Boundary Element Method for 3D Laplace and Stokes Flow Problems with Analytical Technique

Abstract

The analytical technique of element integral in the boundary element method for 3D Laplace and Stokes flow problems is investigated. The boundary integral equations are discretized with constant elements. The local coordinate transformation and polar coordinate transformation techniques are adopted to induce the analytical expressions of element integrals. For 3D Laplace problems, the analytical integral formulae, which are valid for an arbitrary source point, are derived. For 3D Stokes flow problems, analytical evaluation of the integrals, in which the source point and the boundary element are in the same plane, are proposed. These analytical formulae are applicable to arbitrary convex polygonal planar elements. The purpose of numerical examples is to make the case that the analytical expressions are accurate.