Kleanthous, A;
Betcke, T;
Hewett, DP;
Scroggs, MW;
Baran, AJ;
(2019)
Calderón preconditioning of PMCHWT boundary integral equations for scattering by multiple absorbing dielectric particles.
Journal of Quantitative Spectroscopy and Radiative Transfer
, 224
pp. 383-395.
10.1016/j.jqsrt.2018.11.035.
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Abstract
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.
Type: | Article |
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Title: | Calderón preconditioning of PMCHWT boundary integral equations for scattering by multiple absorbing dielectric particles |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1016/j.jqsrt.2018.11.035 |
Publisher version: | https://doi.org/10.1016/j.jqsrt.2018.11.035 |
Language: | English |
Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
Keywords: | Boundary element method, Electromagnetic scattering, Calderón preconditioning, Ice crystals |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
URI: | https://discovery.ucl.ac.uk/id/eprint/10064770 |
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