The complementary derivatives method: a second-order accurate interpolation scheme for non-uniform grid in FDTD simulation

Kermani, M.H.; Ramahi, Omar M.

doi:10.1109/lmwc.2005.863253

Cited by 11 publications

(6 citation statements)

References 6 publications

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“…The first expression for the derivative uses the points and , resulting in (8) The second expression for the -field derivatives uses the points and , resulting in (9) The arithmetic mean of (8) and (9) gives (10) To cancel the first-order truncation error, the third term of the right-hand side of (10) should be zero. To achieve this, we require that (11) Numerical implementation of the CDM can be achieved by simply determining the number of the two FDTD cells that are used to calculate the complementary derivatives. If we assume that one of the -fields is in cell and the other one is in cell (as measured from the interface), and , as defined in Fig.…”

Section: Theory Of the Complementary Derivatives Methods (Cdm)mentioning

confidence: 99%

“…But there is no explanation whether these values can also be used for other experiments or whether each experiment needs different optimized values, thus limiting the generality and practicality of this method. In this paper, we apply the complementary derivatives method (CDM) [11], which guarantees second-order accuracy, to the ADI-FDTD solution of Maxwell's equations of problems containing domains with different grid size. We show that direct application of the CDM to ADI-FDTD disturbs the tri-diagonal structure of the matrix thus increasing the computational complexity in comparison to classical ADI-FDTD formulation.…”

Section: Introductionmentioning

confidence: 99%

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Application of the Complementary Derivatives Method in the ADI-FDTD Solution of Maxwell's Equations

Kermani

Ramahi

2007

IEEE Trans. Antennas Propagat.

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The alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is well suited for simulating structures with large aspect ratios or problems with large gradient fields where different grid sizes can be used to yield greater computational efficiency. However, using different grid sizes increases the truncation error at the interface between domains having different grid sizes. The truncation error is manifested as a spurious reflection from the grid boundary, thus decreasing the simulation accuracy. In this paper, we apply the complementary derivatives method (CDM) to reduce the spurious reflections arising from the use of different grid size domains when using the ADI-FDTD method. It is shown that, the CDM guarantees uniform second-order accuracy throughout the computational domain. When the CDM is implemented in the ADI-FDTD method, the implicit updating equations cannot be written in a tri-diagonal matrix and the computational efficiency of the ADI-FDTD method is not preserved. By employing the Sherman-Morrison formula, we retain the numerical efficiency of the conventional ADI-FDTD. A representative numerical example is presented to demonstrate the accuracy of CDM in the ADI-FDTD simulations.Index Terms-Alternating-direction implicit finite-difference time-domain (ADI-FDTD), complementary derivatives method (CDM), truncation error.

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Section: Theory Of the Complementary Derivatives Methods (Cdm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of the Complementary Derivatives Method in the ADI-FDTD Solution of Maxwell's Equations

Kermani

Ramahi

2007

IEEE Trans. Antennas Propagat.

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“…Considering the accuracy and efficiency of modeling, a non-uniform meshing FDTD technique [9] is applied for the beam waveguide, in wh ich the fine and coarse grids are used for the feed horn and the other regions respectively.…”

Section: A Non-uniform Meshing Fdtd With Symmetric Boundarymentioning

confidence: 99%

Solution and Design Technique for Beam Waveguide Antenna System by Using a Parallel Hybrid-Dimensional FDTD Method

Zhang

Liao

Xiong

et al. 2017

Antennas Wirel. Propag. Lett.

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“…It is also noted that we do not consider several well-known methods, discussed in [17] and its references, to compensate degraded accuracy due to the nonuniform grid in the SG region, since most of these methods can worsen late-time instability by violating the reciprocal property or symmetry of the original Yee updating scheme.…”

Section: Accuracy Improvement Using An Optimal Interpolation Techniquementioning

confidence: 99%

A Novel Nonuniform Subgridding Scheme for FDTD Using an Optimal Interpolation Technique

Kim¹,

Arvas²,

Demir³

et al. 2012

PIER B

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Abstract-Finite-Difference Time-Domain (FDTD) subgridding schemes can significantly improve efficiency of various electromagnetic circuit simulations. However, numerous subgridding schemes suffer from issues associated with stability, efficiency, and material traverse capability. These issues limit general applicability of FDTD subgridding schemes to realistic problems. Herein, a robust nonuniform subgridding scheme is presented that overcomes those weaknesses. The scheme improves simulation accuracy with the aid of greatly increased stability margin and an optimal interpolation technique. It also improves simulation efficiency by allowing the use of time step factors as close as the Courant-Friedrichs-Lewy (CFL) limit. In addition, latetime stability and general applicability are verified through practical microstrip circuit simulation examples.

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The complementary derivatives method: a second-order accurate interpolation scheme for non-uniform grid in FDTD simulation

Cited by 11 publications

References 6 publications

Application of the Complementary Derivatives Method in the ADI-FDTD Solution of Maxwell's Equations

Application of the Complementary Derivatives Method in the ADI-FDTD Solution of Maxwell's Equations

Solution and Design Technique for Beam Waveguide Antenna System by Using a Parallel Hybrid-Dimensional FDTD Method

A Novel Nonuniform Subgridding Scheme for FDTD Using an Optimal Interpolation Technique

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