We implement an exponential integrator for large and sparse systems of ODEs, generated by FE (Finite Element) discretization with mass-lumping of advection-diffusion equations. The relevant exponential-like matrix function is approximated by polynomial interpolation, at a sequence of real Leja points related to the spectrum of the FE matrix (ReLPM, Real Leja Points Method). Application to 2D and 3D advection-dispersion models shows speed-ups of one order of magnitude with respect to a classical variable step-size Crank-Nicolson solver.
The ReLPM exponential integrator for FE discretizations of advection-diffusion equations
CALIARI, Marco;
2004-01-01
Abstract
We implement an exponential integrator for large and sparse systems of ODEs, generated by FE (Finite Element) discretization with mass-lumping of advection-diffusion equations. The relevant exponential-like matrix function is approximated by polynomial interpolation, at a sequence of real Leja points related to the spectrum of the FE matrix (ReLPM, Real Leja Points Method). Application to 2D and 3D advection-dispersion models shows speed-ups of one order of magnitude with respect to a classical variable step-size Crank-Nicolson solver.
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