def compute(prms):
''' Pennes equattion solver
author: Felipe Galarce
email: [email protected]
'''
from functions.inout import readmesh
import os.path
import numpy as np
import time
import sys
dim = 1
non_linear = 1
k = 0.5
cb = 3900
wb = 1.159
Qm = 1091
Ta = 37
if prms['options']['dim'] == 2:
results_dir = prms['io']['results']
mesh_file = './meshes/' + prms['io']['mesh'] + '.h5'
mesh, subdomains, boundaries = readmesh(mesh_file)
# Characterize boundaries
ds = Measure('ds', domain=mesh , subdomain_data=boundaries)
else:
mesh = IntervalMesh(10, 0, 4)
V = FunctionSpace(mesh, "CG", 1)
# variational form
u, v = TrialFunction(V), TestFunction(V)
T = Function(V)
a = inner(k*grad(u), grad(v))*dx - cb*wb*inner(u, v)*dx
L = inner(Qm, v)*dx - cb*wb*inner(Ta, v)*dx
if prms['options']['dim'] == 2:
bc = DirichletBC(V, 40.0, boundaries, 1)
else:
bc = DirichletBC(V, 40.0, 'on_boundary')
solve(a == L, T, bc,
solver_parameters={"linear_solver": "mumps"},
form_compiler_parameters={"optimize": True})
plot(T)
interactive()
def compute(prms):
''' Stokes stationary flow equation solver
author: Felipe Galarce
email: [email protected]
'''
from functions.inout import readmesh
# Extract parameters
mesh_file = prms['io']['mesh']
results_dir = prms['io']['results']
sol,prec = prms['num']['krylov']
mu = prms['phys']['mu']
g_inx = prms['phys']['g_inx']
# Mesh partitioner for parallel distributed systems
#parameters['mesh_partitioner'] = 'ParMETIS' # default: SCOTCH
if prms['num']['dry'] == True:
# perform DRY RUN (e.g. if FFC fails on cluster)
# disable time stepping and vtk output of initial condition
T = -1
prms['io']['vtk'] = 0
print("--> PERFORMING DRY RUN")
# Read mesh, boundaries and subdomains
mesh, boundaries, subdomains = readmesh(mesh_file)
# Define function spaces
P1 = VectorFunctionSpace(mesh, "Lagrange", 1)
B = VectorFunctionSpace(mesh, "Bubble", 4)
V = P1 + B
Q = FunctionSpace(mesh, "CG", 1)
Mini = V*Q
# DC condition over artery walls ("adhesion > cohesion")
noslip = project(Constant((0, 0, 0)), V)
bc = DirichletBC(Mini.sub(0), noslip, subdomains, 2)
# Mark UFL variable with boundaries
ds = Measure('ds', domain=mesh , subdomain_data=subdomains)
# Define variational problem
(u, p) = TrialFunctions(Mini)
(v, q) = TestFunctions(Mini)
f = Constant((0, 0, 0))
a = (mu*inner(grad(u), grad(v)) - div(v)*p + q*div(u))*dx
L = inner(f, v)*dx + inner(Constant((0,g_inx,0)), v)*ds(1)
# Compute solution
w = Function(Mini)
rank = mesh.mpi_comm().Get_rank()
if prec == 'none':
solve(a == L, w, bc, solver_parameters={'linear_solver': sol})
else:
solve(a == L, w, bc, solver_parameters={'linear_solver': sol, 'preconditioner': prec})
# Split the mixed solution using a shallow copy
(u, p) = w.split()
if prms['io']['vtk'] == 1:
ufile_pvd = File(results_dir + "/velocity.pvd")
ufile_pvd << u
pfile_pvd = File(results_dir + "/pressure.pvd")
pfile_pvd << p
def compute(prms):
''' Pennes equattion solver
author: Felipe Galarce
email: [email protected]
'''
from functions.inout import readmesh
import os.path
import numpy as np
import time
import sys
# Extract parameters
mesh_file = './meshes/' + prms['io']['mesh'] + '.h5'
results_dir = prms['io']['results']
dt = float(prms['num']['dt'])
T = float(prms['num']['T'])
# # Parameters for Penne's equation
# rho = float(prms['phys']['rho'])
# rhob = float(prms['phys']['rhob'])
# c = float(prms['phys']['c'])
# cb = float(prms['phys']['cb'])
# k_tissue = float(prms['phys']['k_tissue'])
# k_blood = float(prms['phys']['k_blood'])
# Ta = float(prms['phys']['Ta'])
Tc_min = float(prms['phys']['Tc_min'])
Tc_max = float(prms['phys']['Tc_max'])
# wb = float(prms['phys']['wb'])
# Tf = float(prms['phys']['Tf'])
# hf = float(prms['phys']['hf'])
#
# Qm_mode = prms['phys']['Qm_mode']
# w_mode = prms['phys']['w_mode']
Tmax = prms['phys']['Tmax']
