We propose and analyze the ReLPM (Real Leja Points Method) for evaluating the propagator phi(DeltatB)nu via matrix interpolation polynomials at spectral Leja sequences. Here B is the large, sparse, nonsymmetric matrix arising from stable 2D or 3D finite-difference discretization of linear advection-diffusion equations, and phi(z) is the entire function phi(z) = (e(z) - 1)/z. The corresponding stiff differential system y(t) = By(t) + g,y(0) =y(0), is solved by the exact time marching scheme y(i+1) = y(i) + Deltat(i)phi(Deltat(i)B)(By(i) + g), i = 0, 1,..., where the time-step is controlled simply via the variation percentage of the solution, and can be large. Numerical tests show substantial speed-ups (up to one order of magnitude) with respect to a classical variable step-size Crank-Nicolson solver

Interpolating discrete advection-diffusion propagators at Leja sequences

CALIARI, Marco;
2004-01-01

Abstract

We propose and analyze the ReLPM (Real Leja Points Method) for evaluating the propagator phi(DeltatB)nu via matrix interpolation polynomials at spectral Leja sequences. Here B is the large, sparse, nonsymmetric matrix arising from stable 2D or 3D finite-difference discretization of linear advection-diffusion equations, and phi(z) is the entire function phi(z) = (e(z) - 1)/z. The corresponding stiff differential system y(t) = By(t) + g,y(0) =y(0), is solved by the exact time marching scheme y(i+1) = y(i) + Deltat(i)phi(Deltat(i)B)(By(i) + g), i = 0, 1,..., where the time-step is controlled simply via the variation percentage of the solution, and can be large. Numerical tests show substantial speed-ups (up to one order of magnitude) with respect to a classical variable step-size Crank-Nicolson solver
exponential operator; advection-diffusion problem; sparse matrix; Leja sequence; polynomial interpolation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/312272
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