Electromagnetic scattering by multiple dielectric particles under the illumination of unpolarized high-order Bessel vortex beam

Yu, Mei Ping; Cui, Zhi Wei; Chen, An Tao

doi:10.1016/j.jqsrt.2017.01.005

Cited by 8 publications

(4 citation statements)

References 22 publications

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“…For the multi-particle scattering case (M > 1) one can adopt the same preconditioning strategy and solve the squared system (40) instead of (35). However, since it is the diagonal blocks in (36) that cause the ill-conditioning (the off-diagonal blocks are compact since they map between different boundary components), one might imagine that it is sufficient to precondition block-diagonally by…”

Section: Galerkin Methods and Preconditioningmentioning

confidence: 99%

“…Recalling (36) and (26)- (27), we note that a single application of the matrix A requires 4M (M + 1) matvecs (4 for each off-diagonal block and 8 for each diagonal block), and that a single application of the matrix D requires 8M matvecs. Hence the overall cost of the three formulations (taking into account the initial pre-multiplication of the right-hand-side) is…”

Section: Computational Complexitymentioning

confidence: 99%

“…The use of boundary integral equations and their discretization using boundary element methods (BEMs) is well-established in the electrical engineering community but has only recently started getting serious attention in the atmospheric physics community [34,35,36]. BEM is a "numerically exact" method which can provide highly accurate simulations of scattering by complex ice crystal shapes.…”

Section: And Invariantmentioning

confidence: 99%

“…The results in [34,35] were obtained using a standard desktop machine and were limited to size parameters up to 15, but Bempp supports parallelization and hence with HPC architectures much larger problems can be tackled. We end this brief literature review of BEM in atmospheric physics applications by mentioning recent work by Yu et al [36], in which boundary integral equations were applied to scattering by multiple dielectric particles illuminated by unpolarized high-order Bessel vortex beams, and also by Groth et al [40], where a "hybrid numerical-asymptotic" BEM was presented for 2D high frequency scalar dielectric scattering problems which achieves fixed accuracy with frequency-independent computational cost.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Calderón preconditioning of PMCHWT boundary integral equations for scattering by multiple absorbing dielectric particles

Kleanthous

Betcke

Hewett

et al. 2019

Journal of Quantitative Spectroscopy and Radiative Transfer

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We consider the simulation of electromagnetic scattering by single and multiple isotropic homogeneous dielectric particles using boundary integral equations. Galerkin discretizations of the classical Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) boundary integral equation formulation provide accurate solutions for complex particle geometries, but are well-known to lead to ill-conditioned linear systems. In this paper we carry out an experimental investigation into the performance of Calderón preconditioning techniques for single and multiple absorbing obstacles, which involve a squaring of the PMCHWT operator to produce a well-conditioned second-kind formulation. For single-particle scattering configurations we find that Calderón preconditioning is actually often outperformed by simple "mass-matrix" preconditioning, i.e. working with the strong form of the discretized PMCHWT operator. In the case of scattering by multiple particles we find that a significant saving in computational cost can be obtained by performing block-diagonal Calderón preconditioning in which only the self-interaction blocks are preconditioned. Using the boundary element software library Bempp (www.bempp.com) the numerical performance of the different methods is compared for a range of wavenumbers, particle geometries and complex refractive indices relevant to the scattering of light by atmospheric ice crystals.

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Section: Galerkin Methods and Preconditioningmentioning

confidence: 99%

Section: Computational Complexitymentioning

confidence: 99%