Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Graph Partitioning and Parallel Solvers: Has the Emperor No Clother? (Extended Abstract)
IRREGULAR '98 Proceedings of the 5th International Symposium on Solving Irregularly Structured Problems in Parallel
Variable Reordering for a Parallel Envelope Method
ICPPW '04 Proceedings of the 2004 International Conference on Parallel Processing Workshops
BDDC by a frontal solver and the stress computation in a hip joint replacement
Mathematics and Computers in Simulation
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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.