Abstract
We propose a new domain decomposition waveform relaxation algorithm, which enables using different time steps across subdomains for parallel solving initial-boundary-value problems of linear parabolic equations. Distinct with the classical Schwarz waveform relaxation, the algorithm includes preconditioners to accelerate convergence and has greatly reduced memory requirements. A specific implementation of the local time stepping is also presented and its well-posedness is proved. The preconditioned system is analyzed at the continuous level. Finally, the efficiency of the algorithm is shown through numerical experiments.
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