Just to make sure I'm getting the correct plots for the optimals
Hallo All
I want to have some graphs for the optimal control and the optimal solution for my problem. Thanks to the code
in https:/
here is my code
from dolfin import *
from dolfin_adjoint import *
# Setup
n = 40
mesh = UnitCircleMesh(n)
V = FunctionSpace(mesh, "CG", 1)
###W = FunctionSpace(mesh, "DG", degree = 0)
u = Function(
m = Function(V, name="Control")
v = TestFunction(V)
# Run the forward model once to create the simulation record
F = ( inner(grad(u), grad(v)) + u*v - m*v )*dx
###bc = DirichletBC(V, 0.0, "on_boundary")
solve(F == 0, u)
def max(x, y):
import ufl
x = triangle.x[0]
return ufl.conditional
# the alpha and gamma coefficients which appear in the cost functional
alpha=Constant(1.0)
gamma=Constant(
# The given u_0 , m_0 and b
x = triangle.x
u_0 = 4+1/pi -(1/(4*
m_0 = 4 +(1/(4*
b= (x[0]*x[
# The cost functional
J = Functional(( 0.5*inner(u-u_0, u-u_0) + alpha*0.
# Run the optimisation
reduced_functional = ReducedFunction
# Make sure you have scipy >= 0.11 installed
m_opt = minimize(
# desire solution u_0
proj_udes = project(u_0,V)
plot(u_0, mesh, interactive=True, title="u_0")
# Actual solution
solve(F == 0, u)
plot(u, interactive=True, title="Optimal State")
# L1 error
proj_error = project(u-u_0,V)
plot(proj_error, interactive=True, title="L1-Error")
# Optimal forcing
plot(m_opt, interactive=True, title="Optimal Control")
regardless of the problem or its parameters, I want to make sure if this code is really giving plots for the optimal control and optimal state.
I'm assuming if one wants to plot the optimal state , then one needs to slove a new bilinear form which has the optimal control.
Just I was testing the software on some problems with known solutions and I found a slight diferece.
so, I wanted to make sure if my code is really written in a way that gives the plots of the optimals.
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- Simon Funke
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