Beyond their well-known asymptotic optimality, multigrid methods
are often also the most efficient methods in absolute metrics,
i.e. in time to solution or energy consumption
on large scale parallel supercomputers. This will be studied by
extending Brandt's notion of texbook efficiency for
evaluating the parallel cost efficiency of iterative methods.
The HHG package, a carefully designed multigrid FE framework
will be shown to reach more than ten trillion (
) unknowns
for saddle point systems on current peta-scale machines.
Time permitting, we will also discuss
new techniques that support an algorithmic
recovery from processor failures.
This is joint work with B. Gmeiner, M. Huber, H. Stengel, H. Köstler, C. Waluga, M. Huber, L. John, B. Wohlmuth, M. Mohr, S. Baumann, J. Weismüller, P. Bunge.