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An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques

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Abstract
This work focuses on efficient full-wave solutions of multiscale electromagnetic problems in the time domain. Three local implicitization techniques are proposed and carefully analyzed in order to relax the traditional time step limit of the Finite-Difference Time-Domain (FDTD) method on a nonuniform, staggered, tensor product grid: Newmark, Crank-Nicolson (CN) and Alternating-Direction-Implicit (ADI) implicitization. All of them are applied in preferable directions, alike Hybrid Implicit-Explicit (HIE) methods, as to limit the rank of the sparse linear systems. Both exponential and linear stability are rigorously investigated for arbitrary grid spacings and arbitrary inhomogeneous, possibly lossy, isotropic media. Numerical examples confirm the conservation of energy inside a cavity for a million iterations if the time step is chosen below the proposed, relaxed limit. Apart from the theoretical contributions, new accomplishments such as the development of the leapfrog Alternating-Direction-Hybrid-Implicit-Explicit (ADHIE) FDTD method and a less stringent Courant-like time step limit for the conventional, fully explicit FDTD method on a nonuniform grid, have immediate practical applications. (C) 2017 Elsevier Inc. All rights reserved.
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Please use this url to cite or link to this publication:

Chicago
Van Londersele, Arne, Daniël De Zutter, and Dries Vande Ginste. 2017. “An In-depth Stability Analysis of Nonuniform FDTD Combined with Novel Local Implicitization Techniques.” Journal of Computational Physics 342: 177–193.
APA
Van Londersele, A., De Zutter, D., & Vande Ginste, D. (2017). An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques. JOURNAL OF COMPUTATIONAL PHYSICS, 342, 177–193.
Vancouver
1.
Van Londersele A, De Zutter D, Vande Ginste D. An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques. JOURNAL OF COMPUTATIONAL PHYSICS. 2017;342:177–93.
MLA
Van Londersele, Arne, Daniël De Zutter, and Dries Vande Ginste. “An In-depth Stability Analysis of Nonuniform FDTD Combined with Novel Local Implicitization Techniques.” JOURNAL OF COMPUTATIONAL PHYSICS 342 (2017): 177–193. Print.
@article{8541169,
  abstract     = {This work focuses on efficient full-wave solutions of multiscale electromagnetic problems in the time domain. Three local implicitization techniques are proposed and carefully analyzed in order to relax the traditional time step limit of the Finite-Difference Time-Domain (FDTD) method on a nonuniform, staggered, tensor product grid: Newmark, Crank-Nicolson (CN) and Alternating-Direction-Implicit (ADI) implicitization. All of them are applied in preferable directions, alike Hybrid Implicit-Explicit (HIE) methods, as to limit the rank of the sparse linear systems. Both exponential and linear stability are rigorously investigated for arbitrary grid spacings and arbitrary inhomogeneous, possibly lossy, isotropic media. Numerical examples confirm the conservation of energy inside a cavity for a million iterations if the time step is chosen below the proposed, relaxed limit. Apart from the theoretical contributions, new accomplishments such as the development of the leapfrog Alternating-Direction-Hybrid-Implicit-Explicit (ADHIE) FDTD method and a less stringent Courant-like time step limit for the conventional, fully explicit FDTD method on a nonuniform grid, have immediate practical applications. (C) 2017 Elsevier Inc. All rights reserved.},
  author       = {Van Londersele, Arne and De Zutter, Dani{\"e}l and Vande Ginste, Dries},
  issn         = {0021-9991},
  journal      = {JOURNAL OF COMPUTATIONAL PHYSICS},
  keyword      = {IBCN},
  language     = {eng},
  pages        = {177--193},
  title        = {An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques},
  url          = {http://dx.doi.org/10.1016/j.jcp.2017.04.036},
  volume       = {342},
  year         = {2017},
}

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