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New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations

作     者:Kejia Pan Kang Fu Jin Li Hongling Hu Zhilin Li 

作者机构:School of Mathematics and StatisticsHNP-LAMACentral South UniversityChangsha 410083China MOE-LCSMSchool of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China CRSC&Department of MathematicsNorth Carolina State UniversityRaleighNC 27695-8205USA 

出 版 物:《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报(英文版))

年 卷 期:2023年第16卷第2期

页      面:393-409页

核心收录:

学科分类:07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基  金:supported by the National Natural Science Foundation of China(Grant No.42274101)and the Excellent Youth Foundation of Hunan Province of China(Grant No.2018JJ1042) Hongling Hu was supported by the National Natural Science Foundation of China(Grant No.12071128) the Natural Science Foundation of Hunan Province(Grant No.2021JJ30434).Zhilin Li was partially supported by a Simons Grant No.633724 

主  题:Poisson equation Helmholtz equation sixth-order compact scheme maximum principle staggered grid. 

摘      要:Some new sixth-order compact finite difference schemes for Poisson/Helmholtz equations on rectangular domains in both two-and three-dimensions are developed and *** 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 *** 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 ***,the new compact schemes are exact for 2D and 3D Poisson equations if the solution is a polynomial less than or equal to *** 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 *** examples in both 2D and 3D are presented to verify the effectiveness of the proposed schemes.

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