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Efficient PETSc Solvers for Discontinuous Galerkin Methods Applied to Elliptic Problems

Chiacchiero, Michael Alan (2007) Efficient PETSc Solvers for Discontinuous Galerkin Methods Applied to Elliptic Problems. Master's Thesis, University of Pittsburgh. (Unpublished)

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Abstract

In this thesis we are creating several large scale relatively sparse linear systems generated by the Discontinuous Galerkin Method to numerically solve a two-point boundary value problem over the interval (0,1). These linear systems are then solved on a computer using three iterative Krylov methods all built into a Portable, Extensible Toolkit for Scientific Computation (PETSc). The methods that are used are Conjugate Gradient (CG), Bi-Conjugate Gradient-Stable (Bi-CGStab), and Generalized Minimal Residual (GMRES). The effectiveness and efficiency of these linear solvers are analyzed as two parameters of the system, namely EPS and penalty term SIG, are varied. Also the effects of several preconditioners are analyzed.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Chiacchiero, Michael Alanmac111@pitt.eduMAC111
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairRiviere, Beatriceriviere@pitt.eduRIVIERE
Committee MemberVainchtein, Annaannav@math.pitt.eduAAV4
Committee MemberYotov, Ivanyotov@math.pitt.eduYOTOV
Date: 19 September 2007
Date Type: Completion
Defense Date: 3 August 2007
Approval Date: 19 September 2007
Submission Date: 7 August 2007
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: Cholesky; ILU; Jacobi
Other ID: http://etd.library.pitt.edu/ETD/available/etd-08072007-041832/, etd-08072007-041832
Date Deposited: 10 Nov 2011 19:57
Last Modified: 15 Nov 2016 13:48
URI: http://d-scholarship.pitt.edu/id/eprint/8959

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