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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 ...
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High-Order Split-Step Unconditionally-Stable FDTD Methods and Numerical Analysis
IEEE Transactions on Antennas and Propagation, 2011High-order split-step unconditionally-stable finite-difference time-domain (FDTD) methods in three-dimensional (3-D) domains are presented. Symmetric operator and uniform splitting are adopted simultaneously to split the matrix derived from the classical Maxwell's equations into four sub-matrices.
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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.
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