Reuse of Krylov preconditioner

Question

I am trying to solve a problem several consecutive times using the same matrix. Therefore it is useful to reuse as much as possible from one solve to the next one. For direct solvers I use:

solver = LUSolver()
solver.parameters['reuse_factorization'] = True

This works fine.

I was now trying to do the same with a Krylov solver. I searched around in FEniCS and I found this (very similar to the direct solver):

solver = KrylovSolver('gmres', 'hypre_amg')
solver.parameters['preconditioner']['reuse'] = True

But this returns an error

KeyError: "'reuse' is not a parameter"

Therefore I guess that either this option was removed or the way to use it changed. Can anyone clarify this to me?

Thank you.

Answer 1

Try with

solver.parameters['preconditioner']['structure'] = 'same'

or, if the matrix changes, but the nonzero pattern does not:

solver.parameters['preconditioner']['structure'] = 'same_nonzero_pattern'

I have not found any documentation of this, but you can see it in use for example in Oasis:
https://github.com/mikaem/Oasis/blob/9d0ffaebd4bc8f58fb3bf2fd174f09b48e2c5d73/solvers/NSfracStep/IPCS_ABCN.py#L107

Comments

Thank you Tormod!

I tried that but the times did not change. Do you know why that might be?

-artur palha

---

It seems you are right! I tested the below code with both FEniCS 1.4 and FEniCS 1.5. The results are as follows:

Results from running with FEniCS 1.4. The output shows preconditioner structure and timings in seconds:

same 2.22
different_nonzero_pattern 3.51

With 1.5:

same 2.43
different_nonzero_pattern 2.34

So, with the older version the preconditioner structure statement had an effect, while with the newest version it does not. If this is a bug or a feature I do not know.

The code:

from dolfin import *

import logging
logging.getLogger('FFC').setLevel(logging.WARNING)
logging.getLogger('UFL').setLevel(logging.WARNING)
set_log_level(WARNING)

def solve_poisson(N, M, structure):
    mesh = UnitSquareMesh(N, N)
    V = FunctionSpace(mesh, 'CG', 1)

    # Source term
    f = Expression('-200*pi*pi*sin(pi*x[0])*sin(pi*x[1])')

    # Define Poisson equation bilinear and linear form with du/dn=0
    u = TrialFunction(V)
    v = TestFunction(V)
    eq = inner(nabla_grad(u), nabla_grad(v))*dx - f*v*dx
    a, L = system(eq)

    # Boundary condition
    bc = DirichletBC(V, Constant(0.0), DomainBoundary())

    # Create matrix and vector with appropriate BCs
    A, b = assemble_system(a, L)
    bc.apply(A, b)

    # Solve system
    solution = Function(V)
    solver = KrylovSolver("gmres", "hypre_amg")
    solver.parameters['preconditioner']['structure'] = structure

    for i in range(M):
        solver.solve(A, solution.vector(), b)

import time
for structure in ('same', 'different_nonzero_pattern'):
    t1 = time.time()
    solve_poisson(400, 10, structure)
    print structure, round(time.time() - t1, 2)

---

See the mailing list for the follow up on this:
http://fenicsproject.org/pipermail/fenics/2015-March/002605.html

---

Thanks for the help.

I took some time because I was setting up a code to benchmark the different solvers. I attach just for curiosity (results for version 1.5).

For this benchmark I have tried several solvers (direct and iterative). What I realised is that if the solver is setup in the following way:

solver = dolfin.LUSolver(solver_name)
solver.set_operator(operator_matrix)
solver.solve(vector, right_hand_side)

Then all the reuse will be performed automatically and, as mentioned in the mailing list, once a new operator is set, the pre-processing will be done again for the new operator.

Once again thank you for your help!

---

Hi apalha,

Can you kindly take a look at my question and help me out please.

http://fenicsproject.org/qa/8548/error-during-implementation-of-krylovsolver?show=8553#a8553

Thanks a lot!

---

Hi Tormod Landet,

Can you kindly take a look at my question and help me out please.

http://fenicsproject.org/qa/8548/error-during-implementation-of-krylovsolver?show=8553#a8553

Thanks a lot!