[Trilinos-Users] Thyra::initializeAndReuseOp

[Laurent Griesser]

Hi,

I am new to Trilinos and still not used to the use of linear solvers. I
want to solve a parabolic differential equation. Each time iteration
naturally consists in solving a linear system. From one time iteration to
the other, I would like to reuse my old linear system as much as I can. The
matrix of my linear system is penta-diagonal and this structure doesn't
change from one iteration to the other. Only the matrix coefficients do
change.

I think I can do that with Thyra::initializeAndReuseOp but I am not sure
what this method really does. Does it update my ILU factorization? How
efficient is that compared to the uninitializeOp/initializeOp strategy?

I have partially read the documentation under

http://trilinos.org/docs/dev/packages/thyra/doc/html/classThyra_1_1LinearOpWithSolveFactoryBase.html

They distinguish between

"Reuse of factorizations for small changes in the forward operator"

and

"Updating the linear solver for major changes in the structure of the
forward operator"

What does "small changes" mean? What is the efficiency penalty when I
proceed with the "major changes" method?

With PETSc for example, I don't need to think about this. Usually, I can
write something along those lines:

// linear system setup phase
KSPCreate(PETSC_COMM_SELF, &m_Solver);
KSPSetType(m_Solver, KSPGMRES);
KSPGMRESSetRestart(m_Solver, 1500);
KSPSetTolerances(m_Solver, 1e-5, PETSC_DEFAULT, 1e10, 1500);
KSPGMRESSetOrthogonalization(m_Solver,
KSPGMRESModifiedGramSchmidtOrthogonalization);
PC pc; KSPGetPC(m_Solver, &pc); PCSetType(pc, PCILU);

/*
 * solve parabolic equation
 */
while(t < tf) {
  // update of matrix/rhs
  ...

  // solve linear system
  KSPSetOperators(m_Solver, m_A, m_A, SAME_NONZERO_PATTERN);
  KSPSolve(m_Solver, m_b, m_X);

  // post-processing
  ...
  // time update
  tf += dt;
}

And here, the fact that I mention "SAME_NON_ZERO_PATTERN" tells my solver
that I don't want a complete refactorization. This is exactly what I want
from trilinos. How do I achieve this?

Thanks for your advice,
Laurent
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