An efficient parareal algorithm for a class of time-dependent problems with fractional Laplacian

Shulin Wu

Applied Mathematics and Computation, 2017, vol. 307, issue C, 329-341

Abstract: Time-dependent diffusion equations with fractional Laplacian have received considerable attention in recent years, for which numerical methods play an important role because a simple and analytic solution is often unavailable. We analyze in this paper a parareal algorithm for this kind of problem, which realizes parallel-in-time computation. The algorithm is iterative and uses the 3rd-order SDIRK (singly diagonally implicit Runge-Kutta) method with a small step-size Δt as the F-propagator and the implicit-explicit Euler method with a large step-size ΔT as the G-propagator. The two step-sizes satisfy ΔT/Δt=J with J ≥ 2 being an integer. Using the implicit-explicit Euler method as the G-propagator potentially improves the parallel efficiency, but complicates the convergence analysis. By employing some technical analysis, we provide a sharp estimate of the convergence rate, which is independent of the mesh ratio J and the distribution of the eigenvalues of the coefficient matrix. An extension of the results to problems with time-periodic conditions is also given. Several numerical experiments are carried out to verify the theoretical results.

Keywords: Parareal algorithm; Fractional Laplacian; Implicit-explicit Euler method; 3rd-order SDIRK method; Convergence analysis (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300317301169
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:307:y:2017:i:c:p:329-341

DOI: 10.1016/j.amc.2017.02.012

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().