Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations
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Publication:5161748
DOI10.1137/20M1349667zbMath1490.65081MaRDI QIDQ5161748
Pieter Ghysels, Xiaoye Sherry Li, Lisa Claus, Yang Liu
Publication date: 1 November 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Helmholtz equationrandomized algorithmPoisson equationmultifrontal methodMaxwell equationhigh-frequency wave equationsbutterfly algorithmsparse direct solver
Computational methods for sparse matrices (65F50) Numerical methods for integral equations (65R20) Numerical methods for integral transforms (65R10)
Related Items (2)
Schwarz methods by domain truncation ⋮ A Fast Butterfly-Compressed Hadamard–Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources
Uses Software
Cites Work
- Fast algorithms for spherical harmonic expansions. III
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- Construction and arithmetics of \(\mathcal H\)-matrices
- Hierarchical matrices based on a weak admissibility criterion
- Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices
- L-sweeps: a scalable, parallel preconditioner for the high-frequency Helmholtz equation
- MFEM: a modular finite element methods library
- A unified framework for oscillatory integral transforms: when to use NUFFT or butterfly factorization?
- A hierarchical butterfly LU preconditioner for two-dimensional electromagnetic scattering problems involving open surfaces
- An algorithm for the rapid evaluation of special function transforms
- A fast block low-rank dense solver with applications to finite-element matrices
- Distributed-memory hierarchical interpolative factorization
- An \(\mathcal O(N\log N)\) fast direct solver for partial hierarchically semi-separable matrices. With application to radial basis function interpolation
- Direct Methods for Sparse Matrices
- On the Numerical Rank of the Off-Diagonal Blocks of Schur Complements of Discretized Elliptic PDEs
- Hierarchical Interpolative Factorization for Elliptic Operators: Differential Equations
- Sparse Fourier Transform via Butterfly Algorithm
- A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators
- The Multifrontal Solution of Indefinite Sparse Symmetric Linear
- Updating the Inverse of a Matrix
- The Multifrontal Method for Sparse Matrix Solution: Theory and Practice
- A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
- Directional ‐matrix compression for high‐frequency problems
- The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
- A Fast Direct Solver for Structured Linear Systems by Recursive Skeletonization
- Approximate Separability of the Green's Function of the Helmholtz Equation in the High Frequency Limit
- Interpolative Decomposition Butterfly Factorization
- A Distributed-Memory Algorithm for Computing a Heavy-Weight Perfect Matching on Bipartite Graphs
- Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures
- Improving Multifrontal Methods by Means of Block Low-Rank Representations
- Butterfly Factorization
- Directional Preconditioner for 2D High Frequency Obstacle Scattering
- A Parallel Geometric Multifrontal Solver Using Hierarchically Semiseparable Structure
- Randomized Sparse Direct Solvers
- Direct Solve of Electrically Large Integral Equations for Problem Sizes to 1 M Unknowns
- Bridging the Gap Between Flat and Hierarchical Low-Rank Matrix Formats: The Multilevel Block Low-Rank Format
- Interpolative Butterfly Factorization
- Fast Hierarchical Solvers For Sparse Matrices Using Extended Sparsification and Low-Rank Approximation
- A survey of direct methods for sparse linear systems
- Butterfly Factorization Via Randomized Matrix-Vector Multiplications
- A bibliography on semiseparable matrices
- PaStiX: A high-performance parallel direct solver for sparse symmetric positive definite systems
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