Effectiveness of nonsingular solutions of the boundary problems based on Trefftz methods

Abstract

The paper describes the application of the Trefftz complete and Kupradze functions in two variational formulations, i.e. the original formulation and inverse one, to the solution of the boundary value problems of the two-dimensional Laplace’s equation. In both formulations the solutions and weighting functions are assumed as the series or the separate function of Trefftz complete functions or Kupradze ones. One way or another all methods are named Trefftz methods. They all are nonsingular and, at the same time, they lead to the BEM. The relationship between the groups of Trefftz methods of the original and inverse formulations is perceived.Numerical experiments are conducted for several Laplace problems. The accuracy and simplicity of the methods are discussed. All methods gave comparable results, therefore they may be interchangeably applied to the solution of boundary problems. However the best method group is pointed out.