Demonstration of increasing KSP objects

petsc_garbage.py

from firedrake import *
from firedrake_adjoint import *
from firedrake.petsc import PETSc
from pyadjoint.tape import pause_annotation

mesh = UnitSquareMesh(10, 10)
x, y = SpatialCoordinate(mesh)
Q = FunctionSpace(mesh, "CG", 2)  
Y = TestFunction(Q)

with stop_annotating():
    final_state = Function(Q, name="final_state")
    final_state.interpolate(0.1 * exp(-0.5*(y-1.5)**2/0.1**2))

T_ic = Function(Q, name="T_IC")
T_ic.assign(0)
Told = Function(Q, name="OldTemperature")
Tnew = Function(Q, name="NewTemperature")
Ttheta = 0.5 * Tnew + 0.5 * Told

F_energy = (
    Y * (Tnew - Told) / Constant(1.0e-6) * dx
    + dot(grad(Y), Constant(1.0) * grad(Ttheta)) * dx
)

energy_problem = NonlinearVariationalProblem(F_energy, Tnew)
energy_solver = NonlinearVariationalSolver(energy_problem)

control = Control(T_ic)

Told.assign(T_ic)
Tnew.assign(Told)

for timestep in range(20):
    energy_solver.solve()
    Told.assign(Tnew)

objective = assemble(0.5*(Tnew - final_state)**2 * dx)
pause_annotation()
reduced_functional = ReducedFunctional(objective, control)

h = Function(Q)
from numpy.random import rand

for i in range(10):
    h.vector()[:] = rand(h.vector().local_size())*1e-1
    reduced_functional(T_ic._ad_add(h))
    reduced_functional.derivative()
    PETSc.garbage_view(comm=mesh.comm)