TY - JOUR

T1 - Accelerated Calderón preconditioning for Maxwell transmission problems

AU - Kleanthous, Antigoni

AU - Betcke, Timo

AU - Hewett, David P.

AU - Escapil-Inchauspé, Paul

AU - Jerez-Hanckes, Carlos

AU - Baran, Anthony J.

N1 - Funding Information:
The work of the first author was supported by NERC and the UK Met Office ( CASE PhD studentship to A. Kleanthous, grant NE/N008111/1 ). D.P. Hewett acknowledges support from EPSRC , grant EP/S01375X/1 . P. Escapil-Inchauspé and C. Jerez-Hanckes thank the support of Fondecyt Regular 1171491 .
Publisher Copyright:
© 2022

PY - 2022/6/1

Y1 - 2022/6/1

N2 - We investigate a range of techniques for the acceleration of Calderón (operator) preconditioning in the context of boundary integral equation methods for electromagnetic transmission problems. Our objective is to mitigate as far as possible the high computational cost of the barycentrically-refined meshes necessary for the stable discretisation of operator products. Our focus is on the well-known PMCHWT formulation, but the techniques we introduce can be applied generically. By using barycentric meshes only for the preconditioner and not for the original boundary integral operator, we achieve significant reductions in computational cost by (i) using “reduced” Calderón preconditioners obtained by discarding constituent boundary integral operators that are not essential for regularisation, and (ii) adopting a “bi-parametric” approach [1,2] in which we use a lower quality (cheaper) H-matrix assembly routine for the preconditioner than for the original operator, including a novel approach of discarding far-field interactions in the preconditioner. Using the boundary element software Bempp (www.bempp.com), we compare the performance of different combinations of these techniques in the context of scattering by multiple dielectric particles. Applying our accelerated implementation to 3D electromagnetic scattering by an aggregate consisting of 8 monomer ice crystals of overall diameter 1 cm at 664 GHz leads to a 99% reduction in memory cost and at least a 75% reduction in total computation time compared to a non-accelerated implementation.

AB - We investigate a range of techniques for the acceleration of Calderón (operator) preconditioning in the context of boundary integral equation methods for electromagnetic transmission problems. Our objective is to mitigate as far as possible the high computational cost of the barycentrically-refined meshes necessary for the stable discretisation of operator products. Our focus is on the well-known PMCHWT formulation, but the techniques we introduce can be applied generically. By using barycentric meshes only for the preconditioner and not for the original boundary integral operator, we achieve significant reductions in computational cost by (i) using “reduced” Calderón preconditioners obtained by discarding constituent boundary integral operators that are not essential for regularisation, and (ii) adopting a “bi-parametric” approach [1,2] in which we use a lower quality (cheaper) H-matrix assembly routine for the preconditioner than for the original operator, including a novel approach of discarding far-field interactions in the preconditioner. Using the boundary element software Bempp (www.bempp.com), we compare the performance of different combinations of these techniques in the context of scattering by multiple dielectric particles. Applying our accelerated implementation to 3D electromagnetic scattering by an aggregate consisting of 8 monomer ice crystals of overall diameter 1 cm at 664 GHz leads to a 99% reduction in memory cost and at least a 75% reduction in total computation time compared to a non-accelerated implementation.

KW - Boundary element method (BEM)

KW - Calderón preconditioning

KW - Electromagnetic scattering

UR - http://www.scopus.com/inward/record.url?scp=85125734024&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2022.111099

DO - 10.1016/j.jcp.2022.111099

M3 - Article

AN - SCOPUS:85125734024

VL - 458

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

M1 - 111099

ER -