An Efficient MLACA-SVD Solver for Superconducting Integrated Circuit Analysis

Abstract

Inductance extraction for superconducting integrated circuits requires the accurate solution of structural current distributions. FastHenry is a well known, magnetoquasistatic solver suitable for this task. It is based upon the partial element equivalent circuit, integral equation method, with the structure discretized into hexahedral filaments. It employs the multilevel fast multipole algorithm (MLFMA) for compressed storage of the mutual inductance matrix, which accounts for most of the required memory. This MLFMA implementation is especially memory efficient, given certain approximations and algorithmic parameter choices. However, errors are introduced into the matrix representation. Here, a multilevel adaptive cross approximation solver with singular value decomposition recompression (MLACA-SVD) is presented as an alternative to FastHenry's existing MLFMA solver. MLACA-SVD compresses off-diagonal matrix blocks to a specified error tolerance, based on evaluating selected entries. Quadrature recipes are presented for guaranteed accuracy of matrix entry evaluation. Numerical results for examples of practical interest show that the MLACA-SVD memory scaling versus b (number of filaments) is practically identical to that of FastHenry's MLFMA, and is close to O(blog b). The MLACA-SVD requires less memory for the same solution accuracy, and furthermore offers complete control over matrix approximation errors. For the examples considered, it is found to be a more efficient solver. It is well suited to parallelization.