Adaptive cross approximation for electromagnetic analysis of superconducting circuits

Nel, Abraham Pieter Ben (2019-04)

Thesis (MEng)--Stellenbosch University, 2019.

Thesis

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.

AFRIKAANSE OPSOMMING: Elektromagnetiese analise van supergeleidende geïntegreerde stroombane word gereeld benodig vir induktansie onttrekking. FastHenry is ’n magnetetoquastistiese (MQS) analisehulpmiddel, geskik vir hierdie taak. Dit is gebaseer op die gedeeltelike element ekwivalente stroombaan (GEES), integrale vergelykings metode, met die struktuur gediskretiseer in hexahedrale filamente. Die multivlak vinnige multipool algoritme (MVVMA) implementering in FastHenry is veral doeltreffend ten opsigte van geheue, gegewe sekere benaderings en algoritmiese parameter keuses. Foute word egter in die matriksvoorstelling ingevoer. Hierdie tesis beskryf die implementering van ’n multivlak aanpassingsvaardige kruisbenadering oplosser met enkelvoudige waarde-ontbinding herkompressie (AKO-EWOH) binne FastHenry as ’n alternatief vir die bestaande MVVMA oplosser. Die tesis bied ook twee aangepaste groeperingstrategieë aan om AKO-EWOH se doeltreffendheid verder te verbeter deur interaksies tussen groter groepe te kompres, terwyl die skaleringsuitset in ooreenstemming bly met ’n geldige toelaatbaarheidstoestand. AKO-EWOH kompres skuinsmatige matriksblokke tot ’n gespesifiseerde fouttoleransie, gebaseer op die evaluering van geselekteerde inskrywings. Kwadratuur resepte wat in hierdie tesis aangebied word, bied gewaarborgde akkuraatheid van matriksinskrywing evaluering. Numeriese resultate vir voorbeelde van praktiese belang toon dat die skalering van AKO-EWOH se geheue teenoor die aantal filamente, b, feitlik identies is aan dié van FastHenry se MVVMA, en baie naby is aan O(b log b). Vir die voorbeelde wat oorweeg is, gebruik AKO-EWOH minder geheue vir dieselfde oplossingsakkuraatheid, en bied bowendien volledige beheer oor matriksbenaderings foute. Die resultate vir die groep samesmelting strategieë toon dat vereiste geheue verder verminder word met ongeveer 30%. Die AKO-EWOH-oplosser met samesmelting verg ongeveer vier keer minder geheue as FastHenry se MVVMA, vir soortgelyke akkuraatheidsvlakke.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/106196
This item appears in the following collections: