High-Order Finite Difference Method for Helmholtz Equation in Polar Coordinates

• 作者: Meiling Zhao Na Zhu
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: HIGH-ORDER HELMHOLTZ EQUATION POLAR COORDINATES
• 年，卷（期）: 2019,（3）
• 页码范围: 174-186
• 页数: 13页
• 分类号: O1

摘要

We present a fourth-order finite difference scheme for the Helmholtz equation in polar coordinates. We employ the finite difference format in the interior of the region and derive a nine-point fourth-order scheme. Specially, ghost points outside the region are applied to obtain the approximation for the Neumann boundary condition. We obtain the matrix form of the linear system and the sparsity of the coefficient matrix is favorable for the computation of the Helmholtz equation. The feasibility and accuracy of the method are validated by two test examples which have exact solutions.