Efficient numerical solution of the generalized Dirichlet-Neumann map for linear elliptic PDEs in regular polygon domains
type: Item
instance of: scholarly article
title: Efficient numerical solution of the generalized Dirichlet-Neumann map for linear elliptic PDEs in regular polygon domains
zbMATH Open document ID: 1244.65191
author: A. G. Sifalakis
author: E. Papadopoulou
author: Y. G. Saridakis
published in: Journal of Computational and Applied Mathematics
publication date: 2012-03-19T00:00:00Z
review text: The authors develop, for the two-dimensional Laplace equation, a collocation-type numerical method to study the Dirichlet-Neumann map which uses the derivative of the solution along a direction of an arbitrary angle to the boundary, to compute the derivative of the solution perpendicularly to this direction without solving the problem in the interior of the domain. They prove that in the case of regular polygon domains with the same type of boundary conditions on each side, the coefficient matrix is block circulant and independent of the choice of basis functions. These properties allow the use of the fast Fourier transform, for the efficient solution of the collocation linear system, with significant improvement of the performance for both direct and iterative methods considered. Numerical experiment are included.
reviewed by: Adrian Carabineanu
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 6015762
zbMATH Keywords: Dirichlet-Neumann map
zbMATH Keywords: collocation
zbMATH Keywords: block circulant matrices
zbMATH Keywords: fast Fourier transform
zbMATH Keywords: linear elliptic PDEs
zbMATH Keywords: Laplace equation
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.cam.2011.12.011
OpenAlex ID: W2061143948
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DOI: 10.1016/J.CAM.2011.12.011
description: scientific article; zbMATH DE number 6015762