Tcr = prms['phys']['Tcr']
wb00 = prms['phys']['wb00']
wmax = prms['phys']['wmax']
# if Qm_mode == 'constant':
## Q_meta = float(33800)
# Configuring form compiler
# parameters["form_compiler"]["quadrature_degree"] = 6
parameters["form_compiler"]["optimize"] = True
parameters["form_compiler"]["representation"] = 'quadrature'
## Read mesh, boundaries and subdomains, but first check if the mesh file exists
if not os.path.isfile(mesh_file):
import subprocess
subprocess.call("cp ./meshes/" + prms['io']['mesh'] + ".geo ./", shell=True)
subprocess.call("cp ./functions/xml2hdf5.py ./", shell=True)
subprocess.call("gmsh -2 " + prms['io']['mesh'] + ".geo", shell=True)
subprocess.call("dolfin-convert ./" + prms['io']['mesh'] + ".msh ./" + prms['io']['mesh'] + ".xml ", shell=True)
subprocess.call("python xml2hdf5.py " + prms['io']['mesh'] + ".xml ", shell=True)
subprocess.call("cp " + prms['io']['mesh'] + ".h5 ./meshes/", shell=True)
subprocess.call("rm ./" + prms['io']['mesh'] + ".msh ./" + prms['io']['mesh'] + ".h5 ./" + prms['io']['mesh'] + ".xml ./" + prms['io']['mesh'] + "tissue_box_facet_region.xml " + prms['io']['mesh'] + "_physical_region.xml", shell=True)
mesh, subdomains, boundaries = readmesh(mesh_file)
# Characterize boundaries
ds = Measure('ds', domain=mesh , subdomain_data=boundaries)
# variational form
V = FunctionSpace(mesh, "CG", 1)
phi, v = TrialFunction(V), TestFunction(V)
phi0, phit = interpolate(Constant(prms['phys']['T_inicial']), V), Function(V)
plot(mesh)
interactive()
k = 0.5
cb = 3900
wb = Function(V)
Qm = Function(V)
Ta = 37
k_blood = 0.5
k_tissue = 0.5
rho = 1060
a = rho*cb/dt*inner(phi, v)*dx + inner(k_blood*grad(phi), grad(v))*dx(0) + inner(k_tissue*grad(phi), grad(v))*dx(1)
L = rho*cb/dt*inner(phi0, v)*dx - inner(wb*cb*(Ta), v)*dx - inner(Qm, v)*dx + cb*inner(wb*phi0, v)*dx
# Assemble LHS
A = assemble(a)
# boundary condition
avg_temp = (Tc_max + Tc_min)/2; Amp = (Tc_max - Tc_min)/2
T_boundary = Expression(str(avg_temp) + ' + ' + str(Amp) + '*sin(t/4)' , t = 0)
def HS(x): # Heavy-Side function
return (x > 0).astype(float)
bc = DirichletBC(V, T_boundary, boundaries, 1)
solver = LinearSolver('mumps')
phi_file = File(results_dir + "/temperature.pvd")
rank = mesh.mpi_comm().Get_rank()
t = dt
def Qm_exp(T):
T_arr = T.vector().array()
exponente = (T_arr- 37)/10
dos = 2*np.ones(len(T_arr))
Q = 0.17*np.power(dos, exponente)
# Q = 0.1178*(T_arr - 37) + 0.17
return Q
# mesh dimension and dofmap
gdim = mesh.geometry().dim()
dofmap = V.dofmap(); dofs = dofmap.dofs()
def Wb_(T):
T_arr = T.vector().array();
wb.vector()[:] = wb00*HS(Tcr - T_arr) + (wmax + wb00)/2*HS(T_arr - Tmax) + wmax*(1 + ((wmax - wb00)/wb00)*((T_arr - Tcr)/(Tmax - Tcr)))*(1 - HS(T_arr - Tmax) - HS(Tcr - T_arr))
return wb
start_time = time.time()
while t <= T + dt:
progress = float(t)/float(T + dt)*100.0; time_elapsed = time.time() - start_time
print '\r --> %.2f [ms] | %.0f %% | computing-time-elapsed = %.2f [seg] ' % (t, progress, time_elapsed),
sys.stdout.flush()
# --> SOLVING PENNE'S EQUATION
# assemble RHS
wb = Wb_(phi0)
Qm.vector()[:] = Qm_exp(phi0)
b = assemble(L)
# apply Dirichlet boundary conditions
T_boundary.t = t;
bc.apply(A, b)
# solve linear system
solve(A, phit.vector(), b)
# save solution to file
phi_file << phi0
phi0.assign(phit)
t += dt
def compute(prms):
''' monodomain+minimal equation solver
author: Felipe Galarce
email: [email protected]
'''
from functions.inout import readmesh
# Extract parameters
results_dir = prms['io']['results']
dt = prms['num']['dt']
sol_method, prec, solh_method, prech = prms['num']['krylov']
deg = prms['num']['deg']
n = prms['num']['n']
part = prms['phys']['part']
