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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fictitious domain method ： ウィキペディア英語版 Fictitious domain method In mathematics, the Fictitious domain method is a method to find the solution of a partial differential equations on a complicated domain $D$, by substituting a given problem posed on a domain $D$, with a new problem posed on a simple domain $\backslash Omega$ containing $D$. ==General formulation== Assume in some area $D\; \backslash subset\; \backslash mathbb^n$ we want to find solution $u(x)$ of the equation: : $$ Lu = - \phi(x), x = (x_1, x_2, \dots , x_n) \in D with boundary conditions: : $$ lu = g(x), x \in \partial D \, The basic idea of fictitious domains method is to substitute a given problem posed on a domain $D$, with a new problem posed on a simple shaped domain $\backslash Omega$ containing $D$ ($D\; \backslash subset\; \backslash Omega$). For example, we can choose ''n''-dimensional parallelepiped as $\backslash Omega$. Problem in the extended domain $\backslash Omega$ for the new solution $u\_(x)$: : $$ L_\epsilon u_\epsilon = - \phi^\epsilon(x), x = (x_1, x_2, \dots , x_n) \in \Omega : $$ l_\epsilon u_\epsilon = g^\epsilon(x), x \in \partial \Omega It is necessary to pose the problem in the extended area so that the following condition is fulfilled: : $$ u_\epsilon (x) \xrightarrow(\rightarrow 0 ) u(x), x \in D \, 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fictitious domain method」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.