import numpy as np
from dolfin import *
from multiphenics import *


def E_nu_to_mu_lmbda(E, nu):
    mu = E / (2 * (1.0 + nu))
    lmbda = nu * E / ((1 - 2 * nu) * (1 + nu))
    return (mu, lmbda)


def K_nu_to_E(K, nu):
    return 3 * K * (1 - 2 * nu)


def strain(u):
    return sym(grad(u))


def init_scalar_parameter(p, p_value, index, sub):
    for cell_no in range(len(sub.array())):
        subdomain_no = sub.array()[cell_no]
        if subdomain_no == index:
            p.vector()[cell_no] = p_value
    return p


def init_tensor_parameter(p, p_value, index, sub, dim):
    for cell_no in range(len(sub.array())):
        subdomain_no = sub.array()[cell_no]
        if subdomain_no == index:
            k_j = 0
            for k_i in range(
                    cell_no * np.power(dim, 2),
                    cell_no * np.power(dim, 2) + np.power(dim, 2)):
                p.vector()[k_i] = p_value[k_j]
                k_j = k_j + 1
    return p


def avg_w(x, w):
    return (w * x("+") + (1 - w) * x("-"))


def k_plus(k, n):
    return dot(dot(n("+"), k("+")), n("+"))


def k_minus(k, n):
    return dot(dot(n("-"), k("-")), n("-"))


def weight_e(k, n):
    return k_minus(k, n) / (k_plus(k, n) + k_minus(k, n))


def k_e(k, n):
    return 2 * k_plus(k, n) * k_minus(k, n) / (k_plus(k, n) + k_minus(k, n))


parameters["ghost_mode"] = "shared_facet"  # required by dS

mesh = Mesh("two_mat.xml")
subdomains = MeshFunction("size_t", mesh, "two_mat_physical_region.xml")
boundaries = MeshFunction("size_t", mesh, "two_mat_facet_region.xml")

dx = Measure("dx", domain=mesh, subdomain_data=subdomains)
ds = Measure("ds", domain=mesh, subdomain_data=boundaries)
dS = Measure("dS", domain=mesh, subdomain_data=boundaries)

UCG = VectorElement("CG", mesh.ufl_cell(), 2)
PCG = FiniteElement("CG", mesh.ufl_cell(), 1)
PDG = FiniteElement("DG", mesh.ufl_cell(), 0)

UCG_F = FunctionSpace(mesh, UCG)
PDG_F = FunctionSpace(mesh, PCG + PDG)

W = BlockFunctionSpace([UCG_F, PDG_F],
                       restrict=[None, None])

PM = FunctionSpace(mesh, "DG", 0)
TM = TensorFunctionSpace(mesh, "DG", 0)

n = FacetNormal(mesh)
vc = CellVolume(mesh)
fc = FacetArea(mesh)

h = vc / fc
h_avg = (vc("+") + vc("-")) / (2 * avg(fc))

Id = Identity(mesh.topology().dim())

# Variational formulation
trial = BlockTrialFunction(W)
u, p = block_split(trial)

test = BlockTestFunction(W)
psiu, psip = block_split(test)

w = BlockFunction(W)
w0 = BlockFunction(W)
(u0, p0) = block_split(w0)

K = 1000.e3
nu = 0.25
E = K_nu_to_E(K, nu)

(mu_l, lmbda_l) = E_nu_to_mu_lmbda(E, nu)

f_stress_y = Constant(-1.e3)

f = Constant((0.0, 0.0))  # sink/source for displacement
g = Constant(0.0)  # sink/source for velocity
q = 0.0

p_D1 = 0.0

alpha = 1.0

rho1 = 1200.0
mu1 = 1.e-3
phi1 = 0.3
cf1 = 1.e-9
ct1 = phi1 * cf1
kx1 = 1.e-16
ky1 = 1.e-16

k1 = np.array([kx1, 0., 0., ky1])

rho2 = 1200.0
mu2 = 1.e-3
phi2 = 0.3
cf2 = 1.e-9
ct2 = phi2 * cf2
kx2 = 1.e-12
ky2 = 1.e-12

k2 = np.array([kx2, 0., 0., ky2])

