Reduced Basis Method for the parametrized Electrical Field Integral Equation (EFIE)

Abstract: 

The subsequent discretization of the EFIE is a common approach to solve scattering problems on unbounded domains which is known as the Boundary Element Method (BEM) or Method of Moments (Mom). In many applications, such as optimization, shape recognition or inverse problems, just to mention a few, solving the Boundary Element Method for each new parameter value is too expensive (and unnecessary).

The Reduced Basis Method is accurate, efficient and trustable algorithm in the framework of parametrized problems and in a many-query context. We will present how the Reduced Basis Method is applied to parametrized scattering problems. The novelty is that for the first time the Reduced Basis Method is applied to an integral equation. We will discuss the challenges and present numerical examples.