Sensitivity Analysis of Non-linear Poisson Equation by Element-Free Trefftz Method

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  • エレメントフリ-Trefftz法による非線形Poisson方程式の感度解析
  • エレメントフリー Trefftzホウ ニ ヨル ヒセンケイ Poisson ホウテイシキ ノ カンド カイセキ

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Abstract

A sensitivity analysis scheme of the boundary value problem of Poisson equation by using Trefftz method is described in this paper. An inhomogeneous term of Poisson equation is approximated with the polynomial to derive the particular solution related to Poisson equation. The solution of the problem is approximated with the superposition of the T-complete function of Laplace equation and the derived particular solutions with unknown parameters. The parameters are determined so that the approximated solution satisfies boundary conditions. Since the T-complete functions and the particular solutions are regular, direct differentiation of the expression leads to the sensitivities. The present scheme is applied to some numerical examples.

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