est1_intensity, est1_delay, est1_duration = prms['phys']['est1']
est2_intensity, est2_delay, est2_duration = prms['phys']['est2']
phi_i, r_i, w_i, s_i = prms['phys']['initial_conditions']
T = prms['phys']['T']
sigma_1 = prms['phys']['sigma_1']
betha = prms['phys']['betha']; gamma = prms['phys']['gamma']
amount_fibrosis = prms['phys']['amount_fibrosis']
e1x, e1y = prms['phys']['lamination_direction_main']
e2x, e2y = prms['phys']['lamination_direction_cross']
e1 = Constant((e1x, e1y));
e2 = Constant((e2x, e2y));
b, h = prms['phys']['b'], prms['phys']['h']
# TODO: erase only error and benchmark before simulation if exist previously
if prms['io']['xdmf'] == 1: # TODO: output function
sol = File(results_dir+"/sol.xdmf")
solh = File(results_dir+"/solh.xdmf")
error = open(results_dir + "/error_L2", 'w+')
benchmark = open(results_dir + "/benchmark", 'w+')
# Import minimal model parameters
if part == 'endo':
mat = sio.loadmat('./input/minimal_parameters_endo.mat')
elif part == 'epi':
mat = sio.loadmat('./input/minimal_parameters_epi.mat')
else:
mat = sio.loadmat('./input/minimal_parameters_mid.mat')
p1_phi0 = float(mat['p1_phi0'][0,0])
p2_phiu = float(mat['p2_phiu'][0,0])
p3_thetav = float(mat['p3_thetav'][0,0])
p4_thetaw = float(mat['p4_thetaw'][0,0])
p5_thetav_minus = float(mat['p5_thetav_minus'][0,0])
p6_theta_0 = float(mat['p6_theta_0'][0,0])
p7_tauv1_minus = float(mat['p7_tauv1_minus'][0,0])
p8_tauv2_minus = float(mat['p8_tauv2_minus'][0,0])
p9_tauv_plus = float(mat['p9_tauv_plus'][0,0])
p10_tauw1_minus = float(mat['p10_tauw1_minus'][0,0])
p11_tauw2_minus = float(mat['p11_tauw2_minus'][0,0])
p12_kw_minus = float(mat['p12_kw_minus'][0,0])
p13_phiw_minus = float(mat['p13_phiw_minus'][0,0])
p14_tau_w_plus = float(mat['p14_tau_w_plus'][0,0])
p15_tau_fi = float(mat['p15_tau_fi'][0,0])
p16_tau_o1 = float(mat['p16_tau_o1'][0,0])
p17_tau_o2 = float(mat['p17_tau_o2'][0,0])
p18_tau_so1 = float(mat['p18_tau_so1'][0,0])
p19_tau_so2 = float(mat['p19_tau_so2'][0,0])
p20_k_so = float(mat['p20_k_so'][0,0])
p21_phi_so = float(mat['p21_phi_so'][0,0])
p22_tau_s1 = float(mat['p22_tau_s1'][0,0])
p23_tau_s2 = float(mat['p23_tau_s2'][0,0])
p24_ks = float(mat['p24_ks'][0,0])
p25_phi_s = float(mat['p25_phi_s'][0,0])
p26_tau_si = float(mat['p26_tau_si'][0,0])
p27_tauw_inf = float(mat['p27_tauw_inf'][0,0])
p28_w_inf = float(mat['p28_w_inf'][0,0])
# Mesh partitioner for parallel distributed systems
# TODO: enable PARMETIS (preguntar a david!)
#parameters['mesh_partitioner'] = 'ParMETIS' # default: SCOTCH
# NOTE: parmetis was optimized on the NLHPC cluster
if prms['num']['dry'] == True:
# perform DRY RUN (e.g. if FFC fails on cluster)
# disable time stepping and vtk output of initial condition
T = -1
prms['io']['vtk'] = 0
print("PERFORMING DRY RUN")
def HS(x): # Heavy-Side function
return (x > 0).astype(float)
class DiscontinuousTensor(Expression):# Class with methods to assign tensors to its respective materials
def __init__(self, cell_function, tensors):
self.cell_function = cell_function
self.coeffs = tensors
def value_shape(self):
return (2,2)
def eval_cell(self, values, x, cell):
subdomain_id = self.cell_function[cell.index]
local_coeff = self.coeffs[subdomain_id]
local_coeff.eval_cell(values, x, cell)
# Class with subdomains to mark borders of the domain
class Left(SubDomain):
def inside(self, x, on_boundary):
return near(x[0], 0.0)
class Right(SubDomain):
def inside(self, x, on_boundary):
return near(x[0], b)
class Bottom(SubDomain):
def inside(self, x, on_boundary):
return near(x[1], 0.0)
class Top(SubDomain):
def inside(self, x, on_boundary):
return near(x[1], h)
# Read mesh, boundaries and subdomains
mesh, boundaries, subdomains = readmesh('./meshes/' + amount_fibrosis + '/mesh.h5')
