def solve(self, damp=.2, dynRelax=False):
"""
solve the equation of motion in centeral difference scheme
"""
# get initial coordinate
x = self.getDomain().getX()
# density matrix
kron = util.kronecker(self.getDomain().getDim())
rho = self.__rho * kron
# stress at (n) time step
stress_last = self.getCurrentStress()
# set coefficients for ODE
self.__pde.setValue(D=rho)
self.setRHS(X=-stress_last)
# solve acceleration at (n) time step from ODE
u_tt = self.__pde.getSolution()
# update velocity at (n+1/2) time step
self.__u_t = 1. / (2. + damp * self.__dt) * (
(2. - damp * self.__dt) * self.__u_t + 2. * self.__dt * u_tt)
# get displacement increment
du = self.__dt * self.__u_t
# update strain
D = util.grad(du)
self.__strain += D
# update displacement and domain geometry at (n+1) time step
self.__u += du
self.__domain.setX(x + du)
# !!!!!! apply displacement increment and get boundary force from DE exterior domain, if any
if self.__FEDENodeMap:
DEdu = self.getBoundaryDisplacement(du)
"""
# apply boundary velocity and get boundary traction (deprecated)
self.__Nbc,self.__sceneExt=self.applyDisplIncrement_getTractionDEM(DEdu=DEdu)
"""
# apply boundary velocity and return an asynResult object
arFEfAndSceneExt = self.applyDisplIncrement_getForceDEM(
DEdu=DEdu, dynRelax=dynRelax)
# !!!!!! update stress and scenes from DEM part using strain at (n+1) time step
self.__stress, self.__scenes = self.applyStrain_getStressDEM(
st=D, dynRelax=dynRelax)
"""
# !!!!!! update scenes and return asynResult objects (deprecated)
arScenes = self.applyStrain(st=D)
# !!!!!! retrieve data from asyncResults
# update interior DE scenes
self.__scenes = arScenes.get()
# assign new stresses to gauss points from interior DE scenes
s = self.__pool.map(getStress2D,self.__scenes)
for i in xrange(self.__numGaussPoints):
self.__stress.setValueOfDataPoint(i,s[i])
"""
# if exterior DE domain is given, update scene and boundary force
if self.__FEDENodeMap:
self.__FEf, self.__sceneExt = arFEfAndSceneExt.get()
return self.__u, self.__u_t
def solve(self,damp=.2,dynRelax=False):
"""
solve the equation of motion in centeral difference scheme
"""
# get initial coordinate
x = self.getDomain().getX()
# density matrix
kron = util.kronecker(self.getDomain().getDim())
rho = self.__rho*kron
# stress at (n) time step
stress_last = self.getCurrentStress()
# set coefficients for ODE
self.__pde.setValue(D=rho)
self.setRHS(X=-stress_last)
# solve acceleration at (n) time step from ODE
u_tt = self.__pde.getSolution()
# update velocity at (n+1/2) time step
self.__u_t = 1./(2.+damp*self.__dt)*((2.-damp*self.__dt)*self.__u_t + 2.*self.__dt*u_tt)
# get displacement increment
du = self.__dt*self.__u_t
# update strain
D = util.grad(du)
self.__strain += D
# update displacement and domain geometry at (n+1) time step
self.__u += du
self.__domain.setX(x+du)
# !!!!!! apply displacement increment and get boundary force from DE exterior domain, if any
if self.__FEDENodeMap:
DEdu = self.getBoundaryDisplacement(du)
"""
# apply boundary velocity and get boundary traction (deprecated)
self.__Nbc,self.__sceneExt=self.applyDisplIncrement_getTractionDEM(DEdu=DEdu)
"""
# apply boundary velocity and return an asynResult object
arFEfAndSceneExt=self.applyDisplIncrement_getForceDEM(DEdu=DEdu,dynRelax=dynRelax)
# !!!!!! update stress and scenes from DEM part using strain at (n+1) time step
self.__stress,self.__scenes = self.applyStrain_getStressDEM(st=D,dynRelax=dynRelax)
"""
# !!!!!! update scenes and return asynResult objects (deprecated)
arScenes = self.applyStrain(st=D)
# !!!!!! retrieve data from asyncResults
# update interior DE scenes
self.__scenes = arScenes.get()
# assign new stresses to gauss points from interior DE scenes
s = self.__pool.map(getStress2D,self.__scenes)
for i in xrange(self.__numGaussPoints):
self.__stress.setValueOfDataPoint(i,s[i])
"""
# if exterior DE domain is given, update scene and boundary force
if self.__FEDENodeMap:
self.__FEf,self.__sceneExt = arFEfAndSceneExt.get()
return self.__u, self.__u_t
def solve(self, globalIter=10, solidIter=50):
"""
solve the coupled PDE using fixed-stress split method,
call solveSolid to get displacement
"""
rtol = self.__rtol
x_safe = self.__domain.getX()
k = util.kronecker(self.__domain)
kdr = util.inner(k, util.tensor_mult(self.__S, k)) / 4.
