Transverse electric scattering on inhomogeneous objects: spectrum of integral operator and preconditioning

Abstract

The domain integral equation method with its FFT-based matrix-vector products is a viable alternative to local methods in free-space scattering problems. However, it often suffers from the extremely slow convergence of iterative methods, especially in the transverse electric (TE) case with large or negative permittivity. We identify the nontrivial essential spectrum of the pertaining integral operator as partly responsible for this behavior, and the main reason why a normally efficient deflating preconditioner does not work. We solve this problem by applying an explicit multiplicative regularizing operator, which transforms the system to the form `identity plus compact', yet allows the resulting matrix-vector products to be carried out at the FFT speed. Such a regularized system is then further preconditioned by deflating an apparently stable set of eigenvalues with largest magnitudes, which results in a robust acceleration of the restarted GMRES under constraint memory conditions.

20 pages, 8 figures

References in corpus (2)

• The discrete dipole approximation: an overview and recent developments
• Spectrum of the volume integral operator of electromagnetic scattering

Cited by in corpus (3)

• A Fast Volume Integral Equation Solver with Linear Basis Functions for the Accurate Computation of Electromagnetic Fields in MRI
• Transverse electric scattering on inhomogeneous objects: Singular integral equation, symbol of the operator, and matrix elements
• Spectral structure of electromagnetic scattering on arbitrarily shaped dielectrics