Multiprecision computations with Schwarz methods

Schwarz methods and preconditioners, where the approximate solution of the local problems is performed at a lower precision, i.e., with fewer digits of accuracy than in the underlying (double precision) computation.

Conditions for the appropriate round-off criteria for the lower precision are presented.

It is found experimentally that for the model problems about 5 digits of accuracy are sufficient to achieve the theoretical restrictions, and thus, single precision suffices for the local solves.

Several numerical experiments illustrate the obtained results.