Numerical dispersion and stability analysis of the FDTD technique in lossy dielectrics

Pereda, José Antonio Martín; García, Olmo Fernández; Vegas, Α.; Iglesias, Andrés

doi:10.1109/75.701379

Cited by 50 publications

(48 citation statements)

References 3 publications

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“…µ nc nc (6) where ∆ξ and k ξ are spatial steps and wavenumbers in each x, y and z directions. nc and µ nc are known as the complex numerical permittivity and permeability which are unique to a particular FDTD scheme in doubly lossy media.…”

Section: Dispersion Analysis and Numerical Simulation For Doubly Lossmentioning

confidence: 99%

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Dispersion Analysis of FDTD Schemes for Doubly Lossy Media

Heh¹,

Tan²

2009

PIER B

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Abstract-This paper presents the 3-D dispersion analysis of finitedifference time-domain (FDTD) schemes for doubly lossy media, where both electric and magnetic conductivities are nonzero. Among the FDTD schemes presented are time-average (TA), time-forward (TF), time-backward (TB) and exponential time differencing (ETD). It is first shown that, unlike in electrically lossy media, the attenuation constant in doubly lossy media can be larger than its phase constant. This further calls for careful choice of cell size such that both wavelength and skin depth of the doubly lossy media are properly resolved. From the dispersion analysis, TF generally displays higher phase velocity and attenuation errors due to its first-order temporal accuracy nature compared to second-order ETD and TA. Although both have second-order temporal accuracy, ETD has generally lower phase velocity and attenuation errors than TA. This may be attributed to its closer resemblance to the solution of first-order differential equation. Numerical FDTD simulations in 1-D and 3-D further confirm these findings.

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Section: Dispersion Analysis and Numerical Simulation For Doubly Lossmentioning

confidence: 99%

“…Stability analysis in [6][7][8] showed that for an electrically lossy medium, TA still preserves the stability criterion as the lossless FDTD scheme, i.e., the Courant-Friedrichs-Lewy (CFL) limit. On the other hand, TF and ETD have more relaxed and TB, more stringent stability criterion compared to the lossless CFL limit.…”

Section: Introductionmentioning

confidence: 99%

Dispersion Analysis of FDTD Schemes for Doubly Lossy Media

Heh¹,

Tan²

2009

PIER B

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“…This is the dispersion relationship for lossy material which was previously considered in [22] and more recently studied in [23]. We define the complex permittivity to be…”

Section: Lossy Materialsmentioning

confidence: 99%

Time-Domain Simulations of Problems in Ocean Acoustics

Schneider¹

2006

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the d-ataneeded, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports 10704-01881, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid DMB control number. A total-field scattered-field (TFSF) boundary can be used to introduce incident plane waves into finite-difference time-domain (FDTD) simulations. For fields which are traveling obliquely to the grid axes, there is no simple way to account fully for the effects of the inherent numerical artifacts associated with plane-wave propagation in the FDTD grid. Failure to account for these artifacts causes erroneous fields to leak across the TFSF boundary. The work performed under this grant developed a TFSF boundary for problems involving a planar interface that is theoretically exact. Such a boundary is essential when modeling the scattering from objects in the vicinity of ocean sediment. Although the TFSF boundary assumes a planar interface, the actual interface used in a simulation can take any shape and the space within the total-field region is arbitrary. A suite of C programs was written to implement the boundary. factual summary of the most significant information. PLEASE DO NOT5e. TASK NUMBER. Enter all task numbers as they 15. SUBJECT TERMS. Key words or phrases appear in the report, e.g. 05; RF0330201; T4112.identifying major concepts in the report.5f. WORK UNIT NUMBER. Enter all work unit numbers as they appear in the report, e.g. 001; 16. SECURITY CLASSIFICATION. Enter security AFAPL30480105.classification in accordance with security classification regulations, e.g. U, C, S, etc. If this form contains 6. AUTHOR(S). Enter name(s) of person(s) classified information, stamp classification level on the responsible for writing the report, performing the top and bottom of this page. research, or credited with the content of the report. The form of entry is the last name, first name, middle 17. LIMITATION OF ABSTRACT. This block must be initial, and additional qualifiers separated by commas, completed to assign a distribution limitation to the e.g. Smith, Richard, J, Jr.abstract. Enter UU (Unclassified Unlimited) or SAR (Same as Report). An entry in this block is necessary if 7. PERFORMING ORGANIZATION NAME(S) AND teasrc st elmtd the abstract is to be limited. Abstract A total-field scattered-field (TFSF) boundary can be used to introduce incident plane waves into fi...

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“…The dispersion relation of the FDTD (2,2) scheme in lossy dielectrics is found in Pereda et al (1998). To examine the accuracy of the scheme, we take the ratio of the numerical phase velocityc to the exact c:c…”

Section: Dispersion Analysis Of the Higher Order Schemesmentioning

confidence: 99%

FDTD Algorithm for Microstrip Antennas with Lossy Substrates Using Higher Order Schemes

Prokopidis¹,

Tsiboukis

2004

Electromagnetics

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Higher order spatial schemes are applied to approximate the derivatives of the conducting Maxwell's equations and an analytical study regarding the stability properties and the numerical dispersion of the N-order-in-space and second-order-in-time technique is considered. The hard-to-model effect of dielectric losses on microstrip antennas is investigated and their performance is demonstrated using a fourth-orderin-space and second-order-in-time, finite-difference time-domain scheme in threedimensional calculations.

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Numerical dispersion and stability analysis of the FDTD technique in lossy dielectrics

Cited by 50 publications

References 3 publications

Dispersion Analysis of FDTD Schemes for Doubly Lossy Media

Dispersion Analysis of FDTD Schemes for Doubly Lossy Media

Time-Domain Simulations of Problems in Ocean Acoustics

FDTD Algorithm for Microstrip Antennas with Lossy Substrates Using Higher Order Schemes

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