n = self.getEquivalentPorosity()
perm = self.__permeability * n**3 / (1. - n)**2 * k
kf = self.__bulkFluid
dt = self.__dt
self.__ppde.setValue(A=perm,
D=(n / kf + 1. / kdr) / dt,
Y=(n / kf + 1. / kdr) / dt * self.__pgauss -
self.__meanStressRate / kdr)
p_iter_old = self.__ppde.getSolution()
p_iter_gauss = util.interpolate(p_iter_old,
escript.Function(self.__domain))
u_old, D, sig, s, scene = self.solveSolid(p_iter_gauss=p_iter_gauss,
iter_max=solidIter)
converge = False
iterate = 0
while (not converge) and (iterate < globalIter):
iterate += 1
self.__ppde.setValue(Y=n / kf / dt * self.__pgauss +
1. / kdr / dt * p_iter_gauss -
util.trace(D) / dt)
p_iter = self.__ppde.getSolution()
p_err = util.L2(p_iter - p_iter_old) / util.L2(p_iter)
p_iter_old = p_iter
p_iter_gauss = util.interpolate(p_iter,
escript.Function(self.__domain))
u, D, sig, s, scene = self.solveSolid(p_iter_gauss=p_iter_gauss,
iter_max=solidIter)
u_err = util.L2(u - u_old) / util.L2(u)
u_old = u
converge = (u_err <= rtol and p_err <= rtol * .1)
self.__meanStressRate = (util.trace(sig - self.__stress) / 2. -
p_iter_gauss + self.__pgauss) / dt
self.__pore = p_iter_old
self.__pgauss = p_iter_gauss
self.__domain.setX(x_safe + u_old)
self.__strain += D
self.__stress = sig
self.__S = s
self.__scenes = scene
return u_old
def solveSolid(self, p_iter_gauss=escript.Data(), iter_max=50):
"""
solve the pde for displacement using Newton-Ralphson scheme
"""
k = util.kronecker(self.__domain)
p = p_iter_gauss * k
iterate = 0
rtol = self.__rtol
stress_safe = self.__stress
s_safe = self.__S
x_safe = self.__domain.getX()
self.__upde.setValue(A=s_safe, X=-stress_safe + p, r=self.__r)
#residual0=util.L2(self.__pde.getRightHandSide()) # using force error
u = self.__upde.getSolution() # trial solution, displacement
D = util.grad(u) # trial strain tensor
# !!!!!! obtain stress and tangent operator from DEM part
update_stress, update_s, update_scenes = self.applyStrain_getStressTangentDEM(
st=D)
err = util.Lsup(u) # initial error before iteration
converged = (err < 1.e-12)
while (not converged) and (iterate < iter_max):
#if iterate>iter_max:
# raise RuntimeError,"Convergence for Newton-Raphson failed after %s steps."%(iter_max)
iterate += 1
self.__domain.setX(x_safe + u)
self.__upde.setValue(A=update_s,
X=-update_stress + p,
r=escript.Data())
#residual=util.L2(self.__pde.getRightHandSide())
du = self.__upde.getSolution()
u += du
l, d = util.L2(u), util.L2(du)
err = d / l # displacement error, alternatively using force error 'residual'
converged = (err < rtol)
if err > rtol**3: # only update DEM parts when error is large enough
self.__domain.setX(x_safe)
D = util.grad(u)
update_stress, update_s, update_scenes = self.applyStrain_getStressTangentDEM(
st=D)
"""reset domain geometry to original until global convergence"""
self.__domain.setX(x_safe)
return u, D, update_stress, update_s, update_scenes
def solve(self, globalIter=10, solidIter=50):
"""
solve the coupled PDE using fixed-stress split method,
call solveSolid to get displacement
"""
rtol=self.__rtol
x_safe=self.__domain.getX()
k=util.kronecker(self.__domain)
kdr=util.inner(k,util.tensor_mult(self.__S,k))/4.
