A FEniCS Tutorial - FEniCS Project

7.5 Using a Backend-Specific Solver
The linear algebra backend determines the specific data structures that are
used in the Matrix and Vector classes. For example, with the PETSc backend,
Matrix encapsulates a PETSc matrix storage structure, and Vector encapsulates
a PETSc vector storage structure. Sometimes one wants to perform operations
directly on (say) the underlying PETSc objects. These can be fetched
by
A_PETSc =
down_cast(A).mat() b_PETSc = down_cast(b).vec() U_PETSc =
down_cast(u.vector()).vec()
Here, u is a Function, A is a Matrix, and b is a Vector. The same syntax
applies if we want to fetch the underlying Epetra, uBLAS, or MTL4 matrices
and vectors.
Sometimes one wants to implement tailored solution algorithms, using special
features of the underlying numerical packages. Here is an example where we
create an ML preconditioned Conjugate Gradient solver by programming with
Trilinos-specific objects directly. Given a linear system AU = b, represented
by a Matrix object A, and two Vector objects U and b in a Python program,
the purpose is to set up a solver using the Aztec Conjugate Gradient method
fromTrilinos’Azteclibraryandcombinethatsolverwiththealgebraicmultigrid
preconditioner ML from the ML library in Trilinos. Since the various parts of
Trilinos are mirrored in Python through the PyTrilinos package, we can operate
directly on Trilinos-specific objects.
try:
from PyTrilinos import Epetra, AztecOO, TriUtils, ML
except:
print ’’’You Need to have PyTrilinos with’
Epetra, AztecOO, TriUtils and ML installed
for this demo to run’’’
exit()
from dolfin import *
if not has_la_backend(’Epetra’):
print ’Warning: Dolfin is not compiled with Trilinos’
exit()
parameters[’linear_algebra_backend’] = ’Epetra’
# create matrix A and vector b in the usual way
# u is a Function
# Fetch underlying Epetra objects
A_epetra = down_cast(A).mat()
b_epetra = down_cast(b).vec()
U_epetra = down_cast(u.vector()).vec()
# Sets up the parameters for ML using a python dictionary
ML_param = {"max levels" : 3,
"output" : 10,
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