代用電荷法によるポアソン方程式の数値計算 Numerical Computation of Poisson's Equation by the Charge Simulation Method

この論文にアクセスする

この論文をさがす

著者

    • 森下 博 MORISHITA Hiroshi
    • 兵庫大学経済情報学部経済情報学科 Department of Economics and Information Science, Faculty of Economics and Information Science, Hyogo University
    • 高市 英明 [他] TAKAICHI Hideaki
    • 株式会社理経大阪支店情報機器営業部システム営業三課 3rd System Sales Section, Information Equipment Sales Department, Osaka Branch Office, Rikei Corporation
    • 天野 要 AMANO Kaname
    • 愛媛大学工学部情報工学科 Department of Computer Science, Faculty of Engineering, Ehime University
    • 四ツ谷晶二 YOTSUTANI Shoji
    • 龍谷大学理工学部数理情報学科 Department of Applied Mathematics and Informatics, Faculty of Science and Technology, Ryukoku University

抄録

代用電荷法はラプラス方程式の簡単で精度の高い近似解法として知られている.しかし,調和関数を基本解の1次結合で近似するという計算法の原理から,一般的にポアソン方程式や非線形方程式には適していないと考えられてきた.本諭文では,代用電荷法のポアソン方程式への適用法を提案し,数値実験的にその有効性を検証する.具体的には,ポアソン方程式の解を特解と調和関数の和に分解し,まず前者を基本解を用いて表現し,次に後者を代用電荷法で近似する.ここで,前者の基本解の特異性処理が数値計算上の問題となる.我々は特異点を中心とする極座標を導入してこの特異性を解消する.さらに,変数換で計算領域を矩形領域に帰着させ,数値積分にはシンプソン則を用いる.その結果,全体として精度の高いポアソン方程式の数値計算法を構成することができる.この計算法は,数値積分に要する計算量は小さくないが,計算の並列化は容易で,領域の変形に対する柔軟性に優れている.ここでは主に2次元ポアソン方程式を扱うが,3次元ポアソン方程式の数値計算法と計算例も記す.The charge simulation method is well known as an accurate rapid solver for Laplace's equation,in which the solution is approximated by a linear combination of logarithmic potentials.However,it has been consedered that the method is not suitable for Poisson's equation and nolinear equations.In this paper,we propose a feasible mothod for solving the Dirichelet problem of Poisson's equation using the charge simulation method.We first obtain a particular solution by numerically integrating the logarithmic potential,and reduce the problem to Laplace's equation. Then we solve it by the convertional charge simulation method.In the numerical integration,a difficulty appears due to tne singularity of logarithmic potenteal.We overcome the difficulty by introducing the polar coordinate system around the singular point,and adopt Simpson's rule.On the whole,numerical results of high accuracy can be obtained for Poisson's equation.Some exmples show the effectiveness of the method.A three-dimensional problem is also described in this paper.

The charge simulation method is well known as an accurate, rapid solver for Laplace's equation, in which the solution is approximated by a linear combination of logarithmic potentials. However, it has been considered that the method is not suitable for Poisson's equation and nonlinear equations. In this paper, we propose a feasible method for solving the Dirichlet problem of Poisson's equation using the charge simulation method. We first obtain a particular solution by numerically integrating the logarithmic potential, and reduce the problem to Laplace's equation. Then we solve it by the conventional charge simulation method. In the numerical integration, a difficulty appears due to the singularity of logarithmic potential. We overcome the difficulty by introducing the polar coordinate system around the singular point, and adopt Simpson's rule. On the whole, numerical results of high accuracy can be obtained for Poisson's equation. Some examples show the effectiveness of the method. A three-dimensional problem is also described in this paper.

収録刊行物

  • 情報処理学会論文誌

    情報処理学会論文誌 38(8), 1483-1491, 1997-08-15

    一般社団法人情報処理学会

参考文献:  11件中 1-11件 を表示

被引用文献:  1件中 1-1件 を表示

各種コード

  • NII論文ID(NAID)
    110002721599
  • NII書誌ID(NCID)
    AN00116647
  • 本文言語コード
    JPN
  • 資料種別
    Journal Article
  • ISSN
    1882-7764
  • NDL 記事登録ID
    4274487
  • NDL 雑誌分類
    ZM13(科学技術--科学技術一般--データ処理・計算機)
  • NDL 請求記号
    Z14-741
  • データ提供元
    CJP書誌  CJP引用  NDL  NII-ELS  IPSJ 
ページトップへ