Transformed-space nonuniform pseudospectral time-domain algorithm

Leung, W.C.; Chen, Yinchao

doi:10.1002/1098-2760(20010320)28:6<391::aid-mop1051>3.0.co;2-5

Cited by 11 publications

(7 citation statements)

References 8 publications

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“…These field oscillations, even when small, alter the local fields inside the magnetic material and hence yield incorrect magnetisation distributions within magnetic structures. The Gibbs effect may be reduced through the use of non-uniform grids [34] at the expense of increased difficulty in implementation particularly for complex geometries.…”

Section: Unstaggered Schemesmentioning

confidence: 99%

Sub-Nanosecond Electromagnetic-Micromagnetic Dynamic Simulations Using the Finite-Difference Time-Domain Method

Aziz¹

2009

PIER B

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Abstract-This paper presents an efficient and simple approach of implementing the Landau-Lifshitz-Gilbert (LLG) equation of magnetisation motion within the Finite-difference Time-domain (FDTD) method. This combined electromagnetic-micromagnetic simulation technique is particularly important for modeling electromagnetic interaction with lossy magnetic material in the presence of current and magnetic sources, particularly at very high frequencies. The efficient implementation involves simple two-point spatial interpolations that are applicable to two and three-dimensional FDTD grids, and uses a stable iterative algorithm for the time integration of the LLG equation. A ferromagnetic resonance numerical experiment on a rectangular Permalloy prism excited through its cross-section by a non-uniform pulse field from a transmission line was carried out for the purpose of verifying the combined FDTD-LLG computations. The numerical results were in good agreement with linearised analytical solutions of the LLG equation for uniform and non-uniform precession modes. This paper also presents a brief investigation on the use of non-staggered FDTD grid schemes to model magnetic material using the LLG equation, and indicates that the classical FDTD staggered scheme offers simplicity in implementation and more accuracy for modeling wave interaction with lossy magnetic material than the non-staggered schemes based on Maxwell's equations formulation.

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Section: Unstaggered Schemesmentioning

confidence: 99%

Sub-Nanosecond Electromagnetic-Micromagnetic Dynamic Simulations Using the Finite-Difference Time-Domain Method

Aziz¹

2009

PIER B

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“…Since the initial appearance of the Fourier PSTD algorithm, it has been suggested that using a nonuniform grid might help resolve the Gibbs phenomenon [9] and offer a better handling of the interface. Recently, the space-transformation or mapping technique was applied to Fourier PSTD, using 2 nd -order polynomials as the mapping curve [11,12]. It should be pointed out that the mapping concept in the pseudospectral method is not new [29].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic simulations of metallic materials using the mapped fourier PSTD algorithm

Gao

Mirotznik

Prather

2005

Micro & Optical Tech Letters

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Previously, the regular Fourier pseudospectral time‐domain (PSTD) algorithm was recognized as mainly applicable to simulations of low‐contrast dielectric materials. In this paper, we discuss the difficulties in simulating high‐contrast and particularly metallic materials using the Fourier PSTD method. To overcome these difficulties, we use a nonuniform grid obtained from a specially designed mapping curve that can reduce the Gibbs phenomenon in the mapped space. The convergence property of this technique is then examined. We show dramatic improvements compared with regular Fourier PSTD and finite‐difference time‐domain (FDTD) methods on a uniform grid. As an example application, we apply our method to the modeling of the 2D scattering of a chrome‐projection lithography mask. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 569–575, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20699

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“…16,17 It was suggested that nonuniform (NU) grids, which are suitable for problems in which both large and small features are present at different locations, may also help alleviate (not eliminate) the Gibbs phenomenon when a locally denser grid is placed at the material interface. 16 In the NU PSTD algorithm, 9,16,18 one has to use a NU FFT. [19][20][21][22] Most of the NU FFT algorithms developed thus far apply a similar strategy: i.e., first interpolate the NU sampled data into a uniform grid and then apply the regular FFT.…”

Section: Introductionmentioning

confidence: 99%

Applying a mapped pseudospectral time-domain method in simulating diffractive optical elements

et al. 2004

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A new technique for the analysis of two-dimensional diffractive optical elements, by use of the pseudospectral time-domain (PSTD) method, is presented. In particular, the method uses a nonuniform (NU) grid and a mapping technique to obtain very accurate spatial derivatives in an efficient manner. To this end, we present the formulation of the PSTD method by using a NU grid and compare its application to the analysis with that of the finite-difference time-domain (FDTD) method. Using only a fraction of the memory and a fraction of the computation time used by FDTD, the mapped PSTD was able to obtain very close results to FDTD.

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Transformed-space nonuniform pseudospectral time-domain algorithm

Cited by 11 publications

References 8 publications

Sub-Nanosecond Electromagnetic-Micromagnetic Dynamic Simulations Using the Finite-Difference Time-Domain Method

Sub-Nanosecond Electromagnetic-Micromagnetic Dynamic Simulations Using the Finite-Difference Time-Domain Method

Electromagnetic simulations of metallic materials using the mapped fourier PSTD algorithm

Applying a mapped pseudospectral time-domain method in simulating diffractive optical elements

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