def generate_slow_HTI_PDE_solution(self):
pde = LinearPDESystem(self.domain)
pde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
pde.setSymmetryOn()
dim = pde.getDim()
X = self.domain.getX()
y = Vector([2., 3., 4.][:dim], DiracDeltaFunctions(self.domain))
du = grad(X * X)
D = 2500. * kronecker(dim)
pde.setValue(X=pde.createCoefficient('X'))
sigma = pde.getCoefficient('X')
if dim == 3:
e11 = du[0, 0]
e22 = du[1, 1]
e33 = du[2, 2]
sigma[0, 0] = self.c11 * e11 + self.c13 * (e22 + e33)
sigma[1, 1] = self.c13 * e11 + self.c33 * e22 + self.c23 * e33
sigma[2, 2] = self.c13 * e11 + self.c23 * e22 + self.c33 * e33
s = self.c44 * (du[2, 1] + du[1, 2])
sigma[1, 2] = s
sigma[2, 1] = s
s = self.c66 * (du[2, 0] + du[0, 2])
sigma[0, 2] = s
sigma[2, 0] = s
s = self.c66 * (du[0, 1] + du[1, 0])
sigma[0, 1] = s
sigma[1, 0] = s
else:
e11 = du[0, 0]
e22 = du[1, 1]
sigma[0, 0] = self.c11 * e11 + self.c13 * e22
sigma[1, 1] = self.c13 * e11 + self.c33 * e22
s = self.c66 * (du[1, 0] + du[0, 1])
sigma[0, 1] = s
sigma[1, 0] = s
pde.setValue(D=D, X=-sigma, y_dirac=y)
return pde.getSolution()
def generate_slow_HTI_PDE_solution(self, domain):
pde = LinearPDESystem(domain)
pde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
pde.setSymmetryOn()
dim = pde.getDim()
X = domain.getX()
y = Vector([2.,3.,4.][:dim], DiracDeltaFunctions(domain))
du = grad(X*X)
D = 2500.*kronecker(dim)
pde.setValue(X=pde.createCoefficient('X'))
sigma = pde.getCoefficient('X')
if dim == 3:
e11=du[0,0]
e22=du[1,1]
e33=du[2,2]
sigma[0,0]=self.c11*e11+self.c13*(e22+e33)
sigma[1,1]=self.c13*e11+self.c33*e22+self.c23*e33
sigma[2,2]=self.c13*e11+self.c23*e22+self.c33*e33
s=self.c44*(du[2,1]+du[1,2])
sigma[1,2]=s
sigma[2,1]=s
s=self.c66*(du[2,0]+du[0,2])
sigma[0,2]=s
sigma[2,0]=s
s=self.c66*(du[0,1]+du[1,0])
sigma[0,1]=s
sigma[1,0]=s
else:
e11=du[0,0]
e22=du[1,1]
sigma[0,0]=self.c11*e11+self.c13*e22
sigma[1,1]=self.c13*e11+self.c33*e22
s=self.c66*(du[1,0]+du[0,1])
sigma[0,1]=s
sigma[1,0]=s
pde.setValue(D=D, X=-sigma, y_dirac=y)
return pde.getSolution()
class Subsidence(ForwardModel):
"""
Forward Model for subsidence inversion minimizing
integrate( (inner(w,u)-d)**2)
where u is the surface displacement due to a pressure change P
"""
def __init__(self, domain, w, d, lam, mu, coordinates=None, tol=1e-8):
"""
Creates a new subsidence on the given domain
:param domain: domain of the model
:type domain: `Domain`
:param w: data weighting factors and direction
:type w: ``Vector`` with ``FunctionOnBoundary``
:param d: displacement measured at surface
:type d: ``Scalar`` with ``FunctionOnBoundary``
:param lam: 1st Lame coefficient
:type lam: ``Scalar`` with ``Function``
:param lam: 2st Lame coefficient/Shear modulus
:type lam: ``Scalar`` with ``Function``
:param coordinates: defines coordinate system to be used (not supported yet))
:type coordinates: `ReferenceSystem` or `SpatialCoordinateTransformation`
:param tol: tolerance of underlying PDE
:type tol: positive ``float``
"""
super(Subsidence, self).__init__()
DIM = domain.getDim()
self.__pde = LinearPDESystem(domain)
self.__pde.setSymmetryOn()
self.__pde.getSolverOptions().setTolerance(tol)
#... set coefficients ...
