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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Splitting Numerical Schemes for Two-dimensional Maxwell-Debye Equations
二维 麦克斯韦-德拜方程组 拆分数值方案
2023/4/27
In this talk, we are interested in designing some efficient numerical methods for Maxwell-Debye equations in metamaterials with negative refractive index. Dimensional splitting method is used to reduc...
Evaluation of numerical schemes for capturing shock waves in modeling proppant transport in fractures
Proppant transport Hyperbolic partial differential equations Frac pack Hydraulic fracturing
2018/4/2
In petroleum engineering, the transport phenomenon of proppants in a fracture caused by hydraulic fracturing is captured by hyperbolic partial differential equations (PDEs). The solution of this kind ...
Analysis and Design of Numerical Schemes for Gas Dynamics 2 Artificial Diffusion and Discrete Shock Structure
Numerical Schemes Gas Dynamics Discrete Shock Structure
2015/7/1
The effect of artificial diffusion on discrete shock structures is examined for a family of schemes which includes scalar diffusion, convective upwind and split pressure (CUSP)...
Analysis and Design of Numerical Schemes for Gas Dynamics 1 Artificial Diffusion, Upwind Biasing, Limiters and Their Effect on Accuracy and Multigrid Convergence
Design of Numerical Schemes Gas Dynamics usion Upwind Biasing Limiters Accuracy Multigrid Convergence
2015/7/1
The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This ...
Geometric numerical schemes for the KdV equation
KdV equation symplectic scheme multi-symplectic scheme solitonic gas wave turbulence
2012/5/29
Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-...
Comparison of third order L_0-stable numerical schemes for the two–Dimensional homogeneous diffusion problem subject to specification of mass
Lo − stable Parabolic Problems
2010/9/21
This paper presents a numerical comparison of third order Lo − stable numerical schemes for the two-dimensional parabolic partial differential equations subject to nonlocal boundary conditions. ...
Energy-preserving numerical schemes of high accuracy for one-dimensional Hamiltonian systems
geometric numerical integration long time numerical evolution
2010/12/15
We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered clas...
On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes
Degenerate parabolic equations financial derivatives
2010/10/18
Semi-elliptic stochastic differential equations (SDEs) are common models among practitioners. However, value functions and sensitivities of such models are described by degenerate parabolic partial d...
On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes (with applications to the Libor market model)
Degenerate parabolic equations financial derivatives sen-sitivities Monte-Carlo methods
2010/4/27
Computational parsimony makes reduced factor Libor market models popular among practioners. However, value functions and sensitivities of such models are described by degenerate parabolic (i.e. semiel...