Fully Algebraic Two-Level Overlapping Schwarz Preconditioners for Elasticity Problems

Different parallel two-level overlapping Schwarz preconditioners with Generalized Dryja–Smith–Widlund (GDSW) and Reduced dimension GDSW (RGDSW) coarse spaces for elasticity problems are considered. GDSW type coarse spaces can be constructed from the fully assembled system matrix, but they additionally need the index set of the interface of the corresponding nonoverlapping domain decomposition and the null space of the elasticity operator, i.e., the rigid body motions. In this paper, fully algebraic variants, which are constructed solely from the uniquely distributed system matrix, are compared to the classical variants which make use of this additional information; the fully algebraic variants use an approximation of the interface and an incomplete algebraic null space. Nevertheless, the parallel performance of the fully algebraic variants is competitive compared to the classical variants for a stationary homogeneous model problem and a dynamic heterogenous model problem with coefficient jumps in the shear modulus; the largest parallel computations were performed on 4096 MPI (Message Passing Interface) ranks. The parallel implementations are based on the Trilinos package FROSch.