# mesh for homogenized problem TODO: deducir b y h desde malla exacta para quitarlos de archivo input
mesh_h = RectangleMesh(Point(0.0, 0.0), Point(b, h), n, n, "crossed")
if amount_fibrosis == 'high_fibrosis':
theta_c = 0.4 # proportion of colaggen over the rest of the domain (0.05 healthy, 0.15 moderated y 0.4 high)
theta_f = 0.5 # proportion of fiber over the rest of the domain
elif amount_fibrosis == 'square':
theta_c = 0
theta_f = 0
mesh = UnitSquareMesh(3,3)
mesh_h, boundaries, subdomains = readmesh('./meshes/' + amount_fibrosis + '/mesh.h5')
# Define P1-Lagrange function spaces over meshes
V = FunctionSpace(mesh, "CG", prms['num']['deg'])
Vh = FunctionSpace(mesh_h, "CG", prms['num']['deg']) # function space for test and trial functions
cf = CellFunction("size_t", mesh)
# check if subdomains file exist
if os.path.isfile('./meshes/' + amount_fibrosis + '/subdomains.h5'):
# Import indicatrix function over exact mesh in order to mark fibrotic tissue
cf_file = HDF5File(mesh.mpi_comm(), './meshes/' + amount_fibrosis + '/subdomains.h5', "r")
cf_file.read(cf, "/cf")
cf_file.close()
# ******************************************
# Define difusion tensors for both healthy and fibrotic tissue
sigma_c, sigma_2 = betha*sigma_1, sigma_1/gamma # diffusivity for colagen and cross fibers (sigma_2)
Dh = Constant(((sigma_1, 0), # healthy diffusion tensor
(0, sigma_2)))
Dcol = Constant(((sigma_c*1 , 0.0,), # collagen diffusion tensor
(0.0, sigma_c*1)))
vals = np.zeros(2)
Dh.eval(vals, np.zeros(3))
print vals
# TODO: search for a more convenient form of obtain a component from a ufl constant tensor
D11 = inner(dot(Dh, Constant((1.0, 0))), Constant((1.0, 0)))
print D11
plot(mesh)
interactive()
# Calculate effective tensor for homogenized problem
Deffp = theta_c*Dcol + (1 - theta_c)*Dh - (outer(theta_c*(1 - theta_c)*(Dcol - Dh)*e1, (Dcol - Dh).T*e1))/((1 - theta_c)*inner((Dcol*e1), e1) + theta_c*inner((Dh*e1), e1))
i, j = 0, 0; Deffpij = Deffp[i,j];
Deff = theta_f*Deffp + (1 - theta_f)*Dh - (outer(theta_f*(1 - theta_f)*(Deffp - Dh)*e2, (Deffp - Dh).T*e2))/((1 - theta_f)*inner((Deffp*e2), e2) + theta_f*inner((Dh*e2), e2))
i, j = 0, 0; Deffij = Deff[i,j];
C = DiscontinuousTensor(cf, [Dh, Dcol]) # Assign tensors where they belongs
# ******************************************
# Initialize sub-domain instances
left = Left()
top = Top()
right = Right()
bottom = Bottom()
right.b = b; top.h = h;
# Mark boundaries of the domain
boundaries = FacetFunction("size_t", mesh)
boundaries.set_all(0)
left.mark(boundaries, 1)
top.mark(boundaries, 2)
right.mark(boundaries, 3)
bottom.mark(boundaries, 4)
boundaries_h = FacetFunction("size_t", mesh_h)
boundaries_h.set_all(0)
left.mark(boundaries_h, 1)
top.mark(boundaries_h, 2)
right.mark(boundaries_h, 3)
bottom.mark(boundaries_h, 4)
# ******************************************
# Initial conditions
phi1, r1, w1, s1 = interpolate(Expression(str(phi_i)), V ), interpolate(Expression(str(r_i)), V ), interpolate(Expression(str(w_i)), V ), interpolate(Expression(str(s_i)), V)
phi1h, r1h, w1h, s1h = interpolate(Expression(str(phi_i)), Vh), interpolate(Expression(str(r_i)), Vh), interpolate(Expression(str(w_i)), Vh), interpolate(Expression(str(s_i)), Vh)
# ******************************************
# Inward and outward currents factorization
J, J_h = Function(V), Function(Vh)
# Continuous variational exact problem
u, v = TrialFunction(V), TestFunction(V)
a_K = inner(C * nabla_grad(u), nabla_grad(v)) * dx
a_M = u*v*dx
# Continuous Variational Homogenized Problem
uh, vh = TrialFunction(Vh), TestFunction(Vh)
a_Kh = inner(Deff * grad(uh), grad(vh)) * dx
a_Mh = uh*vh*dx
# Assemble stifness and mass matrix for discretized variational problem
start = time.time()
K = assemble(a_K)
M = assemble(a_M)
A = M + dt*K
