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High-Order Finite Difference Method for Helmholtz Equation in Polar Coordinates
School of Mathematics and Physics, North China Electric Power University, Baoding, China
School of Mathematics and Physics, North China Electric Power University, Baoding, China
- 1 School of Mathematics and Physics, North China Electric Power University, Baoding, China
- 2 School of Mathematics and Physics, North China Electric Power University, Baoding, China
American Journal of Computational Mathematics·Volume 09 (2019)·Pages 174–186·Published 26 August 2019·DOI10.4236/ajcm.2019.93013
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Abstract
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.
KeywordsHigh-OrderHelmholtz EquationPolar Coordinates
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