We present an open-source space-and doubly-time-parallel implementation and evaluate its performance for twodifferent test problems . We use a collocationmethod of arbitrary order to add another level of parallelization in time . We derive an adaptive strategy to select a new $alpha$-circulantpreconditioner for each iteration during runtime for balancing convergencerates, round-off errors and inexactness in the individual time-steps . We present and analyze a parallel implementation of a parallel-in-time method based on preconditioned Richardson iterations. Afteraddressing these more theoretical challenges, we present and evaluate their performance for various test problems. We present a space and doubly . time-based implementation of the

Author(s) : Gayatri Caklovic, Robert Speck, Martin Frank

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Keywords : time - parallel - implementation - present - based -

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