Unconditionally stable algorithms to solve the time-dependent Maxwell equations

Kole, J.S.; Figge, Marc Thilo; Raedt, de Hans

doi:10.1103/physreve.64.066705

Cited by 50 publications

(81 citation statements)

References 35 publications

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“…Kole, Figge and de Raedt noticed (see [6]) that it is possible to split the matrix A into the sum of skew-symmetric matrices, for which the matrix exponential can be computed exactly (KFRmethod). When we have such splitting in the form A = Al + ... + A p (p E IN), then we have U n (!1tA) as a product of exactly computed exponentials exp(~il!1tAi), where~il is some suitable constant (i E {I, ... ,p}).…”

Section: The Kole-figge-de Raedt Methodsmentioning

confidence: 99%

“…This method is also unconditionally stable. use of the methods (see papers [1,5,6,8,10,13]). We consider the Yee-method as a standard solution method, so we compare the methods with the Yee-method.…”

Section: The Krylov-space Methodsmentioning

confidence: 99%

“…(5) (6) is the magnetic field strength, E is the electric permittivity and /-L is the magnetic permeability (see [9] and [13] for more details). The two material parameters can depend on the spatial coordinates.…”

Section: H = (Hx(t X Y Z) Hy(t X Y Z) Hz(t X Y Z))mentioning

confidence: 99%

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Iterative Solution Methods of the Maxwell Equations Using Staggered Grid Spatial Discretization

Horváth

Faragó

Schilders

2004

Scientific Computation

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Section: The Kole-figge-de Raedt Methodsmentioning

confidence: 99%

Section: The Krylov-space Methodsmentioning

confidence: 99%

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Iterative Solution Methods of the Maxwell Equations Using Staggered Grid Spatial Discretization

Horváth

Faragó

Schilders

2004

Scientific Computation

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“…Recently we have introduced a family of unconditionally stable algorithms to solve the TDME [3][4][5]. The operator that governs the time evolution of the electromagnetic (EM) fields is orthogonal and can be written as the matrix exponential of a skew-symmetric matrix [3,5].…”

Section: Introductionmentioning

confidence: 99%

“…The operator that governs the time evolution of the electromagnetic (EM) fields is orthogonal and can be written as the matrix exponential of a skew-symmetric matrix [3,5]. Orthogonal approximations to the time-evolution operator yield unconditionally stable algorithms by construction [13].…”

Section: Introductionmentioning

confidence: 99%

Chebyshev Method to Solve the Time-Dependent Maxwell Equations

Raedt

Michielsen

Kole

et al. 2003

Springer Proceedings in Physics

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Abstract. We present a one-step algorithm to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We compare the results of this algorithm with those obtained from unconditionally stable algorithms and demonstrate that for a range of applications the one-step algorithm may be orders of magnitude more efficient than multiple time-step, finite-difference time-domain algorithms. We discuss both the virtues and limitations of this one-step approach.

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A matrix‐exponential decomposition‐based time‐domain method for band structure calculation of one‐dimensional periodic structures

Wang

Zhang

et al. 2016

Int J Numerical Modelling

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SUMMARYA time-domain method for calculating the band structure of one-dimensional periodic structures is proposed. During the time-stepping of the method, the column vector containing the spatially sampled field data is updated by multiplying with an iteration matrix. The iteration matrix is first obtained by using the matrix-exponential decomposition technique. Then, the small nonzero elements of the matrix are pruned to improve its sparse structure, so that the efficiency of the matrix-vector multiplication involved in each time-step is enhanced. The numerical results show that the method is conditionally stable but is much more stable than the conventional finitedifference time-domain (FDTD) method. The time-step with which the method runs stably can be much larger than the Courant-Friedrichs-Lewy (CFL) limit. And moreover, the method is found to be particularly efficient for the band structure calculation of large-scale structures containing a defect with a very high wave speed, where the conventional FDTD method may generally lose its efficiency severely. For this kind of structures, not only the stability requirement can be significantly relaxed, but also the matrix-pruning operation can be very effectively performed. In the numerical experiments for large-scale quasi-periodic phononic crystal structures containing a defect layer, significantly higher efficiency than the conventional FDTD method can be achieved by the proposed method without an evident accuracy deterioration if the wave speed of the defect layer is relatively high.

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Unconditionally stable algorithms to solve the time-dependent Maxwell equations

Cited by 50 publications

References 35 publications

Iterative Solution Methods of the Maxwell Equations Using Staggered Grid Spatial Discretization

Iterative Solution Methods of the Maxwell Equations Using Staggered Grid Spatial Discretization

Chebyshev Method to Solve the Time-Dependent Maxwell Equations

A matrix‐exponential decomposition‐based time‐domain method for band structure calculation of one‐dimensional periodic structures

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