Kleanthous, Antigoni; (2021) Accelerated Calderón Preconditioning for Electromagnetic Scattering by Multiple Absorbing Dielectric Objects. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

We consider electromagnetic scattering by multiple absorbing dielectric objects using the PMCHWT boundary integral equation formulation. Galerkin discretisation of this formulation leads to ill-conditioned linear systems, and Calderón preconditioning, an operator-based approach, can be used to remedy this. To obtain a stable discretisation of the operator products that arise in this approach, the use of a dual mesh defined on a barycentrically refined grid needs to be considered, increasing memory consumption. Furthermore, to capture the oscillatory solution of the electromagnetic waves, the mesh needs to be refined with respect to frequency, making the simulation of high-frequency problems very expensive. This thesis presents two complementary approaches to minimising memory cost and computation time (for assembly and solution): modification of the preconditioning operator, and a bi-parametric implementation. The former aims to minimise the number of operators used in the preconditioner to reduce the additional matrix-vector products performed, and the memory cost, while still maintaining a sufficient preconditioning effect. The latter uses two distinct sets of parameters during assembly, to minimise assembly and solution time as well as memory. The operator is assembled with a more expensive set of parameters to obtain an accurate solution. The preconditioner, which is discretised using the expensive dual basis functions, is assembled with a cheaper set of parameters. The two approaches are explained in the context of a series of model problems, then applied to realistic ice crystal configurations found in cirrus clouds. They are shown to deliver a reduction of 99% in memory cost and at least 80% in computation time, for the highest frequency considered. The accelerated formulations have been used at the Met Office to create a new database of the scattering properties of atmospheric ice crystals for future numerical weather prediction. A brief description of that work is also presented in the thesis.

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