Computational Electromagnetics for Industrial Applications

Antonini, Giulio; Romano, Daniele; Lombardi, Luigi

doi:10.3390/electronics11121830

Cited by 2 publications

(5 citation statements)

References 9 publications

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“…For brevity, the peak memory size was measured. 1 The conventional method stores the non-zero entries of the coefficient matrices Z (1) , Z (2) , and so on. On the other hand, the fast method stores a part of the non-zero entries regarding the near-field computation (i.e.…”

Section: Resultsmentioning

confidence: 99%

“…Here, the weight w κ,d is given as In the previous study on the construction of the IFMM for transient acoustic scattering problems [24], the Burton-Miller integral equation (BMIE) is targeted. The BMIE, which corresponds to the CFIE in (1), consists of the single-and double-layer potentials and their normal derivatives, which are scalar-valued functions. In addition, to approximate the boundary variables (i.e.…”

Section: Approximation Of Jmentioning

confidence: 99%

“…for each α because the matrix Z (γ) becomes denser as γ becomes larger. On the other hand, Z (1) in the LHS of ( 19) is close to diagonal and, thus, the cost to solve (19) with respect to J α−1 can be assumed to be O(N e ) = O(N s ); the GMRES [40] is utilised as the solver with using 10 −8 as the relative drop tolerance in the numerical analyses in Section 4. Therefore, the computational complexity over all the time steps is estimated as O(N 2 s N t ), which can prohibit the conventional TDBEM from solving large-scale problems.…”

Section: Computational Complexitymentioning

confidence: 99%

“…Sections 3.1-3.3 formulate the fundamental three steps (I)-(III) mentioned in Section 1, i.e. P2M, M2L, and L2P, for the scalar and vector potentials of the CFIE in (1). From these as well as the M2M and L2L formulae, the algorithm of the (multi-level) fast TDBEM is constructed in Section 3.4.…”

Section: Interpolation-based Fmmmentioning

confidence: 99%

“…Full-wave electromagnetic (EM) simulators are strong driving forces to produce scientific and industrial achievements nowadays, e.g. [1] and the references therein. To deal with not only transient response but also frequency response (with the help of Fourier analysis), time-domain methods are useful.…”

Section: Introductionmentioning

confidence: 99%

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A fast time-domain boundary element method for three-dimensional electromagnetic scattering problems

Takahashi

2023

Preprint

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This paper proposes a fast time-domain boundary element method (TDBEM) to solve three-dimensional transient electromagnetic scattering problems regarding perfectly electric conductors in the classical marching-on-in-time manner. The algorithm of the fast TDBEM is a time-domain variant of the interpolation-based fast multipole method (IFMM), which is similar to the time-domain IFMM for acoustic scattering problems investigated in the author's previous studies. The principle of the present IFMM is to interpolate the kernel functions of the electric and magnetic field integral equations (EFIE and MFIE, respectively) so that every kernel function is expressed in a form of separation of variables in terms of both the spatial and temporal variables. Such an expression enables to construct a fast method to evaluate the scalar and vector potentials in the EFIE and MFIE with using so-called multipolemoments and local-coefficients associated with a space-time hierarchy. As opposed to O(N 2 s N t ) of the conventional TDBEM, the computational complexity of the fast TDBEM is estimated as O(N 1+δ s N t ), where N s and N t stand for the spatial and temporal degrees of freedom, respectively, and δ is typically 1/2 or 1/3. The numerical examples presented the advantages of the proposed fast TDBEM over the conventional TDBEM when solving large-scale problems.

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Section: Resultsmentioning

confidence: 99%

Section: Approximation Of Jmentioning

confidence: 99%