def goal_functional_solid(
displacement_solid_array,
velocity_solid_array,
solid,
solid_timeline,
param,
):
global_result = 0.0
macrotimestep = solid_timeline.head
global_size = solid_timeline.size
m = 1
for n in range(global_size):
microtimestep = macrotimestep.head.after
local_size = macrotimestep.size - 1
for k in range(local_size):
print(f"Current contribution: {m}")
result = 0.0
time_step = microtimestep.before.dt
gauss_1, gauss_2 = gauss(microtimestep)
result += (
0.5 * time_step * param.ZETA *
characteristic_function_solid(param) * dot(
grad(
linear_extrapolation(displacement_solid_array, m,
gauss_1, microtimestep)),
grad(
linear_extrapolation(displacement_solid_array, m,
gauss_1, microtimestep)),
) * solid.dx)
result += (
0.5 * time_step * param.ZETA *
characteristic_function_solid(param) * dot(
grad(
linear_extrapolation(displacement_solid_array, m,
gauss_2, microtimestep)),
grad(
linear_extrapolation(displacement_solid_array, m,
gauss_2, microtimestep)),
) * solid.dx)
m += 1
microtimestep = microtimestep.after
global_result += assemble(result)
macrotimestep = macrotimestep.after
return global_result
def adjoint_residual_solid(
displacement_solid,
velocity_solid,
displacement_solid_adjoint,
velocity_solid_adjoint,
displacement_fluid_adjoint,
velocity_fluid_adjoint,
solid: Space,
solid_timeline: TimeLine,
param: Parameters,
):
residuals = []
left = True
macrotimestep = solid_timeline.head
glocal_size = solid_timeline.size
m = 1
for n in range(glocal_size):
microtimestep = macrotimestep.head.after
local_size = macrotimestep.size - 1
for k in range(local_size):
print(f"Current contribution: {m}")
lhs = 0.0
rhs = 0.0
time_step = microtimestep.before.dt
gauss_1, gauss_2 = gauss(microtimestep)
if left:
l = m
microtimestep_adjust = microtimestep
left = False
else:
l = m - 1
if microtimestep.before.before is None:
microtimestep_adjust = (
macrotimestep.microtimestep_before.after)
else:
microtimestep_adjust = microtimestep.before
left = True
lhs += (0.5 * time_step * (
(primal_derivative(velocity_solid, l, gauss_1,
microtimestep_adjust) -
(velocity_solid[m] - velocity_solid[m - 1]) / time_step) *
displacement_solid_adjoint[m]) * solid.dx)
lhs += (0.5 * time_step * (
(primal_derivative(velocity_solid, l, gauss_2,
microtimestep_adjust) -
(velocity_solid[m] - velocity_solid[m - 1]) / time_step) *
displacement_solid_adjoint[m]) * solid.dx)
lhs += (0.5 * time_step *
((primal_derivative(
displacement_solid,
l,
gauss_1,
microtimestep_adjust,
) - (displacement_solid[m] - displacement_solid[m - 1]) /
time_step) * velocity_solid_adjoint[m]) * solid.dx)
lhs += (0.5 * time_step *
((primal_derivative(
displacement_solid,
l,
gauss_2,
microtimestep_adjust,
) - (displacement_solid[m] - displacement_solid[m - 1]) /
time_step) * velocity_solid_adjoint[m]) * solid.dx)
lhs += (0.5 * time_step * form_solid_adjoint(
displacement_solid_adjoint[m],
velocity_solid_adjoint[m],
primal_reconstruction(displacement_solid, l, gauss_1,
microtimestep_adjust) -
linear_extrapolation(displacement_solid, m, gauss_1,
microtimestep),
primal_reconstruction(velocity_solid, l, gauss_1,
microtimestep_adjust) -
linear_extrapolation(velocity_solid, m, gauss_1,
microtimestep),
solid,
param,
))
lhs += (0.5 * time_step * form_solid_adjoint(
displacement_solid_adjoint[m],
velocity_solid_adjoint[m],
primal_reconstruction(displacement_solid, l, gauss_2,
microtimestep_adjust) -
linear_extrapolation(displacement_solid, m, gauss_2,
microtimestep),
primal_reconstruction(velocity_solid, l, gauss_2,
microtimestep_adjust) -
linear_extrapolation(velocity_solid, m, gauss_2,
microtimestep),
solid,
param,
))
lhs -= (0.5 * time_step * param.GAMMA / solid.cell_size *
(primal_reconstruction(displacement_solid, l, gauss_1,
microtimestep_adjust) -
linear_extrapolation(displacement_solid, m, gauss_1,
microtimestep)) *
velocity_fluid_adjoint[m] * solid.ds(1))
lhs -= (0.5 * time_step * param.GAMMA / solid.cell_size *
(primal_reconstruction(displacement_solid, l, gauss_2,
microtimestep_adjust) -
linear_extrapolation(displacement_solid, m, gauss_2,
microtimestep)) *
velocity_fluid_adjoint[m] * solid.ds(1))
lhs -= (0.5 * time_step * param.GAMMA / solid.cell_size *
(primal_reconstruction(velocity_solid, l, gauss_1,
microtimestep_adjust) -
linear_extrapolation(velocity_solid, m, gauss_1,
microtimestep)) *
displacement_fluid_adjoint[m] * solid.ds(1))
