A numerical analysis of the generalised collocation Trefftz method for some 2D Laplace problems.

This paper analyses the generalised collocation Trefftz method which allows to combine the advantages of the T -Trefftz and MFS. The initial idea of the method is to approximate the solution with a linear combination of many basis functions with many source points. The application of only one source point with nonsingular basis function allows for set up linearly independent set. On the other hand, using logarithmic and negative power bases for the source points enables better control over quality of the solution. The validity of the proposed method is conducted for the potential problem in a two-dimensional simply and doubly connected domain without using the domain decomposition. [ABSTRACT FROM AUTHOR]