Convergence of Parareal Algorithms for PDEs with Fractional Laplacian and a Non-Constant Coefficient
Year: 2018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 746–763
Abstract
The convergence of Parareal-Euler and -LIIIC2 algorithms using the backward Euler method as a $\mathscr{G}$-propagator for the linear problem $U^′ (t)+α(t)A^ηU(t)=f(t)$ with a non-constant coefficient $α$ is studied. We propose to employ the propagator $G$ to a constant model $U^′(t)+βA^ ηU(t)=f(t)$ with a special coefficient β instead of applying both propagators $\mathscr{G}$ and $\mathscr{F}$ to the same target model. We established a simple formula to find an optimal parameter $β_{opt}$, minimising the convergence factor for all mesh ratios. Numerical results confirm the proximity of theoretical optimal $β_{opt}$ to the optimal numerical parameter.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.220418.210718
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 746–763
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Stochastic Navier-Stokes equations axisymmetric global existence. Parareal method time-varying problem convergence analysis parameter optimisation.