2020-10-24T20:51:56Z
https://cimec.org.ar/ojs/index.php/cmm/oai
oai:ojs.www.cimec.org.ar:article/913
2009-09-07T19:30:44Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/913
2009-09-07T19:30:44Z
Cuadernos de Matemática y Mecánica
2007
A Preconditioning Mass Matrix to Avoid the Ill-Posed Two-Fluid Model
Articles
Zanotti, Angel L.
Mendez, Carlos G.
Nigro, Norberto M.
Storti, Mario Alberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/913
en
Two-fluid models are central to the simulation of transport
processes in two-phase homogenized systems. Even though this physical
model has been widely accepted, an inherently non-hyperbolic and
non-conservative ill-posed problem arises from the mathematical point
of view. It has been demonstrated that this drawback occurs even for a
very simplified model, i.e., an inviscid model with no interfacial
terms. Lots of efforts have been made to remedy this anomaly and in
the literature two different types of approaches can be found. On one
hand, extra terms with physical origin are added to model the
interphase interaction, but even though this methodology seems to be
realistic, several extra parameters arise from each added term with
the associated difficulty in their estimation. On the other hand,
mathematical based-work has been done to find the way to remove the
complex eigenvalues obtained with two-fluid model
equations. Preconditioned systems, characterized as a projection of
the complex eigenvalues over the real axis, may be one of the choices.
The aim of this paper is to introduce a simple and novel mathematical
strategy based on the application of a preconditioning mass matrix
that circumvents the drawback caused by the non-hyperbolic behavior of
the original model. Although the mass and momentum conservation
equations are modified, the target of this methodology is to present
another way to reach a steady state solution (using a time marching
scheme), greatly valued by researchers in industrial process
design. Attaining this goal is possible because only the temporal term
is affected by the preconditioner. The obtained matrix has two
parameters that correct the non-hyperbolic behavior of the model: the
first one modifies the eigenvalues removing their imaginary part and
the second one recovers the real part of the original
eigenvalues. Besides the theoretical development of the
preconditioning matrix, several numerical results are presented to
show the validity of the method. [To appear in Journal of Applied Mechanics]
oai:ojs.www.cimec.org.ar:article/2385
2009-09-07T19:30:44Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2385
2009-09-07T19:30:44Z
Cuadernos de Matemática y Mecánica
2007
Parabolic mean values and maximal estimates for gradients of temperatures
Articles
Aimar, Hugo A.
Gómez, Ivana
Iaffei, Bibiana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2385
en
The main result of this paper is a pointwise estimate for
the space time gradients of a temperature on a cylindrical
domain in terms of an iteration of two maximal operators. The
result is an extension to the parabolic setting of the elliptic
inequalities proved by D.Jerison and C.Kenig and also by S.Dahlke and
R.DeVore. After an improvement of the parabolic mean value formula and the
analysis of the kernel and the operator that provides the space
derivatives
of temperatures, we obtain a pointwise estimate for space
gradients weighted by powers of the distance to the parabolic
boundary in terms of an iteration of two maximal operators which
are well known in harmonic analysis: the one-sided maximal
Hardy-Littlewood operator in the time variable and the
Calderón maximal operator in the space variable.
Published: Journal of Functional Analysis. Volume 255, Issue 8, 2008, Pages 1939-1956
Link: doi:10.1016/j.jfa.2008.06.006
oai:ojs.www.cimec.org.ar:article/2701
2009-10-02T12:33:31Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2701
2009-10-02T12:33:31Z
Cuadernos de Matemática y Mecánica
2007
Spectral duality for finitely generated nilpotent minimum algebras, with applications
Articles
Aguzzoli, S.
Busaniche, Manuela
Marra, V.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2701
en
We establish a categorical duality for the finitely generated Lindenbaum-Tarski algebras of propositional nilpotent minimum logic. The latter's conjunction is semantically interpreted by a left-continuous (but not continuous) triangular norm; implication is obtained through residuation. Our duality allows one to transfer to nilpotent minimum logic several known results about inutitionistic logic with the prelineari\-ty axiom (also called G\"{o}del-Dummett logic), mutatis mutandis. We give several such applications.
Published: Journal of Logic and Computation 17 (2007), 749-765.
oai:ojs.www.cimec.org.ar:article/3001
2012-02-21T00:04:57Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/3001
2012-02-21T00:04:57Z
Cuadernos de Matemática y Mecánica
2011
Dyadic Fefferman-Stein Inequalities and the Equivalence of Haar Bases on Weighted Lebesgue Spaces
Articles
Aimar, Hugo
Bernardis, Ana
Nowak, Luis
2011-02-15 14:05:30
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/3001
IMAL-CONICET-UNL. UNCOMA
en
In this note we give conditions on two dyadic systems to obtain the equivalence of corresponding Haar systems on dyadic weighted Lebesgue spaces on spaces of homogeneous type. In order to obtain these result we prove a Fefferman-Stein weighted inequality for vector valued dyadic Hardy-
Littlewood maximal operators with dyadic weights in this general setting.
oai:ojs.www.cimec.org.ar:article/2375
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2375
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Convergence and quasi-optimality of adaptive FEM for Steklov eigenvalue problems
Articles
Garau, Eduardo M.
Morin, Pedro
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2375
en
In this article we prove convergence of adaptive finite element methods for Steklov eigenvalue problems under very general assumptions for simple as well as multiple eigenvalues starting from any initial triangulation. We also prove the optimality of the approximations assuming Dörfler's Strategy for marking, when we consider simple eigenvalues.
oai:ojs.www.cimec.org.ar:article/2539
2009-08-15T13:46:05Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2539
2009-08-15T13:46:05Z
Cuadernos de Matemática y Mecánica
2001
Data Oscillation and Convergence of Adaptive FEM
Articles
Morin, Pedro
Nochetto, Ricardo H.
Siebert, Kunibert G.
2009-08-15 10:46:05
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2539
en
Data oscillation is intrinsic information missed by the averaging process associated with finite element methods (FEM) regardless of quadrature. Ensuring a reduction rate of data oscillation, together with an error reduction based on a posteriori error estimators, we construct a simple and efficient adaptive FEM for elliptic PDE with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a finite number of steps. A number of numerical experiments in 2d and 3d yield quasi-optimal meshes along with a competitive performance.
Keywords: A posteriori error estimators, data oscillation, adaptive mesh refinement, convergence, performance, quasi-optimal meshes
AMS Subject Classifications: 65N12, 65N15, 65N30, 65N50, 65Y20
Published: SIAM Journal on Numerical Analysis, Volume 38, Number 2 (2000), 466-488.
oai:ojs.www.cimec.org.ar:article/2986
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2986
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
Generalized Qualification and Qualification Levels for Spectral Regularization Methods
Articles
Herdman, Terry
Spies, Ruben D.
Temperini, Karina G.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2986
CONICET, UNL, AFOSR, DARPA/SPO, NASA LaRC
en
The concept of qualifcation for spectral regularization methods (SRM) for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of
qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualifcation extends the definition introduced
by Mathé and Pereverzev in 2003 (Mathé, P. and Pereverzev, S. V.: "Geometry of linear ill-posed problems in variable Hilbert scales", Inverse Problems, 19(3), 789-803 (2003)), mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also
have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathé and Pereverzev are shown. In particular, SRMs
having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the
context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.
oai:ojs.www.cimec.org.ar:article/458
2009-09-07T19:32:50Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/458
2009-09-07T19:32:50Z
Cuadernos de Matemática y Mecánica
2005
Dimension Functions of Cantor Sets
Articles
García, Ignacio
Molter, Ursula
Scotto, Roberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/458
CONICET
en
We estimate the packing measure of Cantor sets associated to nonincreasing sequences through their decay. This result, dual to one obtained by Besicovitch and Taylor, allows us to characterize the dimension functions recently found by Cabrelli et al for these sets.
Published: Proceedings of the American Mathematical Society, Vol 135 (2007), 3151-3161.
oai:ojs.www.cimec.org.ar:article/1387
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1387
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
On the Uniform Doubling of Hutchinson Orbits of Contractive Mappings
Articles
Aimar, Hugo
Carena, Marilina
Iaffei, Bibiana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1387
en
We are interested in the preservation of doubling properties along the Hutchinson orbit generated by successive applications of contraction mappings on a metric measure space. We construct some elementary examples, built on Muckenhoupt weights, showing that even when the initial and the limit points of the orbit are doubling, no iteration of the IFS remains doubling. We also obtain positive results under some quantitative assumptions on the separation of the images through the IFS. We also explore the completeness, in the Hausdorff-Kantorovich metric, of a version of the doubling property which is suitable for the application of Hutchinson type contractions.
oai:ojs.www.cimec.org.ar:article/2400
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2400
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
Polynomials with all their roots on $S^1$
Articles
Toledano, Ricardo D.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2400
en
We give a characterization of monic polynomials with coefficients in the ring of integers of a Galois number field having all of their roots on the unit circle. Such a characterization is given in terms of finitely many sum of powers of the roots of the considered polynomials.
Published: Lithuanian Mathematical Journal. Vol. 49, Nro 3, (2009), 331-336.
Link: http://www.springer.com/math/journal/10986
oai:ojs.www.cimec.org.ar:article/2972
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2972
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Measuring the level sets of generalized homogeneous functions
Articles
Aimar, Hugo
Gómez, Ivana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2972
en
In this note we prove a formula for the volume of level sets of generalized homogeneous functions in terms of measures supported on the level surfaces. We relate the results to some well known mean value formulas for solutions of PDE.
oai:ojs.www.cimec.org.ar:article/9
2009-07-30T17:24:12Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/9
2009-07-30T17:24:12Z
Cuadernos de Matemática y Mecánica
2005
An interface strip preconditioner for domain decomposition methods: Application to hydrology
Articles
Paz, Rodrigo Rafael
Storti, Mario Alberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/9
CONICET, UNL, ANPCyT
en
In this paper, the efficiency of a parallelizable preconditioner for Domain Decomposition Methods in the context of the solution of non-symmetric linear equations arising from discretization of the Saint-Venant equations, is investigated. The proposed Interface Strip Preconditioner (IS) is based on solving a problem in a narrow strip around the interface. It requires much less memory and computing time than classical Neumann-Neumann preconditioner, and handles correctly the flux splitting among sub-domains that share the interface. The performance of this preconditioner is assessed with an analytical study of Schur complement matrix eigenvalues and numerical experiments conducted in a 2 parallel computational environment (consisting of a Beowulf cluster of twenty-nodes). [International Journal for Numerical Methods in Engineering 62(13), pp. 1873-1894 (2005)]
oai:ojs.www.cimec.org.ar:article/1090
2009-09-07T19:30:44Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1090
2009-09-07T19:30:44Z
Cuadernos de Matemática y Mecánica
2007
Numerical simulations of the flow around a spinning projectile in subsonic regime
Articles
Garibaldi, Javier
Storti, Mario Alberto
Battaglia, Laura
D'Elía, Jorge
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1090
en
The unsteady flow around a 155 mm projectile governed by the Navier-Stokes (NS) equations is numerically solved with a Large Eddy Simulation (LES) scheme, together with the Sub- Grid Scale (SGS) solved by a Smagorinsky model and the van Driest near-wall damping. The computed results are obtained in the subsonic flow regime for a viscous and incompressible Newtonian fluid in order to determine the axial drag coefficient, and they are validated against experimental data. The problem was solved by a monolithic finite element code for parallel computing on a Beowulf cluster.
oai:ojs.www.cimec.org.ar:article/2390
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2390
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
What is a Sobolev space for the Laguerre function systems?
Articles
Bongioanni, Bruno
Torrea, José L.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2390
en
We discuss the concept of Sobolev space associated to the Laguerre operator $ L_\al = - y\,\frac{d^2}{dy^2} - \frac{d}{dy} + \frac{y}{4} + \frac{\al^2}{4y},\quad y\in (0,\infty).$ We show that the natural definition does not fit with the concept of potential space, defined via the potentials $ (L_\al)^{-s}.$ An appropriate Laguerre-Sobolev spaces are defined in order to have the mentioned coincidence. An application is given to the almost everywhere convergence of solutions of the Schr\"odinger equation. Other Laguerre operators are also considered.
