Scalable preconditioned conjugate gradient inversion of vector finite element mass matrices

DOI10.1016/S0377-0427(00)00407-6zbMath0964.65131MaRDI QIDQ1591191

Joe Koning, Dan White, Garry H. Rodrigue

Publication date: 26 June 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Galerkin methodpreconditioningconjugate gradient methodMaxwell's equationsmass matricesinversion algorithmsvector finite elements

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Electromagnetic theory (general) (78A25)

Cites Work

• A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
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• Mixed finite elements in \(\mathbb{R}^3\)
• Optimal block diagonal scaling of block 2-cyclic matrices
• Comparison of splittings used with the conjugate gradient algorithm
• Condition numbers and equilibration of matrices
• A Vector Finite Element Time-Domain Method for Solving Maxwell's Equations on Unstructured Hexahedral Grids
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• Iterative Methods for the Solution of Elliptic Problems on Regions Partitioned into Substructures
• The Condition Number of Equivalence Transformations That Block Diagonalize Matrix Pencils
• On Best Conditioned Matrices
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