C = self.__pde.createCoefficient('A')
for i in range(DIM):
for j in range(DIM):
C[i, i, j, j] += lam
C[i, j, i, j] += mu
C[i, j, j, i] += mu
x = domain.getX()
msk = whereZero(x[DIM - 1]) * kronecker(DIM)[DIM - 1]
for i in range(DIM - 1):
xi = x[i]
msk += (whereZero(xi - inf(xi)) +
whereZero(xi - sup(xi))) * kronecker(DIM)[i]
self.__pde.setValue(A=C, q=msk)
self.__w = interpolate(w, FunctionOnBoundary(domain))
self.__d = interpolate(d, FunctionOnBoundary(domain))
def rescaleWeights(self, scale=1., P_scale=1.):
"""
rescales the weights
:param scale: scale of data weighting factors
:type scale: positive ``float``
:param P_scale: scale of pressure increment
:type P_scale: ``Scalar``
"""
pass
def getArguments(self, P):
"""
Returns precomputed values shared by `getDefect()` and `getGradient()`.
:param P: pressure
:type P: ``Scalar``
:return: displacement u
:rtype: ``Vector``
"""
DIM = self.__pde.getDim()
self.__pde.setValue(y=Data(), X=P * kronecker(DIM))
u = self.__pde.getSolution()
return u,
def getDefect(self, P, u):
"""
Returns the value of the defect.
:param P: pressure
:type P: ``Scalar``
:param u: corresponding displacement
:type u: ``Vector``
:rtype: ``float``
"""
return 0.5 * integrate((inner(u, self.__w) - self.__d)**2)
def getGradient(self, P, u):
"""
Returns the gradient of the defect with respect to susceptibility.
:param P: pressure
:type P: ``Scalar``
:param u: corresponding displacement
:type u: ``Vector``
:rtype: ``Scalar``
"""
d = inner(u, self.__w) - self.__d
self.__pde.setValue(y=d * self.__w, X=Data())
ustar = self.__pde.getSolution()
return div(ustar)
print("\txi = [ %e, %e]" % (inf(xi), sup(xi)))
print("\tgamma = [ %e, %e]" % (inf(gamma), sup(gamma)))
if inf(mu_eff) < 0:
raise ValueError("mu_eff<0")
sigma = 2 * mu_eff * eps_e + lame_eff * trace(eps_e) * k3
if UPDATE_OPERATOR:
pde.setValue(A=mu_eff * (swap_axes(k3Xk3, 0, 3) + swap_axes(k3Xk3, 1, 3)) + lame_eff * k3Xk3)
else:
pde.setValue(A=mu * (swap_axes(k3Xk3, 0, 3) + swap_axes(k3Xk3, 1, 3)) + lame * k3Xk3)
pde.setValue(X=-sigma, y=SIGMA_N * dom.getNormal(), r=dt * v0 - du)
ddu = pde.getSolution()
deps += symmetric(grad(ddu))
du += ddu
norm_ddu = Lsup(ddu)
norm_du = Lsup(du)
print("\t displacement change update = %e of %e" % (norm_ddu, norm_du))
iter += 1
print("deps =", inf(deps), sup(deps))
u += du
n += 1
t += dt
# =========== this is a test for triaxial test ===========================
print("\tYYY t = ", t)
a = (SIGMA_N - lame_eff * VMAX * t) / (lame_eff + mu_eff) / 2
# =========== this is a test for triaxial test ===========================
print("\tYYY a = ", meanValue(a))
r_b=FunctionOnBoundary(dom).getX()[0]
print("volume : ",integrate(r))
#
# step 1:
#
# calculate normal
n_d=dom.getNormal()
t_d=matrixmult(numpy.array([[0.,-1.],[1.,0]]),n_d)
sigma_d=(sign(inner(t_d,U))*alpha_w*t_d-n_d)*Pen*clip(inner(n_d,U),0.)