end = time.time()
time_assembly = end - start
# Assemble stifness and mass matrix for discretized variational homogenized problem
start = time.time()
Kh = assemble(a_Kh)
Mh = assemble(a_Mh)
Ah = Mh + dt*Kh
end = time.time()
time_assembly_h = end - start
benchmark.write(str(time_assembly) + " " + str(time_assembly_h) + "\n")
phi, phih, F_k, F_kh = Function(V), Function(Vh), Function(V), Function(Vh)
# ******************************************
# Auxiliar vectors of the ufl-functions in order to get element-wise operations
r1_arr, w1_arr, s1_arr = r1.vector().array(), w1.vector().array(), s1.vector().array()
r1h_arr, w1h_arr, s1h_arr = r1h.vector().array(), w1h.vector().array(), s1h.vector().array()
# Auxiliary functions to save and export re-scaled potential
aux_out1, aux_out2 = Function(V), Function(Vh)
# ******************************************
# External stimulus (the values of g have to be different to obtain the same stimula in both exact and homogenized tissue)
g1 = Expression('-est1_intensity' , est1_intensity=est1_intensity)
g2 = Expression('-est2_intensity', est2_intensity=est2_intensity)
g1h = Expression('-est1_intensity', est1_intensity=est1_intensity)
g2h = Expression('-est2_intensity', est2_intensity=est2_intensity)
ds = Measure('ds', domain=mesh , subdomain_data=boundaries )
ds_h = Measure('ds', domain=mesh_h, subdomain_data=boundaries_h)
# ******************************************
# Time - loop
# Init Krylov solvers
if prec != 'none' and prech == 'none':
solver, solverh = KrylovSolver(sol_method, prec), KrylovSolver(solh_method)
elif prec != 'none' and prech != 'none':
solver, solverh = KrylovSolver(sol_method, prec), KrylovSolver(solh_method, prech)
elif prec == 'none' and prech == 'none':
solver, solverh = KrylovSolver(sol_method), KrylovSolver(solh_method)
elif prec == 'none' and prech != 'none':
solver, solverh = KrylovSolver(sol_method), KrylovSolver(solh_method, prech)
# the following prevent to evaluate conditional every time-step
if prms['io']['xdmf'] == 1:
counter = 10
else:
counter = 11
rank = mesh.mpi_comm().Get_rank()
t = dt
while t < T:
if rank == 0:
print "solving time step t = %g" % t
#***********************************
# Solving EDO's (Exact Problem)
# Update arrays
phi1_arr = phi1.vector().array()
phi1h_arr = phi1h.vector().array()
eq1 = (1 - HS(phi1_arr - p5_thetav_minus)*p7_tauv1_minus + HS(phi1_arr - p5_thetav_minus)*p8_tauv2_minus);
eq2 = p10_tauw1_minus + (p11_tauw2_minus - p10_tauw1_minus)*(1 + np.tanh(p12_kw_minus*(phi1_arr - p13_phiw_minus)))/2;
eq3 = p18_tau_so1 + (p19_tau_so2 - p18_tau_so1)*(1 + np.tanh(p20_k_so*(phi1_arr - p21_phi_so)))/2;
eq4 = (1 - HS(phi1_arr - p4_thetaw))*p22_tau_s1 + HS(phi1_arr - p4_thetaw)*p23_tau_s2;
eq5 = (1 - HS(phi1_arr - p6_theta_0))*p16_tau_o1 + HS(phi1_arr - p6_theta_0)*p17_tau_o2;
r_inf = (phi1_arr < p5_thetav_minus).astype(float);
w_inf = (1 - HS(phi1_arr - p6_theta_0))*(1 - phi1_arr/p27_tauw_inf) + HS(phi1_arr - p6_theta_0)*p28_w_inf;
# Update gating variables
r1_arr = (r1_arr + (dt*r_inf*(1 - HS(phi1_arr - p3_thetav)))/eq1)/(1 + (dt*(1 - HS(phi1_arr - p3_thetav)))/eq1 + (dt*HS(phi1_arr - p3_thetav))/p9_tauv_plus);
w1_arr = (w1_arr + (dt*w_inf*(1 - HS(phi1_arr - p4_thetaw)))/eq2)/(1 + (dt*(1 - HS(phi1_arr - p4_thetaw)))/eq2 + (dt*HS(phi1_arr - p4_thetaw))/p14_tau_w_plus);
s1_arr = (s1_arr + (dt*(1 + np.tanh(p24_ks*(phi1_arr - p25_phi_s)))/2)/eq4) / (1 + dt/eq4);
# Current factorization
Jfi_i = -1/p15_tau_fi*r1_arr*HS(phi1_arr - p3_thetav) * (p2_phiu - phi1_arr + p3_thetav);
Jfi_e = -r1_arr*HS(phi1_arr - p3_thetav)*p3_thetav*p2_phiu/p15_tau_fi;
Jso_i = (1 - HS(phi1_arr - p4_thetaw))/eq5;
Jso_e = HS(phi1_arr - p4_thetaw)/eq3 - p1_phi0/eq5*(1 - HS(phi1_arr - p4_thetaw));
