@article{oai:nagoya.repo.nii.ac.jp:00008517, author = {KITA, EISUKE and 池田, 洋一 and IKEDA, YOUICHI and 神谷, 紀生 and KAMIYA, NORIO}, issue = {7}, journal = {情報処理学会論文誌}, month = {}, note = {Trefftz法は,支配方程式を満足する非特異なT-complete関数を用いた数値解析法である.これまで,2次元や3次元のラプラス方程式,2次元弾性問題などの数値解析に適用され,その数学的特性が研究されている.これに対して,本論文ではTrefftz法を用いた2次元ポアソン方程式の解法について述べる.ポアソン方程式は非同次項を有するので,支配方程式を満足するT-complete関数を決定することは一般的には困難である.そこで,本論文では,未知関数を含む非同次項をデカルト座標系の多項式で近似し,ラプラス方程式のT-complete関数と近似多項式に対応する特解でポアソン方程式の解を近似する.そして,近似解が境界条件値を満足するようにして,未知パラメータを決定する.いくつかの解析例について提案する方法を適用し,その数学的特性を検討する., Trefftz method is the boundary-type solution procedure using the non-singular T-complete functions satisfying the governing equation. Until now, it is applied to numerical analyses of the two- and three-dimensional Laplace equations and the 2-dimensional elastic problem and the mathematical characteristic is studied. On the other hand, this paper describes the application of the Trefftz method to solve the boundary value problem of two-dimensional Poisson equation. Since the Poisson equation has non-homogeneous term, it is generally difficult to determine the function satisfying the governing equation. In this paper, non-homogeneous term containing an unknown function is approximated by the polynomial in the Cartesian coordinates and then, the solution for the Poisson equation is approximated with the superposition of the T-complete function of the Laplace equation and the particular solutions related to the approximate polynomal. Unknown parameters included in the approximate solution are determined so that the solution satisfies the boundary conditions. The present scheme is applied to some examples in order to study the numerical properties.}, pages = {2272--2280}, title = {Trefftz法による非線形ポアソン方程式の解法}, volume = {43}, year = {2002} }