THE NUMERICAL SOLUTION OF FIRST KIND INTEGRAL EQUATION FOR THE HELMHOLTZ EQUATION ON SMOOTH OPEN ARCS

• 来源期刊: 计算数学(英文版)
• 学科: 数学
• 关键词: Helmholtz equation Quadrature method.
• 年，卷（期）: 2001,（5）
• 页码范围: 489-500
• 页数: 12页
• 分类号: O1
• 语种: 英文

摘要

Consider solving the Dirichlet problem of Helmholtz equation on unbounded region R2\Г with Г a smooth open curve in the plane. We use simple-layer potential to construct a solution. This leads to the solution of a logarithmic integral equation of the first kind for the Helmholtz equation. This equation is reformulated using a special change of variable, leading to a new first kind equation with a smooth solution function. This new equation is split into three parts. Then a quadrature method that takes special advantage of the splitting of the integral equation is used to solve the equation numerically. An error analysis in a Sobolev space setting is given. And numerical results show that fast convergence is clearly exhibited.