Interpolating discrete advection-diffusion propagators at Leja sequences

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:172

Article; Proceedings Paper

Caliari, M ; Vianello, M ; Bergamaschi, L

关键词: exponential operator;    advection-diffusion problem;    sparse matrix;    Leja sequence;    polynomial interpolation;   

DOI  :  10.1016/j.cam.2003.11.015

来源: Elsevier

【 摘 要 】

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. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free