解析解による三次元ヘルムホルツ方程式系の解析 : 選点法の適用につていの基本的な検討(<小特集>音響利用技術-音響情報・音響エネルギー-)

抄録

Three-dimensional Helmholtz equation is one of the important differential equations in engineering. It appears in problems of acoustics, heat conduction and so on. If a domain has an arbitrary shape, the problems cannot be solved by the usual analytic procedure. On the other hand, approximate methods such as the finite element method are not necessarily sufficient for this purpose. This paper deals with a new method of analysis that is based on analytic solutions. In this method, boundary conditions are satisfied approximately at points located on surface of the domain. Eigenvalues and eigenmodes of some domains of revolution, an ellipsoid, a boxy domain and a frustum of pyramid are calculated as numerical examples. Results have good accuracy.