An Explicit Fourth-Order Orthogonal Curvilinear Staggered-Grid FDTD Method for Maxwell's Equations

Xie, Zhongqiang; Chan, Chi Hou; Zhang, Bo

doi:10.1006/jcph.2001.6965

Cited by 44 publications

(35 citation statements)

References 54 publications

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“…A few attempts have been made to accelerate the convergence speed of embedding FDTD methods, giving rise to several fully fourth-order FDTD methods on a medium with material discontinuities by using a simple structured grid [4,[47][48][49], including the curvilinear grid [50]. The single structured grid is logically equivalent to a Cartesian grid.…”

Section: Introductionmentioning

confidence: 99%

“…The single structured grid is logically equivalent to a Cartesian grid. The structured grids used in these fourth-order FDTD methods [47][48][49][50] are, nevertheless, less general than the Cartesian grids of the embedding methods [4,44,45]. In particular, these fourth-order approaches typically require that the electric grid points coincide with the plane interface in 2D configuration, so that the staircasing problem remains unsolved in these high-order methods.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, without appropriate numerical interface schemes, the conventional high-order time-domain methods would be easily degraded to produce loworder accuracy [4]. Therefore, the significant accomplishment of these fourth-order schemes [47][48][49][50] is that the physical jump conditions at material interfaces are correctly enforced up to high-order, so that fourth-order convergence is uniformly assured over the entire domain.…”

Section: Introductionmentioning

confidence: 99%

“…Similar to the embedding methods [4,44,45], the modeling of interfaces results in a local modification of the differential scheme in a preprocessing stage [4,[47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

“…The studies of fourth-order embedding FDTD schemes [4,[47][48][49][50] open up the opportunity for developing other more general and robust high-order interface schemes, which deserve further exploration. There are many important questions remaining unanswered.…”

Section: Introductionmentioning

confidence: 99%

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High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

Zhao

Wang

2004

Journal of Computational Physics

199

164

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This paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high-order finite difference time-domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in one (1D) and two spatial dimensions (2D). By making use of fictitious points, systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage, to arbitrarily high orders of accuracy in principle. While often limited by numerical instability, orders up to 16 in 1D and 2D are achieved. Detailed stability analyses are presented for the present approach to examine the up limit in constructing embedded FDTD methods. As natural generalizations of the high-order FDTD schemes, the proposed derivative matching methods automatically reduce to the standard FDTD schemes when the material interfaces are absent. An interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code. Another feature of the present approach is that it can be robustly implemented with other high accuracy time-domain approaches, such as the multiresolution time-domain (MRTD) method and the local spectral time-domain (LSTD) method, to cope 1 with material interfaces. Numerical experiments on both 1D and 2D problems are carried out to test the convergence, examine the stability, access the efficiency, and explore the limitation of the proposed methods. It is found that operating at their best capacity, the proposed high order schemes are at least a million times more efficient than their fourth order versions in both 1D and 2D. Therefore, it is believed that the proposed hierarchical derivative matching methods are highly accurate, efficient, and robust for CEM.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Similar to the embedding methods [4,44,45], the modeling of interfaces results in a local modification of the differential scheme in a preprocessing stage [4,[47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

Zhao

Wang

2004

Journal of Computational Physics

199

164

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Tensor product derivative matching for wave propagation in inhomogeneous media

Zhao

Wang

2004

Micro & Optical Tech Letters

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We propose a tensor product derivative matching (TPDM) method to restore the accuracy of high‐order finite difference time‐domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in two spatial dimensions (2D). By making use of fictitious points, the TPDM method locally enforces the physical‐jump conditions at material interfaces in a preprocessing stage to arbitrarily high orders of accuracy in principle, based on a structured grid. The proposed method encompasses a variety of schemes of different orders in a single code. In fact, numerical orders from 2 to near 16 are confirmed in the present study. To the best of our knowledge, such high orders have not been reported in the literature for CEM problems involving material interfaces. The limitation and applicability of the present scheme are also analyzed in detail. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 69–77, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20378

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Multidomain pseudospectral time‐domain algorithm in curvilinear coordinates system

Shi

Chen

2007

Micro & Optical Tech Letters

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Multidomain pseudospectral time‐domain (MPSTD) algorithm, previously proposed for a Cartesian coordinates system, is extended to Maxwell's equations in a curvilinear coordinates system and applied to electromagnetic wave problems. A novelty patching technique is derived to effectively implement the boundary conditions at the interface between two adjacent subdomains by using characteristic variables. A perfectly matched layer (PML) in a curvilinear coordinates system is constructed according to a well‐posed PML in a Cartesian coordinates system. Numerical results are presented to illustrate the efficiency and accuracy of the method. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2618–2624, 2007; Published online in Wiley InterScience (www.interscience.wiley.com) DOI 10.1002/mop.22772

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An Explicit Fourth-Order Orthogonal Curvilinear Staggered-Grid FDTD Method for Maxwell's Equations

Cited by 44 publications

References 54 publications

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

Tensor product derivative matching for wave propagation in inhomogeneous media

Multidomain pseudospectral time‐domain algorithm in curvilinear coordinates system

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