# Efficient simulation of unsaturated flow using exponential time integration

Carr, E.J., Moroney, T.J., & Turner, I.W.
(2011)
Efficient simulation of unsaturated flow using exponential time integration.
*Applied Mathematics and Computation*, *217*(14), pp. 6587-6596.

## Abstract

We assess the performance of an exponential integrator for advancing stiff, semidiscrete formulations of the unsaturated Richards equation in time. The scheme is of second order and explicit in nature but requires the action of the matrix function φ(A) where φ(z) = [exp(z) - 1]/z on a suitability defined vector v at each time step. When the matrix A is large and sparse, φ(A)v can be approximated by Krylov subspace methods that require only matrix-vector products with A. We prove that despite the use of this approximation the scheme remains second order. Furthermore, we provide a practical variable-stepsize implementation of the integrator by deriving an estimate of the local error that requires only a single additional function evaluation. Numerical experiments performed on two-dimensional test problems demonstrate that this implementation outperforms second-order, variable-stepsize implementations of the backward differentiation formulae.

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ID Code: | 40705 |
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Item Type: | Journal Article |

Refereed: | Yes |

Keywords: | Exponential integrators , Matrix Function Approximation, Arnoldi Method, Backward Differentiation Formulae, Richards equation, Krylov subspace methods |

DOI: | 10.1016/j.amc.2011.01.041 |

ISSN: | 00963003 |

Subjects: | Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) |

Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > Schools > Mathematical Sciences |

Copyright Owner: | Copyright 2011 Elsevier Inc. |

Deposited On: | 10 Mar 2011 22:59 |

Last Modified: | 19 Aug 2011 01:00 |

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