Calderón preconditioning of PMCHWT boundary integral equations for scattering by multiple absorbing dielectric particles. (February 2019) - Kleanthous, Antigoni; Betcke, Timo; Hewett, David P.; Scroggs, Matthew W.; Baran, Anthony J.
Highlights: For single-particle scattering, mass-matrix preconditioning is often more effective than Calderón preconditioning. For multi-particle scattering, mass-matrix and full Calderón preconditioners perform similarly. For multi-particle scattering, a block-diagonal Calderón preconditioner is faster than the mass-matrix and full Calderón preconditioners. Strong discrete operators require fewer matvecs than their weak counterparts. 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.