A class of linear solvers based on multilevel and supernodal factorization

Yiming Bu

A class of linear solvers based on multilevel and supernodal factorization

Vertaalde titel van de bijdrage: Een klasse van lineaire solvers gebaseerd op multilevel en supernodal factorisatie

Yiming Bu

Technische Mechanica en Numerieke Wiskunde

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De oplossing van grote en schaarse lineaire systemen is een kritieke component van moderne wetenschap en technische simulaties. Iteratieve methoden, namelijk de klasse van moderne Krylov-subruimtemethoden, worden vaak gebruikt om grootschalige lineaire systemen op te lossen. Om de robuustheid en de convergentiesnelheid van de iteratieve methoden te verbeteren, worden preconditioneringstechnieken vaak beschouwd als cruciale componenten van de lineaire systeemoplossing. In dit proefschrift wordt een klasse van algebraïsche multilevel oplossers gepresenteerd voor het conditioneren van algemene lineaire systeemvergelijkingen die voortkomen uit computationele wetenschap en technische toepassingen. Ze kunnen spaarzame patronen produceren en geheugenkosten besparen door recursieve combinatorische algoritmen toe te passen. Robuustheid wordt verbeterd door de factorisatie te combineren met recent ontwikkelde overlappende en compressiestrategieën en door efficiënte lokale oplossers te gebruiken. We hebben de goede prestaties van de voorgestelde strategieën aangetoond met numerieke experimenten op realistische matrixproblemen, ook in vergelijking met enkele van de meest populaire algebraïsche preconditioners die tegenwoordig worden gebruikt.

Vertaalde titel van de bijdrage	Een klasse van lineaire solvers gebaseerd op multilevel en supernodal factorisatie
Originele taal-2	English
Kwalificatie	Doctor of Philosophy
Toekennende instantie	Rijksuniversiteit Groningen
Begeleider(s)/adviseur	Veldman, Arthur, Supervisor Carpentieri, Bruno, Co-supervisor
Datum van toekenning	3-jul.-2018
Plaats van publicatie	[Groningen]
Uitgever	University of Groningen
Gedrukte ISBN's	978-94-034-0727-2
Elektronische ISBN's	978-94-034-0726-5
Status	Published - 2018

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title = "A class of linear solvers based on multilevel and supernodal factorization",

abstract = "The solution of large and sparse linear systems is a critical component of modern science and engineering simulations. Iterative methods, namely the class of modern Krylov subspace methods, are often adopted to solve large-scale linear systems. To improve the robustness and the convergence rate of the iterative methods, preconditioning techniques are often considered crucial components of the linear systems solution. In this thesis, a class of algebraic multilevel solvers is presented for preconditioning general linear systems equations arising from computational science and engineering applications. They can produce sparse patterns and save memory costs by employing recursive combinatorial algorithms. Robustness is enhanced by combining the factorization with recently developed overlapping and compression strategies, and by using efficient local solvers. We have shown the good performance of the proposed strategies with numerical experiments on realistic matrix problems, also in comparison against some of the most popular algebraic preconditioners in use today.",

author = "Yiming Bu",

year = "2018",

language = "English",

isbn = "978-94-034-0727-2",

publisher = "University of Groningen",

school = "University of Groningen",

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TY - BOOK

T1 - A class of linear solvers based on multilevel and supernodal factorization

AU - Bu, Yiming

PY - 2018

Y1 - 2018

N2 - The solution of large and sparse linear systems is a critical component of modern science and engineering simulations. Iterative methods, namely the class of modern Krylov subspace methods, are often adopted to solve large-scale linear systems. To improve the robustness and the convergence rate of the iterative methods, preconditioning techniques are often considered crucial components of the linear systems solution. In this thesis, a class of algebraic multilevel solvers is presented for preconditioning general linear systems equations arising from computational science and engineering applications. They can produce sparse patterns and save memory costs by employing recursive combinatorial algorithms. Robustness is enhanced by combining the factorization with recently developed overlapping and compression strategies, and by using efficient local solvers. We have shown the good performance of the proposed strategies with numerical experiments on realistic matrix problems, also in comparison against some of the most popular algebraic preconditioners in use today.

AB - The solution of large and sparse linear systems is a critical component of modern science and engineering simulations. Iterative methods, namely the class of modern Krylov subspace methods, are often adopted to solve large-scale linear systems. To improve the robustness and the convergence rate of the iterative methods, preconditioning techniques are often considered crucial components of the linear systems solution. In this thesis, a class of algebraic multilevel solvers is presented for preconditioning general linear systems equations arising from computational science and engineering applications. They can produce sparse patterns and save memory costs by employing recursive combinatorial algorithms. Robustness is enhanced by combining the factorization with recently developed overlapping and compression strategies, and by using efficient local solvers. We have shown the good performance of the proposed strategies with numerical experiments on realistic matrix problems, also in comparison against some of the most popular algebraic preconditioners in use today.

M3 - Thesis fully internal (DIV)

SN - 978-94-034-0727-2

PB - University of Groningen

CY - [Groningen]

ER -

A class of linear solvers based on multilevel and supernodal factorization

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