BDDC preconditioners for a space-time finite element discretization of parabolic problems

TL;DR

This paper develops and analyzes BDDC preconditioners for space-time finite element discretizations of parabolic problems, treating time as a spatial coordinate, and demonstrates their robustness through numerical experiments.

Contribution

It introduces BDDC preconditioners tailored for space-time finite element systems, extending domain decomposition methods to unstructured space-time meshes.

Findings

Preconditioners show robustness in numerical tests.

Effective for large-scale space-time finite element systems.

Applicable to unstructured simplicial meshes.

Abstract

This paper deals with balanced domain decomposition by constraints (BDDC) method for solving large-scale linear systems of algebraic equations arising from the space-time finite element discretization of parabolic initial-boundary value problems. The time is considered as just another spatial coordinate, and the finite elements are continuous and piecewise linear on unstructured simplicial space-time meshes. We consider BDDC preconditioned GMRES methods for solving the space-time finite element Schur complement equations on the interface. Numerical studies demonstrate robustness of the preconditioners to some extent.