There is a rather new FETI (Finite element tear and interconnect) domain decomposition method in Elmer that may help in the solution of large of certain large problems. Below are some scalability results (by Juha) that demonstrate rather reasonable scalability.
The problem under study was an academic case of linear elasticity. Weak scaling was studied so that the number of elements for each partition remained at constant 8000. As the largest case was run with 3375 cores this translates to a problem size of abour 80 million unknowns.
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#procs time(s) #iter ================== 27 10.52 26 64 12.30 29 125 9.27 31 216 9.96 31 343 10.26 32 512 11.18 32 729 12.13 33 1000 19.88 33 3375 31.52 35
FETI method is very robust and may also be used for the Poisson equation. Implementation of FETI for other equations (Helmholtz or Stokes) is possible but requires additional work.
PS. The work was supported by PRACE project and the simulations were carried out on Curie supercomputer at CEA.