Hierarchical LU decomposition-based preconditioners for BEM
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Publication:556642
DOI10.1007/s00607-004-0099-6zbMath1071.65031OpenAlexW2088527939MaRDI QIDQ556642
Publication date: 22 June 2005
Published in: Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00607-004-0099-6
Computational methods for sparse matrices (65F50) Boundary value problems for higher-order elliptic equations (35J40) Numerical computation of matrix norms, conditioning, scaling (65F35) Direct numerical methods for linear systems and matrix inversion (65F05) Boundary element methods for boundary value problems involving PDEs (65N38)
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Uses Software
Cites Work
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- Adaptive recompression of \(\mathcal H\)-matrices for BEM
- On the fast matrix multiplication in the boundary element method by panel clustering
- Mosaic-skeleton approximations
- The construction of some efficient preconditioners in the boundary element method
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- Wavelet approximation methods for pseudodifferential equations. I: Stability and convergence
- Effective algorithms with circulant-block matrices
- NETGEN: An advancing front 2D/3D-mesh generator based on abstract rules
- Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients
- Adaptive low-rank approximation of collocation matrices
- Construction and arithmetics of \(\mathcal H\)-matrices
- Approximation of boundary element matrices
- Hierarchical matrices based on a weak admissibility criterion
- Wavelet approximation methods for pseudodifferential equations. II: Matrix compression and fast solution
- A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
- Fast wavelet transforms and numerical algorithms I
- Efficient preconditioners for boundary element matrices based on grey-box algebraic multigrid methods
- Efficient inversion of the Galerkin matrix of general second-order elliptic operators with nonsmooth coefficients
- Wavelets on Manifolds I: Construction and Domain Decomposition
