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Abstract
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The solution of Poisson’s equation is essential for many branches of science and engineering
such as fluid-mechanics, geosciences, and electrostatics. Solution of two-dimensional
Poisson’s equations is carried out by BEM based on Galerkin Vector Method in which the
integrals that appear in the boundary element method are expressed by analytical integration.
In this paper, the Galerkin vector method is developed for more general case than presented
in the previous works. The integrals are computed for constant and linear elements
in BEM. By employing analytical integration in BEM computation, the numerical schemes
and coordinate transformations can be avoided. The presented method can also be used for
the multiple domain case. The results of the analytical integration are employed in BEM
code and the obtained analytical expression will be applied to several examples where
the exact solution exists. The produced results are in good agreement with the exact
solution.
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