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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An inverse Lax-Wendroff procedure for finite difference schemes on the Cartesian grids
笛卡尔网格 有限差分格式 Lax-Wendroff逆过程
2023/11/13
In this talk, we introduce the so-called inverse Lax-Wendroff (ILW) boundary treatment for finite difference approximations on the Cartesian mesh. As the domain boundary may intersect with the grid in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Number of rational points of difference varieties in finite difference fields
有限差分域 差分簇 有理点数
2023/4/13
A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
A sweeping preconditioner for Yee’s finite difference approximation of time-harmonic Maxwell’s equations
Electromagnetic scattering Yee grid finite difference methods perfectly matched layers LDLT factorizations multifrontal method wave propagation in inhomogeneous and anisotropic media matrix preconditioners
2015/7/14
This paper is concerned with the fast iterative solution of linear systems arising from finite difference discretizations in electromagnetics. The sweeping preconditioner with moving perfectly matched...
Verification of a non-hydrostatic dynamical core using the horizontal spectral element method and vertical finite difference method: 2-D aspects
horizontal spectral element method vertical finite difference method
2014/12/19
The non-hydrostatic (NH) compressible Euler equations for dry atmosphere were solved in a simplified two-dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal ...
Global synthetic seismograms using a 2-D finite-difference method
Body waves Computational seismology Wave propagation
2014/4/10
Two-dimensional (2-D) finite-difference (FD) synthetics, which fill the gap between fast 1-D analytic synthetics and time-consuming full 3-D synthetics in our ability to model seismograms, have been u...
The Theory and Application of Upwind Finite Difference Fractional Steps Procedure for Seawater Intrusion
Seawater Intrusion Three-Dimensional Region
2013/3/11
Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differ...
The Best Finite-Difference Scheme for the Helmholtz Equation
The Best Finite-Difference Scheme for the Helmholtz and Laplace’s Equations
2013/1/30
The best finite-difference scheme for the Helmholtz equation is suggested. A method of solving obtained finite-difference scheme is developed. The efficiency and accuracy of method were tested on seve...
A Second Order Finite Difference-Spectral Method for Space Fractional Diffusion Equation
A Second Order Finite Difference-Spectral Method Space Fractional Diffusion Equation
2012/8/7
A high order finite difference-spectral method is derived for solving space fractional diffusion equations, by combining the second order finite difference method in time and the spectral Galerkin met...
Elements of Polya-Schur theory in finite difference setting
Elements Polya-Schur theory finite difference setting Classical Analysis and ODEs
2012/4/16
In this note we attempt to develop an analog of P\'olya-Schur theory describing the class of univariate hyperbolicity preservers in the setting of linear finite difference operators. We study the clas...
Uniform convergence analysis of an upwind finite difference approximations of an homogenous singularly perturbed boundary value problem using grid equidistribution
singular perturbation adaptive grid rate of convergence error estimate
2011/10/13
We derive varepsilon-uniform error estimates for two first-order upwind discretizations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here,...
Consistency Analysis of Finite Difference Approximations to PDE Systems
systems of partial differential equations involution Thomas decomposition finite difference approximations consistency
2011/9/16
Abstract: In the given paper we consider finite difference approximations to systems of polynomially-nonlinear partial differential equations whose coefficients are rational functions over rationals i...
Finite difference approximations for the first-order hyperbolic partial differential equation with point-wise delay
hyperbolic partial differential equation differential difference equation
2011/1/18
Explicit numerical methods based on Lax-Friedrichs and Leap-Frog finite difference approximations are constructed to find the numerical solution of the first-order hyperbolic partial differential equa...
Finite-difference analysis for unsteady squeezing flow of a second grade fluid between circular plates
Non-Newtonian fluids Squeezing flow
2010/9/27
The unsteady two-dimensional flow of non-conducting, incompressible second grade fluid between two circular plates approaching or receding from each other symmetrically is studied. A similarity transf...
Numerical solution to Belousov朲habotinskii model and a comparison with the finite difference method
Traveling wavelets method reaction- diffusion system
2010/9/10
In this work, we find a numerical solution to Belousov – Zhabontinskii system, we use the traveling wavelets method. It is well known that this model describes a chemical reaction. The results obtaine...
An explicit finite difference scheme for a compressible Heisenberg chain equations
compressible Heisenberg chain equations explicitness
2010/9/14
In this paper, we consider a class of compressible Heisenberg chain equations with periodic initial value problem. An explicit finite difference scheme is proposed. Moreover, its convergence and stabi...