Published: Studia Math. 192 (2009), no. 2, 147--172.
oai:ojs.www.cimec.org.ar:article/2707
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2707
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Classification of finitely generated lattice-ordered groups with order-unit
Articles
Busaniche, Manuela
Cabrer, Leonardo
Mundici, D.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2707
en
A unital $\ell$-group $(G,u)$ is an abelian group $G$ equipped with a translation-invariant lattice-order and a distinguished element $u$, called order-unit, whose positive integer multiples eventually dominate each element of $G$. We classify finitely generated unital $\ell$-groups by sequences $\mathcal W = (W_{0},W_{1},\ldots)$ of weighted abstract simplicial complexes, where $W_{t+1}$ is obtained from $W_{t}$ either by the classical Alexander binary stellar operation, or by deleting a maximal simplex of $W_{t}$. A simple criterion is given to recognize when two such sequences classify isomorphic unital $\ell$-groups. Many properties of the unital $\ell$-group $(G,u)$ can be directly read off from its associated sequence: for instance, the properties of being totally ordered, archimedean, finitely presented, simplicial, free.
oai:ojs.www.cimec.org.ar:article/4335
2013-01-18T20:35:47Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/4335
2013-01-18T20:35:47Z
Cuadernos de Matemática y Mecánica
2012
A FFT Preconditioning Technique for the Solution of Incompressible Flow on GPUs
Articles
Storti, Mario Alberto
Paz, Rodrigo Rafael
Dalcin, Lisandro Daniel
Costarelli, Santiago Daniel
Idelsohn, Sergio Rodolfo
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/4335
CONICET, UNL, ANPCyT, ICREA, UPC
en
Graphic Processing Units have received much attention in last years. Compute-intensive algorithms operating on multidimensional arrays that have nearest neighbor dependency and/or exploit data locality can achieve massive speedups. Simulation of problems modeled by time-dependent Partial Differential Equations by using explicit time-stepping methods on structured grids is an instance of such GPU-friendly algorithms. Solvers for transient incompressible fluid flow cannot be developed in a fully explicit manner due to the incompressibility constraint. Segregated algorithms like the fractional step method require the solution of a Poisson problem for the pressure field at each time level. This stage is usually the most time-consuming one. This work discuss a solver for the pressure problem in applications using immersed boundary techniques in order to account for moving solid bodies. This solver is based on standard Conjugate Gradients iterations and depends on the availability of a fast Poisson solver on the whole domain to define a preconditioner. We provide a theoretical and numerical evidence on the advantages of our approach versus classical techniques based on fixed point iterations such as the Iterated Orthogonal Projection method.
oai:ojs.www.cimec.org.ar:article/874
2007-04-27T16:48:12Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/874
2007-04-27T16:48:12Z
Cuadernos de Matemática y Mecánica
2006
Dynamic boundary conditions in CFD
Articles
Storti, Mario Alberto
Nigro, Norberto Marcelo
Paz, Rodrigo Rafael
Dalcín, Lisandro Daniel
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/874
en
The number and type of boundary conditions to be used in the numerical modeling of fluid mechanics problems is normally chosen according to a simplified analysis of the character- istics, and also from the experience of the modeler. The problem is harder at input/output boundaries which are, in most cases, artificial boundaries, so that a bad decision about the boundary conditions to be imposed may affect the precision and stability of the whole computation. For inviscid flows, the analysis of the sense of propagation in the normal di- rection to the boundaries gives the number of conditions to be imposed and, in addition, the conditions that are "absorbing" for the waves impinging normal to the boundary. In practice, it amounts to counting the number of positive and negative eigenvalues of the advective flux Jacobian projected onto the normal. The problem is still harder when the number of incoming characteristics varies during the computation, and to correctly treat these cases poses both mathematical and practical problems. One example considered here is compressible flow where the flow regime at a certain part of an inlet/outlet boundary can change from subsonic to supersonic and the flow can revert. In this work the technique for dynamically imposing the correct number of boundary conditions along the computation, using Lagrange multipliers and penalization is discussed, and several numerical examples are presented. [Submitted to Computer Methods in Applied Mechanics and Engineering (2007)]
oai:ojs.www.cimec.org.ar:article/2381
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2381
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
Convergence of adaptive finite element methods for eigenvalue problems
Articles
Garau, Eduardo M.
Morin, Pedro
Zuppa, Carlos
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2381
en
In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.
Published: Mathematical Models and Methods in Applied Sciences (M3AS), Vol. 19, No. 5 (2009), 721--747.
oai:ojs.www.cimec.org.ar:article/2697
2009-10-02T12:15:27Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2697
2009-10-02T12:15:27Z
Cuadernos de Matemática y Mecánica
2004
Decomposition of BL-chains
Articles
Busaniche, Manuela
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2697
en
A simple and self contained proof of decomposition of BL-chains into ordinal sums of Wajsberg hoops is given.
Published: Algebra Universalis, 52 (2004), 519-525.
oai:ojs.www.cimec.org.ar:article/2997
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2997
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
Galerkin Boundary Elements for Exterior Stokes Flows
Articles
D'Elía, Jorge
Battaglia, Laura
Cardona, Alberto
Storti, Mario Alberto
Franck, Gerardo
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2997
CONICET,ANPCyt,UNL
en
An indirect boundary integral equation for steady Stokes ﬂow around a rigid body in the three-dimensional space is proposed, and is numerically solved by using collocation and Galerkin weight- ing procedures. The resulting double surface integrals of the Galerkin technique that express the pairwise interaction among all boundary elements, which are quadruple integrals, are computed on ﬂat simplex triangles using a regularized quadrature scheme. Numerical examples include the steady creeping ﬂow around the sphere of unit radius and the cube of unit edge length, covering issues on the convergence under mesh reﬁnement and stability under small mesh perturbations.
oai:ojs.www.cimec.org.ar:article/1659
2009-04-28T02:33:33Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1659
2009-04-28T02:33:33Z
Cuadernos de Matemática y Mecánica
2001
Iterative solution of panel method discretizations for 3D potential flow problems. The modal multipolar preconditioning
Articles
D'Elía, Jorge
Storti, Mario Alberto
Idelsohn, Sergio R.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1659
CONICET, UNL, ANPCyT
en
The iterative solution of linear systems arising from panel method
discretization of three-dimensional (3D) exterior potential problems
coming mainly from aero-hydrodynamic engineering problems, is
discussed. We propose an original peconditioning based on an
approximate eigenspace decomposition, that corrects bad conditioning
arising from pair of surfaces that are very close from each other,
which is a very common situation in slender wings and other
aerodynamoc profiles. This preconditioning has been tested with the
standard Bi-Conjugate Gradient (BCG) and Conjugate Gradient Squared
(CGS) iterative methods.
oai:ojs.www.cimec.org.ar:article/2535
2009-08-14T21:45:16Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2535
2009-08-14T21:45:16Z
Cuadernos de Matemática y Mecánica
2003
Surface Diffusion of Graphs: Variational Formulation, Error Analysis and Simulation
Articles
Bänsch, Eberhard
Morin, Pedro
Nochetto, Ricardo H.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2535
en
Abstract: Surface diffusion is a (4th order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. We present a novel variational formulation for graphs and derive a priori error estimates for a time-continuous finite element discretization. We also introduce a semi-implicit time discretization and a Schur complement approach to solve the resulting fully discrete, linear systems. After computational verification of the orders of convergence for polynomial degrees 1 and 2, we show several simulations in 1d and 2d with and without forcing which explore the smoothing effect of surface diffusion as well as the onset of singularities in finite time, such as infinite slopes and cracks.
Keywords: Surface diffusion, fourth-order parabolic problem, finite elements, a priori error estimates, Schur complement, smoothing effect.
AMS Subject Classifications: 35K55, 65M12, 65M15, 65M60, 65Z05.
Published: SIAM Journal on Numerical Analysis, Volume 42, Number 2 (2004), 773--799.
oai:ojs.www.cimec.org.ar:article/2980
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2980
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
Flow Study and Wetting Efficiency of a Perforated-Plate Tray Distributor in a Trickle Bed Reactor
Articles
Ramajo, Damián
Márquez-Damián, Santiago
Raviculé, Marcela
Monsalvo, María
Storti, Mario Alberto
Nigro, Norberto Marcelo
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2980
CONICET,ANPCyt,UNL, Repsol-YPF
en
Trickle bed reactors (TBRs) are massively employed in petrochemical and chemical plants. In general these reactors have one or more beds filled up with catalyst particles. Efficient catalyst utilization relies on a good liquid charge distribution across the catalyst beds. However, normally the distribution is not perfect and some parts of the beds will get less liquid reactants while others will get more than the average. In zones where there is a maldistribution of reactants the reaction will progress in undesirable way leading to deactivation of the catalyst and towards low conversions. Bad tray efficiency due to non-uniform liquid distribution will result in low reactor efficiency and shorten the catalyst's cycle time. The TBR analyzed here is a hydrogenation one that processes C4 (liquid) and hydrogen (gas) to produce butene 1 (also named α butylene). The two-phase charge is introduced through the upper side of the TBR and the liquid phase accumulates on the tray to a certain level swamping the perforated-plate tray. The liquid phase flows down through 68 small holes while the gas phase circulates through 7 gas chimneys. There is another ceramic-ball bed above the catalyst bed with the aim to obtain a better distribution of the charge. In this work a computational fluid dynamics analysis (CFD) employing the Eulerian two-fluid model was carried out with the aim to understand the fluid dynamics of the distribution process and to determine the wetting efficiency of the tray distributor under different operating conditions. The small tray holes were modeled by sinks (drains) and sources, firstly employing numerical and experimental models to obtain the flow rate versus liquid height response. Because of the scarce liquid sloshing above the tray, little differences on the liquid discharge through the holes were found. Due to the low gas fraction of the charge the liquid flows only by gravity following an almost vertical trajectory from the holes to the ceramic ball bed. So, the extension of the wetted zone at the top of the ceramic ball bed is small. A suitable correlation to estimate liquid diffusion inside the ceramic-ball bed was employed, showing that the overall catalyst bed surface is wetted but significant differences on liquid fraction are found. Moreover, a possible additional cause of the low TBR efficiency could be the well known fouling vulnerability of this kind of tray distributors. In this sense, two simple geometric modifications were proposed to enhance tray performance; firstly reducing the amount of gas chimneys to only one, thus adding additional drip points, secondly replacing the holes by short risers in order to reduce the vulnerability to plugging. [Submitted to Int J Chem React Engng ISSN: 1542-6580]
oai:ojs.www.cimec.org.ar:article/266
2006-09-13T12:22:48Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/266
2006-09-13T12:22:48Z
Cuadernos de Matemática y Mecánica
2006
Comparison of Hardy-Littlewood and Dyadic Maximal Functions on Spaces of Homogeneous Type
Articles
Aimar, Hugo A.
Bernardis, Ana L.
