Adaptive cross approximation for electromagnetic analysis of superconducting circuits

[摘要] ENGLISH ABSTRACT: Electromagnetic analysis of superconducting integrated circuits is routinely requiredfor inductance extraction. FastHenry is a magnetoquasistatic (MQS) analysis tool suitablefor this task. It is based on the partial element equivalent circuit (PEEC), integralequation method, with the structure discretised into hexahedral filaments. FastHenry'smultilevel fast multipole algorithm (MLFMA) implementation is especially memory efficient,given certain approximations and algorithmic parameter choices. However, errorsare introduced into the matrix representation. This thesis describes the implementationof a multilevel adaptive cross approximation solver with singular value decomposition recompression(MLACA-SVD) inside FastHenry as an alternative to its existing MLFMAsolver. The thesis also presents two modified grouping strategies to further improveMLACA-SVD efficiency by compressing interactions between larger groups, while maintainingscaling performance consistent with a valid admissibility condition. MLACA-SVDcompresses off-diagonal matrix blocks to a specified error tolerance, based on evaluatingselected entries. Quadrature recipes presented in this thesis provide guaranteed accuracyof matrix entry evaluation.Numerical results for examples of practical interest show that the MLACA-SVD memoryscaling versus number of filaments, denoted b, is practically identical to that of FastHenry'sMLFMA, and is close to O(b log b). The MLACA-SVD requires less memory forthe same solution accuracy, and furthermore offers complete control over matrix approximationerrors. For the examples considered, it is found to be a more efficient solver. Theresults of the group merging strategies show that required memory is further reduced byapproximately 30%. The MLACA-SVD solver with merging requires about four timesless memory than FastHenry's MLFMA, for similar accuracy.

[发布机构] Stellenbosch University