def dJhat(turbine_density):
farm = Farm(domain, turbine, function_space=V, site_ids=1)
farm.turbine_density.assign(turbine_density)
prob_params.tidal_farm = farm
problem = SteadySWProblem(prob_params)
sol_params = CoupledSWSolver.default_parameters()
sol_params.dump_period = 1
solver = CoupledSWSolver(problem, sol_params)
functional = PowerFunctional(problem)
control = Control(farm.turbine_density)
rf = FenicsReducedFunctional(functional, control, solver)
return rf.derivative()
def moola_problem():
adj_reset()
mesh = UnitSquareMesh(256, 256)
V = FunctionSpace(mesh, "CG", 1)
f = interpolate(Constant(1), V)
u = Function(V)
phi = TestFunction(V)
F = inner(grad(u), grad(phi)) * dx - f * phi * dx
bc = DirichletBC(V, Constant(0), "on_boundary")
solve(F == 0, u, bc)
J = Functional(inner(u, u) * dx)
m = Control(f)
rf = ReducedFunctional(J, m)
obj = rf.moola_problem().obj
pf = moola.DolfinPrimalVector(f)
return obj, pf
args.turbines, args.optimize, args.withcuts, args.cost)
sol_params.cache_forward_state = False
solver = CoupledSWSolver(problem, sol_params)
# Define the functional
#if args.withcuts:
# power_functional = PowerFunctional(problem, cut_in_speed=1.0, cut_out_speed=3.)
#else:
# power_functional = PowerFunctional(problem)
#cost_functional = args.cost * CostFunctional(problem)
#functional = power_functional - cost_functional
functional = PowerFunctional(problem)
# Define the control
control = Control(farm.friction_function)
rf = FenicsReducedFunctional(functional, control, solver)
# define optimization problem (link to optizelle)
opt_problem = MaximizationProblem(
rf, bounds=(0., model_turbine.maximum_smeared_friction))
parameters = {
"maximum_iterations": 100,
"optizelle_parameters": {
"msg_level": 10,
"algorithm_class": Optizelle.AlgorithmClass.TrustRegion,
"H_type": Optizelle.Operators.BFGS,
"dir": Optizelle.LineSearchDirection.BFGS,
"ipm": Optizelle.InteriorPointMethod.LogBarrier,
"sigma": 0.5,
problem = SteadySWProblem(prob_params)
sol_params = CoupledSWSolver.default_parameters()
sol_params.dump_period = 1
solver = CoupledSWSolver(problem, sol_params)
functional = PowerFunctional(problem)
control = Control(farm.turbine_density)
rf = FenicsReducedFunctional(functional, control, solver)
return rf.derivative()
# Friction function 1
turbine_density = Constant(0.1)
# Friction function 2
turbine_density = interpolate(
Expression("1e-05*(1 + x[0]*x[0] + 2*x[1]*x[1])"), V)
# Fricyion function 3
turbine_density = interpolate(
Expression("1e-02*(sin(2*pi*x[0]) - cos(2*pi*x[1]))"), V)
# Set control to turbine density
farm = Farm(domain, turbine, function_space=V, site_ids=1)
farm.turbine_density.assign(turbine_density)
control = Control(farm.turbine_density)
# Compute reduced funtional and its derivative
J_dens = Jhat(turbine_density)
dJ_dens = dJhat(turbine_density)
# Compute convergence rates using imported method from dolfin_adjoint
conv_rate = taylor_test(Jhat, control, J_dens, dJ_dens)