A boundary element method for the Laplace equation in a circular domain

Laplace equation governs many types of engineering problems such as torsion, heat conduction, pressure distribution in pipes, seepage and aquifer analysis. Therefore, finding a solution for this equation is of crucial importance. In this article, a boundary element solution for the Laplace equation in a circular domain is presented. Two types of elements including constant elements and linear elements are employed in order to carry out the discretization process. The formulations are given in detail. The corresponding fundamental solution is obtained in a closed-form manner. Numerical results studied in the paper indicate the accuracy of the proposed solution. Furthermore, the obtained numerical results are compared with the exact values which an excellent agreement is observed.

Keywords:

Laplace equation , boundary element method , fundamental solution , constant element , linear element