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Thesis

All-at-once solution of time-dependent PDE problems

Abstract:

In this thesis, we examine the solution to a range of time-dependent Partial Differential Equation (PDE) problems. Throughout, we focus on the development of preconditioners for the all-at-once system, which solves for all time-steps in a single coupled computation. The preconditioners developed are used with existing iterative methods and, due to their specific block structure, could be applied in parallel over time.

We first develop solvers for the heat equation and the transient ...

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Division:
MPLS
Department:
Mathematical Institute
Role:
Author

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Role:
Supervisor
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
UUID:
uuid:60f2985b-6071-47ae-97a9-7813db0194ae
Deposit date:
2017-11-19

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