Iaffei, Bibiana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/266
CONICET
en
We obtain a comparison of the level sets for two maximal functions on a space of homogeneous type: the Hardy-Littlewood maximal function of mean values over balls and the dyadic maximal function of mean values over the
dyadic sets introduced by M. Christ in [4]. As applications to the theory of Ap weights on this setting, we compare the standard and the dyadic Muckenhoupt
classes and we give an alternative proof of reverse Hölder type inequalities.
oai:ojs.www.cimec.org.ar:article/1380
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1380
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
Full Numerical Quadrature in Galerkin Boundary Element Methods
Articles
D'Elía, Jorge
Storti, Mario Alberto
Battaglia, Laura
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1380
CONICET, UNL, ANPCyT
en
When a Galerkin discretization of a boundary integral equation with a weakly singular kernel is performed over triangles, a double surface integral must be evaluated for each pair of them. If these pairs are not contiguous nor the same, the kernel is regular and a Gauss-Legendre quadrature can be employed. But, when they have a common edge or a common vertex, then edge and vertex weak sin- gularities appear, while autointegrals have both facets coincidents and the whole integration domain is weakly singular. Taylor (IEEE Trans. on Antennas and Propagation, 51(7):1630–1637 (2003)) proposed a systematic evaluation, based on a reordering and partition of the integration domain, together a use of the Duffy transformations in order to remove the singularities, in such a way that a Gauss-Legendre quadrature was performed on three coordinates with an analytic one in the fourth one. Since this scheme is a bit restrictive because it was designed for electromagnetic wave propagation kernels, a full numer- ical quadrature on the four coordinates is proposed here in order to handle other kernels, like those of creeping flows. A numerical test is also proposed based on slight modification of the Wang-Atalla one (Comm. in Num. Meth. Eng., 13(0):1–7 (1997)). [Submitted for publicaciont to Communications in Numerical Methods in Engineering]
oai:ojs.www.cimec.org.ar:article/2395
2009-09-07T19:30:44Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2395
2009-09-07T19:30:44Z
Cuadernos de Matemática y Mecánica
2007
Principal fitted components for dimension reduction in regression
Articles
Cook, Dennis
Forzani, Liliana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2395
en
We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components are not invariant or equivariant under full rank linear transformation of the predictors. The development begins with principal fitted components [Cook, R. D. (2007). Fisher lecture: Dimension reduction in regression (with discussion). Statist. Sci. 22 126] and uses normal models for the inverse regression of the predictors on the response to gain reductive information for the forward regression of interest. This approach includes methodology for testing hypotheses about the number of components and about conditional independencies among the predictors.
Published: Statistical Science 2008, Vol. 23, No. 4, 485–501.
DOI: 10.1214/08-STS275
oai:ojs.www.cimec.org.ar:article/2969
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2969
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Odd BMO(R) functions and Carleson measures in the Bessel setting
Articles
Chicco Ruiz, Aníbal
Fariña, J.C.
Rodríguez-Mesa, L.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2969
en
In this paper we characterize the odd functions in BMO(R) by using Carleson measures associated with Poisson and heat semigroups for Bessel operators.
Accepted: Integral Equations and Operator Theory
oai:ojs.www.cimec.org.ar:article/5
2007-02-21T19:04:40Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/5
2007-02-21T19:04:40Z
Cuadernos de Matemática y Mecánica
2006
Strong coupling strategy for fluid structure interaction problems in supersonic regime via fixed point iteration
Articles
Storti, Mario Alberto
Nigro, Norberto Marcelo
Paz, Rodrigo Rafael
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/5
CONICET, UNL, ANPCyT
en
In this paper we present some results on the time integration stability when solving fluid/structure interaction problems with strong coupled staged strategies. The flutter of a flat plate faced with a fluid at Mach between 1.8 and 3 is taken as a benchmark. The precision of differ- ent predictor strategies and the influence of the partitioned strong coupling on stability is discussed. [Submitted to Journal of Sound and Vibration]
oai:ojs.www.cimec.org.ar:article/1017
2009-07-30T17:24:12Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1017
2009-07-30T17:24:12Z
Cuadernos de Matemática y Mecánica
2005
An Interface Strip Preconditioner for Domain Decomposition Methods Application to Hydrology
Articles
Paz, Rodrigo R.
Storti, Mario Alberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1017
en
In this paper, the efficiency of a parallelizable preconditioner for
domain decomposition methods in the context of the solution of
non-symmetric linear equations arising from discretization of the
Saint-Venant equations, is investigated. The proposed interface strip
preconditioner (IS) is based on solving a problem in a narrow strip
around the interface. It requires much less memory and computing time
than classical NeumannNeumann preconditioner, and handles
correctly the flux splitting among sub-domains that share the
interface. The performance of this preconditioner is assessed with an
analytical study of Schur complement matrix eigenvalues and numerical
experiments conducted in a parallel computational environment
(consisting of a Beowulf cluster of 20 nodes). [To appear in Int. J Num. Meth. Engng. ]
oai:ojs.www.cimec.org.ar:article/2386
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2386
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators
Articles
Pradolini, Gladis G.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2386
en
In this article we prove weighted norm inequalities and pointwise estimates between the multilinear fractional integral operator and the multilinear fractional maximal. As a consequence of these estimations we obtain weighted weak and strong inequalities for the multilinear fractional integral operator. In particular, we extend some results given in \cite{CPSS} to the multilinear context. On the other hand we prove weighted pointwise estimates between the multilinear fractional maximal operator ${\cal M}_{\alpha,B}$ associated to a Young function $B$ and the multilinear maximal operators ${\cal M}_{\psi}={\cal M}_{0,\psi}$, $\psi(t)=B(t^{1-\alpha/(nm)})^{{nm}/{(nm-\alpha)}}$. As an application of these estimate we obtain a direct proof of the $L^p-L^q$ boundedness results of ${\cal M}_{\alpha,B}$ for the case $B(t)=t$ and $B_k(t)=t(1+\log^+t)^k$ when $1/q=1/p-\alpha/n$. We also give sufficient conditions on the weights involved in the boundedness results of ${\cal M}_{\alpha,B}$ that generalizes those given in \cite{M} for $B(t)=t$. Finally, we prove some boundedness results in Banach function spaces for a generalized version of the multilinear fractional maximal operator.
oai:ojs.www.cimec.org.ar:article/2702
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2702
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
Free MVn-algebras
Articles
Busaniche, Manuela
Cignoli, Roberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2702
en
In this note we characterize free algebras in varieties of MV-algebras generated by a finite chain ${\bf L}_n$ as algebras of continuous functions from the spectrum of the Boolean skeleton of the free algebra into ${\bf L}_n$.
Published: Algebra Universalis 58 (2008), 335-340.
oai:ojs.www.cimec.org.ar:article/3002
2012-02-21T00:05:24Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/3002
2012-02-21T00:05:24Z
Cuadernos de Matemática y Mecánica
2011
Haar Type Bases in Lorentz Spaces Via Extrapolation
Articles
Aimar, Hugo
Bernardis, Ana
Nowak, Luis
2011-02-15 14:12:58
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/3002
IMAL-CONICET-UNL. UNCOMA
en
In this note we consider Haar systems as unconditional bases for Lorentz spaces defined on spaces of homogeneous type. We also give characterizations of these spaces in terms of the Haar coefficients. The basic tools are the Rubio de Francia extrapolation technique and the characterization of weighted Lebesgue spaces with Haar bases.
oai:ojs.www.cimec.org.ar:article/2376
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2376
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
On Besov regularity of temperatures
Articles
Aimar, Hugo A.
Gómez, Ivana
Iaffei, Bibiana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2376
en
We prove space-time parabolic Besov regularity in terms
of integrability of Besov norms in the space variable for solutions of the
heat equation on cylindrical regions based on Lipschitz domains.
Accepted: The Journal of Fourier Analysis and Applications. January 2010.
oai:ojs.www.cimec.org.ar:article/2540
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2540
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Validation of A 0D/1D Computational Code for the Design of Several Kind of Internal Combustion Engines
Articles
López, Ezequiel José
Nigro, Norberto Marcelo
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2540
ANPCyT, CONICET, UNL
en
A code for computational simulation of internal combustion engines is presented. One-dimensional gas dynamics equations are used for model the ﬂow through pipes and manifolds, and the remaining components in the engine (cylinders, valves, etc.) are modeled by using thermodynamic or 0D models. The numerical code developed is able to simulate spark-ignition and compressionignition, two-stroke and four-stroke, multicylinder and multi-valve engines, naturally aspirated or turbo-charged, and diﬀerent geometries of the combustion chamber. The code was implemented in the scripting language Python, which is a dynamic object-oriented programming language that oﬀers strong support for integration with other languages and tools. The numerical methods used in the discretization of the equations and implementation details are presented. Several test cases are included in order to show the performance of the code.
oai:ojs.www.cimec.org.ar:article/2987
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2987
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
Arbitrary Divergence Speed of the Least-Squares Method in Infinite-Dimensional Inverse Ill-Posed Problems
Articles
Spies, Ruben D.
Temperini, Karina G.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2987
CONICET, UNL, Fundación Antorchas
en
A standard engineering procedure for approximating the solutions of an infinite-dimensional inverse problem of the form Ax = y, where A is a given compact linear operator on a Hilbert space X and y is the given data, is to find a sequence
{XN} of finite-dimensional approximating subspaces of X whose union is dense in X and to construct the sequence {xN} of least squares solutions of the problem in XN.
In 1980, Seidman (Nonconvergence Results for the Application of Least-Squares Estimation to Ill-Posed Problems, Journal of Optimization Theory and Applications, 30, 4, 535-547, 1980) showed that if the problem is ill-posed, then, without any additional assumptions on the exact solution or on the sequence of approximating subspaces {XN}, it cannot be guaranteed that the sequence fxNg will converge to the exact solution. In this article this result is extended in the following sense: it is shown that if X is separable, then for any y in X, y not equal 0, and for any arbitrarily given function s defined over the natural numbers with values in R+, there exists an injective, compact linear operator A and an increasing sequence of finite-dimensional subspaces XN contained in X such that ||xN - A^{-1}y||>= s(N) for all N, where xN is the least squares solution of Ax = y in XN.
oai:ojs.www.cimec.org.ar:article/459
2007-04-27T12:12:42Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/459
2007-04-27T12:12:42Z
Cuadernos de Matemática y Mecánica
2001
On the Composition of the Integral and Derivative Operators of Functional Order
Articles
Hartzstein, Silvia I.
Viviani, Beatriz E.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/459
CONICET
en
The Integral, I_phi, and Derivative, D_phi, operators of order phi, with phi a function of positive lower type and upper type lower than 1, were defined in [HV2] in the setting of spaces of homogeneous-type. These definitions generalize those of the fractional integral and derivative operators of order alpha, where phi(t) = t^alpha, given in [GSV].
In this work we show that the composition T_phi = D_phi I_phi is a singular integral operator. This result in addition with the results obtained in [HV2] of boundedness of I_phi and D_phi or the T1-theorems proved in [HV1] yield the fact that T_phi is a Calderón-Zygmund operator bounded on the generalized Besov, ˙B^{psi,q}_p 1 leq p, q < infty, and Triebel-Lizorkin spaces, ˙F^{psi,q}_p , 1 < p, q < infty, of order psi = psi_ 1/psi_ 2, where psi_1 and psi_2 are two quasi-increasing functions of adequate upper types s_1 and s_2, respectively.
oai:ojs.www.cimec.org.ar:article/1390
2010-11-18T22:44:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1390
2010-11-18T22:44:30Z
Cuadernos de Matemática y Mecánica
2009
Local Absorbent Boundary Condition for Nonlinear Hyperbolic Problems with Unknown Riemann Invariants
Articles
Paz, Rodrigo Rafael
Garelli, Luciano
Storti, Mario Alberto
2009-04-08 20:22:03
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1390
en
A general methodology for developing absorbing boundary conditions for general nonlinear hyperbolic advective-diffusive equations with unknown Riemann invariants is presented. In problems where the Riemann invariants (RI) are known (e.g. the flow in a shallow rectangular channel, the gas flow equations), the imposition of non-reflective boundary conditions is straightforward. In problems where Riemann invariants are unknown (e.g. the flow in a non-rectangular channels, the stratified 2D shallow water flows) it is possible to impose that kind of conditions analyzing the projection of the Jacobians of advective flux functions onto normal directions to fictitious surfaces or boundaries. The advantage of the method is that it is very easy to implement in a finite element code and is only based on computing the advective flux functions (and the their Jacobian projections), then, imposing non-linear constraints via Lagrange Multipliers or Penalty Methods. The application of the dynamic absorbing boundary conditions to typical wave propagation problems with unknown Riemann invariants, like non-linear Saint-Venant system of conservation laws for non-rectangular and non-prismatic 1D channels and stratified 1D/2D shallow water equations, is presented. Also, the new absorbent/dynamic condition can handle automatically the change of Jacobians structure when the flow regime changes from subcritical to supercritical and viceversa, or when recirculating zones are present in regions near fictitious walls.
oai:ojs.www.cimec.org.ar:article/2401
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2401
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Boundedness of the fractional maximal operator on variable exponent Lebesgue spaces: a short proof
Articles
Gorosito, Osvaldo P.
