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Volume 30, Issue 4
A Robust and Accurate Solver of Laplace's Equation with General Boundary Conditions on General Domains in the Plane

Rikard Ojala

DOI: 10.4208/jcm.1201-m3644

J. Comp. Math., 30 (2012), pp. 433-448.

Published online: 2012-08

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  • 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.

  • Keywords

Laplace's equation, Integral equations, Mixed boundary conditions, Robin boundary conditions.

  • AMS Subject Headings

65R20, 65E05.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-30-433, author = {}, title = {A Robust and Accurate Solver of Laplace's Equation with General Boundary Conditions on General Domains in the Plane}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1201-m3644}, url = {http://global-sci.org/intro/article_detail/jcm/8441.html} }
TY - JOUR T1 - A Robust and Accurate Solver of Laplace's Equation with General Boundary Conditions on General Domains in the Plane JO - Journal of Computational Mathematics VL - 4 SP - 433 EP - 448 PY - 2012 DA - 2012/08 SN - 30 DO - http://doi.org/10.4208/jcm.1201-m3644 UR - https://global-sci.org/intro/article_detail/jcm/8441.html KW - Laplace's equation, Integral equations, Mixed boundary conditions, Robin boundary conditions. AB -

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.

Rikard Ojala. (1970). A Robust and Accurate Solver of Laplace's Equation with General Boundary Conditions on General Domains in the Plane. Journal of Computational Mathematics. 30 (4). 433-448. doi:10.4208/jcm.1201-m3644
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