Analysis of Two-Dimensional Problems Described by Helmholtz's Equations Using the Collocation Method. A Study on Domain Decomposition.

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  • 二次元ヘルムホルツ方程式系の選点法による解析　　領域分割法の検討
  • 2ジゲン ヘルムホルツ ホウテイシキケイ ノ センテンホウ ニ ヨル カイセキ リョウイキ ブンカツホウ ノ ケントウ

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The collocation method using analytical solutions has an important inherent issue that causes the loss of the eigen value convergence due to singular points existing in the vicinity of a domain. In our previous study, we proposed a way to cancel it in a specific domain including a notch by adding singular terms to the general solutions. This method, however, can not easily be extended to general singular problems. To overcome this fault, we present a newly improved method that employs a domain decomposition approach in order to relax the effects of any singular points. First, the conditions for continuity between two decomposed domains are derived. Second, the eigen value equations are formulated based on these condition. Finally, using some examples, it is confirmed that the method presented here provides a high acuuracy of eigen values in any problems accompanied by singular points.

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