Global Multitrace, Single-Source Integral Equation for the Scattering by Composite Objects

Abstract

Global multitrace (MT) integral equations offer an appealing option for the integral equation-based description of the scattering of time-harmonic electromagnetic waves by composite objects. They lead to linear systems that are amenable to Calderón preconditioning. However, they also double the number of degrees of freedom at the shared interfaces of the composite object. This contribution introduces a global MT, single-source (SS) formulation for modeling the scattering of time-harmonic waves by composite objects. It is based on a multiplicative rather than an additive combination of the interior and exterior Calderón projectors and a conforming discretization scheme that relies on both primal and dual finite element spaces. Special treatment of perfectly conducting objects is discussed to avoid spurious resonances. This treatment is based on the combined source technique applied in the context of MT, SS integral equations. Numerical experiments demonstrate the method’s correctness by comparing numerical results with analytical solutions and an additive MT formulation. A numerically rigorous study of the convergence rate of the energy norm is conducted. Details are provided on how to generalize the algorithm to handle nonconforming meshes, allowing for greater freedom in device design.