Pradolini, Gladis G.
Salinas, Oscar
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2401
en
We give a simple proof of the boundedness of the fractional maximal operator providing in this way an alternative approach to the one given by C. Capone, D. Cruz Uribe and A. Fiorenza in The fractional maximal operator and fractional integrals on variable L^p spaces, 743--770.
oai:ojs.www.cimec.org.ar:article/2981
2010-06-08T22:40:05Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2981
2010-06-08T22:40:05Z
Cuadernos de Matemática y Mecánica
2009
On local times, density estimation and classification rules for functional data
Articles
Llop, Pamela Nerina
Forzani, Liliana
Fraiman, Ricardo
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2981
en
In this paper we define a $\sqrt{n}$-consistent nonparametric density estimator for functional data. Under mild conditions we obtain strong consistency, strong orders of convergence and derive the asymptotic distribution of the estimator. We propose a nonparametric classification rule based on local times (occupation measure) and include some simulations studies
oai:ojs.www.cimec.org.ar:article/26
2009-07-30T17:24:12Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/26
2009-07-30T17:24:12Z
Cuadernos de Matemática y Mecánica
2005
A Preconditioner for the Schur Complement Matrix
Articles
Storti, Mario Alberto
Dalcín, Lisandro Daniel
Paz, Rodrigo R.
Yommi, Andrea
Sonzogni, Victorio E.
Nigro, Norberto M.
2006-07-04 11:27:15
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/26
CONICET, UNL, ANPCyT
en
A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a problem in a narrow strip around the interface. It requires much less memory and computing time than classical Neumann-Neumann preconditioner and its variants, and handles correctly the flux splitting among subdomains that share the interface. The performance of this preconditioner is assessed with an analytical study of Schur complement matrix eigenvalues and several numerical experiments conducted in a sequential computational environment. Results in a production parallel finite element code are given in a companion paper. [Advances in Engineering Software 37, pp. 754-762 (2006)]
oai:ojs.www.cimec.org.ar:article/1091
2009-09-07T19:30:44Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1091
2009-09-07T19:30:44Z
Cuadernos de Matemática y Mecánica
2007
CFD analysis of a polybutene reactor to diagnose causes of polymer adhesion at inner walls
Articles
Ramajo, Damián
Raviculé, Marcela
Horowitz, Gabriel
Storti, Mario Alberto
Nigro, Norberto Marcelo
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1091
en
In this work the flow patterns inside a polybutene reactor were studied by CFD (Computational Fluid Dynamics) using finite elements. Research was carried out with the aim to find possible causes of excessive adhesion of polymer and catalyst particles at the reactor inner walls. The multi-fluid formulation for a three-phase system formed by liquid reactor mixture, solid catalyst particles and small gas bubbles generated by the reaction was applied. Deposition of solid particles and a non-homogeneous flow distribution over the lower reactor walls were founded. Based on the hypothesis that adhesion phenomena is related to a combination of catalyst-particle precipitation at walls and locally low shear stresses, several operative and constructive modifications were proposed in order to reduce this phenomenon. [Submitted to LAAR]
oai:ojs.www.cimec.org.ar:article/2391
2009-09-07T19:30:44Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2391
2009-09-07T19:30:44Z
Cuadernos de Matemática y Mecánica
2007
Composition of operators in Orlicz spaces
Articles
Bongioanni, Bruno
Harboure, Eleonor
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2391
en
In this work we find sharp conditions for boundedness on Orlicz spaces of the composition of $j$ operators, each one being of restricted weak type $(p,p)$ for some $p>1$, and of strong type $(\infty,\infty)$. Particularly, we find necessary and sufficient conditions to obtain modular inequalities for the $j$-times composition of the Cesàro Maximal function of order $\alpha$. With this approach we treat a kind of strong maximal function related to Cesàro averages over $n$-dimensional rectangles.
Published: Rocky Mountain J. Math. 38 (2008), no. 1, 41--59.
oai:ojs.www.cimec.org.ar:article/2961
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2961
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
An h-Adaptive Solution of the Spherical Blast Wave Problem
Articles
Ríos Rodríguez, Gustavo
Storti, Mario Alberto
López, Ezequiel Javier
Sarraf, Sofía
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2961
ANPCyT, CONICET, UNL
en
Compressible ﬂow problems usually exhibit features in the ﬂow ﬁeld that need a very reﬁned mesh in order to achieve an acceptable accuracy in the numerical solution. Uniform reﬁnement of the whole mesh quickly becomes prohibitive in three dimensions. In these situations, the use of an adaptive technique shows advantageous. Here, a h-reﬁnement/coarsening strategy for unstructured ﬁnite element meshes is described and applied to solve the spherical blast wave problem driven by a point-like intense explosion. The resulting meshes are non-conformal. A 3-D reﬁnement constraint is introduced to enforce a smooth size distribution among neighbor elements in the mesh and a gradient error indicator based on the ﬂow variables is used to track discontinuities. It is shown that the adaption strategy allows to improve the accuracy and to reduce the spurious oscillations in the numerical solution, requiring just a small fraction of the overall computing time.
oai:ojs.www.cimec.org.ar:article/4337
2013-01-20T13:27:33Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/4337
2013-01-20T13:27:33Z
Cuadernos de Matemática y Mecánica
2012
Fastmat: A C++ Library for Multi-Index Array Computations
Articles
Paz, Rodrigo Rafael
Storti, Mario Alberto
Dalcin, Lisandro Daniel
Castro, Hugo Guillermo
Kler, Pablo
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/4337
CONICET, UNL, ANPCyT
en
In this paper we introduce and describe an efficient thread-safe
matrix library for computing element/cell residuals and Jacobians in
Finite Elements and Finite Volumes-like codes. The library provides
a wide range of multi-index tensor operations that are normally used
in scientific numerical computations. The library implements an
algorithm for choosing the optimal computation order when a product
of several tensors is performed (i.e., the so-called `multi-product'
operation). Another key-point of the FastMat approach is that
some computations (for instance the optimal order in the
multi-product operation mentioned before) are computed in the first
iteration of the loop body and stored in a cache object, so
that in the second and subsequent executions these computations are
retrieved from the cache, and then not recomputed. The library is
open source and freely available within the multi-physics parallel
FEM code PETSc-FEM http://www.cimec.org.ar/petscfem and it can
be exploited on distributed and shared memory architectures as well
as in hybrid approaches. We studied the performance of the library
in the context of typical FEM tensor contractions.
oai:ojs.www.cimec.org.ar:article/875
2007-02-21T17:23:26Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/875
2007-02-21T17:23:26Z
Cuadernos de Matemática y Mecánica
2006
MPI for Python: Performance Improvements and MPI2 Extensions
Articles
Dalcin, Lisandro Daniel
Storti, Mario Alberto
Paz, Rodrigo Rafael
D'Elia, Jorge
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/875
en
MPI for Python provides bindings of the Message Passing Interface (MPI) standard for the Python programming language and allows any Python program to exploit multiple processors. In its first release, MPI for Python was constructed on top of the MPI-1 speci- fication defining an object oriented interface that closely followed the MPI-2 C++ bindings, and provided support for communications of general Python objects. In the latest release, this package is improved to enable direct blocking/nonblocking communication of numeric arrays, and to support almost all MPI-2 features. Improvements in communication performance have been tested in a Beowulf class cluster. Results showed a negligible overhead in comparison to compiled C code. MPI for Python is open source and available for download on the web (http: //www.cimec.org.ar/python) [submitted to Journal of Parallel and Distributed Computing (2006)]
oai:ojs.www.cimec.org.ar:article/2382
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2382
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Pointwise estimates for gradients of temperatures in terms of maximal functions
Articles
Aimar, Hugo A.
Gómez, Ivana
Iaffei, Bibiana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2382
en
We give a detailed proof, in the case of one space dimension, of a pointwise upper estimate for the space gradient of a temperature. The operators involved are a one-sided Hardy-Littlewood maximal in time and the Calderón sharp maximal operator in space.
Published: Revista de la Unión Matemática Argentina, vol. 50, no. 2, 105-114, (2009).
oai:ojs.www.cimec.org.ar:article/2698
2009-10-02T12:17:58Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2698
2009-10-02T12:17:58Z
Cuadernos de Matemática y Mecánica
2006
Free algebras in varieties of BL-algebras generated by BLn-chains
Articles
Busaniche, Manuela
Cignoli, Roberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2698
en
Free algebras with an arbitrary number of free generators in varieties of BL-algebras generated by one BL-chain which is an ordinal sum of a finite MV-chain ${\bf L}_n$ and a generalized BL-chain ${\bf B}$ are described in terms of weak Boolean products of BL-algebras that are ordinal sums of subalgebras of ${\bf L}_n$ and free algebras in the variety of basic hoops generated by ${\bf B}.$ The Boolean products are taken over the Stone spaces of the Boolean subalgebras of idempotents of free algebras in the variety of MV-algebras generated by ${\bf L}_n.$
Published: Journal of the Australian Mathematical Society, 80 (2006), 419-439.
oai:ojs.www.cimec.org.ar:article/3003
2012-02-21T00:05:49Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/3003
2012-02-21T00:05:49Z
Cuadernos de Matemática y Mecánica
2011
Modelling and High Performance Simulation of Electrophoretic Techniques in Microfluidic Chips
Articles
Kler, Pablo
Berli, Claudio
Gusrnieri, Fabio Ariel
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/3003
en
Electrophoretic separations comprise a group of analytical tech-
niques such as capillary zone electrophoresis, isoelectric focusing, isota-
chophoresis and free ﬂow electrophoresis. These techniques have been
miniaturized in the last years and now represent one of the most im-
portant applications of the lab-on-a-chip technology. A 3D and time-
dependent numerical model of electrophoresis on microﬂuidic devices is
presented. The model is based on the set of equations that governs elec-
trical phenomena, ﬂuid dynamics, mass transport and chemical reactions.
The relationship between the buﬀer characteristics (ionic strength, pH)
and surface potential of channel walls is taken into consideration. Numer-
ical calculations were performed by using PETSc-FEM, in a Python en-
vironment, employing high performance parallel computing. The method
includes a set of last generation preconditioners and solvers, especially
addressed to 3D microﬂuidic problems, which signiﬁcantly improve the
numerical eﬃciency in comparison with typical commercial software for
multiphysics. In this work, after discussing two validation examples, the
numerical prototyping of a microﬂuidic chip for two-dimensional elec-
trophoresis is presented.
oai:ojs.www.cimec.org.ar:article/1660
2009-04-28T14:55:05Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1660
2009-04-28T14:55:05Z
Cuadernos de Matemática y Mecánica
2001
Computing Ship Wave Resistance from Wave Amplitude with a Non-Local Absorbing Boundary Condition
Articles
Storti, Mario Alberto
D'Elía, Jorge
Idelsohn, Sergio
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1660
CONICET, UNL, ANPCyT
en
A method for computing ship wave resistance from a momentum flux balance is presented. It is based on computing the momentum flux carried by the gravity waves that exit the computational domain through the outlet plane. It can be shown that this method ensures a non-negative wave-resistance, in contrast with straightforward integration of the normal pressure forces. However, this calculation should be performed on a transverse plane located far behind the ship. Traditional Dawson-like methods add a numerical viscosity that dampens the wave pattern so that some amount of momentum flux is lost, and resulting in an error in the momentum balance. The flow field is computed, then, with a centred scheme with absorbing boundary conditions.
oai:ojs.www.cimec.org.ar:article/2536
2009-08-14T21:49:12Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2536
2009-08-14T21:49:12Z
Cuadernos de Matemática y Mecánica
2001
Convergence of Adaptive Finite Element Methods
Articles
Morin, Pedro
Nochetto, Ricardo H.