print("sigma_d =",inf(sigma_d),sup(sigma_d))
momentumStep1.setValue(D=r*ro*kronecker(dom),
Y=r*ro*U+dt*r*[0.,-ro*g],
X=-dt*r*(dev_stress-teta3*p*kronecker(dom)),
y=sigma_d*face_mask*r_b)
U_star=momentumStep1.getSolution()
saveVTK("u.vtu",u=U_star,u0=U)
#
# step 2:
#
# U2=U+teta1*(U_star-U)
U2=U+teta1*U_star
gg2=grad(U2)
div_U2=gg2[0,0]+gg2[1,1]+U2[0]/r
grad_p=grad(p)
pressureStep2.setValue(A=r*dt*B*teta1*teta2/ro*dt*kronecker(dom),
D=r,
Y=-dt*B*r*div_U2,
X=-r*B*dt**2/ro*teta1*(1-teta3)*grad_p)
r_b=FunctionOnBoundary(dom).getX()[0]
print("volume : ",integrate(r))
#
# step 1:
#
# calculate normal
n_d=dom.getNormal()
t_d=matrixmult(numpy.array([[0.,-1.],[1.,0]]),n_d)
sigma_d=(sign(inner(t_d,U))*alpha_w*t_d-n_d)*Pen*clip(inner(n_d,U),0.)
print("sigma_d =",inf(sigma_d),sup(sigma_d))
momentumStep1.setValue(D=r*ro*kronecker(dom),
Y=r*ro*U+dt*r*[0.,-ro*g],
X=-dt*r*(dev_stress-teta3*p*kronecker(dom)),
y=sigma_d*face_mask*r_b)
U_star=momentumStep1.getSolution()
saveVTK("u.vtu",u=U_star,u0=U)
#
# step 2:
#
# U2=U+teta1*(U_star-U)
U2=U+teta1*U_star
gg2=grad(U2)
div_U2=gg2[0,0]+gg2[1,1]+U2[0]/r
grad_p=grad(p)
pressureStep2.setValue(A=r*dt*B*teta1*teta2/ro*dt*kronecker(dom),
D=r,
Y=-dt*B*r*div_U2,
X=-r*B*dt**2/ro*teta1*(1-teta3)*grad_p)
class SonicHTIWave(WaveBase):
"""
Solving the HTI wave equation (along the x_0 axis) with azimuth (rotation around verticle axis)
under the assumption of zero shear wave velocities
The unknowns are the transversal (along x_0) and vertial stress (Q, P)
:note: In case of a two dimensional domain the second spatial dimenion is depth.
"""
def __init__(self, domain, v_p, wavelet, source_tag, source_vector = [1.,0.], eps=0., delta=0., azimuth=0.,
dt=None, p0=None, v0=None, absorption_zone=300*U.m, absorption_cut=1e-2, lumping=True):
"""
initialize the HTI wave solver
:param domain: domain of the problem
:type domain: `Doamin`
:param v_p: vertical p-velocity field
:type v_p: `Scalar`
:param v_s: vertical s-velocity field
:type v_s: `Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param azimuth: azimuth (rotation around verticle axis)
:param gamma: third Thompsen parameter
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param p0: initial solution (Q(t=0), P(t=0)). If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
"""
DIM=domain.getDim()
f=createAbsorptionLayerFunction(v_p.getFunctionSpace().getX(), absorption_zone, absorption_cut)
self.v2_p=v_p**2
self.v2_t=self.v2_p*sqrt(1+2*delta)
self.v2_n=self.v2_p*(1+2*eps)
if p0 == None:
p0=Data(0.,(2,),Solution(domain))
else:
p0=interpolate(p0, Solution(domain ))
if v0 == None:
v0=Data(0.,(2,),Solution(domain))
else:
v0=interpolate(v0, Solution(domain ))
if dt == None:
dt=min(min(inf(domain.getSize()/sqrt(self.v2_p)), inf(domain.getSize()/sqrt(self.v2_t)), inf(domain.getSize()/sqrt(self.v2_n))) , wavelet.getTimeScale())*0.2
super(SonicHTIWave, self).__init__( dt, u0=p0, v0=v0, t0=0.)
