Efficient solvers and preconditioners for the implicit time integration of discontinuous Galerkin methodsPazner, WillcreatorShu, Chi-WangAdvisorPersson, Per-OlofReaderGuzmán, JohnnyReaderBrown University. Department of Applied Mathematicssponsor2018xv, 214 p.born digitalThesis (Ph. D.)--Brown University, 2018thesesIn 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.discontinous Gakerkin methodpreconditionerstime integrationComputational science and engineeringEnglishRPB2018061810.26300/0syb-sb60In CopyrightCollection is open for research.dissertations