A locally adaptive non-intrusive block reduced basis method for scattering applications using the boundary element method

Abstract

In computational electromagnetism, the radar signature of a target usually requires solving repeated electromagnetic scattering problems associated to plane waves illuminating the target with varying frequency and incident angle. When the problem is large scale, strategies based on repeated solver calls usually lead to prohibitive computational costs. This is especially the case when the solver relies on an integral equation discretized using the boundary element method (BEM), as this amounts to solving numerous complex, unsymmetrical and fully populated linear systems. In this work, reduced order models (ROMs) are built in order to rapidly and accurately approximate the solutions for illuminating waves with frequencies and incident angles within bands of interest. In the context of the BEM, the success of a ROM essentially depends on the ability to decouple the frequency from the Green kernels of the underlying integral equation. In this work, we present a methodology for achieving such decoupling that combines the Empirical Interpolation Method (EIM) with the notion of local adaptivity. We use our approximation of the frequency-dependent BEM operator in a locally adaptive non-intrusive reduced basis method. The proposed strategy is fully non-intrusive, in the sense that it only requires the ability to perform matrix–vector products with standard BEM operators. We illustrate our methodology on real-life electromagnetic scattering problems solved by the Combined Field Integral Equation (CFIE) and with matrix–vector products accelerated with the fast-multipole method (FMM).