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- W2328504265 abstract "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." @default.
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- W2328504265 date "1999-01-01" @default.
- W2328504265 modified "2023-10-16" @default.
- W2328504265 title "An Analysis of Two-Dimensional Problems Described by Helmholtz's Equation Using the Collocation Method. A Study on Singularity at Tips of Notched Boundaries." @default.
- W2328504265 doi "https://doi.org/10.1299/kikaic.65.881" @default.
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