def sigma_e(u):
return lambda_ * ufl.nabla_div(u) * fenics.Identity(
2) + 2 * mu * epsilon(u)
def sigma_d(u):
return eta_b * ufl.nabla_div(u) * fenics.Identity(
2) + 2 * eta_s * epsilon(u)
def sigma(u):
return lmbda * nabla_div(u) * Identity(d) + 2 * mu * eps(u)
def xest_implement_2d_myosin(self):
#Parameters
total_time = 1.0
number_of_time_steps = 100
delta_t = total_time / number_of_time_steps
nx = ny = 100
domain_size = 1.0
lambda_ = 5.0
mu = 2.0
gamma = 1.0
eta_b = 0.0
eta_s = 1.0
k_b = 1.0
k_u = 1.0
# zeta_1 = -0.5
zeta_1 = 0.0
zeta_2 = 1.0
mu_a = 1.0
K_0 = 1.0
K_1 = 0.0
K_2 = 0.0
K_3 = 0.0
D = 0.25
alpha = 3
c = 0.1
# Sub domain for Periodic boundary condition
class PeriodicBoundary(fenics.SubDomain):
# Left boundary is "target domain" G
def inside(self, x, on_boundary):
# return True if on left or bottom boundary AND NOT on one of the two corners (0, 1) and (1, 0)
return bool(
(fenics.near(x[0], 0) or fenics.near(x[1], 0)) and
(not ((fenics.near(x[0], 0) and fenics.near(x[1], 1)) or
(fenics.near(x[0], 1) and fenics.near(x[1], 0))))
and on_boundary)
def map(self, x, y):
if fenics.near(x[0], 1) and fenics.near(x[1], 1):
y[0] = x[0] - 1.
y[1] = x[1] - 1.
elif fenics.near(x[0], 1):
y[0] = x[0] - 1.
y[1] = x[1]
else: # near(x[1], 1)
y[0] = x[0]
y[1] = x[1] - 1.
periodic_boundary_condition = PeriodicBoundary()
#Set up finite elements
mesh = fenics.RectangleMesh(fenics.Point(0, 0),
fenics.Point(domain_size, domain_size), nx,
ny)
vector_element = fenics.VectorElement('P', fenics.triangle, 2, dim=2)
single_element = fenics.FiniteElement('P', fenics.triangle, 2)
mixed_element = fenics.MixedElement(vector_element, single_element)
V = fenics.FunctionSpace(
mesh,
mixed_element,
constrained_domain=periodic_boundary_condition)
v, r = fenics.TestFunctions(V)
full_trial_function = fenics.Function(V)
u, rho = fenics.split(full_trial_function)
full_trial_function_n = fenics.Function(V)
u_n, rho_n = fenics.split(full_trial_function_n)
#Define non-linear weak formulation
def epsilon(u):
return 0.5 * (fenics.nabla_grad(u) + fenics.nabla_grad(u).T
) #return sym(nabla_grad(u))
def sigma_e(u):
return lambda_ * ufl.nabla_div(u) * fenics.Identity(
2) + 2 * mu * epsilon(u)
def sigma_d(u):
return eta_b * ufl.nabla_div(u) * fenics.Identity(
2) + 2 * eta_s * epsilon(u)
# def sigma_a(u,rho):
# return ( -zeta_1*rho/(1+zeta_2*rho)*mu_a*fenics.Identity(2)*(K_0+K_1*ufl.nabla_div(u)+
# K_2*ufl.nabla_div(u)*ufl.nabla_div(u)+K_3*ufl.nabla_div(u)*ufl.nabla_div(u)*ufl.nabla_div(u)))
def sigma_a(u, rho):
return -zeta_1 * rho / (
1 + zeta_2 * rho) * mu_a * fenics.Identity(2) * (K_0)
F = (gamma * fenics.dot(u, v) * fenics.dx -
gamma * fenics.dot(u_n, v) * fenics.dx +
fenics.inner(sigma_d(u), fenics.nabla_grad(v)) * fenics.dx -
fenics.inner(sigma_d(u_n), fenics.nabla_grad(v)) * fenics.dx -
delta_t *
fenics.inner(sigma_e(u) + sigma_a(u, rho), fenics.nabla_grad(v)) *
