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Across-the-space parallelism still remains the most mature, convenient and natural way to parallelize large scale problems. One of the major problems here is that implicit time stepping is often difficult to parallelize due to the structure of the system. Approximate implicit schemes have been suggested to circumvent the problem (M.A. Botchev et al., Appl. Numer. Math. 31 (3) (1999) 239). These schemes...
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