TITLE:
High-Order Finite Difference Method for Helmholtz Equation in Polar Coordinates
AUTHORS:
Na Zhu, Meiling Zhao
KEYWORDS:
High-Order, Helmholtz Equation, Polar Coordinates
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.9 No.3,
August
30,
2019
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.