Siebert, Kunibert G.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2536
en
Adaptive finite element methods (FEM) have been widely used in applications for over 20 years now. In practice, they converge starting from coarse grids, although no mathematical theory has been able to prove this assertion. Ensuring an error reduction rate based on a posteriori error estimators, together with a reduction rate of data oscillation (information missed by the underlying averaging process), we construct a simple and efficient adaptive FEM for elliptic partial differential equations. We prove that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a finite number of steps. A number of numerical experiments in two and three dimensions yield quasi-optimal meshes along with a competitive performance. Extensions to higher order elements and applications to saddle point problems are discussed as well.
Keywords: A posteriori error estimators, data oscillation, adaptive mesh refinement, convergence, Stokes, Uzawa
AMS Subject Classifications: 65N12, 65N15, 65N30, 65N50, 65Y20
Published: SIAM Review, 44 (2002) 631--658.
oai:ojs.www.cimec.org.ar:article/2982
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2982
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
On convex regression estimators
Articles
Aguilera, Néstor E.
Forzani, Liliana
Morin, Pedro
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2982
en
A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we convexify it by taking the convex envelope of a sample of the approximation obtained.
We prove that the uniform rate of convergence of the estimator is maintained after the convexification is applied.
The finite sample properties of the new estimator are investigated by means of a simulation study and the application of the new method is demonstrated in examples.
Keywords: approximation, convex regression, convexity, data-smoothing, nonparametric regression
Submitted: mayo 2010.
oai:ojs.www.cimec.org.ar:article/267
2006-09-13T12:17:20Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/267
2006-09-13T12:17:20Z
Cuadernos de Matemática y Mecánica
2006
Multiresolution Approximations and Unconditional Bases on Weighted Lebesgue Spaces on Spaces of Homogeneous Type
Articles
Aimar, Hugo A.
Bernardis, Ana L.
Iaffei, Bibiana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/267
en
Starting from a slight modification of the dyadic sets introduced by M. Christ in [M. Christ, A T(b) theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math. 60/61 (1990) 601–628] on a space of homogeneous type (X, d, µ), an MRA type structure and a Haar system H controled by the quasi distance d, can be constructed in this general setting in such a way that H is an orthonormal basis for L2(dµ). This paper is devoted
to explore under which conditions on the measure measure nu, the system H is also an unconditional basis for the Lebesgue spaces Lp(dnu). As a consequence, we obtain a characterization of these spaces in terms of the H–coefficients.
oai:ojs.www.cimec.org.ar:article/1383
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1383
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
High Performance Simulations of Electrokinetic Flow and Transport in Microfluidic Chips
Articles
Kler, Pablo
Dalcín, Lisandro
Guarnieri, Fabio Ariel
Storti, Mario Alberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1383
CONICET, UNL, ANPCyT
en
This article discusses high performance numerical simulations of electroki- netic flow and transport phenomena in microfluidic chips. Modeling grounds on conservation equations of mass, momentum and electric charge in the framework of continuum mechanics. Two examples of interest in microfluidics are consid- ered as study cases. Three dimension effects and whole chip geometries are taking into account. All numerical simulations presented are performed with PETSc-FEM within a Python programming environment employing parralel computing. Computation time and parallel efficiency are measured in order to study additive Schwarz method performance as domain decomposition technique in solving common ill-conditioned microfluidics problems. [Submitted to Comp. Method in Applied Mech Engng]
oai:ojs.www.cimec.org.ar:article/2396
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2396
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
Likelihood-based sufficient dimension reduction
Articles
Cook, Dennis
Forzani, Liliana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2396
en
We obtain the maximum likelihood estimator of the central subspace under conditional normality of the predictors given the response. Analytically and in simulations we found that our new estimator can preform much better than sliced inverse regression, sliced average variance estimation and directional regression, and that it seems quite robust to deviations from normality.
Published: J. Amer. Statist. Assoc. 104 (2009), no. 485, 197--208.
oai:ojs.www.cimec.org.ar:article/2968
2009-12-04T16:24:25Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2968
2009-12-04T16:24:25Z
Cuadernos de Matemática y Mecánica
2008
Maximal operators, Riesz transforms and Littlewood–Paley functions associated with Bessel operators on BMO
Articles
Betancor, J.J.
Chicco Ruiz, Aníbal
Fariña, J.C.
Rodríguez-Mesa, L.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2968
en
In this paper we study boundedness properties of certain harmonic analysis operators (maximal operators for heat and Poisson semigroups, Riesz transform and Littlewood-Paley g-functions) associated with Bessel operators, on the space BMO_o (R) that consists of the odd functions with bounded mean oscillation on R
Published: Journal of Mathematical Analysis and Applications 363 (1), 310-326.
oai:ojs.www.cimec.org.ar:article/6
2007-04-27T12:12:42Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/6
2007-04-27T12:12:42Z
Cuadernos de Matemática y Mecánica
2001
Hot-pressing process modeling for medium density fiberboard (MDF)
Articles
Nigro, Norberto Marcelo
Storti, Mario Alberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/6
CONICET, UNL, ANPCyT
en
In this paper we present a numerical solution for the mathematical modeling of the hot-pressing process applied to medium density fiber- board. The model is based in the work of Humphrey [1982], Humphrey and Bolton [1989] and Carvalho and Costa [1998], with some modifica- tions and extensions in order to take into account mainly the convec- tive effects on the phase change term and also a conservative numerical treatment of the resulting system of partial differential equations. [International Journal of Mathematics and Mathematical Sciences 26, pp. 713-729 (2001)]
oai:ojs.www.cimec.org.ar:article/1018
2009-09-07T19:30:44Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1018
2009-09-07T19:30:44Z
Cuadernos de Matemática y Mecánica
2007
Numerical simulation of the Ahmed vehicle model near-wake
Articles
Franck, Gerardo
Nigro, Norberto M.
Storti, Mario Alberto
D'Elia, Jorge
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1018
en
The near-wake structure of the flow around the Ahmed vehicle model
is numerically achieved by a time-averaged procedure of the unsteady
flow modeled by the Navier-Stokes equations with a Large Eddy
Simulation (LES) model for the turbulence . The Reynolds (based on
the model length) and the Mach numbers are fixed in 4.25 million and
0.18, respectively. A viscous and incompressible fluid model of
Newtonian type is assumed. A LES technique together with the
Smagorinsky model as Subgrid Scale Modeling (SGM) and the van
Driest near-wall damping is employed. The coherent macro structures in
the near-wake are estimated through the second invariant of the
velocity gradient (Q-criterion) applied on the time-average
flow. A monolithic computational code is employed, which is based on
the finite element method with equal order basis functions (linear)
for pressure and velocity and uses a Streamline Upwind Petrov-Galerkin
(SUPG) scheme combined with a Pressure Stabilizing
Petrov-Galerkin(PSPG) one. Parallel computing on a Beowulf
cluster with a domain decomposition technique for solving the
algebraic system is used. [Submitted to Int J Num Meth Fluids]
oai:ojs.www.cimec.org.ar:article/2387
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2387
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
Weighted inequalities for negative powers of Schrödinger operators
Articles
Bongioanni, Bruno
Harboure, Eleonor
Salinas, Oscar
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2387
en
In this article we obtain boundedness of the operator $(-\Delta~+~V)^{-\alpha/2}$ from $L^{p,\infty}(w)$ into weighted bounded mean oscillation type spaces $BMO_\LL^{\beta}(w)$ under appropriate conditions on the weight $w$. We also show that these weighted spaces also have a point-wise description for $0 < \beta < 1$. Finally, we study the behaviour of the operator $(-\Delta~+~V)^{-\alpha/2}$ when acting on $BMO_\LL^{\beta}(w)$.
Published: J. Math. Anal. Appl. 348 (2008), no. 1, 12--27.
oai:ojs.www.cimec.org.ar:article/2704
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2704
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Constructive logic with strong negation as a substructural logic
Articles
Busaniche, Manuela
Cignoli, Roberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2704
en
Spinks and Veroff have shown that constructive logic with strong negation (CLSN for short), can be considered as a substructural logic. We use algebraic tools developed to study substructural logics to investigate some axiomatic extensions of CLSN. For instance we prove that Nilpotent Minimum Logic is the extension of CLSN by the prelinearity axiom. This generalizes the well known result by Monteiro and Vakarelov that three-valued \Lukasiewicz logic is an extension of CLSN. A Glivenko-like theorem relating CLSN and three-valued \Lukasiewicz logic is proved.
Accepted: Journal of Logic and Computation ; doi: 10.1093/logcom/exn081.
oai:ojs.www.cimec.org.ar:article/3729
2012-02-21T00:06:08Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/3729
2012-02-21T00:06:08Z
Cuadernos de Matemática y Mecánica
2011
Parabolic Besov Regularity for the Heat Equation
Articles
Aimar, Hugo
Gómez, Ivana
2011-02-15 14:24:28
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/3729
The research was supported by CONICET, UNL and ANPCyT.
en
We obtain parabolic Besov smoothness improvement for temperatures on cylindrical regions based on Lipschitz domains. The results extend those for harmonic functions obtained by S. Dahlke and R. DeVore in “Besov regularity for elliptic boundary value problems” published in Communications in Partial Differential Equations 22, no.1-2, 1-16, 1997.
oai:ojs.www.cimec.org.ar:article/2377
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2377
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
On convex functions and the finite element method
Articles
Aguilera, Néstor E.
Morin, Pedro
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2377
en
Many problems of theoretical and practical interest involve finding a convex or concave function. For instance, optimization problems such as finding the projection on the convex functions in $H^k(\Omega)$, or some problems in economics.
In the continuous setting and assuming smoothness, the convexity constraints may be given locally by asking the Hessian matrix to be positive semidefinite, but in making discrete approximations two difficulties arise: the continuous solutions may be not smooth, and an adequate discrete version of the Hessian must be given.
In this paper we propose a finite element description of the Hessian, and prove convergence under very general conditions, even when the continuous solution is not smooth, working on any dimension, and requiring a linear number of constraints in the number of nodes.
Using semidefinite programming codes, we show concrete examples of approximations to optimization problems.
Published: SIAM J. Numer. Anal. Vol 47, Issue 4 (2009), 3139--3157.
http://dx.doi.org/10.1137/080720917
oai:ojs.www.cimec.org.ar:article/2669
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2669
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
A smooth family of Cantor sets
Articles
García, Ignacio
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2669
en
We show that the Cantor set $C_p$ associated to the sequence $\{1/n^p\}_n$, $p>1$, is a smooth attractor. Moreover, it is smoothly conjugate to the $2^{-p}$-middle Cantor set. We also study the convolution of Hausdorff measures supported on these sets and the structure and size of the sumset $C_p+C_q$.
oai:ojs.www.cimec.org.ar:article/2988
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2988
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
An h-Adaptive Solution of the Spherical Blast Wave Problem
Articles
Ríos Rodríguez, Gustavo
Storti, Mario Alberto
López, Ezequiel
Sarraf, Sofía
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2988
CONICET,ANPCyt,UNL
en
Shock waves and contact discontinuities usually appear in compressible ﬂows, requiring a ﬁne mesh in order to achieve an acceptable accuracy of the numerical solution. The usage of a mesh adaptation strategy is convenient as uniform reﬁnement of the whole mesh becomes prohibitive in three-dimensional problems. An unsteady h-adaptive strategy for unstructured ﬁnite element meshes is introduced. The non-conformity of the reﬁned mesh and a bounded decrease in the geometrical quality of the elements are some features of the reﬁnement algorithm. A three-dimensional extension of the well known reﬁnement constraint for two-dimensional meshes is used to enforce a smooth size transition among neighbour elements with different levels of reﬁnement. A density-based gradient indicator is used to track discontinuities. The solution procedure is partially parallelized, i.e: the inviscid ﬂow equations are solved in parallel with a streamline upwind Petrov-Galerkin ﬁnite element formulation with shock capturing terms while the adaptation of the mesh is sequentially performed. Results are presented for a spherical blast wave driven by a point-like explosion with an initial pressure jump of 105 atmospheres. The adapted solution is compared to that computed on a ﬁxed mesh. Also, results provided by the theory of self-similar solutions are considered for the analysis. In this particular problem, adapting the mesh to the solution accounts for approximately 4% of the total simulation time and the reﬁnement algorithm scales almost linearly with the size of the problem.
oai:ojs.www.cimec.org.ar:article/460
2006-09-18T19:28:11Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/460
2006-09-18T19:28:11Z
Cuadernos de Matemática y Mecánica
2002
Integral and Derivative Operators of Functional Order on Generalized Besov and Triebel-Lizorkin Spaces in the Setting of Spaces of Homogeneous TypeE
Articles
Hartzstein, Silvia I.
