Sensitivity analysis scheme of boundary value problem of 2D Poisson equation by using Trefftz method

This paper describes the sensitivity analysis of the boundary value problem of two-dimensional Poisson equation by using Trefftz method. A non-homogeneous term of two-dimensional Poisson equation is approximated with a polynomial function in the Cartesian coordinates to derive a particular solution. The unknown function of the boundary value problem is approximate with the superposition of the T-complete functions of Laplace equation and the derived particular solution with unknown parameters. The parameters are determined so that the approximate solution satisfies boundary conditions. Since the T-complete functions and the particular solution are regular, direct differentiation of the expression results leads to the sensitivity expressions. The boundary-specified value and the shape parameter are taken as the variables of the sensitivity analysis to formulate the sensitivity analysis methods. The present scheme is applied to some numerical examples in order to confirm the validity of the present algorithm.