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High-Order Unconditionally Stable Two-Step Leapfrog ADI-FDTD Methods and Numerical Analysis
IEEE Transactions on Antennas and Propagation, 2013High-order unconditionally stable two-step leapfrog alternating direction implicit-finite-difference time-domain (ADI-FDTD) methods in three-dimensional (3-D) domains are presented. Based on the exponential evolution operator (EEO), the Maxwell's equations in a matrix form can be split into four subprocedures first, and then two subprocedures are ...
Yong-Dan Kong, Qing-Xin Chu, Rong-Lin Li
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Applied Numerical Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhengguang Liu, Shuangshuang Chen
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhengguang Liu, Shuangshuang Chen
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Towards the development of unconditionally stable time-domain meshless numerical methods
2009 IEEE MTT-S International Microwave Symposium Digest, 2009Meshless methods have recently emerged as robust numerical techniques for electromagnetic modeling in time domain. In those methods, a problem domain is represented by scattered spatial nodes instead of numerical meshes, thus the conformal modeling of boundaries and solution refinements can be conveniently achieved.
null Yiqiang Yu, Zhizhang Chen
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An unconditionally gradient stable numerical method for solving the Allen–Cahn equation
Physica A: Statistical Mechanics and its Applications, 2009Abstract We consider an unconditionally gradient stable scheme for solving the Allen–Cahn equation representing a model for anti-phase domain coarsening in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy ...
Jeong-Whan Choi +3 more
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Numerical Dispersion Analysis of the Unconditionally Stable Three-Dimensional LOD-FDTD Method
IEEE Transactions on Antennas and Propagation, 2010The numerical dispersion characteristics of the recently developed three-dimensional unconditionally stable locally- one-dimensional finite-difference time-domain (LOD-FDTD) method are derived analytically. The effect of grid size and the Courant Friedrich Lewy (CFL) limits on dispersion are studied in detail.
Iftikhar Ahmed, Eng-Kee Chua, Er-Ping Li
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International Journal for Numerical Methods in Engineering, 1982
AbstractThird‐ and fourth‐order accurate Nørsett rational approximations to the exponential and associated semi‐implicit Runge–Kutta methods are used for the construction of efficient, accurate and unconditionally stable schemes for the direct numerical integration of the linear, nonhomogeneous, second‐order equations of structural dynamics.
Dougalis, Vassilios A. +1 more
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AbstractThird‐ and fourth‐order accurate Nørsett rational approximations to the exponential and associated semi‐implicit Runge–Kutta methods are used for the construction of efficient, accurate and unconditionally stable schemes for the direct numerical integration of the linear, nonhomogeneous, second‐order equations of structural dynamics.
Dougalis, Vassilios A. +1 more
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IEEE Transactions on Antennas and Propagation, 2012
An one-step arbitrary-order leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is presented. Its unconditional stability is analytically proven and numerically verified. Its numerical properties are shown to be identical to those of the conventional ADI-FDTD and LOD-FDTD methods.
Shun-Chuan Yang +3 more
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An one-step arbitrary-order leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is presented. Its unconditional stability is analytically proven and numerically verified. Its numerical properties are shown to be identical to those of the conventional ADI-FDTD and LOD-FDTD methods.
Shun-Chuan Yang +3 more
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Numerical Methods for Partial Differential Equations, 2021
We consider numerical approximations for a modified phase field crystal model with a strong nonlinear vacancy potential. Based on the invariant energy quadratization approach and stabilized strategies, we develop linear, unconditionally energy stable ...
Shuaichao Pei, Yanren Hou, Wenjing Yan
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We consider numerical approximations for a modified phase field crystal model with a strong nonlinear vacancy potential. Based on the invariant energy quadratization approach and stabilized strategies, we develop linear, unconditionally energy stable ...
Shuaichao Pei, Yanren Hou, Wenjing Yan
semanticscholar +1 more source