On factored discretizations of the Laplacian for the fast solution of Poisson's equation on general regions

DOI10.1007/BF01934917zbMath0559.65076OpenAlexW1997657631MaRDI QIDQ2266361

Werner Liniger

Publication date: 1984

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01934917

zbMATH Keywords

stabilityPoisson's equationpreconditioned conjugate gradient methodPoisson solverssparse Cholesky decompositionfactorization of the Laplace operator

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (1)

On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations

Uses Software

• symrcm

Cites Work

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• Generalized Nested Dissection
• A Finite Element-Capacitance Matrix Method for the Neumann Problem for Laplace’s Equation
• On the Numerical Solution of Helmholtz's Equation by the Capacitance Matrix Method
• Marching Algorithms for Elliptic Boundary Value Problems. I: The Constant Coefficient Case
• Marching Algorithms for Elliptic Boundary Value Problems. II: The Variable Coefficient Case
• Capacitance Matrix Methods for the Helmholtz Equation on General Three-Dimensional Regions
• The Direct Solution of the Discrete Poisson Equation on a Rectangle
• On Direct Methods for Solving Poisson’s Equations

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