  The interface to the MUMPS solver was updated in the JOREK MHD code to
support Block Low Rank (BLR) compression and an interface to the new PaStiX
solver version 6 has been implemented supporting BLR as well. First tests were
carried out with JOREK, which solves a large sparse matrix system iteratively
in each time step. For the preconditioning, a direct solver is applied in the
code to sub-matrices, and at this point BLR was applied with the results being
summarized in this report. For a simple case with a linearly growing mode,
results with both solvers look promising with a considerable reduction of the
memory consumption by several ten percent was obtained. A direct increase in
performance was seen in particular configurations already.
  The choice of the BLR accuracy parameter $\epsilon$ proves to be critical in
this simple test and also in more realistic simulations, which were carried out
only with MUMPS due to the limited time available. The more realistic test
showed an increase in run time when using BLR, which was mitigated when using
larger values of $\epsilon$. However, the GMRes iterative solver does not reach
convergence anymore when $\epsilon$ is too large, since the preconditioner
becomes too inaccurate in that case. It is thus critical to use an $\epsilon$
as large as possible, while still reaching convergence. More tests regarding
this optimum will be necessary in the future. BLR can also lead to an indirect
speed-up in particular cases, when the simulation can be run on a smaller
number of compute nodes due to the reduced memory consumption.

Performance;Mathematical Software