TY - GEN

T1 - Fully Algebraic Two-Level Overlapping Schwarz Preconditioners for Elasticity Problems

AU - Heinlein, Alexander

AU - Hochmuth, Christian

AU - Klawonn, Axel

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85106449555&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-55874-1_52

DO - 10.1007/978-3-030-55874-1_52

M3 - Conference contribution

AN - SCOPUS:85106449555

SN - 9783030558734

T3 - Lecture Notes in Computational Science and Engineering

SP - 531

EP - 539

BT - Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference

A2 - Vermolen, Fred J.

A2 - Vuik, Cornelis

PB - Springer

T2 - European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019

Y2 - 30 September 2019 through 4 October 2019

ER -