A General Procedure for Introducing Structured Nonorthogonal Discretization Grids Into High-Order Finite-Difference Time-Domain Methods

Armenta, Roberto B.; Sarris, Costas D.

doi:10.1109/tmtt.2010.2049921

Cited by 10 publications

(3 citation statements)

References 23 publications

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“…Now, FDTD has become one of the most popular methods in computational electromagnetics (CEM), but it still has much potential towards higher accuracy, faster speed, broader applications, and larger computational capacity. For instance, a lot of research results on FDTD have been presented to improve its second-order accuracy and reduce the error from geometric staircase approximation (such as the high-order FDTD [3] and conformal FDTD [4]- [7]). Meanwhile, parallel programming technologies (OpenMP, MPI, and GPU [8], [9]) have been greatly applied in FDTD simulations.…”

Section: Introductionmentioning

confidence: 99%

Novel Adaptive Steady-State Criteria for Finite-Difference Time-Domain Method

You

Tan

Cui

2014

IEEE Trans. Microwave Theory Techn.

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Two novel adaptive steady-state criteria are proposed to adaptively determine whether the steady state has been achieved in finite-difference time-domain (FDTD) method. The proposed criteria are established by the total electromagnetic energy in the computational region. To reduce the computational burden of electromagnetic energy calculation, a new approach is presented to replace the volume integral of energy with a surface integral. In addition, after newly defined attenuation coefficient and stability coefficient, novel adaptive steady-state criteria are proposed to overcome the premature convergence, nonmonotonicity, and nonconvergence challenges, which are serious in traditional adaptive steady-state criteria. At the end of this paper, numerical examples are given to demonstrate the effectiveness and superiority of our proposed criteria.

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Section: Introductionmentioning

confidence: 99%

Novel Adaptive Steady-State Criteria for Finite-Difference Time-Domain Method

You

Tan

Cui

2014

IEEE Trans. Microwave Theory Techn.

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show abstract

“…Amid the broad assortment of numerical tools, the contribution of the finite‐difference time‐domain (FDTD) algorithm to the investigation of waveguide and antenna devices has been widely acknowledged, furnishing beneficial outcomes, along with its various powerful high‐order renditions . Nevertheless, its applicability to contemporary scenarios is proven cumbersome, especially on a wideband basis, as most of the devices have many geometric details, arbitrary discontinuities, or involve dispersive materials, which call for prolonged simulations because of the Courant stability condition.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, an extensive decrease of dispersion errors is achieved, even when time-steps are chosen appreciably beyond stability limits. These advanced simulation competences are successfully applied to diverse real-world setups and composite configurations, thus validating the efficiency and universality of the proposed methodology.Amid the broad assortment of numerical tools, the contribution of the finite-difference time-domain (FDTD) algorithm [8] to the investigation of waveguide and antenna devices has been widely acknowledged, furnishing beneficial outcomes, along with its various powerful high-order renditions [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Nevertheless, its applicability to contemporary scenarios is proven cumbersome, especially on a wideband basis, as most of the devices have many geometric details, arbitrary discontinuities, or involve dispersive materials, which call for prolonged simulations because of the Courant stability condition.…”

mentioning

confidence: 99%

Hybrid unconditionally stable high‐order nonstandard schemes with optimal error‐controllable spectral resolution for complex microwave problems

Kantartzis

2012

Int J Numerical Modelling

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A hybrid unconditionally stable time-domain technique for the precise analysis and wideband performance characterization of 3D microwave systems is developed in this paper. Founded on a nontraditional differential discretization basis, the proposed technique launches a class of robust operators via an error-controllable procedure that offers enhanced spectral resolution and optimal spatial stencils. The key asset of the frequency-dependent algorithm is the novel high-order nonstandard approximators, whose tensorial properties preserve the hyperbolic character of Maxwell's equations. In this manner, the resulting formulation remains completely explicit and generates effective dual meshes free of artificial vector parasites and spurious modes. Moreover, the preceding schemes are fruitfully hybridized, in the context of nonoverlapping subspaces, with an alternating-direction implicit finite-element time-domain method in an effort to handle abruptly varying media boundaries and intricate geometries. Hence, an extensive decrease of dispersion errors is achieved, even when time-steps are chosen appreciably beyond stability limits. These advanced simulation competences are successfully applied to diverse real-world setups and composite configurations, thus validating the efficiency and universality of the proposed methodology.Amid the broad assortment of numerical tools, the contribution of the finite-difference time-domain (FDTD) algorithm [8] to the investigation of waveguide and antenna devices has been widely acknowledged, furnishing beneficial outcomes, along with its various powerful high-order renditions [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Nevertheless, its applicability to contemporary scenarios is proven cumbersome, especially on a wideband basis, as most of the devices have many geometric details, arbitrary discontinuities, or involve dispersive materials, which call for prolonged simulations because of the Courant stability condition. Furthermore, the large electrical size of some cases dictates fine lattice resolutions together with the enforcement of nonphysical assumptions. Toward the circumvention of the stability limit, the alternating-direction implicit (ADI) concept has, lately, offered a promising means, which can allow the use of large time-steps during the update of field components [28,29]. In fact, since its initial advent, the ADI-FDTD algorithm became the topic of a systematic examination [30][31][32], whose principal deductions unveiled a serious shortcoming in practical implementations; the appearance of gradually increasing dispersion errors as time-steps depart from the Courant limit. For the mitigation of this problem, various efficient techniques have been, hitherto, presented for Cartesian [33][34][35][36][37][38][39][40][41] and nonorthogonal lattices [42,43].It is the objective of this paper to introduce a 3D frequency-dependent unconditionally stable timedomain methodology, based on a family of high-order nonstandard schemes, for the accurate modeling ...

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Boundary Modeling and High-Order Convergence in Finite-Difference Methods

Armenta

Sarris

2014

Computational Electromagnetics—Retrospective and Outlook

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A General Procedure for Introducing Structured Nonorthogonal Discretization Grids Into High-Order Finite-Difference Time-Domain Methods

Cited by 10 publications

References 23 publications

Novel Adaptive Steady-State Criteria for Finite-Difference Time-Domain Method

Novel Adaptive Steady-State Criteria for Finite-Difference Time-Domain Method

Hybrid unconditionally stable high‐order nonstandard schemes with optimal error‐controllable spectral resolution for complex microwave problems

Boundary Modeling and High-Order Convergence in Finite-Difference Methods

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