Year: 2023
Author: Hongling Hu, Kejia Pan, Zhilin Li, Kang Fu, Jin Li, Hongling Hu, Zhilin Li
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 2 : pp. 393–409
Abstract
Some new sixth-order compact finite difference schemes for Poisson/Helmholtz equations on rectangular domains in both two- and three-dimensions are developed and analyzed. Different from a few sixth-order compact finite difference schemes in the literature, the finite difference and weight coefficients of the new methods have analytic simple expressions. One of the new ideas is to use a weighted combination of the source term at staggered grid points which is important for grid points near the boundary and avoids partial derivatives of the source term. Furthermore, the new compact schemes are exact for 2D and 3D Poisson equations if the solution is a polynomial less than or equal to 6. The coefficient matrices of the new schemes are $M$-matrices for Helmholtz equations with wave number $K≤0,$ which guarantee the discrete maximum principle and lead to the convergence of the new sixth-order compact schemes. Numerical examples in both 2D and 3D are presented to verify the effectiveness of the proposed schemes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0073
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 2 : pp. 393–409
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Poisson equation Helmholtz equation sixth-order compact scheme maximum principle staggered grid.