fenics.dx + rho * r * fenics.dx - rho_n * r * fenics.dx +
ufl.nabla_div(rho * u) * r * fenics.dx -
ufl.nabla_div(rho * u_n) * r * fenics.dx - D * delta_t *
fenics.dot(fenics.nabla_grad(rho), fenics.nabla_grad(r)) *
fenics.dx + delta_t *
(-k_u * rho * fenics.exp(alpha * ufl.nabla_div(u)) + k_b *
(1 - c * ufl.nabla_div(u))) * r * fenics.dx)
# F = ( gamma*fenics.dot(u,v)*fenics.dx - gamma*fenics.dot(u_n,v)*fenics.dx + fenics.inner(sigma_d(u),fenics.nabla_grad(v))*fenics.dx -
# fenics.inner(sigma_d(u_n),fenics.nabla_grad(v))*fenics.dx - delta_t*fenics.inner(sigma_e(u)+sigma_a(u,rho),fenics.nabla_grad(v))*fenics.dx
# +rho*r*fenics.dx-rho_n*r*fenics.dx + ufl.nabla_div(rho*u)*r*fenics.dx - ufl.nabla_div(rho*u_n)*r*fenics.dx -
# D*delta_t*fenics.dot(fenics.nabla_grad(rho),fenics.nabla_grad(r))*fenics.dx +delta_t*(-k_u*rho*fenics.exp(alpha*ufl.nabla_div(u))+k_b*(1-c*ufl.nabla_div(u))))
vtkfile_rho = fenics.File(
os.path.join(os.path.dirname(__file__), 'output', 'myosin_2d',
'solution_rho.pvd'))
vtkfile_u = fenics.File(
os.path.join(os.path.dirname(__file__), 'output', 'myosin_2d',
'solution_u.pvd'))
# rho_0 = fenics.Expression(((('0.0'),('0.0'),('0.0')),('sin(x[0])')), degree=1 )
# full_trial_function_n = fenics.project(rho_0, V)
time = 0.0
for time_index in range(number_of_time_steps):
# Update current time
time += delta_t
# Compute solution
fenics.solve(F == 0, full_trial_function)
# Save to file and plot solution
vis_u, vis_rho = full_trial_function.split()
vtkfile_rho << (vis_rho, time)
vtkfile_u << (vis_u, time)
full_trial_function_n.assign(full_trial_function)
def sigma1(u):
return lmbda * nabla_div(u) * Identity(d) + 2.0 * mu * eps1(u)
def sigma(u):
return lambda_*nabla_div(u)*Identity(d) + 2*mu*epsilon(u)
def sigma(u):
return lmbda * nabla_div(u) * Identity(2) + 2 * mu * epsilon(u)
def solve_Laplace(Sim_setup,Solver_type,Vertices_array,Domains,core,VTA_IFFT,output):
set_log_active(False) #turns off debugging info
Sim_setup.mesh.coordinates()
Sim_setup.mesh.init()
# to get conductivity (and permittivity if EQS formulation) mapped accrodingly to the subdomains. k_val_r is just a list of conductivities (S/mm!) in a specific order to scale the cond. tensor
kappa,k_val_r=get_dielectric_properties_from_subdomains(Sim_setup.mesh,Sim_setup.subdomains,Sim_setup.Laplace_eq,Domains.Float_contacts,Sim_setup.conductivities,Sim_setup.rel_permittivities,Sim_setup.sine_freq)
if int(Sim_setup.sine_freq)==int(Sim_setup.signal_freq):
file=File('/opt/Patient/Field_solutions/Conductivity_map_'+str(Sim_setup.signal_freq)+'Hz.pvd')
file<<kappa[0]
if Sim_setup.Laplace_eq == 'EQS':
file=File('/opt/Patient/Field_solutions/Permittivity_map_'+str(Sim_setup.signal_freq)+'Hz.pvd')
file<<kappa[1]
# to get tensor scaled by the conductivity map
if Sim_setup.anisotropy==1:
Cond_tensor=get_scaled_cond_tensor(Sim_setup.mesh,Sim_setup.subdomains,Sim_setup.sine_freq,Sim_setup.signal_freq,Sim_setup.unscaled_tensor,k_val_r)
