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Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model

Computers & Mathematics with Applications, 2021
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Huanrong Li   +3 more
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Numerical dispersion analysis of an efficient unconditionally stable three-dimensional LOD-FDTD method

2013 IEEE International Conference on Signal Processing, Communication and Computing (ICSPCC 2013), 2013
In this paper, an improved three-dimensional (3D) locally one-dimensional finite-difference time-domain (LOD-FDTD) method is presented. In the proposed method, the time step is divided into three sub-steps. Dispersion control parameters are inducted into X, Y and Z directions.
Min Su, Bo Yi, Pei-Guo Liu
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Maximum norm error analysis of an unconditionally stable semi‐implicit scheme for multi‐dimensional Allen–Cahn equations

Numerical Methods for Partial Differential Equations, 2018
In this paper, a linearized finite difference scheme is proposed for solving the multi‐dimensional Allen–Cahn equation. In the scheme, a modified leap‐frog scheme is used for the time discretization, the nonlinear term is treated in a semi‐implicit way ...
Dongdong He, Kejia Pan
semanticscholar   +1 more source

Three-Dimensional Unconditionally Stable LOD-FDTD Methods With Low Numerical Dispersion in the Desired Directions

IEEE Transactions on Antennas and Propagation, 2016
In order to get low numerical dispersion in the desired directions, four-step locally one-dimensional finite-difference time-domain (LOD4-FDTD), five-step LOD-FDTD (LOD5-FDTD), and six-step LOD-FDTD (LOD6-FDTD) methods are developed here. These methods are derived from the three-step LOD-FDTD method, and each of their substeps has variation in either ...
Alok Kumar Saxena   +1 more
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Numerical analysis for high-order six-stages split-step unconditionally-stable FDTD methods

2012 International Conference on Microwave and Millimeter Wave Technology (ICMMT), 2012
High-order six-stages split-step unconditionally-stable finite-difference time-domain (FDTD) methods are presented. Along the positive and negative of the x, y, and z coordinate directions, the Maxwell's matrix is split into six submatrices, and the time step is divided into six sub-steps. In addition, high-order central finite-difference operators are
Yong-Dan Kong, Qing-Xin Chu
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A compact fourth‐order unconditionally stable six‐stages split‐step FDTD method and numerical analysis

Microwave and Optical Technology Letters, 2014
ABSTRACTA compact fourth‐order six‐stages split‐step finite‐difference time‐domain method is developed, which is based on the compact fourth‐order scheme. The proposed method improves the efficiency of computation by reducing the bandwidth of the matrix to be inversed from seven to five for the fourth‐order scheme.
Yong‐Dan Kong   +2 more
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Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system

Numerical Methods for Partial Differential Equations
AbstractWe develop two totally decoupled, linear and second‐order accurate numerical methods that are unconditionally energy stable for solving the Cahn–Hilliard–Darcy equations for two phase flows in porous media or in a Hele‐Shaw cell. The implicit‐explicit Crank–Nicolson leapfrog method is employed for the discretization of the Cahn–Hiliard equation
Yali Gao, Daozhi Han
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An Unconditionally L∞ — stable method of fractional steps for numerical solution of convective diffusion problems

2006
Developing a stable and efficient numerical method for solving the convective diffusion problems continues to be an active and challenging research area because of its importance in prediction of heat and mass transfer and fluid flow. Tests of the diverse methods of this area in the literature reveal that two types of problems appear quite frequently ...
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