A Robust and Accurate Solver of Laplace's Equation with General Boundary Conditions on General Domains in the Plane
Year: 2012
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 4 : pp. 433–448
Abstract
A robust and general solver for Laplace's equation on the interior of a simply connected domain in the plane is described and tested. The solver handles general piecewise smooth domains and Dirichlet, Neumann, and Robin boundary conditions. It is based on an integral equation formulation of the problem. Difficulties due to changes in boundary conditions and corners, cusps, or other examples of non-smoothness of the boundary are handled using a recent technique called recursive compressed inverse preconditioning. The result is a rapid and very accurate solver which is general in scope, and its performance is demonstrated via some challenging numerical tests.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1201-m3644
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 4 : pp. 433–448
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Laplace's equation Integral equations Mixed boundary conditions Robin boundary conditions.