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
It has been evident that the theory and methods of dynamic derivatives are playing an increasingly important role in hybrid modeling and computations. Being constructed on various kinds of hybrid grids, that is, tim...It has been evident that the theory and methods of dynamic derivatives are playing an increasingly important role in hybrid modeling and computations. Being constructed on various kinds of hybrid grids, that is, time scales, dynamic derivatives offer superior accuracy and flexibility in approximating mathematically important natural processes with hard-to-predict singularities, such as the epidemic growth with unpredictable jump sizes and option market changes with high uncertainties, as compared with conventional derivatives. In this article, we shall review the novel new concepts, explore delicate relations between the most frequently used second-order dynamic derivatives and conventional derivatives. We shall investigate necessary conditions for guaranteeing the consistency between the two derivatives. We will show that such a consistency may never exist in general. This implies that the dynamic derivatives provide entirely different new tools for sensitive modeling and approximations on hybrid grids. Rigorous error analysis will be given via asymptotic expansions for further modeling and computational applications. Numerical experiments will also be given.展开更多
由电磁学的基本规律麦克斯韦方程差分形式即时域有限差分(Finite Different Time Domain,FDTD)导出不均匀网格的FDTD差分形式,即不均匀网格的时域有限差分法(Non Uniform Grid Finite Different TimeDomain,NU-FDTD),并提出了在腔体孔...由电磁学的基本规律麦克斯韦方程差分形式即时域有限差分(Finite Different Time Domain,FDTD)导出不均匀网格的FDTD差分形式,即不均匀网格的时域有限差分法(Non Uniform Grid Finite Different TimeDomain,NU-FDTD),并提出了在腔体孔缝电磁耦合分析中采用NU-FDTD时,网格和时间步长划分的原则是:导体边界采用局部均匀细网格法,其它空间采用渐变不均匀法。实验结果表明,这种方法不仅节省计算时间,而且精度高。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.
文摘It has been evident that the theory and methods of dynamic derivatives are playing an increasingly important role in hybrid modeling and computations. Being constructed on various kinds of hybrid grids, that is, time scales, dynamic derivatives offer superior accuracy and flexibility in approximating mathematically important natural processes with hard-to-predict singularities, such as the epidemic growth with unpredictable jump sizes and option market changes with high uncertainties, as compared with conventional derivatives. In this article, we shall review the novel new concepts, explore delicate relations between the most frequently used second-order dynamic derivatives and conventional derivatives. We shall investigate necessary conditions for guaranteeing the consistency between the two derivatives. We will show that such a consistency may never exist in general. This implies that the dynamic derivatives provide entirely different new tools for sensitive modeling and approximations on hybrid grids. Rigorous error analysis will be given via asymptotic expansions for further modeling and computational applications. Numerical experiments will also be given.
文摘由电磁学的基本规律麦克斯韦方程差分形式即时域有限差分(Finite Different Time Domain,FDTD)导出不均匀网格的FDTD差分形式,即不均匀网格的时域有限差分法(Non Uniform Grid Finite Different TimeDomain,NU-FDTD),并提出了在腔体孔缝电磁耦合分析中采用NU-FDTD时,网格和时间步长划分的原则是:导体边界采用局部均匀细网格法,其它空间采用渐变不均匀法。实验结果表明,这种方法不仅节省计算时间,而且精度高。
