About the Parallel Versatile Implementation of Finite Element Tearing and Interconnect Methods

Abstract

The FETI (Finite Element Tearing and Interconnect) method is a well-established domain decomposition technique for solving large systems of equations which usually result from the discretisation of partial differential equations. Nowadays, many different versions of FETI are available, each one of them trying to exploit certain characteristics of the physical problem being solved. This broad family of FETI solvers makes necessary to think in informatic solutions which take care not only of the computational performance, but also of the flexibility of the code. Hard-coded solutions must be clearly avoided in order to give support to existing and future FETI versions which have different requirements concerning coarse spaces, preconditioners, direct and iterative solvers and projections. In this work, the issues related to satisfying those requirements in the parallel implementation of FETI methods are studied. An object-oriented design is adopted for ensuring the flexibility needed for the future development of additional FETI versions. A particular emphasis is placed in the implementation of these methods as extensions to the PETSc (Portable, Extensible Toolkit for Scientific Computation) library. A performance test is conducted in order to show the capabilities of the developed library.