Jsi_e = -HS(phi1_arr - p4_thetaw)*w1_arr*s1_arr/p26_tau_si;
J.vector()[:]= Jsi_e + Jso_e + Jfi_e + (Jfi_i + Jso_i)*phi1_arr
# Solving EDO's (Homogenized Problem)
eq1 = (1 - HS(phi1h_arr - p5_thetav_minus)*p7_tauv1_minus + HS(phi1h_arr - p5_thetav_minus)*p8_tauv2_minus);
eq2 = p10_tauw1_minus + (p11_tauw2_minus - p10_tauw1_minus)*(1 + np.tanh(p12_kw_minus*(phi1h_arr - p13_phiw_minus)))/2;
eq3 = p18_tau_so1 + (p19_tau_so2 - p18_tau_so1)*(1 + np.tanh(p20_k_so*(phi1h_arr - p21_phi_so)))/2;
eq4 = (1 - HS(phi1h_arr - p4_thetaw))*p22_tau_s1 + HS(phi1h_arr - p4_thetaw)*p23_tau_s2;
eq5 = (1 - HS(phi1h_arr - p6_theta_0))*p16_tau_o1 + HS(phi1h_arr - p6_theta_0)*p17_tau_o2;
r_inf = (phi1h_arr < p5_thetav_minus).astype(float);
w_inf = (1 - HS(phi1h_arr - p6_theta_0))*(1 - phi1h_arr/p27_tauw_inf) + HS(phi1h_arr - p6_theta_0)*p28_w_inf;
# Update gating variables
r1h_arr = (r1h_arr + (dt*r_inf*(1 - HS(phi1h_arr - p3_thetav)))/eq1)/(1 + (dt*(1 - HS(phi1h_arr - p3_thetav)))/eq1 + (dt*HS(phi1h_arr - p3_thetav))/p9_tauv_plus);
w1h_arr = (w1h_arr + (dt*w_inf*(1 - HS(phi1h_arr - p4_thetaw)))/eq2)/(1 + (dt*(1 - HS(phi1h_arr - p4_thetaw)))/eq2 + (dt*HS(phi1h_arr - p4_thetaw))/p14_tau_w_plus);
s1h_arr = (s1h_arr + (dt*(1 + np.tanh(p24_ks*(phi1h_arr - p25_phi_s)))/2)/eq4) / (1 + dt/eq4);
# Current factorization
Jfi_i = -1/p15_tau_fi*r1h_arr*HS(phi1h_arr - p3_thetav) * (p2_phiu - phi1h_arr + p3_thetav);
Jfi_e = -r1h_arr*HS(phi1h_arr - p3_thetav)*p3_thetav*p2_phiu/p15_tau_fi;
Jso_i = (1 - HS(phi1h_arr - p4_thetaw))/eq5;
Jso_e = HS(phi1h_arr - p4_thetaw)/eq3 - p1_phi0/eq5*(1 - HS(phi1h_arr - p4_thetaw));
Jsi_e = -HS(phi1h_arr - p4_thetaw)*w1h_arr*s1h_arr/p26_tau_si;
J_h.vector()[:]= Jsi_e + Jso_e + Jfi_e + (Jfi_i + Jso_i)*phi1h_arr
#**********************************
# Solving PDE
if (t >= est1_delay)*(t <= est1_delay + est1_duration):
G = assemble(g1*v *ds(1) )
Gh = assemble(g1*vh*ds_h(1))
elif (t >= est2_delay)*(t <= est2_delay + est2_duration):
G = assemble(g2*v *ds(4) )
Gh = assemble(g2*vh*ds_h(4))
else:
G, Gh = 0, 0;
F_k.vector()[:] = J.vector()
b = M*phi1.vector() - dt*M*F_k.vector() + dt*G
F_kh.vector()[:] = J_h.vector()
bh = Mh*phi1h.vector() - dt*Mh*F_kh.vector() + dt*Gh
start = time.time()
solver.solve(A , phi.vector(), b)
end = time.time(); time_solve = end - start
start = time.time()
solverh.solve(Ah, phih.vector(), bh)
end = time.time(); time_solve_h = end - start
phi1.assign(phi)
phi1h.assign(phih)
"""
#**********************************
# Evaluate L2-norm
phi_hi = interpolate(phih, V)
m2 = inner(phi-phi_hi, phi - phi_hi)*dx
m3 = inner(phi, phi)*dx
l2_norm_dif = assemble(m2)
l2_norm = assemble(m3)
error_rel = abs(l2_norm_dif/(l2_norm + (t <= est1_delay)))
print "error = %g" % error_rel
"""
#**********************************
# Export solutions to VTK (re-scaled to physiologycal values)
if counter == 10:
aux_out1.vector()[:] = 85.7*phi.vector() - 84
aux_out2.vector()[:] = 85.7*phih.vector() - 84
sol << aux_out1, t
solh << aux_out2, t
counter = 0
counter += 1
#error.write(str(t) + " " + str(error_rel) + "\n")
benchmark.write(str(time_solve) + " " + str(time_solve_h) + "\n")
t = t + dt
def compute(prms):
''' Pennes equattion solver
author: Felipe Galarce
email: [email protected]
'''
from functions.inout import readmesh
import os.path
# Extract parameters
mesh_file = './meshes/' + prms['io']['mesh'] + '.h5'
results_dir = prms['io']['results']
dt = float(prms['num']['dt'])
T = float(prms['num']['T'])
# Parameters for Penne's equation
rho = float(prms['phys']['rho'])
rhob = float(prms['phys']['rhob'])
c = float(prms['phys']['c'])
cb = float(prms['phys']['cb'])
k = float(prms['phys']['k'])
Ta = float(prms['phys']['Ta'])
Tc = float(prms['phys']['Tc'])
wb = float(prms['phys']['wb'])
Tf = float(prms['phys']['Tf'])