rho_values = [rho1, rho2]
mu_values = [mu1, mu2]
phi_values = [phi1, phi2]
ct_values = [ct1, ct2]
k_values = [k1, k2]

rho = Function(PM)
mu = Function(PM)
phi = Function(PM)
ct = Function(PM)
k = Function(TM)

rho = init_scalar_parameter(rho, rho_values[0], 500, subdomains)
mu = init_scalar_parameter(mu, mu_values[0], 500, subdomains)
phi = init_scalar_parameter(phi, phi_values[0], 500, subdomains)
ct = init_scalar_parameter(ct, ct_values[0], 500, subdomains)
k = init_tensor_parameter(k, k_values[0], 500, subdomains, mesh.topology().dim())

rho = init_scalar_parameter(rho, rho_values[1], 501, subdomains)
mu = init_scalar_parameter(mu, mu_values[1], 501, subdomains)
phi = init_scalar_parameter(phi, phi_values[1], 501, subdomains)
ct = init_scalar_parameter(ct, ct_values[1], 501, subdomains)
k = init_tensor_parameter(k, k_values[1], 501, subdomains, mesh.topology().dim())

T = 300.0
t = 0.0
dt = 5.0
penalty1 = 1.0
penalty2 = 10.0

xdmu = XDMFFile(mesh.mpi_comm(), "displacement_cg.xdmf")
xdmp = XDMFFile(mesh.mpi_comm(), "pressure_eg.xdmf")

bcd1 = DirichletBC(W.sub(0).sub(0), 0.0, boundaries, 1)  # Zero normal displacement for solid on left side
bcd3 = DirichletBC(W.sub(0).sub(0), 0.0, boundaries, 3)  # Zero normal displacement for solid on right side
bcd4 = DirichletBC(W.sub(0).sub(1), 0.0, boundaries, 4)  # Zero normal displacement for solid on bottom side
bcs = BlockDirichletBC([bcd1, bcd3, bcd4])

theta = 1.0

a = inner(2 * mu_l * strain(u) + lmbda_l * div(u) * Id, sym(grad(psiu))) * dx

b = inner(-alpha * p * Id, sym(grad(psiu))) * dx

c = rho * alpha * div(u) * psip * dx

d = (phi * rho * ct * p * psip * dx + dt * dot(rho * k / mu * grad(p), grad(psip)) * dx
     - dt * dot(avg_w(rho * k / mu * grad(p), weight_e(k, n)), jump(psip, n)) * dS
     - theta * dt * dot(avg_w(rho * k / mu * grad(psip), weight_e(k, n)), jump(p, n)) * dS
     + dt * penalty1 / h_avg * avg(rho) * k_e(k, n) / avg(mu) * dot(jump(p, n), jump(psip, n)) * dS
     - dt * dot(rho * k / mu * grad(p), psip * n) * ds(2)
     - dt * dot(rho * k / mu * grad(psip), p * n) * ds(2)
     + dt * (penalty2 / h * rho / mu * dot(dot(n, k), n) * dot(p * n, psip * n)) * ds(2))

lhs = [[a, b],
       [c, d]]

f_u = (inner(f, psiu) * dx
       + dot(f_stress_y * n, psiu) * ds(2))

f_p = (rho * alpha * div(u0) * psip * dx
       + phi * rho * ct * p0 * psip * dx + dt * g * psip * dx
       - dt * dot(p_D1 * n, rho * k / mu * grad(psip)) * ds(2)
       + dt * (penalty2 / h * rho / mu * dot(dot(n, k), n) * dot(p_D1 * n, psip * n)) * ds(2))

rhs = [f_u, f_p]

AA = block_assemble(lhs)
FF = block_assemble(rhs)
bcs.apply(AA)
bcs.apply(FF)

while (t < T):
    t += dt

    AA = block_assemble(lhs)
    FF = block_assemble(rhs)
    bcs.apply(AA)
    bcs.apply(FF)

    block_solve(AA, w.block_vector(), FF, "mumps")

    u, p = block_split(w)
    block_assign(w0, w)

    u.rename("u", "displacement")
    p.rename("p", "pressure")

    xdmu.write(u, t)
    xdmp.write(p, t)
