[Trilinos-Users] BELOS GMRES preconditioner

Deepak Garg deepak.garg at ingv.it
Mon Jul 2 18:16:45 EDT 2018


I am using GMRES solver of BELOS package from Trilinos (12.10.1). My system
is emanating from finite element method: Ax=b where A is assembled
Epetra_CrsMatrix. I have tried to solve the system with PseudoBlockGmres
and ILU preconditioner from ifpack library. The solver is taking plenty of
time to solve the equations. It can be due to poor conditioning of the
system. To remedy this I want to construct my own preconditioner with the
following steps:

1.  First, I want to construct a matrix C which must be a nodal block
diagonal matrix of A. For
      example if A is 4X4 matrix and each node has two dofs then

       C =   a11  a12    0     0
                a21  a22    0     0
                 0       0      a31  a32
                 0       0      a41  a42

Q: How can I extract this block diagonal matrix from Epetra_Crs matrix?

2.   Next I want to decompose C into LU format i.e.  C = LU, where L and U
are lower and upper
       triangular matrices.

Q: How can I achieve that?

3.   Next I want to solve the following preconditioned system by gmres

      (L^-1 A U^-1) (Ux) = (L^-1 b)

Q: How can I construct this system?

Many thanks in advance,
Deepak Garg
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