Summary
After stating an abstract convergence result for the parareal algorithm used in the parallelization in time of general partial differential equations, we analyze the stability and convergence properties of the algorithm for equations with constant coefficients. We show that suitably damping coarse schemes ensure unconditional stability of the parareal algorithm and analyze how the regularity of the initial condition influences convergence in the absence of sufficient damping.
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Bal, G. (2005). On the Convergence and the Stability of the Parareal Algorithm to Solve Partial Differential Equations. In: Barth, T.J., et al. Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26825-1_43
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DOI: https://doi.org/10.1007/3-540-26825-1_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22523-2
Online ISBN: 978-3-540-26825-3
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