GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
A comparison of some dynamic load-balancing algorithms for a parallel adaptive flow solver
Parallel Computing - Special issue on graph partioning and parallel computing
SIAM Journal on Scientific Computing
A New Paradigm for Parallel Adaptive Meshing Algorithms
SIAM Journal on Scientific Computing
Euro-Par '01 Proceedings of the 7th International Euro-Par Conference Manchester on Parallel Processing
Domain decomposition preconditioning for parallel PDE software
Engineering computational technology
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In this paper we extend our previous work on the use of domain decomposition (DD) preconditioning for the parallel finite element (FE) solution of three-dimensional elliptic problems [3, 6] and convection-dominated problems [7, 8] to include the use of local mesh refinement. The preconditioner that we use is based upon a hierarchical finite element mesh that is partitioned at the coarsest level. The individual subdomain problems are then solved on meshes that have a single layer of overlap at each level of refinement in the mesh. Results are presented to demonstrate that this preconditioner leads to iteration counts that appear to be independent of the level of refinement in the final mesh, even in the case where this refinement is local in nature: as produced by an adaptive finite element solver for example.