else:
Cond_tensor=False #just to initialize
#In case of current-controlled stimulation, Dirichlet_bc or the whole potential distribution will be scaled afterwards (due to the system's linearity)
V_space,Dirichlet_bc,ground_index,facets=get_solution_space_and_Dirichlet_BC(Sim_setup.external_grounding,Sim_setup.c_c,Sim_setup.mesh,Sim_setup.subdomains,Sim_setup.boundaries,Sim_setup.element_order,Sim_setup.Laplace_eq,Domains.Contacts,Domains.fi)
#ground index refers to the ground in .med/.msh file
# to solve the Laplace equation div(kappa*grad(phi))=0 (variational form: a(u,v)=L(v))
phi_sol=define_variational_form_and_solve(V_space,Dirichlet_bc,kappa,Sim_setup.Laplace_eq,Cond_tensor,Solver_type)
if Sim_setup.Laplace_eq=='EQS':
(phi_r,phi_i)=phi_sol.split(deepcopy=True)
else:
phi_r=phi_sol
phi_i=Function(V_space)
phi_i.vector()[:] = 0.0
#save unscaled real solution for plotting
if int(Sim_setup.sine_freq)==int(Sim_setup.signal_freq):
file=File('/opt/Patient/Field_solutions/Phi_real_unscaled_'+str(Sim_setup.signal_freq)+'Hz.pvd')
file<<phi_r,Sim_setup.mesh
if Sim_setup.external_grounding==True:
file=File('/opt/Patient/Field_solutions/ground_facets'+str(Sim_setup.signal_freq)+'Hz.pvd')
file<<facets
print("DoFs on the mesh for "+Sim_setup.Laplace_eq+" : ", (max(V_space.dofmap().dofs())+1))
if Sim_setup.c_c==1 or Sim_setup.CPE_status==1: #we compute E-field, currents and impedances only for current-controlled or if CPE is used
J_ground=get_current(Sim_setup.mesh,facets,Sim_setup.boundaries,Sim_setup.element_order,Sim_setup.Laplace_eq,Domains.Contacts,kappa,Cond_tensor,phi_r,phi_i,ground_index)
#If EQS, J_ground is a complex number
#V_across=max(Domains.fi[:], key=abs) # voltage drop in the system
#V_across=abs(max(Domains.fi[:])-min(Domains.fi[:])) # voltage drop in the system
if Sim_setup.external_grounding==True and (Sim_setup.c_c==1 or len(Domains.fi)==1):
V_max=max(Domains.fi[:], key=abs)
V_min=0.0
elif -1*Domains.fi[0]==Domains.fi[1]: # V_across is needed only for 2 active contact systems
V_min=-1*abs(Domains.fi[0])
V_max=abs(Domains.fi[0])
else:
V_min=min(Domains.fi[:], key=abs)
V_max=max(Domains.fi[:], key=abs)
V_across=V_max-V_min # this can be negative
Z_tissue = V_across/J_ground # Tissue impedance
if int(Sim_setup.sine_freq)==int(Sim_setup.signal_freq):
print("Tissue impedance at the signal freq.: ",Z_tissue)
if Sim_setup.CPE_status==1: # in this case we need to estimate the voltage drop over the CPE and adjust the Derichlet BC accordingly
if len(Domains.fi)>2:
print("Currently, CPE can be used only for simulations with two contacts. Please, assign the rest to 'None'")
raise SystemExit
Dirichlet_bc_with_CPE,total_impedance=get_CPE_corrected_Dirichlet_BC(Sim_setup.external_grounding,facets,Sim_setup.boundaries,Sim_setup.CPE_param,Sim_setup.Laplace_eq,Sim_setup.sine_freq,Sim_setup.signal_freq,Domains.Contacts,Domains.fi,V_across,Z_tissue,V_space)
