Fast multi-core CEM solvers and flux trapping analysis for superconducting structures

Jackman, Kyle (2018-03)

Thesis (PhD)--Stellenbosch University, 2018.

Thesis

ENGLISH ABSTRACT: The dissertation presents the development of a numerical field solver, called TetraHenry (TTH), for inductance extraction and flux trapping analysis of superconducting integrated circuits. The solver uses tetrahedral elements to model multidirectional current flow in complex three-dimensional superconducting volumes; whereas two dimensional triangular elements are used for sheet currents in thin superconducting films. Triangular meshing significantly reduces the number of unknowns and provides the capability to analyse chipscale superconducting layouts. Support for piecewise homogenous dielectric materials are implemented, which enables frequency-depended impedance extraction. The Fast Multipole Method for the Biot-Savart law, which enables the simulation of magnetic materials, is derived. The effects of external magnetic fields on the performance of superconducting circuits are analysed. The amount of flux through each hole or moat can be specified using the Volume Loop basis function; enabling flux trapping analysis and inductance extraction around holes. The full derivation of the integral equations for volume and sheet currents are discussed. The Method of Moments is used to obtain a system of linear equations, which is solved with a preconditioned GMRES solver. Matrix-vector multiplication is accelerated with the Fast Multipole method. The accuracy and performance of the numerical solver are evaluated, by comparing simulated results to existing software.

AFRIKAANSE OPSOMMING: Die dissertasie bied aan die ontwikkeling van ’n numeriese veldoplosser, genaamd TetraHenry (TTH), vir induktansie onttrekking en vloed-vasvang analise van supergeleier geïntegreerde stroombane. Die veldoplosser gebruik tetrahedraal elemente om stroomvloei binne komplekse driedimensionele supergeleidende volumes te modelleer; terwyl tweedimensionele driehoekige elemente gebruik word vir stroomvloei in dun supergeleier filamente. Driehoekige elemente verminder die aantal onbekendes aansienlik en bied die vermoë om supergeleier uitlegte op groot skaal te analiseer. Ondersteuning vir stuksgewyse homogene diëlektriese materiale word geïmplementeer, wat frekwensie-afhanklike impedansie onttrekking moontlik maak. Die “Fast Multipole” metode vir die Biot Savart wet, wat die simulering van magnetiese materiale moontlik maak, word afgelei. Die effekte van eksterne magnetiese velde op supergeleier stroombane word ontleed. Vloed-vasvang analise en induktansie onttrekking rondom gate word uitgevoer met behulp van Volume Lus funksies. Die volledige afleiding van die integraalvergelykings vir volume en oppervlakstrome word bespreek. Die Metode van Momente word gebruik om ’n stelsel van lineêre vergelykings te verkry, wat opgelos word met ’n voorafbepaalde GMRES iteratiewe oplosser. Matriks-vektor vermenigvuldiging word versnel met die “Fast Multipole” metode. Die akkuraatheid en spoed van die numeriese enjin word geëvalueer deur gesimuleerde resultate te vergelyk met bestaande sagteware.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/103747
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