Static load balancing applied to Schur complement method

• Published in: Computers & structures Vol. 85; no. 9; pp. 489 - 498
• Main Authors: Medek, Ondřej, Kruis, Jaroslav, Bittnar, Zdeněk, Tvrdík, Pavel
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2007
• Subjects: Domain decomposition; Finite element methods; Mesh partitioning; Multilevel graph partitioning; Parallel solvers; Schur complement method; Static load balancing; Time-dependent problems; Multilevel graph partitioning; Time-dependent problems; Static load balancing; Mesh partitioning; Schur complement method; Parallel solvers; Finite element methods; Domain decomposition
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2006.08.025

A finite element method often leads to large sparse symmetric and positive definite systems of linear equations. We consider parallel solvers based on the Schur complement method on homogeneous parallel machines with distributed memory. A finite element mesh is partitioned by graph partitioning. Such partitioning results in submeshes with similar numbers of elements and, consequently, submatrices of similar sizes. The submatrices are partially factorised. The time spent on the partial factorisation can be different, i.e., disbalanced, because methods exploiting the sparsity of submatrices are used. This paper proposes a Quality Balancing heuristic that modifies classic mesh partitioning so that the partial factorisation times are balanced, which saves overall computation time, especially for time dependent mechanical and nonstationary transport problems.