Applied numerical linear algebra
Applied numerical linear algebra
Parallel multilevel k-way partitioning scheme for irregular graphs
Supercomputing '96 Proceedings of the 1996 ACM/IEEE conference on Supercomputing
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Evaluation of Three Unstructured Multigrid Methods on 3D Finite Element
Evaluation of Three Unstructured Multigrid Methods on 3D Finite Element
Parallel multigrid smoothing: polynomial versus Gauss--Seidel
Journal of Computational Physics
Proceedings of the 2004 ACM/IEEE conference on Supercomputing
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Sparse Tiling for Stationary Iterative Methods
International Journal of High Performance Computing Applications
Mumford and Shah Functional: VLSI Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A distributed memory parallel Gauss-Seidel algorithm for linear algebraic systems
Computers & Mathematics with Applications
Distributed gradient-domain processing of planar and spherical images
ACM Transactions on Graphics (TOG)
Combining performance aspects of irregular gauss-seidel via sparse tiling
LCPC'02 Proceedings of the 15th international conference on Languages and Compilers for Parallel Computing
ASCOS: an asymmetric network structure COntext similarity measure
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
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Gauss-Seidel is a popular multigrid smoother as it is provably optimal on structured grids and exhibits superior performance on unstructured grids. Gauss-Seidel is not used to our knowledge on distributed memory machines as it is not obvious how to parallelize it effectively. We, among others, have found that Krylov solvers preconditioned with Jacobi, block Jacobi or overlapped Schwarz are effective on unstructured problems. Gauss-Seidel does however have some attractive properties, namely: fast convergence, no global communication (ie, no dot products) and fewer flops per iteration as one can incorporate an initial guess naturally. This paper discusses an algorithm for parallelizing Gauss-Seidel for distributed memory computers for use as a multigrid smoother and compares its performance with preconditioned conjugate gradients on unstructured linear elasticity problems with up to 76 million degrees of freedom.