The Mathematical Institute, University of Oxford, Eprints Archive

Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method

Smears, Iain (2015) Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method. Technical Report. Unspecified. (Submitted)

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Abstract

The discontinuous Galerkin time-stepping method has many advantageous properties for solving parabolic equations. However, its practical use has been limited by the large and challenging nonsymmetric systems to be solved at each time-step. This work develops a fully robust and efficient preconditioning strategy for solving these systems. We first construct a left preconditioner, based on inf-sup theory, that transforms the linear system to a symmetric positive definite problem that can be solved by the preconditioned conjugate gradient (PCG) algorithm. We then prove that the transformed system can be further preconditioned by an ideal block diagonal preconditioner, leading to a condition number κ bounded by 4 for any time-step size, any approximation order and any positive self-adjoint spatial operators. Numerical experiments demonstrate the low condition numbers and fast convergence of the algorithm for both ideal and approximate preconditioners, and show the feasibility of the high-order solution of large problems.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1894
Deposited By: Helen Taylor
Deposited On:03 Sep 2015 06:50
Last Modified:03 Sep 2015 06:50

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