f=open('/opt/Patient/Field_solutions/Impedance'+str(core)+'.csv','ab')
np.savetxt(f, total_impedance, delimiter=" ")
f.close()
# to solve the Laplace equation for the adjusted Dirichlet
phi_sol_CPE=define_variational_form_and_solve(V_space,Dirichlet_bc_with_CPE,kappa,Sim_setup.Laplace_eq,Cond_tensor,Solver_type)
if Sim_setup.Laplace_eq=='EQS':
(phi_r_CPE,phi_i_CPE)=phi_sol_CPE.split(deepcopy=True)
else:
phi_r_CPE=phi_sol_CPE
phi_i_CPE=Function(V_space)
phi_i_CPE.vector()[:] = 0.0
J_ground_CPE=get_current(Sim_setup.mesh,facets,Sim_setup.boundaries,Sim_setup.element_order,Sim_setup.Laplace_eq,Domains.Contacts,kappa,Cond_tensor,phi_r_CPE,phi_i_CPE,ground_index)
# just resaving
phi_sol,phi_r,phi_i,J_ground=(phi_sol_CPE,phi_r_CPE,phi_i_CPE,J_ground_CPE)
# if Full_IFFT==1:
# Hdf=HDF5File(Sim_setup.mesh.mpi_comm(), "/opt/Patient/Field_solutions_functions/solution"+str(np.round(Sim_setup.sine_freq,6))+".h5", "w")
# Hdf.write(Sim_setup.mesh, "mesh")
# if Sim_setup.CPE_status!=1:
# Hdf.write(phi_sol, "solution_full")
# if Sim_setup.c_c==1:
# with open('/opt/Patient/Field_solutions_functions/current_scale'+str(np.round(Sim_setup.sine_freq,6))+'.file', 'wb') as f:
# pickle.dump(np.array([np.real(J_ground),np.imag(J_ground)]), f)
# Hdf.close()
#else:
if VTA_IFFT==1:
Sim_type='Astrom' # fixed for now
if Sim_type=='Astrom' or Sim_type=='Butson':
# Solve for rescaled
Dirichlet_bc_scaled=[]
for bc_i in range(len(Domains.Contacts)): #CPE estimation is valid only for one activa and one ground contact configuration
if Sim_setup.Laplace_eq == 'EQS':
if Domains.fi[bc_i]==0.0:
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(0), 0.0, Sim_setup.boundaries,Domains.Contacts[bc_i]))
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(1), 0.0, Sim_setup.boundaries,Domains.Contacts[bc_i]))
else:
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(0), np.real((Domains.fi[bc_i])/J_ground),Sim_setup.boundaries,Domains.Contacts[bc_i]))
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(1), np.imag((Domains.fi[bc_i])/J_ground),Sim_setup.boundaries,Domains.Contacts[bc_i]))
else:
if Domains.fi[bc_i]==0.0:
Dirichlet_bc_scaled.append(DirichletBC(V_space, 0.0, Sim_setup.boundaries,Domains.Contacts[bc_i]))
else:
Dirichlet_bc_scaled.append(DirichletBC(V_space, np.real((Domains.fi[bc_i])/J_ground),Sim_setup.boundaries,Domains.Contacts[bc_i]))
if Sim_setup.external_grounding==True:
if Sim_setup.Laplace_eq == 'EQS':
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(0),0.0,facets,1))
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(1),0.0,facets,1))
else:
Dirichlet_bc_scaled.append(DirichletBC(V_space,0.0,facets,1))
phi_sol_check=define_variational_form_and_solve(V_space,Dirichlet_bc_scaled,kappa,Sim_setup.Laplace_eq,Cond_tensor,Solver_type)
if Sim_setup.Laplace_eq=='EQS':
(phi_r_check,phi_i_check)=phi_sol_check.split(deepcopy=True)
else:
phi_r_check=phi_sol_check
