## Galerkin BEM for 3D Laplace Equation

Download GBEM_LAP, a package for solving the 3D Laplace equation based on a piecewise **linear** Galerkin Boundary Element Method.

# Piecewise linear Galerkin method

The potential and flux are assumed to be linear over each boundary element. It can be shown (see [2,3,4]) that the Galerkin surface integrals

can be employed to successfully compute and on the boundary where is an exterior point to and stands for the support of the function Moreover, is a linear test function defined over the flat triangle and is a linear shape function defined over the flat triangle In addition, the following potentials

are utilized to effectively calculate at interior points The analytic expressions for and over a flat triangle are given in [1].

# References

- [1] S. Nintcheu Fata.

Explicit expressions for 3D boundary integrals in potential theory.

*Int. J. Num. Meth. Eng.*, 78(1):32-47, 2009. - [2] S. Nintcheu Fata and L. J. Gray.

Semi-analytic integration of hypersingular Galerkin BIEs for three-dimensional potential problems.

*J. Comput. Appl. Math.*, 231(2):561-576, 2009. - [3] S. Nintcheu Fata and L. J. Gray.

On the implementation of 3D Galerkin boundary integral equations.

*Eng. Anal. Boundary Elem.*, 34(1):60-65, 2010. - [4] S. Nintcheu Fata.

Semi-analytic treatment of nearly-singular Galerkin surface integrals.

*Appl. Numer. Math.*, 60(10):974-993, 2010.