WT5”BZ]A high-order-accurate difference scheme with unconditional stability is developed for the diffusion equation on nonuniform grids. The theoretical analysis shows that the accuracy of this scheme is between thir...WT5”BZ]A high-order-accurate difference scheme with unconditional stability is developed for the diffusion equation on nonuniform grids. The theoretical analysis shows that the accuracy of this scheme is between third order and fourth order, and fourth-order accuracy is achieved in the case of the same grid steps being used within the computational domain. Two numerical examples are given to demonst ate the advantages of the proposed scheme. Compared with the conventional difference scheme, more accurate numerical solution can be obtained by using the proposed scheme even with relatively larger grid sizes. It is also pointed out that the appropriate structure of the nonuniform grid can not only make the proposed scheme more practical, but lead to a solution superior to that for a uniform grid structure. [WT5”HZ]展开更多
Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large-scale media. It is necessary to use a nonuniform g...Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large-scale media. It is necessary to use a nonuniform grid, where upsampling the wavefield from the coarse grid to the fine grid is essential for reducing artifacts. In this paper, we suggest a local refinement scheme using the Fourier interpolation, which is superior to traditional interpolation methods since it is theoretically exact if the input wavefield is band limited.Traditional interpolation methods would fail at high upsampling ratios(say 50); in contrast, our scheme still works well in the same situations, and the upsampling ratio can be any positive integer. A high upsampling ratio allows us to greatly reduce the computational burden and memory demand in the presence of tiny structures and large-scale models, especially for 3D cases.展开更多
By using nonuniform(geometric)grid network,a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type.Singl...By using nonuniform(geometric)grid network,a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type.Single cell discretization to the elliptic equation makes it easier to compute and exhibit stability of the numerical solutions.The monotone and irreducible property of the Jacobian matrix to the system of difference equations analyses the converging behavior of the numerical solution values.As an experiment,applications of the compact scheme to Schr¨odinger equations,sine-Gordon equations,elliptic Allen–Cahn equation and Poisson’s equation have been presented with root mean squared errors of exact and approximate solution values.The results corroborate the reliability and efficiency of the scheme.展开更多
基金ProjectsupportedbytheMajorStateBasicResearchDevelopmentProgram (No .G19990 436 )andthe"Trans CenturyTrainingProgramFoundationfo
文摘WT5”BZ]A high-order-accurate difference scheme with unconditional stability is developed for the diffusion equation on nonuniform grids. The theoretical analysis shows that the accuracy of this scheme is between third order and fourth order, and fourth-order accuracy is achieved in the case of the same grid steps being used within the computational domain. Two numerical examples are given to demonst ate the advantages of the proposed scheme. Compared with the conventional difference scheme, more accurate numerical solution can be obtained by using the proposed scheme even with relatively larger grid sizes. It is also pointed out that the appropriate structure of the nonuniform grid can not only make the proposed scheme more practical, but lead to a solution superior to that for a uniform grid structure. [WT5”HZ]
基金supported by the National Natural Science Foundation of China (Grant No.41130418)the National Major Project of China (under grant 2017ZX05008-007)+1 种基金supports from the Youth Innovation Promotion Association CAS (2012054)Foundation for Excellent Member of the Youth Innovation Promotion Association (2016)
文摘Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large-scale media. It is necessary to use a nonuniform grid, where upsampling the wavefield from the coarse grid to the fine grid is essential for reducing artifacts. In this paper, we suggest a local refinement scheme using the Fourier interpolation, which is superior to traditional interpolation methods since it is theoretically exact if the input wavefield is band limited.Traditional interpolation methods would fail at high upsampling ratios(say 50); in contrast, our scheme still works well in the same situations, and the upsampling ratio can be any positive integer. A high upsampling ratio allows us to greatly reduce the computational burden and memory demand in the presence of tiny structures and large-scale models, especially for 3D cases.
基金Science and Engineering Research Board(DST,Govt.of India)Grant No.SR/FTP/MS-020/2011Chinese Academy of Sciences President’s International Fellowship Initiative,Grant No.2015PM034。
文摘By using nonuniform(geometric)grid network,a new high-order finite-difference compact scheme has been obtained for the numerical solution of three-space dimensions partial differential equations of elliptic type.Single cell discretization to the elliptic equation makes it easier to compute and exhibit stability of the numerical solutions.The monotone and irreducible property of the Jacobian matrix to the system of difference equations analyses the converging behavior of the numerical solution values.As an experiment,applications of the compact scheme to Schr¨odinger equations,sine-Gordon equations,elliptic Allen–Cahn equation and Poisson’s equation have been presented with root mean squared errors of exact and approximate solution values.The results corroborate the reliability and efficiency of the scheme.