phi_i_check=Function(V_space)
phi_i_check.vector()[:] = 0.0
J_ground,E_field_r,E_field_im=get_current(Sim_setup.mesh,facets,Sim_setup.boundaries,Sim_setup.element_order,Sim_setup.Laplace_eq,Domains.Contacts,kappa,Cond_tensor,phi_r_check,phi_i_check,ground_index,get_E_field=True)
if Sim_type=='Astrom':
W_amp=FunctionSpace(Sim_setup.mesh,'DG',Sim_setup.element_order-1)
w_amp = TestFunction(W_amp)
Pv_amp = TrialFunction(W_amp)
E_amp_real = Function(W_amp)
a_local = inner(w_amp, Pv_amp) * dx
L_local = inner(w_amp, sqrt(dot(E_field_r,E_field_r))) * dx
A_local, b_local = assemble_system(a_local, L_local, bcs=[])
local_solver = PETScKrylovSolver('bicgstab')
local_solver.solve(A_local,E_amp_real.vector(),b_local)
#E_amp_real.vector()[:]=E_amp_real.vector()
E_amp_imag = Function(W_amp)
a_local = inner(w_amp, Pv_amp) * dx
L_local = inner(w_amp, sqrt(dot(E_field_im,E_field_im))) * dx
A_local, b_local = assemble_system(a_local, L_local, bcs=[])
local_solver = PETScKrylovSolver('bicgstab')
local_solver.solve(A_local,E_amp_imag.vector(),b_local)
elif Sim_type=='Butson':
from ufl import nabla_div
W_amp=FunctionSpace(Sim_setup.mesh,'DG',Sim_setup.element_order-1)
w_amp = TestFunction(W_amp)
Pv_amp = TrialFunction(W_amp)
Second_deriv= Function(W_amp)
a_local = inner(w_amp, Pv_amp) * dx
L_local = inner(w_amp, nabla_div(E_field_r)) * dx
A_local, b_local = assemble_system(a_local, L_local, bcs=[])
local_solver = PETScKrylovSolver('bicgstab')
local_solver.solve(A_local,Second_deriv.vector(),b_local)
W_amp=FunctionSpace(Sim_setup.mesh,'DG',Sim_setup.element_order-1)
w_amp = TestFunction(W_amp)
Pv_amp = TrialFunction(W_amp)
Second_deriv_imag= Function(W_amp)
a_local = inner(w_amp, Pv_amp) * dx
L_local = inner(w_amp, nabla_div(E_field_im)) * dx
A_local, b_local = assemble_system(a_local, L_local, bcs=[])
local_solver = PETScKrylovSolver('bicgstab')
local_solver.solve(A_local,Second_deriv_imag.vector(),b_local)
Phi_ROI=np.zeros((Vertices_array.shape[0],5),float)
#VTA=0.0
for inx in range(Vertices_array.shape[0]):
pnt=Point(Vertices_array[inx,0],Vertices_array[inx,1],Vertices_array[inx,2])
if Sim_setup.mesh.bounding_box_tree().compute_first_entity_collision(pnt)<Sim_setup.mesh.num_cells()*100:
Phi_ROI[inx,0]=Vertices_array[inx,0]
Phi_ROI[inx,1]=Vertices_array[inx,1]
Phi_ROI[inx,2]=Vertices_array[inx,2]
#if Sim_setup.c_c==1:
if Sim_type=='Butson':
Phi_ROI[inx,3]=Second_deriv(pnt) # already scaled
Phi_ROI[inx,4]=Second_deriv_imag(pnt) # already scaled
elif Sim_type=='Astrom':
Phi_ROI[inx,3]=E_amp_real(pnt) # already scaled
Phi_ROI[inx,4]=E_amp_imag(pnt) # already scaled
#if Sim_setup.sine_freq==Sim_setup.signal_freq and abs(Phi_ROI[inx,3])>=0.3:
# VTA+=0.1**3
else: # we assign 0.0 here
Phi_ROI[inx,3]=0.0
Phi_ROI[inx,4]=0.0
#print("Couldn't probe the potential at the point ",Vertices_array[inx,0],Vertices_array[inx,1],Vertices_array[inx,2])
#print("check the neuron array, exiting....")
