def step(self):
"""
Take one time step
"""
ls = LSFactory()
self.p = ls.direct(self.lhs, self.rhs)
return self.p
def solve(self, max_direct=40000, callback=False, **kwargs):
""" Reassemble and solve linear system.
After the funtion has been called, the attributes lhs and rhs are
updated according to the parameter states. Also, the attribute x
gives the pressure given the current state.
TODO: Provide an option to save solver information if multiple
systems are to be solved with the same left hand side.
The function attempts to set up the best linear solver based on the
system size. The setup and parameter choices here are still
experimental.
Parameters:
max_direct (int): Maximum number of unknowns where a direct solver
is applied. If a direct solver can be applied this is usually
the most efficient option. However, if the system size is
too large compared to available memory, a direct solver becomes
extremely slow.
callback (boolean, optional): If True iteration information will be
output when an iterative solver is applied (system size larger
than max_direct)
Returns:
np.array: Pressure state.
"""
logger.error('Solve elliptic model')
# Discretize
tic = time.time()
logger.warning('Discretize')
self.lhs, self.rhs = self.reassemble()
logger.warning('Done. Elapsed time ' + str(time.time() - tic))
# Solve
tic = time.time()
ls = LSFactory()
if self.rhs.size < max_direct:
logger.warning('Solve linear system using direct solver')
self.x = ls.direct(self.lhs, self.rhs)
else:
logger.warning('Solve linear system using GMRES')
precond = self._setup_preconditioner()
# precond = ls.ilu(self.lhs)
slv = ls.gmres(self.lhs)
self.x, info = slv(self.rhs,
M=precond,
callback=callback,
maxiter=10000,
restart=1500,
tol=1e-8)
if info == 0:
logger.warning('GMRES succeeded.')
else:
logger.warning('GMRES failed with status ' + str(info))
logger.warning('Done. Elapsed time ' + str(time.time() - tic))
return self.x
def solve(self):
""" Discretize and solve linear system by a direct solver.
The saddle point structure of the dual discretization implies that
other block solvers are needed. TODO.
"""
ls = LSFactory()
self.x = ls.direct(*self.reassemble())
return self.x
def solve(self):
""" Discretize and solve linear system by a direct solver.
The saddle point structure of the dual discretization implies that
other block solvers are needed. TODO.
"""
ls = LSFactory()
lhs, rhs = self.reassemble()
import scipy.io as sps_io
sps_io.mmwrite("matrix.mtx", lhs)
self.x = ls.direct(lhs, rhs)
return self.x
def solve(self, max_direct=40000, callback=False, **kwargs):
"""
This is an adaption of the elliptic solver to the Schur complement
elimination. The only change can be found in the if self.el statement.
"""
# Discretize
tic = time.time()
logger.info("Discretize")
self.lhs, self.rhs = self.reassemble()
if self.el:
to_be_eliminated = SC.dofs_of_dimension(other.grid(), other.lhs,
eldim)
self.lhs, self.rhs, _, _, _ = SC.eliminate_dofs(
other.lhs, other.rhs, to_be_eliminated)
logger.info("Done. Elapsed time " + str(time.time() - tic))
# Solve
tic = time.time()
ls = LSFactory()
if self.rhs.size < max_direct:
logger.info("Solve linear system using direct solver")
self.x = ls.direct(self.lhs, self.rhs)
else:
logger.info("Solve linear system using GMRES")
precond = self._setup_preconditioner()
# precond = ls.ilu(self.lhs)
slv = ls.gmres(self.lhs)
self.x, info = slv(
self.rhs,
M=precond,
callback=callback,
maxiter=10000,
restart=1500,
tol=1e-8,
)
if info == 0:
logger.info("GMRES succeeded.")
else:
logger.error("GMRES failed with status " + str(info))
logger.info("Done. Elapsed time " + str(time.time() - tic))
return self.x
def _assign_solvers(self):
mat, ind = self._obtain_submatrix()
all_ind = np.arange(self.rhs.size)
not_ind = [np.setdiff1d(all_ind, i) for i in ind]
factory = LSFactory()
num_mat = len(mat)
solvers = np.empty(num_mat, dtype=np.object)
for i, A in enumerate(mat):
sz = A.shape[0]
if sz < 5000:
solvers[i] = factory.direct(A)
else:
# amg solver is pyamg is installed, if not ilu
try:
solvers[i] = factory.amg(A, as_precond=True)
except ImportError:
solvers[i] = factory.ilu(A)
return solvers, ind, not_ind
def solve(self,
max_direct=40000,
callback=False,
discretize=True,
**kwargs):
""" Reassemble and solve linear system.
After the funtion has been called, the attributes lhs and rhs are
updated according to the parameter states. Also, the attribute x
gives the pressure given the current state.
The function attempts to set up the best linear solver based on the
system size. The setup and parameter choices here are still
experimental.
Parameters:
max_direct (int): Maximum number of unknowns where a direct solver
is applied. If a direct solver can be applied this is usually
the most efficient option. However, if the system size is
too large compared to available memory, a direct solver becomes
extremely slow.
callback (boolean, optional): If True iteration information will be
output when an iterative solver is applied (system size larger
than max_direct)
Returns:
np.array: Pressure state.
"""
# Discretize
tic = time.time()
if discretize:
logger.info("Discretize")
self.lhs, self.rhs = self.reassemble(**kwargs)
self.is_factorized = False
logger.info("Done. Elapsed time " + str(time.time() - tic))
else:
self.rhs = self._stress_disc.rhs(self.grid(), self.data())
# Solve
tic = time.time()
ls = LSFactory()
if self.rhs.size < max_direct:
logger.info("Solve linear system using direct solver")
if not self.is_factorized:
logger.info("Making LU decomposition")
self.lhs = self.lhs.tocsc()
self.lhs = sps.linalg.factorized(self.lhs)
self.is_factorized = True
logger.info("Done. Elapsed time " + str(time.time() - tic))
logger.info("Solve linear system using direct solver")
tic = time.time()
self.x = self.lhs(self.rhs)
else:
logger.info("Solve linear system using GMRES")
precond = self._setup_preconditioner()
# precond = ls.ilu(self.lhs)
slv = ls.gmres(self.lhs)
self.x, info = slv(
self.rhs,
M=precond,
callback=callback,
maxiter=10000,
restart=1500,
tol=1e-8,
)
if info == 0:
logger.info("GMRES succeeded.")
else:
logger.error("GMRES failed with status " + str(info))
logger.info("Done. Elapsed time " + str(time.time() - tic))
return self.x