Efficient solvers and preconditioners for the implicit time integration of discontinuous Galerkin methods

Pazner, Will

Full Metadata

Overview

Year:: 2018
Contributor:: Pazner, Will (creator); Shu, Chi-Wang (Advisor); Persson, Per-Olof (Reader); Guzmán, Johnny (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: discontinous Gakerkin method; preconditioners; time integration; Computational science and engineering
Extent:: xv, 214 p.
DOI: https://doi.org/10.26300/0syb-sb60

Files

Description

Abstract:: In this work, we develop and analyze solvers and preconditioners designed for the implicit time integration of discontinuous Galerkin (DG) discretizations. The discontinuous Galerkin method is a high-order accurate finite element method for the numerical solution of partial differential equations on unstructured meshes. The temporal integration of such discretizations by means of implicit methods has the important advantage of avoiding restrictive stability conditions on the size of the time step. Because of the large number of degrees of freedom and potentially poorly-conditioned nature of the resulting algebraic systems of equations, sophisticated solvers and preconditioners are a requirement for good performance. This thesis focuses on the iterative solution of the resulting linear systems by means of Krylov subspace solvers. We develop and study preconditioners that allow of the efficient use of fully-implicit Runge-Kutta methods, which have previously been considered prohibitively expensive. These methods have the additional advantage that they allow for parallelism in the temporal dimension. Additionally, we develop an implicit tensor-product solver that makes use of a construction known as the Kronecker-product singular value decomposition to obtain asymptotically-improved computational complexities on quadrilateral and hexahedral meshes. Finally, we study the effect of polygonal mesh geometries on the convergence of iterative linear solvers. The applicability of these methods is demonstrated on a wide range of large-scale, two- and three-dimensional test cases.
Notes:: Thesis (Ph. D.)--Brown University, 2018

Content

Access Conditions

Rights: In Copyright
Restrictions on Use: Collection is open for research.

Citation

Pazner, Will, "Efficient solvers and preconditioners for the implicit time integration of discontinuous Galerkin methods" (2018). Applied Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://doi.org/10.26300/0syb-sb60

Relations

Collection:

Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.
...