#raise SystemExit
fre_vector=[Sim_setup.sine_freq]*Phi_ROI.shape[0]
comb=np.vstack((Phi_ROI[:,0],Phi_ROI[:,1],Phi_ROI[:,2],Phi_ROI[:,3],Phi_ROI[:,4],fre_vector)).T
f = h5py.File('/opt/Patient/Field_solutions/sol_cor'+str(core)+'.h5','a')
f.create_dataset(str(Sim_setup.sine_freq), data=comb)
f.close()
if Sim_setup.c_c==1:
comb_Z=np.vstack((np.real(Z_tissue),np.imag(Z_tissue),Sim_setup.sine_freq)).T
f=open('/opt/Patient/Field_solutions/Impedance'+str(core)+'.csv','ab')
np.savetxt(f, comb_Z, delimiter=" ")
f.close()
# if Sim_setup.sine_freq==Sim_setup.signal_freq and Sim_setup.c_c==1: # re-solve with the scaled potential just to check (to match 1 A)
# Dirichlet_bc_scaled=[]
# for bc_i in range(len(Domains.Contacts)): #CPE estimation is valid only for one activa and one ground contact configuration
# if Sim_setup.Laplace_eq == 'EQS':
# if Domains.fi[bc_i]==0.0:
# Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(0), 0.0, Sim_setup.boundaries,Domains.Contacts[bc_i]))
# Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(1), 0.0, Sim_setup.boundaries,Domains.Contacts[bc_i]))
# else:
# Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(0), np.real((Domains.fi[bc_i])/J_ground),Sim_setup.boundaries,Domains.Contacts[bc_i]))
# Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(1), np.imag((Domains.fi[bc_i])/J_ground),Sim_setup.boundaries,Domains.Contacts[bc_i]))
# else:
# if Domains.fi[bc_i]==0.0:
# Dirichlet_bc_scaled.append(DirichletBC(V_space, 0.0, Sim_setup.boundaries,Domains.Contacts[bc_i]))
# else:
# Dirichlet_bc_scaled.append(DirichletBC(V_space, np.real((Domains.fi[bc_i])/J_ground),Sim_setup.boundaries,Domains.Contacts[bc_i]))
#
# phi_sol_check=define_variational_form_and_solve(V_space,Dirichlet_bc_scaled,kappa,Sim_setup.Laplace_eq,Cond_tensor,Solver_type)
#
# if Sim_setup.Laplace_eq=='EQS':
# (phi_r_check,phi_i_check)=phi_sol_check.split(deepcopy=True)
# else:
# phi_r_check=phi_sol_check
# phi_i_check=Function(V_space)
# phi_i_check.vector()[:] = 0.0
#J_ground=get_current(Sim_setup.mesh,Sim_setup.boundaries,Sim_setup.element_order,Sim_setup.Laplace_eq,Domains.Contacts,kappa,Cond_tensor,phi_r_check,phi_i_check,ground_index)
if Sim_setup.sine_freq==Sim_setup.signal_freq:
print("Current through the ground after normalizing to 1 A at the signal freq.: ",J_ground)
file=File('/opt/Patient/Field_solutions/'+str(Sim_setup.Laplace_eq)+str(Sim_setup.signal_freq)+'_phi_r_1A.pvd')
file<<phi_r_check
output.put(1)
else:
Phi_ROI=np.zeros((Vertices_array.shape[0],5),float)
for inx in range(Vertices_array.shape[0]):
pnt=Point(Vertices_array[inx,0],Vertices_array[inx,1],Vertices_array[inx,2])
if Sim_setup.mesh.bounding_box_tree().compute_first_entity_collision(pnt)<Sim_setup.mesh.num_cells()*100:
Phi_ROI[inx,0]=Vertices_array[inx,0]
Phi_ROI[inx,1]=Vertices_array[inx,1]
Phi_ROI[inx,2]=Vertices_array[inx,2]
if Sim_setup.c_c==1:
Phi_ROI[inx,3]=np.real((phi_r(pnt)+1j*phi_i(pnt))/J_ground) #*1A is left out here
Phi_ROI[inx,4]=np.imag((phi_r(pnt)+1j*phi_i(pnt))/J_ground) #*1A is left out here
else:
Phi_ROI[inx,3]=phi_r(pnt)
Phi_ROI[inx,4]=phi_i(pnt)
else:
print("Couldn't probe the potential at the point ",Vertices_array[inx,0],Vertices_array[inx,1],Vertices_array[inx,2])
print("check the neuron array, exiting....")
