Directional $\mathcal{H}^2$ Compression Algorithm: Optimisations and Application to a Discontinuous Galerkin BEM for the Helmholtz Equation
DOI10.4208/cicp.OA-2021-0241zbMath1491.35144OpenAlexW4229022388MaRDI QIDQ5077715
Nadir-Alexandre Messaï, Sebastien Pernet, Abdesselam Bouguerra
Publication date: 19 May 2022
Published in: Communications in Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4208/cicp.oa-2021-0241
Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation
- A Nitsche-based domain decomposition method for hypersingular integral equations
- Efficient numerical methods for non-local operators. \(\mathcal H^2\)-matrix compression, algorithms and analysis.
- Local a-posteriori error indicators for the Galerkin discretization of boundary integral equations
- Variable order panel clustering
- A fast adaptive multipole algorithm in three dimensions
- \(\mathcal H^2\)-matrix approximation of integral operators by interpolation
- Residual-based a posteriori error estimate for hypersingular equation on surfaces
- A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
- The fast multipole method: Numerical implementation
- Fast multipole accelerated singular boundary method for the 3D Helmholtz equation in low frequency regime
- \textit{hp} non-conforming \textit{a priori} error analysis of an interior penalty discontinuous Galerkin BEM for the Helmholtz equation
- Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis
- Discontinuous Galerkin \(hp\)-BEM with quasi-uniform meshes
- A nonconforming domain decomposition approximation for the Helmholtz screen problem with hypersingular operator
- The boundary element method with Lagrangian multipliers
- Boundary Integral Operators on Lipschitz Domains: Elementary Results
- Directional ‐matrix compression for high‐frequency problems
- Hybrid Matrix Compression for High-Frequency Problems
- A fast multipole method for Maxwell equations stable at all frequencies
- Spectral Elements for the Integral Equations of Time-Harmonic Maxwell Problems
- An ${\cal H}^{2}$-Matrix-Based Integral-Equation Solver of Reduced Complexity and Controlled Accuracy for Solving Electrodynamic Problems
- A Parallel Butterfly Algorithm
- An a posteriori error estimate for a first-kind integral equation
- Acoustic and electromagnetic equations. Integral representations for harmonic problems
This page was built for publication: Directional $\mathcal{H}^2$ Compression Algorithm: Optimisations and Application to a Discontinuous Galerkin BEM for the Helmholtz Equation