self.__wavelet=wavelet
self.__mypde=LinearPDESystem(domain)
if lumping: self.__mypde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=kronecker(2), X=self.__mypde.createCoefficient('X'))
self.__source_tag=source_tag
self.__r=Vector(0, DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
def _getAcceleration(self, t, u):
"""
returns the acceleraton for time `t` and solution `u` at time `t`
"""
dQ = grad(u[0])[0]
dP = grad(u[1])[1:]
sigma=self.__mypde.getCoefficient('X')
sigma[0,0] = self.v2_n*dQ
sigma[0,1:] = self.v2_t*dP
sigma[1,0] = self.v2_t*dQ
sigma[1,1:] = self.v2_p*dP
self.__mypde.setValue(X=-sigma, y_dirac= self.__r * self.__wavelet.getValue(t))
return self.__mypde.getSolution()
class TTIWave(WaveBase):
"""
Solving the 2D TTI wave equation with
`sigma_xx= c11*e_xx + c13*e_zz + c15*e_xz`
`sigma_zz= c13*e_xx + c33*e_zz + c35*e_xz`
`sigma_xz= c15*e_xx + c35*e_zz + c55*e_xz`
the coefficients `c11`, `c13`, etc are calculated from the tompsen parameters `eps`, `delta` and the tilt `theta`
:note: currently only the 2D case is supported.
"""
def __init__(self, domain, v_p, v_s, wavelet, source_tag,
source_vector = [0.,1.], eps=0., delta=0., theta=0., rho=1.,
dt=None, u0=None, v0=None, absorption_zone=300*U.m,
absorption_cut=1e-2, lumping=True):
"""
initialize the TTI wave solver
:param domain: domain of the problem
:type domain: `Domain`
:param v_p: vertical p-velocity field
:type v_p: `Scalar`
:param v_s: vertical s-velocity field
:type v_s: `Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param delta: second Thompsen parameter
:param theta: tilting (in Rad)
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param u0: initial solution. If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
"""
DIM=domain.getDim()
if not DIM == 2:
raise ValueError("Only 2D is supported.")
f=createAbsorptionLayerFunction(Function(domain).getX(), absorption_zone, absorption_cut)
v_p=v_p*f
v_s=v_s*f
if u0 == None:
u0=Vector(0.,Solution(domain))
else:
u0=interpolate(p0, Solution(domain ))
if v0 == None:
v0=Vector(0.,Solution(domain))
else:
v0=interpolate(v0, Solution(domain ))
if dt == None:
dt=min((1./5.)*min(inf(domain.getSize()/v_p), inf(domain.getSize()/v_s)), wavelet.getTimeScale())
super(TTIWave, self).__init__( dt, u0=u0, v0=v0, t0=0.)