hf = float(prms['phys']['hf'])
# parameters for elasticity equations
alpha = float(prms['phys']['alpha'])
nu = float(prms['phys']['nu'])
G = float(prms['phys']['G'])
Qm_mode = prms['phys']['Qm_mode']
if Qm_mode == 'constant':
Q_meta = float(33800)
# Configuring form compiler
# parameters["form_compiler"]["quadrature_degree"] = 6
parameters["form_compiler"]["optimize"] = True
parameters["form_compiler"]["representation"] = 'quadrature'
## Read mesh, boundaries and subdomains, but first check if the mesh file exists
if not os.path.isfile(mesh_file):
import subprocess
subprocess.call("cp ./meshes/" + prms['io']['mesh'] + ".geo ./", shell=True)
subprocess.call("cp ./functions/xml2hdf5.py ./", shell=True)
subprocess.call("gmsh -2 " + prms['io']['mesh'] + ".geo", shell=True)
subprocess.call("dolfin-convert ./" + prms['io']['mesh'] + ".msh ./" + prms['io']['mesh'] + ".xml ", shell=True)
subprocess.call("python xml2hdf5.py " + prms['io']['mesh'] + ".xml ", shell=True)
subprocess.call("cp " + prms['io']['mesh'] + ".h5 ./meshes/", shell=True)
subprocess.call("rm ./" + prms['io']['mesh'] + ".msh ./" + prms['io']['mesh'] + ".h5 ./" + prms['io']['mesh'] + ".xml ./" + prms['io']['mesh'] + "tissue_box_facet_region.xml " + prms['io']['mesh'] + "_physical_region.xml", shell=True)
mesh, subdomains, boundaries = readmesh(mesh_file)
# Characterize boundaries
ds = Measure('ds', domain=mesh , subdomain_data=boundaries)
# ============= HEAT EQUATION ===============
# variational form
V = FunctionSpace(mesh, "CG", 1)
phi, v = TrialFunction(V), TestFunction(V)
phi0, phit = Function(V), Function(V)
a = rho*c/dt*inner(phi, v)*dx + k*inner(grad(phi), grad(v))*dx + cb*wb*inner(phi, v)*dx
L = rho*c/dt*inner(phi0, v)*dx + inner(Constant(Q_meta), v)*dx + cb*wb*inner(Constant(Ta), v)*dx - inner(hf*phi0 - Constant(Tf), v)*ds(5)
# point sources
delta1 = PointSource(V, Point(0.009, 0.032, 0.04), float(prms['phys']['Pu']))
delta2 = PointSource(V, Point(0.009, 0.04, 0.028), float(prms['phys']['Pu']))
delta3 = PointSource(V, Point(0.009, 0.04, 0.028), float(prms['phys']['Pu']))
# Assemble LHS
A = assemble(a)
# boundary condition
bc = DirichletBC(V, Expression(str(Tc)), boundaries, 1)
# Configure solver and file to save solution
solver = KrylovSolver('cg', 'amg')
solver.parameters['report'] = False
# solver.parameters['preconditioner']['structure'] = 'same'
solver.parameters['nonzero_initial_guess'] = True
phi_file = File(results_dir + "/temperature.pvd")
# ============= ELASTICITY EQUATIONS ===============
def update(u, u0, v0, a0, beta, gamma, dt):
"""Update fields at the end of each time step."""
# Get vectors (references)
u_vec, u0_vec = u.vector(), u0.vector()
v0_vec, a0_vec = v0.vector(), a0.vector()
# Update acceleration and velocity
# a = 1/(2*beta)*((u - u0 - v0*dt)/(0.5*dt*dt) - (1-2*beta)*a0)
a_vec = (1.0/(2.0*beta))*( (u_vec - u0_vec - v0_vec*dt)/(0.5*dt*dt) - (1.0-2.0*beta)*a0_vec )
# v = dt * ((1-gamma)*a0 + gamma*a) + v0
v_vec = dt*((1.0-gamma)*a0_vec + gamma*a_vec) + v0_vec
# Update (u0 <- u0)
v0.vector()[:], a0.vector()[:] = v_vec, a_vec
u0.vector()[:] = u.vector()
# Newmark scheme parameters and function to compute acceleration
beta = 0.25
gamma = 0.50
def ddot_u(u):
return ((u - u0 - dt*v0)/(beta*dt*dt) - a0*(1 - 2*beta)/(2*beta))
#Function Spaces
VV = VectorFunctionSpace(mesh, "Lagrange", 1) # displacement space
uu, vv = TrialFunction(VV), TestFunction(VV)
u0, v0, a0 = Function(VV), Function(VV), Function(VV)
displacements = Function(VV)
# symetric parts of test and trial functions
eps_u, eps_v = sym(grad(uu)), sym(grad(vv))
# Lamme's Parameters
lmbda, mu = 2.0*G*nu/(1 - 2*nu), G
sig_u = lmbda*tr(eps_u)*Identity(2) + 2.*mu*eps_u
# variational form
F = inner(ddot_u(uu), vv)*dx + inner(sig_u, eps_v)*dx
