Comparison of different methods for choosing the collocation points in the boundary collocation method for 2D-harmonic problems with special purpose Trefftz functions

Based on special purpose Trefftz functions, this paper presents a comparison of different methods for choosing collocation points when a boundary collocation method is used to fulfill the boundary conditions. First, it is shown that for some geometries when applying a boundary collocation method with special purpose Trefftz functions, equidistant collocation points give unacceptable results. Next, for four 2-D harmonic boundary value problems, four cases of different placements of the collocation points are described and compared. Based on the results of the comparison of the test methods for the location of the collocation points it is shown that one of the proposed methods for placing the collocation points is simple to implement and accurate. The essence of this method is an adaptive determination of the consequent collocation points.