边界是光滑开弧Helmholtz方程的边界积分法
Boundary Integral Method for Helmholtz Equation with a Smooth Open Arc Boundary
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摘要: 由Helmholtz方程Dirchlet问题产生的第一类积分方程的核具有对数奇性,并且积分方程的解在开弧端点具有r^-1/2奇数。将积分方程的核分成两部分,一部分包含特殊的奇性,另一部分不包含奇性,然后应用Galerkin法和配置法,最后讨论了近似解的收敛性。Abstract: The kernel in the first integral equation arising from Dirichlet problem of Helmholtz equation has a logarithmic singularity and the solution for the integral equation has r-1/2\|singularity at the endpoints of the open arc. The kernel is splitted into two parts so that the one contains a special singularity and the other doesn't contain any singularity. Galerkin method and collocation method are used and a convergence analysis is given.