Parareal
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Related Articles from SNS
Linear Convergence of Parareal Algorithm for Semilinear Parabolic Equations
arXiv:2606.03516v1 Announce Type: new Abstract: Long-time simulations of evolution equations present substantial computational challenges due to the inherently sequential nature of conventional time-stepping schemes. The parareal method, a leading parallel-in-time (PinT) algorithm, offers a promising approach to overcome the challenge by introducing concurrency in the time domain. While its convergence theory is well-established for linear problems, extending the theory to nonlinear...
A Parareal Algorithm with Low-Rank Coarse Solvers
arXiv:2508.08873v2 Announce Type: replace Abstract: We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from truncated SVD approximations of the transfer operators mapping initial values for a given time interval to the solution at the end of the interval. By leveraging randomized singular value decompositions, these low-rank approximations are obtained embarrassingly parallel by computing local fine solutions...