Adaptive Directional Compression of High-Frequency Helmholtz Boundary Element Matrices
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Steffen Börm
Abstract
Boundary element methods for the high-frequency Helmholtz equation require efficient compression techniques for the resulting matrices. Directional interpolation converges exponentially and is very robust and fast, but high accuracies lead to very large storage requirements. This problem can be solved by combining interpolation with algebraic recompression techniques that significantly reduce the storage requirements while keeping the accuracy and robustness and only moderately increasing the runtime.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Sino–German Computational and Applied Mathematics
- An Adaptive Finite Element Scheme for the Hellinger–Reissner Elasticity Mixed Eigenvalue Problem
- Adaptive Directional Compression of High-Frequency Helmholtz Boundary Element Matrices
- Hierarchical Argyris Finite Element Method for Adaptive and Multigrid Algorithms
- On the Threshold Condition for Dörfler Marking
- An Unfitted dG Scheme for Coupled Bulk-Surface PDEs on Complex Geometries
- Dimensionally Consistent Preconditioning for Saddle-Point Problems
- An Optimal Multilevel Method with One Smoothing Step for the Morley Element
- Kernel Embedding Based Variational Approach for Low-Dimensional Approximation of Dynamical Systems
- 𝑯(curl 2)-Conforming Spectral Element Method for Quad-Curl Problems
- Defects in Active Nematics – Algorithms for Identification and Tracking
- Dual-Weighted Residual A Posteriori Error Estimates for a Penalized Phase-Field Slit Discontinuity Problem
- Fast Tensor Product Schwarz Smoothers for High-Order Discontinuous Galerkin Methods
- Error Analysis of an Unconditionally Energy Stable Local Discontinuous Galerkin Scheme for the Cahn–Hilliard Equation with Concentration-Dependent Mobility
Artikel in diesem Heft
- Frontmatter
- Sino–German Computational and Applied Mathematics
- An Adaptive Finite Element Scheme for the Hellinger–Reissner Elasticity Mixed Eigenvalue Problem
- Adaptive Directional Compression of High-Frequency Helmholtz Boundary Element Matrices
- Hierarchical Argyris Finite Element Method for Adaptive and Multigrid Algorithms
- On the Threshold Condition for Dörfler Marking
- An Unfitted dG Scheme for Coupled Bulk-Surface PDEs on Complex Geometries
- Dimensionally Consistent Preconditioning for Saddle-Point Problems
- An Optimal Multilevel Method with One Smoothing Step for the Morley Element
- Kernel Embedding Based Variational Approach for Low-Dimensional Approximation of Dynamical Systems
- 𝑯(curl 2)-Conforming Spectral Element Method for Quad-Curl Problems
- Defects in Active Nematics – Algorithms for Identification and Tracking
- Dual-Weighted Residual A Posteriori Error Estimates for a Penalized Phase-Field Slit Discontinuity Problem
- Fast Tensor Product Schwarz Smoothers for High-Order Discontinuous Galerkin Methods
- Error Analysis of an Unconditionally Energy Stable Local Discontinuous Galerkin Scheme for the Cahn–Hilliard Equation with Concentration-Dependent Mobility
