Spurious fields suppression in domain decomposition algorithms using Lagrange multipliers

Abstract

Various domain decomposition methods (DDM) have been developed as popular divide-and-conquer strategies to solve numerical electromagnetic problems of unprecedented scale. The DDM techniques invariably divide the original large problem into multiple smaller sub-problems, solve each sub-problem separately, and then, re-couple them into a continuous global solution over the entire domain. Key to all DDM approaches is the proper merging of all subdomain solutions. Bi-directional Robin boundary conditions have been popular in connecting non-overlapping individual solutions with remarkable success. However, similar to traditional absorbing boundary conditions, Robin conditions become inadequate when subdomain boundaries are partitioned in a way that dominant modes run parallel to the boundaries. Under these circumstances, spurious fields can occur along the subdomain boundaries that contaminate the accuracy of the entire solution. In this paper, extra constraints in the form of Lagrange multipliers are incorporated to suppress spurious fields in the fully overlapping DDM setup.