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A HIGH-ORDER-ACCURATE DIFFERENCE SCHEME WITH UNCONDITIONAL STABILITY FOR THE DIFFUSION EQUATION ON nonuniform gridS

Journal of Hydrodynamics 2001年第1期13卷 92-98页

作者： Wang Xuan, Yang Zhi-feng State Key Laboratory of Environment Simulation and Pollution Control, Institute of Environmental Sciences, Beijing Normal University, Beijing 100875, China[WT5”HZ] Beijing Normal Univ. Beijing 100875 China

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]

关键词： ]finite difference scheme diffusion equation nonuniform grid high accuracy computational fluid dynamics

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Geometric grid network and third-order compact scheme for solving nonlinear variable coefficients 3D elliptic PDEs

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International Journal of Modeling, Simulation, and Scientific Computing 2018年第6期9卷 72-99页

作者： Navnit Jha Venu Gopal Bhagat Singh Department of Mathematics South Asian University ChanakyapuriNew Delhi 110070India The School of Mathematical Sciences University of Science and Technology of China Hefei Anhui 230026P.R.China

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 *** cell discretization to the elliptic equation makes it easier to compute and exhibit stability of the numerical *** monotone and irreducible property of the Jacobian matrix to the system of difference equations analyses the converging behavior of the numerical solution *** 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 *** results corroborate the reliability and efficiency of the scheme.

关键词： Finite-difference method nonuniform grid compact operator monotone matrix sine-Gordon equation elliptic Allen-Cahn equation.

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散乱数据的数值微分及其误差估计

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高等学校计算数学学报 2003年第1期25卷 81-90页

作者：贾现正王彦博程晋复旦大学数学系复旦大学数学系上海 200433

1 背景及问题的提出导数是数学分析中的一个基本的慨念。对于数学工作者来讲,计算导数不是一项特别困难的工作。但是,对于研究实际问题的科学工作者来讲,这项工作就不是一件简单的工作了,首先,求导数的问题是一个典型的Hadamard意义下... 详细信息

1 背景及问题的提出导数是数学分析中的一个基本的慨念。对于数学工作者来讲,计算导数不是一项特别困难的工作。但是,对于研究实际问题的科学工作者来讲,这项工作就不是一件简单的工作了,首先,求导数的问题是一个典型的Hadamard意义下的不适定问题([5],[12]等)

关键词： numerical differentiation scattered data nonuniform grid natural cubic spline.

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Exact local refinement using Fourier interpolation for nonuniformgrid modeling

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Earth and Planetary Physics 2017年第1期1卷 58-62页

作者： JinHai Zhang ZhenXing Yao Key Laboratory of Earth and Planetary Physics Institute of Geology and Geophysics Chinese Academy of Sciences

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 *** 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.

关键词： local refinement varying grid tiny structures fourier interpolation nonuniform grid

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