Optimized integral equation domain decomposition methods for scattering by large and deep cavities

Electromagnetic scattering analysis of large and deep cavities embedded in an arbitrarily shaped host body is of high interest to the engineering community. The objective of this work is to investigate an effective boundary integral equation domain decomposition method for solving the cavity scattering problems. The key features of the proposed work include: (i) the introduction of individual electric and magnetic traces as unknowns for each sub-region, (ii) the development of a multi-trace combined field integral equation formulation for decomposed boundary value problem, and (iii) the derivation of optimized multiplicative Schwarz preconditioning using complete second order transmission condition. The proposed method can be viewed as an effective preconditioning scheme for the integral equation based solution of the cavity scattering problems. The strength and flexibility of the proposed method will be illustrated by means of several representative numerical examples.