A comparison of the semidiscontinuous element and multiple node with auxiliary boundary collocation approaches for the boundary element method

Abstract

Several approaches have been considered to resolve boundary element formulation problems associated with geometric corners and edges as well as discontinuous boundary conditions. The semidiscontinuous element and multiple node approaches are perhaps the two most widely used methods. In the semidiscontinuous element approach, functional and collocation nodes are moved off geometric corners, edges, and lines of discontinuous boundary conditions. In the multiple node approach, multiple nodes are placed at corners, and double nodes are placed along edges and along lines of discontinuous boundary conditions. The purpose of this paper is to elucidate the differences between these two approaches and perform a direct comparison of the approaches by considering several numerical example problems.