Boundary element modeling with variable nodal and collocation point locations

Abstract

In both the real variable and Complex Variable Boundary Element Methods (CVBEM), nodal points are typically located on the problem boundary and then various techniques are used to fit boundary condition values at the nodal point locations such as collocation (equating approximation function to boundary condition values at a discrete set of locations on the boundary) or least squares minimization on the boundary, among others. In this paper, the CVBEM is used to examine the significant improvement in approximation accuracy achieved by using as additional approximation variables the actual nodal point locations (both on the problem boundary as well as exterior of the problem domain union boundary), and to also use as additional approximation variables the locations where boundary conditions are fitted (i.e. collocation points). The developed concepts also apply directly to the more commonly used real variable boundary element technique. Our results show that significant improvement in modeling accuracy is achieved by including the nodal point coordinates and also the collocation point coordinates as additional variables to be optimized.