A hybrid ADI and SBTD scheme for unconditionally stable time-domain solutions of Maxwell's equations

Zhenyu Huang; George Pan; Rodolfo Diaz

doi:10.1109/TADVP.2007.909453

A hybrid ADI and SBTD scheme for unconditionally stable time-domain solutions of Maxwell's equations

Zhenyu Huang, George Pan, Rodolfo Diaz

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Based upon the sampling bi-orthogonal algorithm and alternating direction implicit scheme, we present an unconditionally stable time-domain method, SB-ADI. Similar to the ADI scheme, this method is a second-order approximation in temporal discretization. However, theoretically, the new method produces no spatial discretization error due to the sampling property and compact support of the SBTD algorithm. Dispersion and stability analysis are presented. In a numerical example of 2-D electromagnetic bandgap structure, the new method has reduced the ℓ² error by a factor of 3.5 at 16% increase of CPU time with respect to the standard ADI.

Original language	English (US)
Pages (from-to)	219-226
Number of pages	8
Journal	IEEE Transactions on Advanced Packaging
Volume	31
Issue number	1
DOIs	https://doi.org/10.1109/TADVP.2007.909453
State	Published - Feb 2008

Keywords

Alternating-direction implicit (ADI)
Finite-difference time-domain (FDTD)
Maxwell's equations
Sampling bi-orthogonal time domain
Stability

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TADVP.2007.909453

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abstract = "Based upon the sampling bi-orthogonal algorithm and alternating direction implicit scheme, we present an unconditionally stable time-domain method, SB-ADI. Similar to the ADI scheme, this method is a second-order approximation in temporal discretization. However, theoretically, the new method produces no spatial discretization error due to the sampling property and compact support of the SBTD algorithm. Dispersion and stability analysis are presented. In a numerical example of 2-D electromagnetic bandgap structure, the new method has reduced the ℓ2 error by a factor of 3.5 at 16% increase of CPU time with respect to the standard ADI.",

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AU - Diaz, Rodolfo

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N2 - Based upon the sampling bi-orthogonal algorithm and alternating direction implicit scheme, we present an unconditionally stable time-domain method, SB-ADI. Similar to the ADI scheme, this method is a second-order approximation in temporal discretization. However, theoretically, the new method produces no spatial discretization error due to the sampling property and compact support of the SBTD algorithm. Dispersion and stability analysis are presented. In a numerical example of 2-D electromagnetic bandgap structure, the new method has reduced the ℓ2 error by a factor of 3.5 at 16% increase of CPU time with respect to the standard ADI.

AB - Based upon the sampling bi-orthogonal algorithm and alternating direction implicit scheme, we present an unconditionally stable time-domain method, SB-ADI. Similar to the ADI scheme, this method is a second-order approximation in temporal discretization. However, theoretically, the new method produces no spatial discretization error due to the sampling property and compact support of the SBTD algorithm. Dispersion and stability analysis are presented. In a numerical example of 2-D electromagnetic bandgap structure, the new method has reduced the ℓ2 error by a factor of 3.5 at 16% increase of CPU time with respect to the standard ADI.

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KW - Finite-difference time-domain (FDTD)

KW - Maxwell's equations

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KW - Stability

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A hybrid ADI and SBTD scheme for unconditionally stable time-domain solutions of Maxwell's equations

Abstract

Keywords

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