Journal ArticleDOI
Unconditionally stable Crank-Nicolson scheme for solving two-dimensional Maxwell's equations
C. Sun,C.W. Trueman +1 more
TLDR
In this article, the Douglas-Gunn algorithm is used to subdivide the update procedure into two sub-steps, at each sub-step only a tri-diagonal matrix needs to be solved for one field component, and other two field components are updated explicitly in one step.Abstract:
The Crank-Nicolson method is an unconditionally stable, implicit numerical scheme with second-order accuracy in both time and space. When applied to solve Maxwell's equations in two-dimensions, the resulting matrix is block tri-diagonal, which is very expensive to solve. The Douglas-Gunn algorithm is used to subdivide the update procedure into two sub-steps. At each sub-step only a tri-diagonal matrix needs to be solved for one field component. The other two field components are updated explicitly in one step. The numerical dispersion relations are given for the original Crank-Nicolson scheme and for the Douglas-Gunn modification. The predicted numerical dispersion is shown to agree with numerical experiments, and its numerical anisotropy is shown to be much smaller than that of the ADI-FDTD.read more
Citations
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Journal ArticleDOI
A Three-Dimensional Semi-Implicit FDTD Scheme for Calculation of Shielding Effectiveness of Enclosure With Thin Slots
Juan Chen,Jianguo Wang +1 more
TL;DR: In this article, the authors extended the hybrid implicit-explicit finite-difference time domain (HIE-FDTD) scheme for a 2D transverse electric (TE) wave to a full 3D electromagnetic wave.
Journal ArticleDOI
Approximate Crank-Nicolson schemes for the 2-D finite-difference time-domain method for TE/sub z/ waves
TL;DR: In this paper, two implicit finite-difference time-domain (FDTD) methods are presented for a two-dimensional TE/sub z/ wave, which are based on the unconditionally stable Crank-Nicolson scheme.
Journal ArticleDOI
Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method
TL;DR: In this paper, a factorization-splitting scheme using two substeps was proposed to decompose the generalized Crank-Nicolson (CN) matrix into two simple matrices with the terms not factored confined to one sub-step.
Journal ArticleDOI
Unconditionally-stable FDTD method based on Crank-Nicolson scheme for solving three-dimensional Maxwell equations
G. Sun,C.W. Trueman +1 more
TL;DR: The approximate factorization-splitting (CNAFS) method as mentioned in this paper is an efficient implementation of the Crank-Nicolson scheme for solving the 3D Maxwell equations in the time domain, using much less CPU time and memory than a direct implementation.
Journal ArticleDOI
Explicit Time-Domain Finite-Element Method Stabilized for an Arbitrarily Large Time Step
Qing He,Houle Gan,Dan Jiao +2 more
TL;DR: In this paper, the root cause of the instability of an explicit time-domain finite-element method is quantitatively identified and an unconditionally stable explicit method is successfully created which is stable and accurate for a time step solely determined by accuracy regardless of how large the time step is.
References
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Journal ArticleDOI
Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
Abstract: Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for a boundary condition involving perfectly conducting surfaces. An example is given of the scattering of an electromagnetic pulse by a perfectly conducting cylinder.
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A new FDTD algorithm based on alternating-direction implicit method
TL;DR: In this article, a new finite-difference time-domain (FDTD) algorithm is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint.
Journal ArticleDOI
Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method
TL;DR: In this article, an unconditionally stable three-dimensional (3-D) finite-difference time-method (FDTD) is presented where the time step used is no longer restricted by stability but by accuracy.
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On the accuracy of the ADI-FDTD method
TL;DR: In this article, an analytical study of the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method for solving time-varying Maxwell's equations and compare its accuracy with that of the Crank-Nicolson (CN) and Yee FDTD schemes is presented.