A fast direct solver for a fourth order finite difference scheme for Poisson's equation on the unit disc in polar coordinates

DOI10.1007/s11075-015-9971-zzbMath1332.65153OpenAlexW2068765684MaRDI QIDQ907579

Lyndsey Wright, Bernard Bialecki

Publication date: 25 January 2016

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-015-9971-z

zbMATH Keywords

convergencenumerical examplesfast Fourier transformsfinite difference schemePoisson's equationpolar coordinateslocal truncation errormatrix decomposition algorithm

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for discrete and fast Fourier transforms (65T50) Finite difference methods for boundary value problems involving PDEs (65N06) Direct numerical methods for linear systems and matrix inversion (65F05)

Cites Work

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• A simple compact fourth-order Poisson solver on polar geometry
• Fast direct solvers for Poisson equation on 2D polar and spherical geometries
• High-Order Finite-Differences Schemes to Solve Poisson's Equation in Polar Coordinates
• A fourth‐order difference scheme for quasilinear poisson equation in polar co‐ordinates
• Matrix Decomposition Algorithms for Modified Spline Collocation for Helmholtz Problems

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