A Chimera Method Based on Dirichlet-Dirichlet Coupling and Pasting Penalization Operators

Abstract

A chimera method for pasting different meshes in the context of the finite element method is presented. The method is based both on transferring the solution on one mesh to the boundary of the other via Dirichlet boundary conditions and interpolation, and also with a penalization "pasting" operator. One of the advantages of the proposed method is that no changes in topology arise during the computations. The second advantage is that the solution can be obtained iteratively with a convergence rate that is similar to that one for an equivalent non-chimera mesh, and the matrix-vector operator can be computed by completely decouple operations on both meshes. For symmetric positive-definite operators the resulting system is not symmetric positive-definite, however the solution can be obtained with biconjugate gradient stabilized method, so the memory requirement is almost the same as for the conjugate gradient method, which could be used for an equivalent non-chimera mesh. Several examples are presented assessing the precision and computational cost of the method.