Parallelization methods for space-time problems

Let's now return to a time-evolution problem, of the heat, wave or even Schrödinger type. To calculate an approximate solution in space and time, we prefer to choose a scheme that is implicit in time in the first and third cases, and explicit in the second. A uniform time discretization over the domain will then produce a natural parallelization in the explicit case, without the need to iterate between processors. For an implicit scheme, on the other hand, we have to solve an elliptic equation at each time step (see the beginning of section 1.4 of [AF 1 375] ). This can be solved by one of the domain...