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

2018/10/29 by Langer, Ulrich, Yang, Huidong
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1810.12159

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.

Related

• Space-time balancing domain decomposition
• Space-Time Finite Element Methods for Parabolic Evolution Problems with Non-smooth Solutions
• Adaptive space-time finite element methods for non-autonomous parabolic\n problems with distributional sources
• A Stabilized Unfitted Space-time Finite Element Method for Parabolic Problems on Moving Domains
• Simultaneous space-time finite element methods for parabolic optimal control problems