Browsing by Author "Nel, Abraham Pieter Ben"

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    Adaptive cross approximation for electromagnetic analysis of superconducting circuits
    (Stellenbosch : Stellenbosch University, 2019-04) Nel, Abraham Pieter Ben; Botha, Matthys M.; Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering.
    ENGLISH ABSTRACT: Electromagnetic analysis of superconducting integrated circuits is routinely required for inductance extraction. FastHenry is a magnetoquasistatic (MQS) analysis tool suitable for this task. It is based on the partial element equivalent circuit (PEEC), integral equation method, with the structure discretised into hexahedral filaments. FastHenry’s multilevel fast multipole algorithm (MLFMA) implementation is especially memory efficient, given certain approximations and algorithmic parameter choices. However, errors are introduced into the matrix representation. This thesis describes the implementation of a multilevel adaptive cross approximation solver with singular value decomposition recompression (MLACA-SVD) inside FastHenry as an alternative to its existing MLFMA solver. The thesis also presents two modified grouping strategies to further improve MLACA-SVD efficiency by compressing interactions between larger groups, while maintaining scaling performance consistent with a valid admissibility condition. MLACA-SVD compresses off-diagonal matrix blocks to a specified error tolerance, based on evaluating selected entries. Quadrature recipes presented in this thesis provide guaranteed accuracy of matrix entry evaluation. Numerical results for examples of practical interest show that the MLACA-SVD memory scaling versus number of filaments, denoted b, is practically identical to that of FastHenry’s MLFMA, and is close to O(b log 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. The results of the group merging strategies show that required memory is further reduced by approximately 30%. The MLACA-SVD solver with merging requires about four times less memory than FastHenry’s MLFMA, for similar accuracy.