Interconnected hierarchical structures for fast direct elliptic solution
From MaRDI portal
Publication:2113659
DOI10.1007/s10915-022-01761-7zbMath1487.65031OpenAlexW4214538033MaRDI QIDQ2113659
Xiaofeng Ou, Jian-Lin Xia, Maarten V. de Hoop, Xiao Liu
Publication date: 14 March 2022
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-022-01761-7
elliptic equationbasis reusefast sparse direct solverinterconnected hierarchical structureneighbor treeSchur complement update
Complexity and performance of numerical algorithms (65Y20) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
- A direct solver for variable coefficient elliptic PDEs discretized via a composite spectral collocation method
- A fast direct solver for elliptic problems on general meshes in 2D
- Fast construction of hierarchical matrix representation from matrix-vector multiplication
- Acoustic inverse scattering via Helmholtz operator factorization and optimization
- Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients
- Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices
- A spectrally accurate direct solution technique for frequency-domain scattering problems with variable media
- Distributed-memory hierarchical interpolative factorization
- An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling
- Parallel Randomized and Matrix-Free Direct Solvers for Large Structured Dense Linear Systems
- Superfast and Stable Structured Solvers for Toeplitz Least Squares via Randomized Sampling
- On the Complexity of Some Hierarchical Structured Matrix Algorithms
- A Direct Solver with $O(N)$ Complexity for Variable Coefficient Elliptic PDEs Discretized via a High-Order Composite Spectral Collocation Method
- A Fast Randomized Eigensolver with Structured LDL Factorization Update
- 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
- Hierarchical Interpolative Factorization for Elliptic Operators: Differential Equations
- A Fast Randomized Algorithm for Computing a Hierarchically Semiseparable Representation of a Matrix
- The Use of Linear Graphs in Gauss Elimination
- 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
- An introduction to hierarchical matrices
- A Superfast Structured Solver for Toeplitz Linear Systems via Randomized Sampling
- Schur complement domain decomposition methods for the solution of multiple scattering problems
- Fast Factorization Update for General Elliptic Equations Under Multiple Coefficient Updates
- Robust and Accurate Stopping Criteria for Adaptive Randomized Sampling in Matrix-Free Hierarchically Semiseparable Construction
- 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
- Randomized Sparse Direct Solvers
- A Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions
- Nested Dissection of a Regular Finite Element Mesh