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. 65876596.

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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 matrixvector products with A. We prove that despite the use of this approximation the scheme remains second order. Furthermore, we provide a practical variablestepsize implementation of the integrator by deriving an estimate of the local error that requires only a single additional function evaluation. Numerical experiments performed on twodimensional test problems demonstrate that this implementation outperforms secondorder, variablestepsize implementations of the backward differentiation formulae.
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ID Code:  40705 

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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