A Parallel Geometric Multifrontal Solver Using Hierarchically Semiseparable Structure
From MaRDI portal
Publication:5270753
DOI10.1145/2830569zbMath1369.65050OpenAlexW2318669552WikidataQ113310218 ScholiaQ113310218MaRDI QIDQ5270753
Maarten V. de Hoop, Shen Wang, Jian-Lin Xia, François-Henry Rouet, Xiaoye Sherry Li
Publication date: 30 June 2017
Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1145/2830569
Computational methods for sparse matrices (65F50) Parallel numerical computation (65Y05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
Related Items (15)
A Preconditioned Finite Element Solution of the Coupled Pressure-Temperature Equations Used to Model Trace Gas Sensors ⋮ Distributed-memory hierarchical interpolative factorization ⋮ A Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions ⋮ On the Complexity of the Block Low-Rank Multifrontal Factorization ⋮ hm-toolbox: MATLAB Software for HODLR and HSS Matrices ⋮ Matrices with Hierarchical Low-Rank Structures ⋮ An Additive Overlapping Domain Decomposition Method for the Helmholtz Equation ⋮ Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations ⋮ Robust and Effective eSIF Preconditioning for General Dense SPD Matrices ⋮ A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation ⋮ Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients ⋮ An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling ⋮ Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations ⋮ Parallel Skeletonization for Integral Equations in Evolving Multiply-Connected Domains ⋮ Improving Multifrontal Methods by Means of Block Low-Rank Representations
Uses Software
Cites Work
- Unnamed Item
- Acoustic inverse scattering via Helmholtz operator factorization and optimization
- A fast direct solver for a class of elliptic partial differential equations
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- On a new class of structured matrices
- Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients
- Introduction to hierarchical matrices with applications.
- A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
- A fast block low-rank dense solver with applications to finite-element matrices
- Computations with quasiseparable polynomials and matrices
- Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
- Divide and Conquer Low-Rank Preconditioners for Symmetric Matrices
- On the Complexity of Some Hierarchical Structured Matrix Algorithms
- A fast, memory efficient and robust sparse preconditioner based on a multifrontal approach with applications to finite‐element matrices
- On the Numerical Rank of the Off-Diagonal Blocks of Schur Complements of Discretized Elliptic PDEs
- Fast algorithms for hierarchically semiseparable matrices
- Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation
- The Role of Elimination Trees in Sparse Factorization
- Superfast Multifrontal Method for Large Structured Linear Systems of Equations
- The Multifrontal Solution of Indefinite Sparse Symmetric Linear
- The Multifrontal Method for Sparse Matrix Solution: Theory and Practice
- ScaLAPACK Users' Guide
- An introduction to hierarchical matrices
- Improving Multifrontal Methods by Means of Block Low-Rank Representations
- A Fast $ULV$ Decomposition Solver for Hierarchically Semiseparable Representations
- Efficient Structured Multifrontal Factorization for General Large Sparse Matrices
- Efficient Scalable Algorithms for Solving Dense Linear Systems with Hierarchically Semiseparable Structures
- SuperLU_DIST
- Some Fast Algorithms for Sequentially Semiseparable Representations
- Nested Dissection of a Regular Finite Element Mesh
- A bibliography on semiseparable matrices
This page was built for publication: A Parallel Geometric Multifrontal Solver Using Hierarchically Semiseparable Structure
