Solving the Laplace’s Equation by the FDM and BEM Using Mixed Boundary Conditions

Hassan Ghassemi^1, , Saeid Panahi¹ and Ahmad Reza Kohansal²

¹Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran

²Department of Shipbuilding, Faculty of Engineering, Persian Gulf University, Bousher, Iran

Cite this paper

Hassan Ghassemi, Saeid Panahi and Ahmad Reza Kohansal. Solving the Laplace’s Equation by the FDM and BEM Using Mixed Boundary Conditions. American Journal of Applied Mathematics and Statistics. 2016; 4(2):37-42. doi: 10.12691/AJAMS-4-2-2

Abstract

This paper presents to solve the Laplace’s equation by two methods i.e. the finite difference method (FDM) and the boundary element method (BEM). The body is ellipse and boundary conditions are mixed. In the BEM, the integration domain needs to be discretized into small elements. The boundary integral equation derived using Green’s theorem by applying Green’s identity for any point in the surface. The methods are applied to examine an example of square domain with mixed boundary condition. Both types of numerical models are computed and compared with analytical solution. The results obtained agree perfectly with those obtained from exact solution.

Keywords

Mixed boundary condition, Boundary element Method, Finite Difference Method

Copyright

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