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DTSTAMP:20210916T132450Z
LOCATION:Jean-Jacques Rousseau
DTSTART;TZID=Europe/Stockholm:20210707T113000
DTEND;TZID=Europe/Stockholm:20210707T120000
UID:submissions.pasc-conference.org_PASC21_sess161_msa245@linklings.com
SUMMARY:Massively Parallel Multigrid with Direct Coarse Grid Solvers
DESCRIPTION:Minisymposium\n\nMassively Parallel Multigrid with Direct Coar
 se Grid Solvers\n\nLeleux, Buttari, Mary, Ruede, Wohlmuth\n\nExtreme scale
  simulation requires fast and scalable algorithms, such as multigrid metho
 ds. To achieve asymptotically optimal complexity, it is essential to emplo
 y a hierarchy of grids. The cost to solve the coarsest grid system can oft
 en be neglected in sequential computings, but cannot be ignored in massive
 ly parallel executions. In this case, the coarsest grid can be large and i
 ts efficient solution becomes a challenging task. We propose solving the c
 oarse grid system using modern, approximate sparse direct methods and inve
 stigate the expected gains compared with traditional iterative methods. Si
 nce the coarse grid system only requires an approximate solution, we show 
 that we can leverage block low-rank techniques, combined with the use of s
 ingle precision arithmetic, to significantly reduce the computational requ
 irements of the direct solver. In the case of extreme scale computing, the
  coarse grid system is too large for a sequential solution, but too small 
 to permit massively parallel efficiency. We show that the agglomeration of
  the coarse grid system to a subset of processors is necessary for the spa
 rse direct solver to achieve performance. We demonstrate the efficiency of
  the proposed method on a Stokes-type saddle point system solved with a mo
 nolithic Uzawa multigrid method. In particular, we show that the use of an
  approximate sparse direct solver for the coarse grid system can outperfor
 m that of a preconditioned minimal residual iterative method. This is demo
 nstrated for the multigrid solution of systems of order up to 1E11 degrees
  of freedom on a petascale supercomputer using 43200 processes.\n\nDomain:
  CS and Math, Emerging Applications, Solid Earth Dynamics, Engineering
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