Interpolating discrete advection–diffusion propagators at Leja sequences
Journal of Computational and Applied Mathematics, ISSN: 0377-0427, Vol: 172, Issue: 1, Page: 79-99
2004
- 52Citations
- 17Captures
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Article Description
We propose and analyze the ReLPM (Real Leja Points Method) for evaluating the propagator ϕ (Δ tB ) v 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 ϕ ( z ) is the entire function ϕ ( z )=(e z −1)/ z. The corresponding stiff differential system ẏ(t)=By(t)+g,y(0)=y0, is solved by the exact time marching scheme y i+1 = y i +Δ t i ϕ (Δ t i B )( B y 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.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0377042704000998; http://dx.doi.org/10.1016/j.cam.2003.11.015; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=4444264388&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S0377042704000998; https://api.elsevier.com/content/article/PII:S0377042704000998?httpAccept=text/xml; https://api.elsevier.com/content/article/PII:S0377042704000998?httpAccept=text/plain; https://dx.doi.org/10.1016/j.cam.2003.11.015
Elsevier BV
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