Viviani, Beatriz E.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/460
CONICET
en
In this work we define the Integral, I_phi, and Derivative, D_phi, operators of order phi, in the setting of spaces of homogeneous-type, where phi is a function of positive lower type and upper type lower than 1.
We show that I_phi and D_phi are bounded from Lipschitz spaces Lambda^{xi} to Lambda^{xi phi} and Lambda^{xi/phi} respectively, with suitable restrictions on the quasi-increasing function xi for each case.
We also prove that I_phi and D_phi are bounded from the generalized Besov ˙B^{psi ,q}_p , with 1 leq p, q < infty, and Triebel-Lizorkin spaces ˙F^{psi ,q}_p , with 1 < p, q < infty, of order psi to those of order phi psi and psi /phi respectively, where psi is the quotient of two quasi-increasing functions of adequate upper types.
oai:ojs.www.cimec.org.ar:article/1382
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1382
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Validación del Código PETSc-FEM en Fenómenos Convectivos
Articles
Ferreiro, Alejandro
Nigro, Norberto
Dalcín, Lisandro
Storti, Mario
2009-04-08 20:22:03
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1382
CONICET, UNL, ANPCyT, UNSE
es
La transferencia de calor por convección está asociada a fenómenos fluidodinámicos, estudiados en múltiples aplicaciones de interés científico e industrial. Tales fenómenos presentan una amplia diversidad de escalas, lo cual configura un importante condicionamiento para su simulación computacional, restringiendo su implementación casi exclusivamente al procesamiento en paralelo. Actualmente, este procesamiento se implementa en computadoras personales con tratamiento computacional distribuido. Los “clusters” de procesadores INTEL x86 que operan bajo el sistema operativo GNU/Linux (clusters Beowulf), son grupos de computadoras personales que actuando en conjunto e interconectadas a través de dispositivos de alta velocidad, pueden resolver problemas de envergadura. El código de Elementos Finitos PETSc- FEM (Parallel Extensible Toolkit for Scientific Computations – Finite Element Method), se ejecuta en “clusters” Beowulf con una arquitectura orientada hacia Fluidodinámica Computacional. Este software, desarrollado en el Centro Internacional de Métodos Computacionales en Ingeniería, está escrito en C++ bajo una filosofía de programación orientada a objetos. El mismo, está basado en las librerías PETSc/MPI (Parallel Extensible Toolkit for Scientific Computations/ Message Passing Interface). En el presente trabajo, se expone su validación satisfactoria en procesos de convección de calor, a partir del análisis de resultados logrados con ensayos numéricos en una cavidad bidimensional. [Publicado originalmente en Revista Nuevas Propuestas, No 43/44. Santiago del Estero, 2008]
oai:ojs.www.cimec.org.ar:article/2532
2009-08-14T21:20:18Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2532
2009-08-14T21:20:18Z
Cuadernos de Matemática y Mecánica
2006
A variational shape optimization approach for image segmentation with a Mumford-Shah functional
Articles
Dogan, Gunay
Morin, Pedro
Nochetto, Ricardo H.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2532
en
We introduce a novel computational method for a Mumford-Shah functional, which decomposes a given image into smooth regions separated by closed curves. Casting this as a shape optimization problem, we develop a gradient descent approach at the continuous level that yields non-linear PDE flows. We propose time discretizations that linearize the problem, and space discretization by continuous piecewise linear finite elements. The method incorporates topological changes, such as splitting and merging for detection of multiple objects, space-time adaptivity and a coarse-to-fine approach to process large images efficiently. We present several simulations that illustrate the performance of the method, and investigate the model sensitivity to various parameters.
Keywords: image segmentation, Mumford-Shah, shape optimization, finite element method
AMS Subject Classifications: 49M15,49M25,65D15,65K10,68T45,90C99
Published: SIAM Journal on Scientific Computing 30 (2008), no. 6, 3028--3049.
oai:ojs.www.cimec.org.ar:article/2977
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2977
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
Bounded renormalization with continuous penalization for level set interface capturing methods
Articles
Battaglia, Laura
Storti, Mario Alberto
D'Elía, Jorge
2010-06-07 08:59:29
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2977
CONICET,ANPCyt,UNL
en
In this work, a reinitialization procedure oriented to regularize the Level Set (LS) function field is presented. In LS approximations for two-fluid flow simulations, a scalar function indicates the presence of one or another phase and the interface between them. In general, the advection of such function produces a degradation of some properties of the LS function, such as the smoothness of the transition between phases and the correct position of the interface. The methodology introduced here, denominated Bounded Renormalization with Continuous Penalization, consists in solving by the finite element method a partial differential equation with certain distinguishing properties with the aim of keeping the desirable properties of the LS function. The performance of the strategy is evaluated for several typical cases in one, two and three-dimensional domains, for both the advection and the renormalization stages. [Submitted to publication in Int J Num Meth Eng ISSN: 0029-5981]
oai:ojs.www.cimec.org.ar:article/216
2009-08-14T19:53:59Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/216
2009-08-14T19:53:59Z
Cuadernos de Matemática y Mecánica
2002
Finite Element Methods for Surface Diffusion
Articles
Bansch, Eberhard
Morin, Pedro
Nochetto, Ricardo
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/216
CONICET-UNL
en
Surface diffusion is a (4th order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. We present a novel variational formulation for the parametric case, develop a finite element method, and propose a Schur complement approach to solve the resulting linear systems. We also introduce a new graph formulation and state an optimal a priori error estimate. We conclude with several significant simulations, some with pinch-off in finite time.
Keywords: Surface diffusion, fourth-order parabolic problem, finite elements, a priori error estimates, Schur complement, smoothing effect, pinch-off.
AMS Subject Classifications: 35K55, 65M12, 65M15, 65M60, 65Z05
Published: Free Boundary Problems. International Series of Num. Math., vol. 147, 53--63, Birkhäuser (2003)
oai:ojs.www.cimec.org.ar:article/1092
2010-11-19T13:14:23Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1092
2010-11-19T13:14:23Z
Cuadernos de Matemática y Mecánica
2007
Tensorial Equations for Three-Dimensional Laminar Boundary Layer Flows
Articles
Storti, Mario Alberto
D'Elía, Jorge
Battaglia, Laura
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1092
en
For a laminar and attached steady flow along a smooth three-dimensional surface of an incompressible, isothermal and viscous fluid of Newtonian type, the boundary layer equations written in orthogonal curvilinear coordinates and involving curvature terms are relatively well known, but a covariant formulation that has not neither of them is rather not further considered. The more conventional boundary layer equations are written as two-dimensional partial differential equations over the body surface itself but, since in many cases these surfaces are not flat, the curvature tensor or the two principal curvatures of the flow domain must be into account. On the other hand, the present work is focused on a covariant formulation of the three-dimensional boundary layer equations without any curvature terms. The formulation also uses an orthogonal curvilinear coordinates given by the two surface coordinates plus a third normal to the body surface. The lack of curvature terms is due to that the boundary layer equations are rewritten as three-dimensional partial differential equations in an Euclidean domain and, since this is a flat space, the flow domain has not curvature terms and only remains the surface metric tensor in the continuity equation. In particular, it is shown that the developed equations are covariant under a linear coordinate transformation on the two surface coordinates, and a scaling one along the normal coordinate to the body surface. As a practical use of them, the boundary layer flow on the surface of a sphere in an axisymmetrical flow is numericaly computed using a pseudo-spectral approach.
oai:ojs.www.cimec.org.ar:article/2392
2009-08-04T16:14:18Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2392
2009-08-04T16:14:18Z
Cuadernos de Matemática y Mecánica
2006
Sobolev spaces associated to the harmonic oscillator.
Articles
Bongioanni, Bruno
Torrea, José L.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2392
en
We define the Hermite Sobolev spaces naturally associated to the harmonic oscillator $H= -\Delta +|x|^2.$ Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.
Published: Proc. Indian Acad. Sci. Math. Sci. 116 (2006), no. 3, 337--360.
oai:ojs.www.cimec.org.ar:article/2962
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2962
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Equivalence of Haar bases associated to different dyadic systems
Articles
Aimar, Hugo A.
Bernardis, Ana L.
Nowak, Luis
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2962
en
In this note we give sufficient conditions on two dyadic systems on a space of homogeneous type in order to obtain the equivalence of corresponding Haar systems on Lebesgue spaces. The main tool is the vector valued Fefferman-Stein inequality for the Hardy-Littlewood maximal operator.
Accepted: Journal of Geometric Analysis. November 2009.
oai:ojs.www.cimec.org.ar:article/876
2007-02-21T18:46:37Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/876
2007-02-21T18:46:37Z
Cuadernos de Matemática y Mecánica
2006
Simultaneous Untangling and Smoothing of Moving Mesh
Articles
Lopez, Ezequiel J.
Nigro, Norberto Marcelo
Storti, Mario Alberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/876
en
In this paper a usefull technique for simultaneous untangling and smoothing of meshes is presented. It is based as an extension of an earlier smoothing strategy developed by the authors and employed to solve the computational mesh dynamics stage in fluid-structure interaction problems. In moving grid problems the mesh untangling is necessary to remedy the drawback produced by the elements inversion arisen from the boundary motion making the mesh invalid. The original smoothing strategy is defined in terms of the minimization of a functional associated with the mesh distortion employing an indicator of the element geometric quality. This functional becomes discontinuous when an element has null volume, making impossible to ob- tain a valid mesh from an invalid one. To circumvent this drawback, the original functional is transformed in order to guarantee its continuity for the whole space of volume values getting in this way the untangling technique. The regularization depends on one parameter, allowing to recover the original functional when this parameter tends to zero. This feature is very important because at first it is necessary to regularize the functional for making the untangling possible, i.e. to make the mesh valid, but then, it is advisable to use the original functional to make the smoothing optimal. This technique is applied to several test cases, including 2D and 3D meshes with simplicial elements. An additional example serves as a guide to show how this technique may be employed for mesh genera- tion too. [Submitted to Int J N Meth Engng (2006)]
oai:ojs.www.cimec.org.ar:article/2383
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2383
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Balls as subspaces of homogeneous type: on a construction due to R. Macías and C. Segovia
Articles
Aimar, Hugo A.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2383
en
oai:ojs.www.cimec.org.ar:article/2699
2009-10-02T12:25:42Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2699
2009-10-02T12:25:42Z
Cuadernos de Matemática y Mecánica
2006
Free nilpotent minimum algebras
Articles
Busaniche, Manuela
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2699
en
In the present paper we give a description of the free algebra over an arbitrary set of generators in the variety of nilpotent minimum algebras. Such description is given in terms of a weak boolean product of directly indecomposable algebras over the boolean space corresponding to the boolean subalgebra of the free NM-algebra.