raise SystemExit
fre_vector=[Sim_setup.sine_freq]*Phi_ROI.shape[0]
comb=np.vstack((Phi_ROI[:,0],Phi_ROI[:,1],Phi_ROI[:,2],Phi_ROI[:,3],Phi_ROI[:,4],fre_vector)).T
f = h5py.File('/opt/Patient/Field_solutions/sol_cor'+str(core)+'.h5','a')
f.create_dataset(str(Sim_setup.sine_freq), data=comb)
f.close()
if Sim_setup.c_c==1:
comb_Z=np.vstack((np.real(Z_tissue),np.imag(Z_tissue),Sim_setup.sine_freq)).T
f=open('/opt/Patient/Field_solutions/Impedance'+str(core)+'.csv','ab')
np.savetxt(f, comb_Z, delimiter=" ")
f.close()
if Sim_setup.sine_freq==Sim_setup.signal_freq and Sim_setup.c_c==1: # re-solve with the scaled potential just to check (to match 1 A)
Dirichlet_bc_scaled=[]
for bc_i in range(len(Domains.Contacts)): #CPE estimation is valid only for one activa and one ground contact configuration
if Sim_setup.Laplace_eq == 'EQS':
if Domains.fi[bc_i]==0.0:
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(0), 0.0, Sim_setup.boundaries,Domains.Contacts[bc_i]))
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(1), 0.0, Sim_setup.boundaries,Domains.Contacts[bc_i]))
else:
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(0), np.real((Domains.fi[bc_i])/J_ground),Sim_setup.boundaries,Domains.Contacts[bc_i]))
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(1), np.imag((Domains.fi[bc_i])/J_ground),Sim_setup.boundaries,Domains.Contacts[bc_i]))
else:
if Domains.fi[bc_i]==0.0:
Dirichlet_bc_scaled.append(DirichletBC(V_space, 0.0, Sim_setup.boundaries,Domains.Contacts[bc_i]))
else:
Dirichlet_bc_scaled.append(DirichletBC(V_space, np.real((Domains.fi[bc_i])/J_ground),Sim_setup.boundaries,Domains.Contacts[bc_i]))
if Sim_setup.external_grounding==True:
if Sim_setup.Laplace_eq == 'EQS':
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(0),0.0,facets,1))
Dirichlet_bc_scaled.append(DirichletBC(V_space.sub(1),0.0,facets,1))
else:
Dirichlet_bc_scaled.append(DirichletBC(V_space,0.0,facets,1))
phi_sol_check=define_variational_form_and_solve(V_space,Dirichlet_bc_scaled,kappa,Sim_setup.Laplace_eq,Cond_tensor,Solver_type)
if Sim_setup.Laplace_eq=='EQS':
(phi_r_check,phi_i_check)=phi_sol_check.split(deepcopy=True)
else:
phi_r_check=phi_sol_check
phi_i_check=Function(V_space)
phi_i_check.vector()[:] = 0.0
J_ground=get_current(Sim_setup.mesh,facets,Sim_setup.boundaries,Sim_setup.element_order,Sim_setup.Laplace_eq,Domains.Contacts,kappa,Cond_tensor,phi_r_check,phi_i_check,ground_index)
print("Current through the ground after normalizing to 1 A at the signal freq.: ",J_ground)
file=File('/opt/Patient/Field_solutions/'+str(Sim_setup.Laplace_eq)+str(Sim_setup.signal_freq)+'_phi_r_1A.pvd')
file<<phi_r_check
output.put(1)
bc_R = DirichletBC(V, p_R, boundary_R)
bcs = [bc_L, bc_R]
# Defining variational problem
p = TrialFunction(V)
v = TestFunction(V)
d = 2
I = Identity(d)
x, y = SpatialCoordinate(mesh)
M = max_value(Constant(0.10), exp(-(10 * y - 1.0 * sin(10 * x) - 5.0)**2))
K = M * I
#K = Constant(1.0)
a = dot(K * grad(p), grad(v)) * dx
f1 = as_vector((-2 * x, 0))
f = nabla_div(dot(-K, f1))
L = inner(f, v) * dx
# Computing solutions
p = Function(V)
solve(a == L, p, bcs)
u_bar = -K * grad(p)
# Projecting the Velocity profile
W = VectorFunctionSpace(mesh, 'P', 1)
u_bar1 = project(u_bar, W)
# Evaluating difference between Numerical pressure, p and Exact pressure, p_e
p_e_f = interpolate(p_e, V)
diff_p = Function(V)
diff_p.vector()[:] = p.vector() - p_e_f.vector()