The LEM exponential integrator for advection-diffusion-reaction equations

Authors:
Marco Caliari;Marco Vianello;Luca Bergamaschi
Affiliations:
Department of Pure and Applied Mathematics, University of Padova, via Trieste 63, 35121 Padova, Italy;Department of Pure and Applied Mathematics, University of Padova, via Trieste 63, 35121 Padova, Italy;Department of Mathematics Methods and Models for Applied Sciences, University of Padova, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

We implement a second-order exponential integrator for semidiscretized advection-diffusion-reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja-Euler-Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.