Hierarchical Cholesky decomposition of sparse matrices arising from curl–curl-equation

DOI10.1515/jnma.2007.031zbMath1135.65015OpenAlexW4246966070MaRDI QIDQ5446877

I. Ibragimov, K. Straube, Sergej Rjasanow

Publication date: 6 March 2008

Published in: Journal of Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jnma.2007.031

zbMATH Keywords

algorithmsfinite element methodnumerical examplesclusteringMaxwell's equationssparse matrixpreconditionerreorderinghierarchical matrixapproximate Cholesky decomposition

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) PDEs in connection with optics and electromagnetic theory (35Q60) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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) Direct numerical methods for linear systems and matrix inversion (65F05)

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Uses Software

• MESHPART

Cites Work

• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• Adaptive low-rank approximation of collocation matrices
• The Evolution of the Minimum Degree Ordering Algorithm
• Rank-Revealing QR Factorizations and the Singular Value Decomposition
• Errata: A Stable Generalized Eigenvalue Problem
• Geometric Mesh Partitioning: Implementation and Experiments
• An Approximate Minimum Degree Ordering Algorithm
• H-matrix Preconditioners in Convection-Dominated Problems
• Nested Dissection of a Regular Finite Element Mesh