a_elasticity, L_elasticity = lhs(F), rhs(F)
rank = mesh.mpi_comm().Get_rank()
t = dt
coupling_term = Function(VV)
x_label = VV.sub(0).dofmap().dofs()
y_label = VV.sub(1).dofmap().dofs()
# # TODO: FIX BC
# bc_disp = DirichletBC(VV, Expression(("0.0", "0.0")), boundaries, 1)
print 'time [ms]: '
while t <= T + dt:
if rank == 0: print '%g\t' % t,
# --> SOLVING PENNE'S EQUATION
# assemble RHS
b = assemble(L)
# if t == dt:
# delta1.apply(b)
# delta2.apply(b)
# delta3.apply(b)
# apply Dirichlet boundary conditions
bc.apply(A, b)
# solve linear system
solver.solve(A, phit.vector(), b)
# save solution to file
phi_file << phi0
# --> SOLVING ELASTICITY EQUATIONS
A_elasticity = assemble(a_elasticity);
b_elasticity = assemble(L_elasticity)
# coupling term
coupling_term_arr = -2.0*G*alpha*(1 + nu)/(1 - 2*nu)*(phit.vector().array() - Tc)
coupling_term.vector()[x_label] = coupling_term_arr
coupling_term.vector()[y_label] = coupling_term_arr
VF = assemble(inner(coupling_term, vv)*dx)
b_elasticity = b_elasticity + VF
# solve linear system
bc_disp.apply(A_elasticity, b_elasticity)
solve(A_elasticity, displacements.vector(), b_elasticity, 'gmres', 'ilu')
# deform mesh accordingly to displacements field
plot(phit)
plot(displacements)
plot(mesh)
ALE.move(mesh, displacements)
# interactive()
update(displacements, u0, v0, a0, beta, gamma, dt)
phi0.assign(phit)
t += dt
def compute(prms):
''' Pennes equattion solver
author: Felipe Galarce
email: [email protected]
'''
from functions.inout import readmesh
import os.path
import numpy as np
import time
import sys
non_linear = 1
# Parameters for Penne's equation
cb = float(prms['phys']['cb'])
k = float(prms['phys']['k_tissue'])
Tc = float(prms['phys']['Tc'])
Tmax = prms['phys']['Tmax']
Tcr = prms['phys']['Tcr']
wb00 = prms['phys']['wb00']
wmax = prms['phys']['wmax']
Ta = prms['phys']['Ta']
Tc = 35
Ta = 37
Tsurr = Tc
h_newton = 100
Rrad = 15 # TODO: fix this value
def HS(x): # Heavy-Side function
return (x > 0).astype(float)
def Wb_(T):
T_arr = T.vector().array();
wb.vector()[:] = wb00*HS(Tcr - T_arr) + (wmax + wb00)/2*HS(T_arr - Tmax) + wmax*(1 + ((wmax - wb00)/wb00)*((T_arr - Tcr)/(Tmax - Tcr)))*(1 - HS(T_arr - Tmax) - HS(Tcr - T_arr))
return wb
def Qm_exp(T):
T_arr = T.vector().array()
exponente = (T_arr- 37)/10
dos = 2*np.ones(len(T_arr))
Qm.vector()[:] = 0.17*np.power(dos, exponente)
return Qm
if prms['options']['dim'] != 1:
results_dir = prms['io']['results']
mesh_file = './meshes/' + prms['io']['mesh'] + '.h5'
mesh, subdomains, boundaries = readmesh(mesh_file)
# Characterize boundaries
ds = Measure('ds', domain=mesh , subdomain_data=boundaries)
else:
mesh = IntervalMesh(100, 0, 0.05)
V = FunctionSpace(mesh, "CG", 1)
wb, Qm = Function(V), Function(V)
du = TrialFunction(V)
v = TestFunction(V)
u_ = Function(V) # the most recently computed solution
F = inner(k*grad(u_), grad(v))*dx \
- cb*inner(Wb_(u_)*u_, v)*dx \
+ inner(Qm_exp(u_), v)*dx \
+ cb*wb*inner(Ta, v)*dx \
+ h_newton*inner(Constant(Tc - Ta), v)*dx
#- 1.0/Rrad*inner(Constant(Tc - Tsurr), v)*dx
J = derivative(F, u_, du) # Gateaux derivative in dir. of du
if prms['options']['dim'] == 3:
bc = DirichletBC(V, Tc, boundaries, 2)
elif prms['options']['dim'] == 2:
bc = DirichletBC(V, Tc, boundaries, 1)
else:
bc = DirichletBC(V, Tc, 'on_boundary')
problem = NonlinearVariationalProblem(F, u_, bc, J)
solver = NonlinearVariationalSolver(problem)
prm = solver.parameters
prm['newton_solver']['absolute_tolerance'] = 1E-8
prm['newton_solver']['relative_tolerance'] = 1E-7
prm['newton_solver']['maximum_iterations'] = 25
prm['newton_solver']['relaxation_parameter'] = 1.0
set_log_level(PROGRESS)
solver.solve()
out_file = File('./results/Skin2Blood.pvd')
out_file << u_
plot(u_)
interactive()
