シュワルツの交代法を利用した境界値問題の分割統治法  [in Japanese] A Divide and Conquer Method for Solving Boundary Value Problems based on Shwartz's Alternating Method  [in Japanese]

境界値問題を領域分割によって解く方法について検討した。先ず、問題の領域は重なり部分を有する形で二つの領域に分割される。それぞれの領域における境界値問題を交互に解き、二つの領域の解が共通領域で一致するようにもっていく。2次元の境界値問題を代用電荷法で解く状況を考え、2分割、5分割、10分割の場合を例にとり、解を接続する数値実験を行ない、重なり部分が外相、解の接続は容易であるが、引導時間の点で分割の効果が上がらないと言える。

A method for solving a boundary value problem by dividing the region is discussed. At first, the region under concern is divided into two regions with a citron common area. Then the boundary value problem on each region is solved step by step, so that the field on each region coincide on the common area. By using the charge simulation method, several numerical experiments are done. It is found out that the big boundary value problem can be divided and fairly well conquered by this technique. However the overhead on the number of unknown constants is relatively large and the merit of division on computing time is limited.