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- W2803516107 abstract "In this paper, we present an idea toward parallel coarse grid correction (CGC) for the parareal algorithm. It is well known that such a CGC procedure is often the bottleneck of speedup of the parareal algorithm. For an ODE system with initial-value condition $u(0)=u_0$ the idea can be explained as follows. First, we apply the $mathcal{G}$-propagator to the same ODE system but with a special condition $u(0)=alpha u(T)$, where $alphainmathbb{R}$ is a crux parameter. Second, in each iteration of the parareal algorithm the CGC procedure will be carried out by the so-called diagonalization technique established recently. The parameter $alpha$ controls both the roundoff error arising from such a diagonalization technique and the convergence rate of the resulting parareal algorithm. We show that there exists some threshold $alpha^*$ such that the parareal algorithm with diagonalization-based CGC possesses the same convergence rate as that of the parareal algorithm with classical CGC if $|alpha|leq alpha^*$. With $|alpha|=alpha^*$, we show that the condition number associated with the diagonalization technique is a moderate quantity of order $mathcal{O}(1)$ (and therefore the roundoff error is small) and is independent of the length of the time interval. Numerical results are given to support our findings." @default.
- W2803516107 created "2018-06-01" @default.
- W2803516107 creator A5021118595 @default.
- W2803516107 date "2018-01-01" @default.
- W2803516107 modified "2023-09-30" @default.
- W2803516107 title "Toward Parallel Coarse Grid Correction for the Parareal Algorithm" @default.
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- W2803516107 doi "https://doi.org/10.1137/17m1141102" @default.
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