def form_fluid(
displacement_fluid,
velocity_fluid,
phi_fluid,
psi_fluid,
fluid: Space,
param: Parameters,
):
return (
param.NU * dot(grad(velocity_fluid), grad(phi_fluid)) * fluid.dx
+ dot(param.BETA, grad(velocity_fluid)) * phi_fluid * fluid.dx
+ dot(grad(displacement_fluid), grad(psi_fluid)) * fluid.dx
- dot(grad(displacement_fluid), fluid.normal_vector)
* psi_fluid
* fluid.ds(1)
- param.NU
* dot(grad(velocity_fluid), fluid.normal_vector)
* phi_fluid
* fluid.ds(1)
+ param.GAMMA
/ fluid.cell_size
* displacement_fluid
* psi_fluid
* fluid.ds(1)
+ param.GAMMA
/ fluid.cell_size
* velocity_fluid
* phi_fluid
* fluid.ds(1)
)
def form_fluid_adjoint(
displacement_fluid_adjoint,
velocity_fluid_adjoint,
xi_fluid,
eta_fluid,
fluid: Space,
param: Parameters,
):
return (
param.NU
* dot(grad(eta_fluid), grad(displacement_fluid_adjoint))
* fluid.dx
+ dot(param.BETA, grad(eta_fluid))
* displacement_fluid_adjoint
* fluid.dx
+ dot(grad(xi_fluid), grad(velocity_fluid_adjoint)) * fluid.dx
- dot(grad(xi_fluid), fluid.normal_vector)
* velocity_fluid_adjoint
* fluid.ds(1)
- param.NU
* dot(grad(eta_fluid), fluid.normal_vector)
* displacement_fluid_adjoint
* fluid.ds(1)
+ param.GAMMA
/ fluid.cell_size
* xi_fluid
* velocity_fluid_adjoint
* fluid.ds(1)
+ param.GAMMA
/ fluid.cell_size
* eta_fluid
* displacement_fluid_adjoint
* fluid.ds(1)
)
def functional_fluid(
displacement_fluid_old,
velocity_fluid_old,
displacement_fluid_interface,
velocity_fluid_interface,
displacement_fluid_old_interface,
velocity_fluid_old_interface,
phi_fluid,
psi_fluid,
fluid: Space,
param: Parameters,
time,
time_step,
):
return (
velocity_fluid_old * phi_fluid * fluid.dx
- 0.5
* time_step
* form_fluid(
displacement_fluid_old,
velocity_fluid_old,
phi_fluid,
psi_fluid,
fluid,
param,
)
+ 0.5
* time_step
* param.GAMMA
/ fluid.cell_size
* displacement_fluid_interface
* psi_fluid
* fluid.ds(1)
+ 0.5
* time_step
* param.GAMMA
/ fluid.cell_size
* velocity_fluid_interface
* phi_fluid
* fluid.ds(1)
+ 0.5
* time_step
* param.GAMMA
/ fluid.cell_size
* displacement_fluid_old_interface
* psi_fluid
* fluid.ds(1)
+ 0.5
* time_step
* param.GAMMA
/ fluid.cell_size
* velocity_fluid_old_interface
* phi_fluid
* fluid.ds(1)
+ time_step * external_force(time) * phi_fluid * fluid.dx
)
def nodesquare():
space = Space()
space.add_dimension("x")
space.add_dimension("y")
nodelist = []
for i in range(-1, 2):
for j in range(-1, 2):
nodelist.append(space.nodegen([i, j]))
for i in [0, 1, 2, 3, 4, 5, 6, 7, 8]:
nodelist[4].link(nodelist[i])
return nodelist
def functional_fluid_adjoint_initial(
displacement_fluid_adjoint_old,
velocity_fluid_adjoint_old,
displacement_fluid_adjoint_interface,
velocity_fluid_adjoint_interface,
displacement_fluid_adjoint_old_interface,
velocity_fluid_adjoint_old_interface,
xi_fluid,
eta_fluid,
fluid: Space,
param: Parameters,
time,
time_step,
microtimestep_before: MicroTimeStep,
microtimestep: MicroTimeStep,
):
return (
0.5
* time_step
* param.NU
* dot(grad(eta_fluid), fluid.normal_vector)
* displacement_fluid_adjoint_interface
* fluid.ds(1)
+ 2.0 * param.NU
* characteristic_function_fluid(param)
* dot(
goal_functional(
microtimestep_before, microtimestep, "primal_velocity"
)[1],
grad(eta_fluid),
)
* fluid.dx
