Efficient simulation of unsaturated flow using exponential time integration
Data(s) |
2011
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Resumo |
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. |
Formato |
application/pdf |
Identificador | |
Publicador |
Elsevier Inc. |
Relação |
http://eprints.qut.edu.au/40705/1/c40705.pdf DOI:10.1016/j.amc.2011.01.041 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. |
Direitos |
Copyright 2011 Elsevier Inc. |
Fonte |
Faculty of Science and Technology; Mathematical Sciences |
Palavras-Chave | #010200 APPLIED MATHEMATICS #010300 NUMERICAL AND COMPUTATIONAL MATHEMATICS #Exponential integrators #Matrix Function Approximation #Arnoldi Method #Backward Differentiation Formulae #Richards equation #Krylov subspace methods |
Tipo |
Journal Article |