lhs -= (0.5 * time_step * param.GAMMA / solid.cell_size *
(primal_reconstruction(velocity_solid, l, gauss_2,
microtimestep_adjust) -
linear_extrapolation(velocity_solid, m, gauss_2,
microtimestep)) *
displacement_fluid_adjoint[m] * solid.ds(1))
rhs += (0.5 * time_step * 2.0 * param.ZETA *
characteristic_function_solid(param) * dot(
grad(
linear_extrapolation(displacement_solid, m,
gauss_1, microtimestep)),
grad(
primal_reconstruction(
displacement_solid,
l,
gauss_1,
microtimestep_adjust,
) - linear_extrapolation(displacement_solid, m,
gauss_1, microtimestep)),
) * solid.dx)
rhs += (0.5 * time_step * 2.0 * param.ZETA *
characteristic_function_solid(param) * dot(
grad(
linear_extrapolation(displacement_solid, m,
gauss_2, microtimestep)),
grad(
primal_reconstruction(
displacement_solid,
l,
gauss_2,
microtimestep_adjust,
) - linear_extrapolation(displacement_solid, m,
gauss_2, microtimestep)),
) * solid.dx)
m += 1
microtimestep = microtimestep.after
residuals.append(assemble(0.5 * rhs - 0.5 * lhs))
macrotimestep = macrotimestep.after
return residuals
def primal_residual_solid(
displacement_solid_array,
velocity_solid_array,
displacement_fluid_array,
velocity_fluid_array,
displacement_solid_adjoint_array,
velocity_solid_adjoint_array,
solid: Space,
solid_timeline: TimeLine,
param: Parameters,
):
residuals = []
macrotimestep = solid_timeline.head
global_size = solid_timeline.size
m = 1
for n in range(global_size):
microtimestep = macrotimestep.head.after
local_size = macrotimestep.size - 1
for k in range(local_size):
print(f"Current contribution: {m}")
lhs = 0.0
rhs = 0.0
time_step = microtimestep.before.dt
gauss_1, gauss_2 = gauss(microtimestep)
lhs += (0.5 * time_step *
((velocity_solid_array[m] - velocity_solid_array[m - 1]) /
time_step * (adjoint_reconstruction(
displacement_solid_adjoint_array,
m,
gauss_1,
microtimestep,
macrotimestep,
) - displacement_solid_adjoint_array[m])) * solid.dx)
lhs += (0.5 * time_step *
((velocity_solid_array[m] - velocity_solid_array[m - 1]) /
time_step * (adjoint_reconstruction(
displacement_solid_adjoint_array,
m,
gauss_2,
microtimestep,
macrotimestep,
) - displacement_solid_adjoint_array[m])) * solid.dx)
lhs += (0.5 * time_step *
((displacement_solid_array[m] -
displacement_solid_array[m - 1]) / time_step *
(adjoint_reconstruction(
velocity_solid_adjoint_array,
m,
gauss_1,
microtimestep,
macrotimestep,
) - velocity_solid_adjoint_array[m])) * solid.dx)
lhs += (0.5 * time_step *
((displacement_solid_array[m] -
displacement_solid_array[m - 1]) / time_step *
(adjoint_reconstruction(
velocity_solid_adjoint_array,
m,
gauss_2,
microtimestep,
macrotimestep,
) - velocity_solid_adjoint_array[m])) * solid.dx)
lhs += (0.5 * time_step * form_solid(
linear_extrapolation(displacement_solid_array, m, gauss_1,
microtimestep),
linear_extrapolation(velocity_solid_array, m, gauss_1,
microtimestep),
adjoint_reconstruction(
displacement_solid_adjoint_array,
m,
gauss_1,
microtimestep,
macrotimestep,
) - displacement_solid_adjoint_array[m],
adjoint_reconstruction(
velocity_solid_adjoint_array,
m,
gauss_1,
microtimestep,
macrotimestep,
) - velocity_solid_adjoint_array[m],
solid,
param,
))
lhs += (0.5 * time_step * form_solid(
linear_extrapolation(displacement_solid_array, m, gauss_2,
microtimestep),
linear_extrapolation(velocity_solid_array, m, gauss_2,
microtimestep),
adjoint_reconstruction(
displacement_solid_adjoint_array,
m,
gauss_2,
microtimestep,
macrotimestep,
) - displacement_solid_adjoint_array[m],
adjoint_reconstruction(
velocity_solid_adjoint_array,
m,
gauss_2,
microtimestep,
macrotimestep,
) - velocity_solid_adjoint_array[m],
solid,
param,
))
lhs += (0.5 * time_step * param.NU * dot(
grad(
linear_extrapolation(velocity_fluid_array, m, gauss_1,
microtimestep)),
solid.normal_vector,
) * (adjoint_reconstruction(
displacement_solid_adjoint_array,
m,
gauss_1,
microtimestep,
macrotimestep,
) - displacement_solid_adjoint_array[m]) * solid.ds(1))
lhs += (0.5 * time_step * param.NU * dot(
grad(
linear_extrapolation(velocity_fluid_array, m, gauss_2,
microtimestep)),
solid.normal_vector,
) * (adjoint_reconstruction(
displacement_solid_adjoint_array,
m,
gauss_2,
microtimestep,
macrotimestep,
) - displacement_solid_adjoint_array[m]) * solid.ds(1))
m += 1
microtimestep = microtimestep.after
residuals.append(assemble(0.5 * rhs - 0.5 * lhs))
macrotimestep = macrotimestep.after
return residuals