def diagnostic_solve(self, u0, h, s, dirichlet_ids, tol=1e-6, **kwargs):
r"""Solve for the ice velocity from the thickness and surface
elevation
Parameters
----------
u0 : firedrake.Function
Initial guess for the ice velocity; the Dirichlet boundaries
are taken from `u0`
h : firedrake.Function
Ice thickness
s : firedrake.Function
Ice surface elevation
dirichlet_ids : list of int
list of integer IDs denoting the parts of the boundary where
Dirichlet boundary conditions should be applied
tol : float
dimensionless tolerance for when to terminate Newton's method
Returns
-------
u : firedrake.Function
Ice velocity
Other parameters
----------------
**kwargs
All other keyword arguments will be passed on to the
`viscosity`, `friction`, `gravity`, and `terminus` functions
that were set when this model object was initialized
"""
u = u0.copy(deepcopy=True)
boundary_ids = u.ufl_domain().exterior_facets.unique_markers
side_wall_ids = kwargs.get('side_wall_ids', [])
kwargs['side_wall_ids'] = side_wall_ids
kwargs['ice_front_ids'] = list(
set(boundary_ids) - set(dirichlet_ids) - set(side_wall_ids))
bcs = firedrake.DirichletBC(u.function_space(),
firedrake.as_vector((0, 0)), dirichlet_ids)
params = {'quadrature_degree': self.quadrature_degree(u, h, **kwargs)}
action = self.action(u=u, h=h, s=s, **kwargs)
scale = self.scale(u=u, h=h, s=s, **kwargs)
problem = MinimizationProblem(action, scale, u, bcs, params)
solver = NewtonSolver(problem, tol)
solver.solve()
return u
class IcepackSolver:
def __init__(self,
model,
fields,
solver_parameters,
dirichlet_ids=[],
side_wall_ids=[]):
r"""Diagnostic solver implementation using hand-written Newton line
search optimization algorithm"""
self._model = model
self._fields = fields
self._solver_parameters = solver_parameters.copy()
self._tolerance = self._solver_parameters.pop('tolerance', 1e-12)
self._max_iterations = self._solver_parameters.pop(
'max_iterations', 50)
self._dirichlet_ids = dirichlet_ids
self._side_wall_ids = side_wall_ids
def setup(self, **kwargs):
for name, field in kwargs.items():
if name in self._fields.keys():
self._fields[name].assign(field)
else:
if isinstance(field, firedrake.Constant):
self._fields[name] = firedrake.Constant(field)
elif isinstance(field, firedrake.Function):
self._fields[name] = field.copy(deepcopy=True)
else:
raise TypeError(
'Input fields must be Constant or Function!')
# Create homogeneous BCs for the Dirichlet part of the boundary
u = self._fields.get('velocity', self._fields.get('u'))
V = u.function_space()
# NOTE: This will have to change when we do Stokes!
bcs = firedrake.DirichletBC(V, Constant((0, 0)), self._dirichlet_ids)
if not self._dirichlet_ids:
bcs = None
# Find the numeric IDs for the ice front
boundary_ids = u.ufl_domain().exterior_facets.unique_markers
ice_front_ids_comp = set(self._dirichlet_ids + self._side_wall_ids)
ice_front_ids = list(set(boundary_ids) - ice_front_ids_comp)
# Create the action and scale functionals
_kwargs = {
'side_wall_ids': self._side_wall_ids,
'ice_front_ids': ice_front_ids
}
action = self._model.action(**self._fields, **_kwargs)
scale = self._model.scale(**self._fields, **_kwargs)
# Set up a minimization problem and solver
quadrature_degree = self._model.quadrature_degree(**self._fields)
params = {'quadrature_degree': quadrature_degree}
problem = MinimizationProblem(action, scale, u, bcs, params)
self._solver = NewtonSolver(problem,
self._tolerance,
solver_parameters=self._solver_parameters,
max_iterations=self._max_iterations)
def solve(self, **kwargs):
r"""Solve the diagnostic model physics for the ice velocity"""
if not hasattr(self, '_solver'):
self.setup(**kwargs)
else:
for name, field in kwargs.items():
self._fields[name].assign(field)
# Solve the minimization problem and return the velocity field
self._solver.solve()
u = self._fields.get('velocity', self._fields.get('u'))
return u.copy(deepcopy=True)