A direct solver for elliptic PDEs in three dimensions based on hierarchical merging of Poincaré-Steklov operators

DOI10.1016/j.cam.2016.05.013zbMath1346.65062OpenAlexW2417419892MaRDI QIDQ738994

Per-Gunnar Martinsson, Sijia Hao

Publication date: 16 August 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.05.013

zbMATH Keywords

direct solvercollocationnumerical experimentoscillatory solutionlinear complexityhigh order discretizationnested dissectionvariable coefficientHelmholtz-type equationsmultidomain spectral methodmultifrontal solverstructured matrix algebra

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Complexity and performance of numerical algorithms (65Y20)

Related Items (7)

The ultraspherical spectral element method ⋮ An accelerated Poisson solver based on multidomain spectral discretization ⋮ A spectral element method for modelling streamer discharges in low-temperature atmospheric-pressure plasmas ⋮ Distributed-memory hierarchical interpolative factorization ⋮ Asymmetric transport computations in Dirac models of topological insulators ⋮ An Iterative Solver for the HPS Discretization Applied to Three Dimensional Helmholtz Problems ⋮ Randomized GPU Algorithms for the Construction of Hierarchical Matrices from Matrix-Vector Operations

Uses Software

• Matlab
• hlib
• CSparse

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• A direct solver for variable coefficient elliptic PDEs discretized via a composite spectral collocation method
• An \(O(N)\) algorithm for constructing the solution operator to 2D elliptic boundary value problems in the absence of body loads
• A fast direct solver for elliptic problems on general meshes in 2D
• Efficient numerical methods for non-local operators. \(\mathcal H^2\)-matrix compression, algorithms and analysis.
• A fast direct solver for a class of elliptic partial differential equations
• A direct solver with \(O(N)\) complexity for integral equations on one-dimensional domains
• Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• Construction and arithmetics of \(\mathcal H\)-matrices
• A spectrally accurate direct solution technique for frequency-domain scattering problems with variable media
• Domain decomposition based \({\mathcal H}\)-LU preconditioning
• Randomized algorithms for the low-rank approximation of matrices
• On the Numerical Rank of the Off-Diagonal Blocks of Schur Complements of Discretized Elliptic PDEs
• Fast algorithms for hierarchically semiseparable matrices
• Direct Methods for Sparse Linear Systems
• Superfast Multifrontal Method for Large Structured Linear Systems of Equations
• Spectral Methods in MATLAB
• A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator
• Efficient Structured Multifrontal Factorization for General Large Sparse Matrices
• Randomized Sparse Direct Solvers
• On the Compression of Low Rank Matrices
• Nested Dissection of a Regular Finite Element Mesh

This page was built for publication: A direct solver for elliptic PDEs in three dimensions based on hierarchical merging of Poincaré-Steklov operators