Published: Mathematical Logic Quarterly, 52 N3 (2006), 219-236.
oai:ojs.www.cimec.org.ar:article/2999
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2999
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
Haarlet Analysis of Lipschitz Regularity in Metric Measure Spaces
Articles
Aimar, Hugo
Bernardis, Ana
Nowak, Luis
2011-02-15 12:42:52
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2999
en
In this note we shall give a simple characterization of Lipschitz
spaces on spaces of homogeneous type via Haar coefficients. As a consequence of our main result we obtain a new proof of the equivalence of the Campanato and Lipschitz classes on space of homogeneous type due to Macías and Segovia.
oai:ojs.www.cimec.org.ar:article/1661
2009-04-28T17:36:14Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1661
2009-04-28T17:36:14Z
Cuadernos de Matemática y Mecánica
2001
Algebraic Discrete Non-Local (DNL) Absorbing Boundary Condition for the Ship Wave Resistance Problem
Articles
Storti, Mario Alberto
D'Elía, Jorge
Idelsohn, Sergio
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1661
CONICET, UNL, ANPCyT
en
An absorbing boundary condition for the ship wave resistance problem is presented. In contrast to the Dawson-like methods, it avoids the use of numerical viscosities in the discretization, so that a centered scheme can be used for the free surface operator. The absorbing boundary condition is “completely absorbing,” in the sense that the solution is independent of the position of the downstream boundary and is derived from straightforward analysis of the resulting constant-coefficients difference equations, assuming that the mesh is 1D-structured (in the longitudinal direction) and requires the eigen-decomposition of a matrix one dimension lower than the system matrix. The use of a centered scheme for the free surface operator allows a full finite element discretization. The drag is computed by a momentum flux balance. This method is more accurate and guarantees positive resistances.
oai:ojs.www.cimec.org.ar:article/2537
2009-08-14T21:52:35Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2537
2009-08-14T21:52:35Z
Cuadernos de Matemática y Mecánica
2001
An adaptive Uzawa FEM for the Stokes Problem: Convergence without the inf-sup Condition
Articles
Bänsch, Eberhard
Morin, Pedro
Nochetto, Ricardo H.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2537
en
We introduce and study an adaptive finite element method for the Stokes system based on an Uzawa outer iteration to update the pressure and an elliptic adaptive inner iteration for velocity. We show linear convergence in terms of the outer iteration counter for the pairs of spaces consisting of continuous finite elements of degree k for velocity whereas for pressure the elements can be either discontinuous of degree k-1 or continuous of degree k-1 and k. The popular Taylor-Hood family is the sole example of stable elements included in the theory, which in turn relies on the stability of the continuous problem and thus makes no use of the discrete inf-sup condition. We discuss the realization and complexity of the elliptic adaptive inner solver, and provide consistent computational evidence that the resulting meshes are quasi-optimal.
Keywords: A posteriori error estimators, adaptive mesh refinement, convergence, data oscillation, performance, quasi-optimal meshes
AMS Subject Classifications: 65N12, 65N15, 65N30, 65N50, 65Y20
Published: SIAM Journal on Numerical Analysis, Volume 40, Number 4 (2002), 1207-1229.
oai:ojs.www.cimec.org.ar:article/2984
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2984
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
Convergence of an adaptive Ka\v canov FEM for quasi-linear problems
Articles
Garau, Eduardo M.
Morin, Pedro
Zuppa, Carlos
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2984
en
We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Kacanov iteration and a mesh adaptation step is performed after each linear solve. The method is thus inexact because we do not solve the discrete nonlinear problems exactly, but rather perform one iteration of a fixed point method (Kacanov), using the approximation of the previous mesh as an initial guess. The convergence of the method is proved for any reasonable marking strategy and starting from any initial mesh. We conclude with some numerical experiments that illustrate the theory.
oai:ojs.www.cimec.org.ar:article/2397
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2397
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
Weak type $(1,1)$ of maximal operators on metric measure spaces
Articles
Carena, Marilina
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2397
en
A discretization method for the study of the weak type $(1,1)$ for the maximal of a sequence of convolution operators on $\mathbb R^n$ has been introduced by Miguel de Guzm\'an and Teresa Carrillo, by replacing the integrable functions by finite sums of Dirac deltas. Trying to extend the above mentioned result to integral operators defined on metric measure spaces, a general setting containing at once continuous, discrete and mixed contexts, a caveat comes from the result in \emph{On restricted weak type $(1,1)$; the discrete case} (Akcoglu M.; Baxter J.; Bellow A.; Jones R., Israel J. Math. 124 (2001), 285--297). There a sequence of convolution operators in $\ell^1(\mathbb Z)$ is constructed such that the maximal operator is of restricted weak type $(1,1)$, or equivalently of weak type $(1,1)$ over finite sums of Dirac deltas, but not of weak type $(1,1)$.
The purpose of this note is twofold. First we prove that, in a general metric measure space with a measure that is absolutely continuous with respect to some doubling measure, the weak type $(1,1)$ of the maximal operator associated to a given sequence of integral operators is equivalent to the weak type $(1,1)$ over linear combinations of Dirac deltas with positive integer coefficients. Second, for the non-atomic case we obtain as a corollary that any of these weak type properties is equivalent to the weak type $(1,1)$ over finite sums of Dirac deltas supported at different points.
oai:ojs.www.cimec.org.ar:article/1385
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1385
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
Completeness of Muckenhoupt Classes
Articles
Aimar, Hugo
Carena, Marilina
Iaffei, Bibiana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1385
en
In this note we prove that the Hausdorff distance between compact sets and the Kantorovich distance between measures, provide an adequate setting for the convergence of Muckenhoupt weights. The results which we prove on compact metric spaces with finite metric dimension can be applied to classical fractals.
oai:ojs.www.cimec.org.ar:article/2398
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2398
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
On approximation of maximal operators
Articles
Aimar, Hugo A.
Carena, Marilina
Iaffei, Bibiana
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2398
en
We prove that the weak type (1, 1) for the maximal of a sequence of integral operators on a metric measure space X, follows from the uniform weak type on Dirac deltas of the restriction of the operators to a sequence of approximations of X.
oai:ojs.www.cimec.org.ar:article/2970
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2970
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Integration of the Composite Mesh Technique with the Multigrid Method
Articles
Sarraf, Sofía
López, Ezequiel Javier
Bergallo, Marta Beatriz
Sonzogni, Victorio Enrique
Ríos Rodríguez, Gustavo
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2970
ANPCyT, CONICET, UNL
en
The Composite Finite Element Mesh method is useful for discretization error estimation and, in addition, for solution improvement with no appreciable increment in the computational cost. The technique consists in redeﬁne over a given mesh the linear operator that arises from the discretization of a partial diﬀerential equation. This operator is modiﬁed according to an appropriate linear combination between the operators of the given mesh and of a coarse mesh, which must be a coarsening of the ﬁrst one. On the other hand, Multigrid methods solve a linear system using systems of several sizes resulting from diﬀerent discretization levels. This feature motivates the study of the application of the Multigrid strategy in conjunction with the Composite Mesh technique. In this work, we propose a scheme for solving the linear system arising from the Composite Mesh strategy using a Multigrid method. Particularly, we use a geometric version of the Multigrid technique. The proposal is based on a modiﬁcation of the operators in some levels of the Multigrid algorithm in order to achieve both, the advantages of Multigrid for linear systems resolution and the solution improvement that could be achieved with the Composite Mesh strategy. Several elliptic test problems with analytical solution are presented, where the convergence rates are analyzed and the decrease in discretization errors is quantiﬁed.
oai:ojs.www.cimec.org.ar:article/7
2009-07-30T17:24:12Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/7
2009-07-30T17:24:12Z
Cuadernos de Matemática y Mecánica
2005
On the efficiency and quality of numerical solutions in CFD problems using the Interface Strip Preconditioner for domain decomposition methods
Articles
Paz, Rodrigo Rafael
Nigro, Norberto Marcelo
Storti, Mario Alberto
2006-06-24 12:10:56
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/7
CONICET, UNL, ANPCyT
en
In this paper, the efficiency and the quality of the solutions obtained with a new parallelizable preconditioner for Domain Decomposition Methods (DDM) by means of Finite Element discretization of partial differential equations arising in the context of CFD problems is studied. We compare the convergence to the analytical solution or measured data for problems that have been considered as `benchmarks' in the computational fluid dynamic literature. For this purpose, we study the solution obtained via parallelized iterative methods that have been extensively used (e.g. CG and GMRES global iteration and its variants) in CFD computations and those obtained with the Interface Strip (IS) preconditioner for the Schur Complement method. The idea is to present the new solver as an alternative to obtain more accurate and faster solutions in the context of monolithic and non-monolithic CFD schemes. For this purpose, the confined internal flows and external viscous compressible/incompressible flow around (complex-shape) bodies are considered.[International Journal for Numerical Methods in Fluids 52, pp. 89-118 (2006)]
oai:ojs.www.cimec.org.ar:article/1019
2009-07-30T17:24:12Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1019
2009-07-30T17:24:12Z
Cuadernos de Matemática y Mecánica
2005
Added mass of an oscillating hemisphere at very-low and very-high frequencies
Articles
Storti, Mario Alberto
D'Elia, Jorge
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1019
en
A floating hemisphere under forced harmonic oscillation at very-low
and very-high frequencies is considered. The problem is reduced to an
elliptic one, that is, the Laplace operator in the exterior domain
with Dirichlet and Neumann boundary conditions. Asymptotic values of
the added mass are found with an analytic prolongation for the surge
mode, and with a semi-numerical computation with spherical harmonics
for the heave mode. The general procedure is based on the use of
spherical harmonics and its derivation is based on a physical insight
rather than a mathematical one. This case can be used to test the
accuracy achieved by numerical codes based on other formulations as
finite or boundary elements. [To appear in Journal Fluids Engineering ASME]
oai:ojs.www.cimec.org.ar:article/2388
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2388
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Riesz transforms related to Schrödinger operators acting on BMO type spaces.
Articles
Bongioanni, Bruno
Harboure, Eleonor
Salinas, Oscar
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2388
en
In this work we obtain boundedness on suitable weighted $BMO$ type spaces of Riesz transforms, and their adjoints, associated to the Schr\"odinger operator $-\Delta+V$, where $V$ satisfies a reverse H\"older inequality. Our results are new even in the unweighted case.
Accepted: J. Math. Anal. Appl.
oai:ojs.www.cimec.org.ar:article/2705
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2705
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Residuated lattices as algebraic semantics for paraconsistent Nelson logic
Articles
Busaniche, Manuela
Cignoli, Roberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2705
en
The class of NPc-lattices is introduced as a quasivariety of commutative residuated lattices, and it is shown that the class of pairs $(\A, A^+)$ such that $\A$ is an NPc-lattice and $A^+$ is its positive cone, is a matrix semantics for Nelson paraconsistent logic.
Published: Journal of Logic and Computation (2009), doi: 10.1093/logcom/exp028.
oai:ojs.www.cimec.org.ar:article/3730
2012-02-21T00:06:26Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/3730
2012-02-21T00:06:26Z
Cuadernos de Matemática y Mecánica
2011
Tug-of-war games and the infinity Laplacian with spatial dependence
Articles
Gómez, Ivana
Rossi, Julio Daniel
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/3730
The research was supported by Ministerio de Ciencia e Innovación grant MTM2008-05824, Spain and CONICET, Argentina.
en
In this paper we look for PDEs that arise as limits of values of Tug-of-War games when the possible movements of the game are taken in a family of sets that are not necessarily euclidean balls. In this way we find existence of viscosity solutions to the Dirichlet problem for an equation of the form -(x) = 0, that is, an infinity Laplacian with spatial dependence. Here J_{x}(Dv(x)) is a vector that depends on the the spatial location and the gradient of the solution.
oai:ojs.www.cimec.org.ar:article/2379
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2379
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
Approximating optimization problems over convex functions
Articles
Aguilera, Néstor E.
Morin, Pedro
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2379
en
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some problems in economics.
In the continuous setting and assuming smoothness, the convexity constraints may be given locally by asking the Hessian matrix to be positive semidefinite, but in making discrete approximations two difficulties arise: the continuous solutions may be not smooth, and functions with positive semidefinite discrete Hessian need not be convex in a discrete sense.
Previous work has concentrated on non-local descriptions of convexity, making the number of constraints to grow super-linearly with the number of nodes even in dimension 2, and these descriptions are very difficult to extend to higher dimensions.
In this paper we propose a finite difference approximation using positive semidefinite programs and discrete Hessians, and prove convergence under very general conditions, even when the continuous solution is not smooth, working on any dimension, and requiring a linear number of constraints in the number of nodes.
Using semidefinite programming codes, we show concrete examples of approximations to problems in two and three dimensions.
