Multigrid Method for Maxwell's Equations
SIAM Journal on Numerical Analysis
Parallel multigrid solver for 3D unstructured finite element problems
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Two-grid Method for Linear Elasticity on Unstructured Meshes
SIAM Journal on Scientific Computing
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Multigrid
A distributed memory unstructured gauss-seidel algorithm for multigrid smoothers
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
An Iterative Method with Convergence Rate Chosen a priori
An Iterative Method with Convergence Rate Chosen a priori
Proceedings of the 2004 ACM/IEEE conference on Supercomputing
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Journal of Computational Physics
A distributed memory parallel Gauss-Seidel algorithm for linear algebraic systems
Computers & Mathematics with Applications
Journal of Computational Physics
Enhancing the performance of multigrid smoothers in simultaneous multithreading architectures
VECPAR'06 Proceedings of the 7th international conference on High performance computing for computational science
A fast parallel Poisson solver on irregular domains applied to beam dynamics simulations
Journal of Computational Physics
Multi-level µ-finite element analysis for human bone structures
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Analysis and Computation of Compatible Least-Squares Methods for div-curl Equations
SIAM Journal on Numerical Analysis
Multigrid Smoothers for Ultraparallel Computing
SIAM Journal on Scientific Computing
Improvements of a fast parallel poisson solver on irregular domains
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
Smoothed aggregation spectral element agglomeration AMG: SA-ρAMGe
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
A highly scalable matrix-free multigrid solver for μFE analysis based on a pointer-less octree
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
Journal of Computational Physics
Hi-index | 31.47 |
Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.