Split-Field Domain Decomposition Parallel Algorithm With Fast Convergence for Electromagnetic Analysis

Abstract

In this work, we propose a new split-field domain-decomposition (DD) algorithm. Different from conventional DD methods where interface fields are treated as a whole and shared in common between adjacent subdomains, we split the field on the interface into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> components, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> is the number of subdomains sharing the interface, and solve one component of the interface field in each subdomain. The resultant numerical scheme allows for each subdomain to be directly solved in a decoupled manner, and meanwhile captures the global coupling among subdomains iteratively with fast and guaranteed convergence. Numerical simulations of large-scale electromagnetic structures such as integrated circuits and packages demonstrate the accuracy and efficiency of the proposed DD algorithm, and the resultant parallel solver.