def point_integral_step(self, model):
# Set-up forms
mesh = UnitSquareMesh(10, 10)
V = FunctionSpace(mesh, "CG", 1)
S = state_space(mesh, model.num_states())
Me = MixedElement((V.ufl_element(), S.ufl_element()))
VS = FunctionSpace(mesh, Me)
vs = Function(VS)
vs.assign(project(model.initial_conditions(), VS))
(v, s) = split(vs)
(w, r) = TestFunctions(VS)
rhs = inner(model.F(v, s), r) + inner(-model.I(v, s), w)
form = rhs * dP
# Set-up scheme
time = Constant(0.0)
scheme = BackwardEuler(form, vs, time)
scheme.t().assign(float(time))
# Create and step solver
solver = PointIntegralSolver(scheme)
solver.parameters["newton_solver"]["relative_tolerance"] = 1e-6
solver.parameters["newton_solver"]["report"] = False
dt = 0.1
solver.step(dt)
return vs
def ode_test_form(request):
Model = eval(request.param)
model = Model()
mesh = UnitSquareMesh(10, 10)
V = FunctionSpace(mesh, "CG", 1)
S = state_space(mesh, model.num_states())
Mx = MixedElement((V.ufl_element(), S.ufl_element()))
VS = FunctionSpace(mesh, Mx)
vs = Function(VS)
vs.assign(project(model.initial_conditions(), VS))
(v, s) = split(vs)
(w, r) = TestFunctions(VS)
rhs = inner(model.F(v, s), r) + inner(-model.I(v, s), w)
form = rhs * dP
return form
def __init__(self, mesh, time, model, I_s=None, params=None):
# Store input
self._mesh = mesh
self._time = time
self._model = model
# Extract some information from cell model
self._F = self._model.F
self._I_ion = self._model.I
self._num_states = self._model.num_states()
# Handle stimulus
self._I_s = handle_markerwise(I_s, GenericFunction)
# Initialize and update parameters if given
self.parameters = self.default_parameters()
if params is not None:
self.parameters.update(params)
# Create (mixed) function space for potential + states
v_family = self.parameters["V_polynomial_family"]
v_degree = self.parameters["V_polynomial_degree"]
s_family = self.parameters["S_polynomial_family"]
s_degree = self.parameters["S_polynomial_degree"]
if (v_family == s_family and s_degree == v_degree):
self.VS = VectorFunctionSpace(self._mesh,
v_family,
v_degree,
dim=self._num_states + 1)
else:
V = FunctionSpace(self._mesh, v_family, v_degree)
S = state_space(self._mesh, self._num_states, s_family, s_degree)
#Mx = MixedElement(V.ufl_element(), S.ufl_element())
#self.VS = FunctionSpace(self._mesh, Mx)
self.VS = MixedFunctionSpace(V, S)
# Initialize solution fields
self.vs_ = Function(self.VS, name="vs_")
self.vs = Function(self.VS, name="vs")