二次元ヘルムホルツ方程式系の選点法による解析 : 切り欠き部の特異性を考慮した解析法の検討

概要

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If a domain of the target of analysis is convex, the solution of the two dimensional problem described by Helmholtz's equation is regular on the whole domain and the usual collocation method can be applied. On the other hand, if domains have notched boundaries, the tips of notches become singular points of the flux. For such cases, the solutions used in the convex domain problems can not be applied, because they never express any singularity. This paper shows that the analytical method for the convex domains previously proposed by the authors can be extended to the problems of notched domains. A general solution for the new method consists of two parts. One of them is the same as the solution for the convex domains and the other is a series that expresses the singularity at the notch tips. Numerical results of eigenmode obtained by this method satisfy boundary conditions and eigenvalues have excellent accuracy.
一般社団法人日本機械学会の論文
1999-03-25