n=self.getEquivalentPorosity()
perm=self.__permeability*n**3/(1.-n)**2*k
kf=self.__bulkFluid
dt=self.__dt
self.__ppde.setValue(A=perm,D=(n/kf+1./kdr)/dt,Y=(n/kf+1./kdr)/dt*self.__pgauss-self.__meanStressRate/kdr)
p_iter_old=self.__ppde.getSolution()
p_iter_gauss=util.interpolate(p_iter_old,escript.Function(self.__domain))
u_old,D,sig,s,scene=self.solveSolid(p_iter_gauss=p_iter_gauss,iter_max=solidIter)
converge=False
iterate=0
while (not converge) and (iterate<globalIter):
iterate += 1
self.__ppde.setValue(Y=n/kf/dt*self.__pgauss+1./kdr/dt*p_iter_gauss-util.trace(D)/dt)
p_iter=self.__ppde.getSolution()
p_err=util.L2(p_iter-p_iter_old)/util.L2(p_iter)
p_iter_old=p_iter
p_iter_gauss=util.interpolate(p_iter,escript.Function(self.__domain))
u,D,sig,s,scene=self.solveSolid(p_iter_gauss=p_iter_gauss,iter_max=solidIter)
u_err=util.L2(u-u_old)/util.L2(u)
u_old=u
converge=(u_err<=rtol and p_err <= rtol*.1)
self.__meanStressRate=(util.trace(sig-self.__stress)/2.-p_iter_gauss+self.__pgauss)/dt
self.__pore=p_iter_old
self.__pgauss=p_iter_gauss
self.__domain.setX(x_safe+u_old)
self.__strain+=D
self.__stress=sig
self.__S=s
self.__scenes=scene
return u_old
def solveSolid(self, p_iter_gauss=escript.Data(), iter_max=50):
"""
solve the pde for displacement using Newton-Ralphson scheme
"""
k=util.kronecker(self.__domain)
p=p_iter_gauss*k
iterate=0
rtol=self.__rtol
stress_safe=self.__stress
s_safe=self.__S
x_safe=self.__domain.getX()
self.__upde.setValue(A=s_safe, X=-stress_safe+p, r=self.__r)
#residual0=util.L2(self.__pde.getRightHandSide()) # using force error
u=self.__upde.getSolution() # trial solution, displacement
D=util.grad(u) # trial strain tensor
# !!!!!! obtain stress and tangent operator from DEM part
update_stress,update_s,update_scenes=self.applyStrain_getStressTangentDEM(st=D)
err=util.Lsup(u) # initial error before iteration
converged=(err<1.e-12)
while (not converged) and (iterate<iter_max):
#if iterate>iter_max:
# raise RuntimeError,"Convergence for Newton-Raphson failed after %s steps."%(iter_max)
iterate+=1
self.__domain.setX(x_safe+u)
self.__upde.setValue(A=update_s,X=-update_stress+p,r=escript.Data())
#residual=util.L2(self.__pde.getRightHandSide())
du=self.__upde.getSolution()
u+=du
l,d=util.L2(u),util.L2(du)
err=d/l # displacement error, alternatively using force error 'residual'
converged=(err<rtol)
if err>rtol**3: # only update DEM parts when error is large enough
self.__domain.setX(x_safe)
D=util.grad(u)
update_stress,update_s,update_scenes=self.applyStrain_getStressTangentDEM(st=D)
"""reset domain geometry to original until global convergence"""
self.__domain.setX(x_safe)
return u,D,update_stress,update_s,update_scenes