[Trilinos-Users] thinking about a "deflated solver"

Riccardo Rossi rrossi at cimne.upc.edu
Sun Apr 27 13:30:26 MDT 2014

Dear List,

 I am toying with the idea (that is, for the moment simply starting to
think how I would do it) of implementing a “deflation solver”, based on
subdomain deflations to improve the weak scalability of additive schwarz

 The essential step to do this is to define a sparse matrix W, so that

W(i,j) = 1 on all of the “js” which are owned by the processor I (this is
hence very similar to the restrictor matrix in Additive Shwarz)

 this allow to define a coarse matrix

Adeflated = Wtranspose * Aglobal * W

 with size Ndomains*Ndomains, which can be solved together with the single
domains provding a provable guarantee of weak scalability.

 I had a look at EpetraExt and the matrix-matrix multiplication facilities
in there shall allow me to implement this quite easily.

 The point is that since this matrix will be very small, it will be most
probably convenient to have it on a single processor. How shall I do this

My plan was to first do the multiplication letting EpetraExt decide the
graph distribution across processors, and then to move the matrix to a
single processor. I however do not have a clear idea on how I should do
this efficiently. I would be grateful if someone could point me to the
correct function to do this or propose a better approach.

 The second thing that would be interesting is to use a threaded
preconditioner on the local problemes. I am aware of some efficient
OpenMP-only solvers which could be used on the different subdomains (for
example the pastix solver has an OpenMP-threades ILU which could be used
nicely in this context.

To be able to construct such preconditioners one shoulk however have a
classical CSR matrix representation of the local problem.

Does epetra provide capabilities to do this? Again I would be grateful for
suggestions on the appropriate functions

 thank you in advance

Riccardo Rossi


*Riccardo Rossi*

PhD, Civil Engineer

member of the Kratos Team: www.cimne.com/kratos

lecturer at Universitat Politècnica de Catalunya, BarcelonaTech (UPC)

Research fellow at International Center for Numerical Methods in
Engineering (CIMNE)

C/ Gran Capità, s/n, Campus Nord UPC, Ed. C1, Despatx C9

08034 – Barcelona – Spain – www.cimne.com  -

T.(+34) 93 401 56 96 skype: *rougered4*



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