self.__wavelet=wavelet
self.__mypde=LinearPDESystem(domain)
if lumping: self.__mypde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=rho*kronecker(DIM), X=self.__mypde.createCoefficient('X'))
self.__source_tag=source_tag
self.__r=Vector(0, DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
c0_33=v_p**2 * rho
c0_66=v_s**2 * rho
c0_11=(1+2*eps) * c0_33
c0_13=sqrt(2*c0_33*(c0_33-c0_66) * delta + (c0_33-c0_66)**2)-c0_66
self.c11= c0_11*cos(theta)**4 - 2*c0_13*cos(theta)**4 + 2*c0_13*cos(theta)**2 + c0_33*sin(theta)**4 - 4*c0_66*cos(theta)**4 + 4*c0_66*cos(theta)**2
self.c13= -c0_11*cos(theta)**4 + c0_11*cos(theta)**2 + c0_13*sin(theta)**4 + c0_13*cos(theta)**4 - c0_33*cos(theta)**4 + c0_33*cos(theta)**2 + 4*c0_66*cos(theta)**4 - 4*c0_66*cos(theta)**2
self.c16= (-2*c0_11*cos(theta)**2 - 4*c0_13*sin(theta)**2 + 2*c0_13 + 2*c0_33*sin(theta)**2 - 8*c0_66*sin(theta)**2 + 4*c0_66)*sin(theta)*cos(theta)/2
self.c33= c0_11*sin(theta)**4 - 2*c0_13*cos(theta)**4 + 2*c0_13*cos(theta)**2 + c0_33*cos(theta)**4 - 4*c0_66*cos(theta)**4 + 4*c0_66*cos(theta)**2
self.c36= (2*c0_11*cos(theta)**2 - 2*c0_11 + 4*c0_13*sin(theta)**2 - 2*c0_13 + 2*c0_33*cos(theta)**2 + 8*c0_66*sin(theta)**2 - 4*c0_66)*sin(theta)*cos(theta)/2
self.c66= -c0_11*cos(theta)**4 + c0_11*cos(theta)**2 + 2*c0_13*cos(theta)**4 - 2*c0_13*cos(theta)**2 - c0_33*cos(theta)**4 + c0_33*cos(theta)**2 + c0_66*sin(theta)**4 + 3*c0_66*cos(theta)**4 - 2*c0_66*cos(theta)**2
def _getAcceleration(self, t, u):
"""
returns the acceleraton for time `t` and solution `u` at time `t`
"""
du = grad(u)
sigma=self.__mypde.getCoefficient('X')
e_xx=du[0,0]
e_zz=du[1,1]
e_xz=du[0,1]+du[1,0]
sigma[0,0]= self.c11 * e_xx + self.c13 * e_zz + self.c16 * e_xz
sigma[1,1]= self.c13 * e_xx + self.c33 * e_zz + self.c36 * e_xz
sigma_xz = self.c16 * e_xx + self.c36 * e_zz + self.c66 * e_xz
sigma[0,1]=sigma_xz
sigma[1,0]=sigma_xz
self.__mypde.setValue(X=-sigma, y_dirac= self.__r * self.__wavelet.getValue(t))
return self.__mypde.getSolution()
class HTIWave(WaveBase):
"""
Solving the HTI wave equation (along the x_0 axis)
:note: In case of a two dimensional domain a horizontal domain is considered, i.e. the depth component is dropped.
"""
def __init__(self, domain, v_p, v_s, wavelet, source_tag,
source_vector = [1.,0.,0.], eps=0., gamma=0., delta=0., rho=1.,
dt=None, u0=None, v0=None, absorption_zone=None,
absorption_cut=1e-2, lumping=True, disable_fast_assemblers=False):
"""
initialize the VTI wave solver
:param domain: domain of the problem
:type domain: `Domain`
:param v_p: vertical p-velocity field
:type v_p: `Scalar`
:param v_s: vertical s-velocity field
:type v_s: `Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param delta: second Thompsen parameter
:param gamma: third Thompsen parameter
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param u0: initial solution. If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
:param disable_fast_assemblers: if True, forces use of slower and more general PDE assemblers
"""
DIM=domain.getDim()
self.fastAssembler = hasattr(domain, "createAssembler") and not disable_fast_assemblers
f=createAbsorptionLayerFunction(v_p.getFunctionSpace().getX(), absorption_zone, absorption_cut)
v_p=v_p*f
v_s=v_s*f
if u0 == None:
u0=Vector(0.,Solution(domain))
else:
u0=interpolate(p0, Solution(domain ))
if v0 == None:
v0=Vector(0.,Solution(domain))
else:
v0=interpolate(v0, Solution(domain ))
if dt == None:
dt=min((1./5.)*min(inf(domain.getSize()/v_p), inf(domain.getSize()/v_s)), wavelet.getTimeScale())
super(HTIWave, self).__init__( dt, u0=u0, v0=v0, t0=0.)
