2019•Keisan Rikigaku Koenkai koen ronbunshu/Keisan Rikigaku Kouenkai kouen rombunshuuOpen access

A boundary element method for 1-periodic boundary value problems in 2D Helmholtz’ equation and its application

Hiroya NAKASHIMA, Hiroshi ISAKARI, Toru TAKAHASHI, Toshiro MATSUMOTO

Abstract

The boundary element method is used as an efficient analysis method for the 1-periodic boundary value problem in the 2D Helmholtz equation. However, in the boundary element method for 1-periodic problem, we need to evaluate slowly-convergent Green’s functions. In this research, we implement a fast boundary element method with the Ewald method. We also show the application of the proposed boundary element method to a topology optimisation problem.

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Key concepts: Boundary knot method, Boundary element method, Singular boundary method, Helmholtz equation, Mathematical analysis, Boundary value problem, Mathematics, Mixed boundary condition