Electromagnetic time domain modeling using an improved meshless method

Razmjoo, H.; Movahhedi, Masoud; Hakimi, Ahmad; Bahonar, Shahid

doi:10.1109/mwsym.2011.5972878

Cited by 8 publications

(13 citation statements)

References 10 publications

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“…As this figure shows, the method is stable and the obtained resonant frequency, based on Figure 7(a), has acceptable accuracy. However, as seen in Figure 6(a), by choosing a great Dt, non-physical dispersion in the attenuation of the response amplitude, which is also evident in Razmjoo et al (2011a), appear in simulation result. This matter is due to this fact that the phase velocity of numerical wave modes can differ from c by an amount varying with the wavelength.…”

Section: Improved Meshless Methodsmentioning

confidence: 86%

Unconditionally stable improved meshless methods for electromagnetic time-domain modeling

Razmjoo

Movahhedi

2013

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose -In this paper, a modified meshless method, as one of the numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to solving time-domain wave equation. The paper aims to discuss these issues. Design/methodology/approach -In space domain, the fields at the collocation points are expanded into a series of new Shepard's functions which have been suggested recently and are treated with a meshless method procedure. For time discretization of the second-order time-derivative, two finite-difference schemes, i.e. backward difference and Newmark-b techniques, are proposed. Findings -Both schemes are implicit and always stable and have unconditional stability with different orders of accuracy and numerical dispersion. The unconditional stability of the proposed methods is analytically proven and numerically verified. Moreover, two numerical examples for electromagnetic field computation are also presented to investigate characteristics of the proposed methods. Originality/value -The paper presents two unconditionally stable schemes for meshless methods in time-domain electromagnetic problems.

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Section: Improved Meshless Methodsmentioning

confidence: 86%

Unconditionally stable improved meshless methods for electromagnetic time-domain modeling

Razmjoo

Movahhedi

2013

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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“…The vector potential technique was introduced to solve time-domain electromagnetic fields with finite differences in [6,9]. Various meshless implementations have been later reported [10][11][12][13]. In this paper, we propose an efficient implementation of the time-domain meshless radial point interpolation method (RPIM) based on the local calculation of the magnetic vector potential (A) in small support domains.…”

Section: Introductionmentioning

confidence: 99%

Time‐domain vector potential technique for the meshless radial point interpolation method

Shaterian

Kaufmann

2015

Numerical Meth Engineering

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A time-domain meshless algorithm based on vector potentials is introduced for the analysis of transient electromagnetic fields. The proposed numerical algorithm is a modification of the radial point interpolation method, where radial basis functions are used for local interpolation of the vector potentials and their derivatives. In the proposed implementation, solving the second-order vector potential wave equation intrinsically enforces the divergence-free property of the electric and magnetic fields. Furthermore, the computational effort associated with the generation of a dual node distribution (as required for solving the first-order Maxwell's equations) is avoided. The proposed method is validated with several examples of 2D waveguides and filters, and the convergence is empirically demonstrated in terms of node density or size of local support domains. It is further shown that inhomogeneous node distributions can provide increased convergence rates, that is, the same accuracy with smaller number of nodes compared with a solution for homogeneous node distribution. A comparison of the magnetic vector potential technique with conventional radial point interpolation method is performed, highlighting the superiority of the divergence-free formulation.

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“…However, one of the major problems that is high computational cost, still exists in meshless method. Recently, some direct meshless methods have been proposed to solve the time consumption issue [3][4][5][6][7]. The direct and conventional (indirect) meshless methods are different just in construction of the shape functions, whereas the direct meshless method proposes the shape functions, directly [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, some direct meshless methods have been proposed to solve the time consumption issue [3][4][5][6][7]. The direct and conventional (indirect) meshless methods are different just in construction of the shape functions, whereas the direct meshless method proposes the shape functions, directly [3][4][5][6][7]. This novel method caused a great reduction in time consumption, because of cancelling the first matrix inversion calculation step and improved the accuracy by proposing an analytical shape function, which its derivatives exist, analytically [7].…”

Section: Introductionmentioning

confidence: 99%

Criterion for selecting the shape functions in electromagnetic meshless methods

Afsari

Movahhedi

2013

IET Science, Measurement & Technology

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The root of this study, comes from the lack of regularity where exists in shape function selection in meshless methods. Up to now, shape functions in meshless methods were being established by basis functions. In other words, there was no predictable rule by which the shape functions be predetermined, without any need to basis functions. In presented approach, the authors are going to establish a criterion, which is based on both analytical and simulation results; helps select an approximately well-behaved shape function for which the shape parameters have been predetermined. This work focused on both Laplace and wave equations as the most important equations in electrostatic and electromagnetic problems to show the validation of the proposed approach in computational electromagnetics. Comparing the results with radial point interpolation method as the most common existing meshless method, finite-element method and finite-difference method, the criterion shows extremely good accuracy despite a great reduction in time consumption rate for selecting a compatible shape function.

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Electromagnetic time domain modeling using an improved meshless method

Cited by 8 publications

References 10 publications

Unconditionally stable improved meshless methods for electromagnetic time-domain modeling

Unconditionally stable improved meshless methods for electromagnetic time-domain modeling

Time‐domain vector potential technique for the meshless radial point interpolation method

Criterion for selecting the shape functions in electromagnetic meshless methods

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