self.__wavelet=wavelet
self.c33 = v_p**2 * rho
self.c44 = v_s**2 * rho
self.c11 = (1+2*eps) * self.c33
self.c66 = (1+2*gamma) * self.c44
self.c13 = sqrt(2*self.c33*(self.c33-self.c44) * delta + (self.c33-self.c44)**2)-self.c44
self.c23 = self.c33-2*self.c66
if self.fastAssembler:
C = [("c11", self.c11),
("c23", self.c23), ("c13", self.c13), ("c33", self.c33),
("c44", self.c44), ("c66", self.c66)]
if "speckley" in domain.getDescription().lower():
C = [(n, interpolate(d, ReducedFunction(domain))) for n,d in C]
self.__mypde=WavePDE(domain, C)
else:
self.__mypde=LinearPDESystem(domain)
self.__mypde.setValue(X=self.__mypde.createCoefficient('X'))
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=rho*kronecker(DIM))
self.__source_tag=source_tag
if DIM == 2:
source_vector= [source_vector[0],source_vector[2]]
self.__r=Vector(0, DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
def setQ(self,q):
"""
sets the PDE q value
:param q: the value to set
"""
self.__mypde.setValue(q=q)
def _getAcceleration(self, t, u):
"""
returns the acceleraton for time `t` and solution `u` at time `t`
"""
du = grad(u)
if self.fastAssembler:
self.__mypde.setValue(du=du, y_dirac= self.__r * self.__wavelet.getValue(t))
else:
sigma=self.__mypde.getCoefficient('X')
if self.__mypde.getDim() == 3:
e11=du[0,0]
e22=du[1,1]
e33=du[2,2]
sigma[0,0]=self.c11*e11+self.c13*(e22+e33)
sigma[1,1]=self.c13*e11+self.c33*e22+self.c23*e33
sigma[2,2]=self.c13*e11+self.c23*e22+self.c33*e33
s=self.c44*(du[2,1]+du[1,2])
sigma[1,2]=s
sigma[2,1]=s
s=self.c66*(du[2,0]+du[0,2])
sigma[0,2]=s
sigma[2,0]=s
s=self.c66*(du[0,1]+du[1,0])
sigma[0,1]=s
sigma[1,0]=s
else:
e11=du[0,0]
e22=du[1,1]
sigma[0,0]=self.c11*e11+self.c13*e22
sigma[1,1]=self.c13*e11+self.c33*e22
s=self.c66*(du[1,0]+du[0,1])
sigma[0,1]=s
sigma[1,0]=s
self.__mypde.setValue(X=-sigma, y_dirac= self.__r * self.__wavelet.getValue(t))
return self.__mypde.getSolution()
raise ValueError("mu_eff<0")
sigma = 2 * mu_eff * eps_e + lame_eff * trace(eps_e) * k3
if (UPDATE_OPERATOR):
pde.setValue(A=mu_eff *
(swap_axes(k3Xk3, 0, 3) + swap_axes(k3Xk3, 1, 3)) +
lame_eff * k3Xk3)
else:
pde.setValue(A=mu *
(swap_axes(k3Xk3, 0, 3) + swap_axes(k3Xk3, 1, 3)) +
lame * k3Xk3)
pde.setValue(X=-sigma, y=SIGMA_N * dom.getNormal(), r=dt * v0 - du)
ddu = pde.getSolution()
deps += symmetric(grad(ddu))
du += ddu
norm_ddu = Lsup(ddu)
norm_du = Lsup(du)
print("\t displacement change update = %e of %e" % (norm_ddu, norm_du))
iter += 1
print("deps =", inf(deps), sup(deps))
u += du
n += 1
t += dt
#=========== this is a test for triaxial test ===========================
print("\tYYY t = ", t)
a = (SIGMA_N - lame_eff * VMAX * t) / (lame_eff + mu_eff) / 2
#=========== this is a test for triaxial test ===========================
print("\tYYY a = ", meanValue(a))