Sensitivity analysis of the Poisson equation using the Trefftz method

摘要

A sensitivity analysis scheme for the boundary value problem of the three-dimensional Poisson equation by using the Trefftz method is described in this paper. In the present scheme, the inhomogeneous term of the three-dimensional Poisson equation is approximated with the polynomial function in Cartesian coordinates to derive the related particular solution. The use of the particular solution transforms the boundary value problem of the Poisson equation into that of the Laplace equation. Since the unknown parameters included into the particular solution depend on the unknown function, the derived boundary value problem is solved by the iterative process. The function is approximated with the superposition of the T-complete functions and the particular solution. Therefore, direct differentiation of the solution leads to the sensitivities. The boundary-specified value is taken as the variable for the sensitivity analysis and then the sensitivity analysis formulations are described.