)
def functional_solid_adjoint_initial(
displacement_solid_adjoint_old,
velocity_solid_adjoint_old,
displacement_solid_adjoint_interface,
velocity_solid_adjoint_interface,
displacement_solid_adjoint_old_interface,
velocity_solid_adjoint_old_interface,
xi_solid,
eta_solid,
solid: Space,
param: Parameters,
time,
time_step,
microtimestep_before: MicroTimeStep,
microtimestep: MicroTimeStep,
):
return (
0.5
* time_step
* param.GAMMA
/ solid.cell_size
* xi_solid
* velocity_solid_adjoint_interface
* solid.ds(1)
+ 0.5
* time_step
* param.GAMMA
/ solid.cell_size
* eta_solid
* displacement_solid_adjoint_interface
* solid.ds(1)
+ 2.0 * param.ZETA
* characteristic_function_solid(param)
* dot(
goal_functional(
microtimestep_before, microtimestep, "primal_displacement"
)[1],
grad(xi_solid),
)
* solid.dx
)
def functional_solid(
displacement_solid_old,
velocity_solid_old,
displacement_solid_interface,
velocity_solid_interface,
displacement_solid_old_interface,
velocity_solid_old_interface,
phi_solid,
psi_solid,
solid: Space,
param: Parameters,
time,
time_step,
):
return (
velocity_solid_old * phi_solid * solid.dx
+ displacement_solid_old * psi_solid * solid.dx
- 0.5
* time_step
* form_solid(
displacement_solid_old,
velocity_solid_old,
phi_solid,
psi_solid,
solid,
param,
)
- 0.5
* time_step
* param.NU
* dot(grad(velocity_solid_interface), solid.normal_vector)
* phi_solid
* solid.ds(1)
- 0.5
* time_step
* param.NU
* dot(grad(velocity_solid_old_interface), solid.normal_vector)
* phi_solid
* solid.ds(1)
)
def form_solid(
displacement_solid,
velocity_solid,
phi_solid,
psi_solid,
solid: Space,
param: Parameters,
):
return (
param.ZETA * dot(grad(displacement_solid), grad(phi_solid)) * solid.dx
+ param.DELTA * dot(grad(velocity_solid), grad(phi_solid)) * solid.dx
- velocity_solid * psi_solid * solid.dx
- param.DELTA
* dot(grad(velocity_solid), solid.normal_vector)
* phi_solid
* solid.ds(1)
)
def form_solid_adjoint(
displacement_solid_adjoint,
velocity_solid_adjoint,
xi_solid,
eta_solid,
solid: Space,
param: Parameters,
):
return (
param.ZETA
* dot(grad(xi_solid), grad(displacement_solid_adjoint))
* solid.dx
+ param.DELTA
* dot(grad(eta_solid), grad(displacement_solid_adjoint))
* solid.dx
- eta_solid * velocity_solid_adjoint * solid.dx
- param.DELTA
* dot(grad(eta_solid), solid.normal_vector)
* displacement_solid_adjoint
* solid.ds(1)
)
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
param.NUMBER_ELEMENTS_VERTICAL,
diagonal="right",
)
mesh_s = RectangleMesh(
Point(0.0, -1.0),
Point(4.0, 0.0),
param.NUMBER_ELEMENTS_HORIZONTAL,
param.NUMBER_ELEMENTS_VERTICAL,
diagonal="left",
)
boundary_mesh = BoundaryMesh(mesh_f, "exterior")
inner_boundary = Inner_boundary()
mesh_i = SubMesh(boundary_mesh, inner_boundary)
# Create function spaces
fluid = Space(mesh_f, param.LOCAL_MESH_SIZE_FLUID)
solid = Space(mesh_s, param.LOCAL_MESH_SIZE_SOLID)
interface = Space(mesh_i)
# Create time interval structures
fluid_timeline = TimeLine()
fluid_timeline.unify(
param.TIME_STEP, param.LOCAL_MESH_SIZE_FLUID, param.GLOBAL_MESH_SIZE
)
solid_timeline = TimeLine()
solid_timeline.unify(
param.TIME_STEP, param.LOCAL_MESH_SIZE_SOLID, param.GLOBAL_MESH_SIZE
)
# Set deoupling method
if param.RELAXATION: