GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Efficient solution of parabolic equations by Krylov approximation methods
SIAM Journal on Scientific and Statistical Computing
A Krylov projection method for systems of ODEs
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
An exponential method of numerical integration of ordinary differential equations
Communications of the ACM
Computing a matrix function for exponential integrators
Journal of Computational and Applied Mathematics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Journal of Computational Physics
EXPINT---A MATLAB package for exponential integrators
ACM Transactions on Mathematical Software (TOMS)
Stopping Criteria for Rational Matrix Functions of Hermitian and Symmetric Matrices
SIAM Journal on Scientific Computing
Acceleration Techniques for Approximating the Matrix Exponential Operator
SIAM Journal on Matrix Analysis and Applications
Implementation of exponential Rosenbrock-type integrators
Applied Numerical Mathematics
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
Journal of Computational Physics
Hi-index | 31.45 |
A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly ''Jacobian-free'' - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.