BDDC preconditioners for a space-time finite element discretization of parabolic problems
For researchers solving parabolic PDEs with space-time methods, this work provides a domain decomposition preconditioner, though the robustness is only partial.
This paper develops BDDC preconditioners for solving linear systems from space-time finite element discretizations of parabolic problems, treating time as an additional spatial coordinate. Numerical experiments show the preconditioners are robust to some extent.
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.