def Jhat(val):
cell_params[param_name].assign(val)
ics = Function(project(model.initial_conditions(), solver.VS),
name="ics")
self._run(solver, ics)
(vs_, vs) = solver.solution_fields()
return assemble(form(vs))
def main(N, dt, T, theta):
if dolfin_adjoint:
adj_reset()
# Create cardiac model
mesh = UnitSquareMesh(N, N)
time = Constant(0.0)
cell_model = NoCellModel()
ac_str = "cos(t)*cos(2*pi*x[0])*cos(2*pi*x[1]) + 4*pow(pi, 2)*cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)"
stimulus = Expression(ac_str, t=time, degree=3)
heart = CardiacModel(mesh, time, 1.0, 1.0, cell_model, stimulus=stimulus)
# Set-up solver
ps = BasicSplittingSolver.default_parameters()
ps["theta"] = theta
ps["BasicBidomainSolver"]["linear_variational_solver"][
"linear_solver"] = "direct"
solver = BasicSplittingSolver(heart, params=ps)
# Define exact solution (Note: v is returned at end of time
# interval(s), u is computed at somewhere in the time interval
# depending on theta)
v_exact = Expression("cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)", t=T, degree=3)
u_exact = Expression("-cos(2*pi*x[0])*cos(2*pi*x[1])*sin(t)/2.0",
t=T - (1 - theta) * dt,
degree=3)
# Define initial condition(s)
vs0 = Function(solver.VS)
(vs_, vs, vur) = solver.solution_fields()
vs_.assign(vs0)
# Solve
solutions = solver.solve((0, T), dt)
for (timestep, (vs_, vs, vur)) in solutions:
continue
# Compute errors
(v, s) = vs.split(deepcopy=True)
v_error = errornorm(v_exact, v, "L2", degree_rise=2)
(v, u, r) = vur.split(deepcopy=True)
u_error = errornorm(u_exact, u, "L2", degree_rise=2)
return (v_error, u_error, mesh.hmin(), dt, T)
def tlm_adj_setup_cellmodel_parameters(self, cell_model, Scheme):
mesh = UnitIntervalMesh(3)
Model = cell_model.__class__
# Initiate solver, with model and Scheme
cell_params = Model.default_parameters()
param_name = cellmodel_parameters_seeds[Model][0]
cell_params[param_name] = Constant(cell_params[param_name],
name=param_name)
model = Model(params=cell_params)
solver = self._setup_solver(model, Scheme, mesh)
info_green("Running forward %s with %s (setup)" % (model, Scheme))
ics = Function(project(model.initial_conditions(), solver.VS),
name="ics")
self._run(solver, ics)
# Define functional
(vs_, vs) = solver.solution_fields()
form = lambda w: inner(w, w) * dx
J = Functional(form(vs) * dt[FINISH_TIME])
# Compute value of functional with current ics
Jics = assemble(form(vs))
# Set-up runner
def Jhat(val):
cell_params[param_name].assign(val)
ics = Function(project(model.initial_conditions(), solver.VS),
name="ics")
self._run(solver, ics)
(vs_, vs) = solver.solution_fields()
return assemble(form(vs))
# Stop annotating
solver.parameters["enable_adjoint"] = False
m = ConstantControl(cell_params[param_name])
return J, Jhat, m, Jics