Published: Numerische Mathematik 111 (2008), 1-34; DOI: 10.1007/s00211-008-0176-4.
oai:ojs.www.cimec.org.ar:article/2695
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2695
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Regularity of the Schrödinger equation for the harmonic oscillator
Articles
Bongioanni, Bruno
Rogers, Keith M.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2695
en
We consider the Schrödinger equation for the harmonic oscillator $i \partial_t u = Hu$, where $H = -\Delta + |x|^2$, with initial data in the Hermite-Sobolev space $H^{-s/2} L^2(\real^n)$. We obtain smoothing and maximal estimates and apply these to perturbations of the equation and almost everywhhere convergence problems.
Accepted: Arkiv för matematik
oai:ojs.www.cimec.org.ar:article/2994
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2994
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
End-Point Estimates for Iterated Commutators of Multilinear Singular Integrals
Articles
Pérez, Carlos
Pradolini, Gladis
Torres, Rodolfo H.
Trujillo-González, Rodrigo
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2994
en
Iterated commutators of multilinear Calderón-Zygmund operators and pointwise multiplication with functions in BMO are studied in products of Lebesgue spaces. Both strong type and weak end-point estimates are obtained, including weighted results involving the vectors weights of the multilinear Calderón-Zygmund
theory recently introduced in the literature. Some better than expected estimates for certain multilinear operators are presented too.
oai:ojs.www.cimec.org.ar:article/457
2009-07-31T22:36:23Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/457
2009-07-31T22:36:23Z
Cuadernos de Matemática y Mecánica
1980
A Well Behaved Quasi-distance for Spaces of Homogeneous Type
Articles
Macías, Roberto A.
Segovia, Carlos
2009-07-31 19:36:23
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/457
CONICET
en
For any space of homogeneous type a quasi-distance equivalent to the original one is obtained satisfying that, if B and B' are balls such the center of the B' belongs to B and the radius of B' is smaller than the radius of B then, the measure of the intersection of B and B' is smaller than a constant fraction of the measure of the B'. An application to weighted norm inequalities for Hardy-Littlewood maximal function, which extends a result of A. P. Calderón, is given.
oai:ojs.www.cimec.org.ar:article/1391
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1391
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Aeroelastic study of the start-up of a rocket engine nozzle
Articles
Garelli, Luciano
Paz, Rodrigo Rafael
Storti, Mario Alberto
2009-04-08 20:22:03
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1391
en
The aim of this paper is to analyze the aeroelastic processes developed during the starting phase of a rocket engine via a coupling fluid/structure code. This analysis gives a better understanding of the behavior of the structure as the shock waves propagate inside the engine nozzle. The gasdynamics Euler equations are solved for the fluid, and constitutive linear elastic solid under the assumption of large displacements and rotations with no material damping is adopted for the structure. The coupling of each subproblem is carried out with a Gauß-Seidel algorithm over the fluid and structure states. For the fluid problem an ALE (Arbitrary Lagrangian-Eulerian Formulation) formulation is used. It allows to define a reference system following the moving boundaries while the structure is deformed. The code is validated with a study of the flutter phenomena that may occur when a supersonic compressible fluid flows over a flat solid plate. Regarding the rocket engine ignition problem, a modal analysis of the structure is performed in order to analyze the eigenfrequency shifts when considering the coupling with the fluid flow. [Submitted to Computers and Fluids 2009]
oai:ojs.www.cimec.org.ar:article/2533
2009-09-07T19:30:44Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2533
2009-09-07T19:30:44Z
Cuadernos de Matemática y Mecánica
2007
Convergence of finite elements adapted for weaker norms
Articles
Morin, Pedro
Siebert, Kunibert G.
Veeser, Andreas
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2533
en
We consider finite elements that are adapted to a (semi)norm that is weaker than the one of the trial space. We establish convergence of the finite element solutions to the exact one under the following conditions: refinement relies on unique quasi-regular element subdivisions and generates locally quasi-uniform grids; the finite element spaces are conforming, nested, and satisfy the inf-sup condition; the error estimator is reliable and appropriately locally efficient; the indicator of a non-marked element is bounded by the estimator contribution associated with the marked elements, and each marked element is subdivided at least once. This abstract convergence result is illustrated by two examples.
Keywords: Adaptivity, conforming finite elements, convergence, weaker (semi)norms, mesh-dependent norms
Published: Applied and Industrial Matematics in Italy II, Selected Contributions from the 8th SIMAI Conference, Vincenzo Cutello, Giorgio Fotia, Luigia Puccio, eds. Series on Advances in Mathematics for Applied Sciences - Vol. 75. World Scientific, 2007.
oai:ojs.www.cimec.org.ar:article/2978
2011-09-26T01:17:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2978
2011-09-26T01:17:03Z
Cuadernos de Matemática y Mecánica
2010
Simulation of free surface flows by a finite element interface capturing technique
Articles
Battaglia, Laura
Storti, Mario Alberto
D'Elía, Jorge
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2978
CONICET,ANPCyt,UNL
en
Transient free surface flows are numerically simulated by a finite element interface capturing method based on a level set approach. The methodology consists of the solution of two-fluid viscous incompressible flows for a single domain, where the liquid phase is identified by positive values of the level set function, the gaseous one by negative ones, and the free surface by the zero level set. The numerical solution at each time step is performed in three stages: (i) a two-fluid Navier--Stokes stage, (ii) an advection stage for the transport of the level set function, and (iii) a bounded reinitialization with continuous penalization stage for keeping smoothness of the level set function. The proposed procedure, and particularly the renormalization stage, are evaluated in two typical two and three-dimensional problems. [Submitted to Int. J Comp Fluid Dynamics, ISSN 1061-8562]
oai:ojs.www.cimec.org.ar:article/230
2009-08-14T21:35:03Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/230
2009-08-14T21:35:03Z
Cuadernos de Matemática y Mecánica
2003
A finite element method for surface diffusion: the parametric case
Articles
Morin, Pedro
Bänsch, Eberhard
Nochetto, Ricardo H.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/230
CONICET - UNL
en
Abstract: Surface diffusion is a (4th order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. We present a novel variational formulation for parametric surfaces with or without boundaries. The method is semi-implicit, requires no explicit parametrization, and yields a linear system of elliptic PDE to solve at each time step. We next develop a finite element method, propose a Schur complement approach to solve the resulting linear systems, and show several significant simulations, some with pinch-off in finite time. We introduce a mesh regularization algorithm, which helps prevent mesh distortion, and discuss the use of time and space adaptivity to increase accuracy while reducing complexity.
Keywords: Surface diffusion, fourth-order parabolic problem, finite elements, Schur complement, smoothing effect, pinch-off.
AMS Subject Classifications: 35K55, 65M12, 65M15, 65M60, 65Z05.
Published: Journal of Computational Physics 203 (2005) 321--343.
Published: Journal of Computational Physics 203 (2005) 321--343.
oai:ojs.www.cimec.org.ar:article/1318
2009-12-04T16:20:34Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/1318
2009-12-04T16:20:34Z
Cuadernos de Matemática y Mecánica
2008
An h-Adaptive Unstructured Mesh Refinement Strategy for Unsteady Problems
Articles
Ríos Rodríguez, Gustavo
Nigro, Norberto Marcelo
Storti, Mario Alberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/1318
CONICET, UNL, ANPCyT
en
An h-adaptive unstructured mesh refinement strategy to solve unsteady problems by the finite element method is presented. The maximum level of refinement for the mesh is prescribed beforehand. The core operation of the strategy, namely the elements refinement, is described in detail. It is shown through numerical tests that one of the advantages of the chosen refinement procedure is to keep bounded the decrease of the mesh's quality. The type of element is not changed and no transition templates are used, therefore hanging nodes appear in the adapted mesh. The 1-irregular nodes refinement constraint is applied and the refinement process driven by this criterion is recursive. Both the strength and weakness of the adaptivity algorithm are mentioned, based on clock time measures and implementation issues. To show the proper working of the strategy, an axisymmetric, compressible non-viscous starting flow in a bell-shaped nozzle is solved over an unstructured mesh of hexaedra. [Submitted for publication to Latin American Applied Research]
oai:ojs.www.cimec.org.ar:article/2393
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2393
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
LDR a package for likelihood-based sufficient dimension reduction
Articles
Cook, Dennis
Forzani, Liliana
Tomassi, Diego
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2393
en
We introduce a software package running under Matlab that implements several recently proposed likelihood-based methods for sufficient dimension reduction. Current capabilities include estimation of reduced subspaces with a fixed dimension d, as well as estimation of d by use of likelihood-ratio testing, permutation testing and information criteria. The methods are suitable for preprocessing data for both regression and classification. Implementations of related estimators are also available. Although the software is more oriented to command-line operation, a graphical user interface is also provided for prototype computations.
oai:ojs.www.cimec.org.ar:article/2963
2010-06-08T22:34:30Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/2963
2010-06-08T22:34:30Z
Cuadernos de Matemática y Mecánica
2009
Weighted local BMO spaces and the local Hardy-Littlewood maximal operator
Articles
Chicco Ruiz, Aníbal
Harboure, Eleonor O.
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/2963
en
oai:ojs.www.cimec.org.ar:article/3
2007-02-21T01:20:37Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/3
2007-02-21T01:20:37Z
Cuadernos de Matemática y Mecánica
2006
Sloshing in a Multi-Physics Parallel Programming Paradigm
Articles
Battaglia, Laura
D'Elía, Jorge
Storti, Mario Alberto
Nigro, Norberto Marcelo
2006-06-24 09:51:45
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/3
CONICET, UNL, ANPCyT
en
In this work, transient free surface flows of a viscous incompressible fluid are numerically solved through parallel computation. Transient free surface flows are boundary-value problems of moving type that involve geometrical non-linearities. In contrast to more conventional CFD problems, the computational flow domain is partially bounded by a free surface which is not known a priori, since its shape must be computed as part of the solution. In steady-flow the free surface is obtained by an iterative process, but when the free surface evolves with time the problem is more difficult, generating large distortions in the computational flow domain. The incompressible Navier-Stokes numerical solver is based on the finite element method with equal order elements for pressure and velocity (linear elements), and it uses a Streamline Upwind/Petrov-Galerkin (SUPG) scheme combined with a Pressure-Stabilizing/Petrov-Galerkin (PSPG) one. At each time step, the fluid equations are solved with constant pressure and null viscous traction conditions at the free surface and the velocities obtained in this way are used for updating the positions of the surface nodes. Then, a pseudo elastic problem is solved in the fluid domain in order to relocate the interior nodes so as to keep mesh distortion controlled. This has been implemented in PETSc-FEM by running two parallel instances of the code and exchanging information between them. Some numerical examples are presented. [Journal of Applied Mechanics (JAM-ASME) vol 73, pp. 1017-1025 (2006)]
oai:ojs.www.cimec.org.ar:article/877
2007-04-27T03:25:57Z
cmm:ART
v2
https://cimec.org.ar/ojs/index.php/cmm/article/view/877
2007-04-27T03:25:57Z
Cuadernos de Matemática y Mecánica
2006
Numerical simulations of axisymmetric inertial waves in a rotating sphere by finite elements
Articles
D'Elia, Jorge
Nigro, Noberto
Storti, Mario Alberto
url:https://cimec.org.ar/ojs/index.php/cmm/article/view/877
en
Axisymmetric inertial waves of a viscous fluid that fill a perturbed
rotating spherical container are numerically simulated by finite
elements. A laminar flow of an incompressible viscous fluid of
Newtonian type is assumed in the numerical simulations. A monolithic
computational code is employed, which is based on stabilized finite
elements by means of a Streamline Upwind Petrov Galerkin (SUPG) and
Pressure Stabilized Petrov Galerkin
(PSPG) composed scheme. The Reynolds number is fixed as 50 000, while the ranges of the Rossby and Ekman
numbers are 0.2 Ro 1 and 2 × 10-5 Ek 10-4 , respectively. Some flow visualizations are performed. The
pressure coefficient spectrum at the centre of the sphere is plotted as a function of the frequency ratio and some
resonant frequencies are identified. The position of these resonant frequencies are in good agreement with previous
experimental and analytical ones in the inviscid limit.
[To appear in International Journal of Computational Fluid Dynamics.Author Posting. (c) Taylor & Francis, 2007. ]
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