First- and second-order sensitivity analysis schemes by collocation-type Trefftz method - Kita, Eisuke; Kamiya, Norio; Ikeda, Youichi (Computer Assisted Methods in Engineering and Science, 1997)
This paper presents the boundary-type schemes of the first- and the second-order sensitivity analyses by Trefftz method. In the Trefftz method, physical quantities are approximated by the superposition of the T-complete functions satisfying the governing equations. Since the T-complete functions are regular, the approximate expressions of the quantities are also regular. Therefore, direct differentiation of them leads to the expressions of the sensitivities. Firstly, the Trefftz method for the two-dimensional potential problem is formulated by means of the collocation method. Then, the first- and the second-order sensitivity analysis schemes are explained with the simple numerical examples for their verification.