Direct and iterative solution of the generalized Dirichlet-Neumann map for elliptic PDEs on square domains

DOI10.1016/j.cam.2008.07.025zbMath1183.65154OpenAlexW1978066612MaRDI QIDQ1012512

E. P. Papadopoulou, A. G. Sifalakis, Yiannis G. Saridakis, Scott R. Fulton

Publication date: 21 April 2009

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.2008.07.025

zbMATH Keywords

numerical experimentsiterative methodsGMREScollocationsuccessive overrelaxationelliptic PDEsDirichlet-Neumann mapJacobiGauss-Seidelglobal relationgeneralized minimal residualBi-CGSTABstabilized bi-conjugate gradient

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) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (4)

Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons ⋮ A Hybrid Analytical-Numerical Technique for Elliptic PDEs ⋮ On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains ⋮ Efficient numerical solution of the generalized Dirichlet-Neumann map for linear elliptic PDEs in regular polygon domains

Cites Work

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• An analytical method for linear elliptic PDEs and its numerical implementation
• Efficient numerical solution of the generalized Dirichlet-Neumann map for linear elliptic PDEs in regular polygon domains
• The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation
• Two–dimensional linear partial differential equations in a convex polygon
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Numerical Linear Algebra for High-Performance Computers
• A unified transform method for solving linear and certain nonlinear PDEs

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