Performance of MLACA with Modified Grouping for Superconducting Circuit Analysis

Abstract

Inductance extraction for superconducting integrated circuits requires knowledge of the structural current distribution. FastHenry is a well-known magnetoquasistatic analysis tool for solving the current distribution. FastHenry is based upon the partial element equivalent circuit (PEEC), volume integral equation method. It is a method of moments (MoM) formulation. FastHenry employs the multilevel fast multipole algorithm (MLFMA) for compressed storage of the mutual inductance matrix. Recently, a multilevel adaptive cross approximation solver with singular value decomposition recompression (MLACA-SVD), and with modified grouping strategies for increased efficiency, has been proposed as an alternative fast solver within FastHenry. This paper presents further results with MLACA-SVD and group merging, for a volumetric superconducting structure, such that unknowns are distributed roughly evenly throughout a cubic domain. This is in contrast to the predominantly planar structures considered before. The results show that the group merging schemes are broadly applicable to general volumetric structures, for increased efficiency. The results could be relevant to other applications of FastHenry and of ACA.