Sensitivity Analysis of Potential Problem by Regular- and Singular-function Trefftz Method

Abstract

Trefftz method is the boundary-type solution procedure which uses the function satisfying the governing equation as the approximation function of the solution of the problem. The regular T-complete function and the singular fundamental solution are employed as the approximation function. In this paper, the Trefftz methods formulated by the T-complete function and the fundamental solution are referred to “regular-function Trefftz method” [3,5–8,11,12,14] and “singular-function Trefftz method” [1, 4, 9, 10, 13], respectively. In the former, the regular expressions of the physical quantaties can be obtained because the regular T-complete function is employed. However, the condition number of the system of equations to be solved becomes large. In the latter, the source points are placed outside the object domain and the solution of the problem is approximated by the linear combination of the fundamental solution. Therefore, also in this case, the formulation is regular but the computational accuracy is strongly dependednt on the placement of the collocation points.