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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 47, 2005 - Issue 3
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Original Articles

TWO CARTESIAN GRID METHODS FOR SOLVING THE POISSON PROBLEM IN AN ARBITRARY DOMAIN

Pages 291-302 | Received 05 Aug 2004, Accepted 10 Sep 2004, Published online: 24 Feb 2007
 

ABSTRACT

Two methods for solving the Poisson problem on an automatically generated Cartesian grid are proposed. The first method is a combination of the finite-element method and the boundary-element method. The second method is a combination of the finite-difference method and the method of fundamental solutions. Both methods split the problem into an inhomogeneous differential equation with homogeneous boundary conditions and a homogeneous differential equation with inhomogeneous boundary conditions. Numerical tests of the two methods using a sample problem reveal that they yield satisfactory results.

The author would like to acknowledge financial support from the Thailand Research Fund.

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