def setUpPDE(self):
"""
Return the underlying PDE.
:rtype: `LinearPDE`
"""
if self.__pde is None:
dom=self.__domain
x = dom.getX()
DIM=dom.getDim()
q=whereZero(x[DIM-1]-inf(x[DIM-1]))
for i in range(DIM-1):
xi=x[i]
q+=whereZero(xi-inf(xi))+whereZero(xi-sup(xi))
pde=LinearPDE(dom, numEquations=1)
pde.getSolverOptions().setTolerance(self.__tol)
pde.setSymmetryOn()
A=pde.createCoefficient('A')
X=pde.createCoefficient('X')
pde.setValue(A=A, X=X, q=q)
else:
pde=self.__pde
pde.resetRightHandSideCoefficients()
return pde
def __init__(self, domain, pml_condition=None, frequency=None, vp=None, fix_boundary=True):
"""
Initialise the class with domain, boundary conditions and frequency.
Setup PDE
:param domain: the domain : setup with Dirac points
:type domain: `Domain`
:param pml_condition:
:type pml_condition:
:param frequency:
:type frequency:
:param vp: velocity field
:type vp: `Data`
:param fix_boundary: if true fix all the boundaries except the top
:type fix_boundary: `bool`
"""
Dim=domain.getDim()
self.pde=LinearPDE(domain, numEquations=1, numSolutions=1, isComplex=True)
self.pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
self.pml=pml_condition
if not self.pml:
self.pde.setValue(A=kronecker(domain))
self.J=1.
if fix_boundary:
x=domain.getX()
q=whereZero(x[Dim-1]-inf(x[Dim-1]))
for i in range(Dim-1):
q+=whereZero(x[i]-inf(x[i]))+whereZero(x[i]-sup(x[i]))
self.pde.setValue(q=q)
self.setFrequency(frequency)
self.setVp(vp)
def test_PDE2D(self):
dx_tests = 0.1
sigma0 = 1.
electrodes = [(0.5 - 2 * dx_tests, 1.), (0.5 - dx_tests, 1.),
(0.5 + dx_tests, 1.), (0.5 + 2 * dx_tests, 1.)]
domain = finRectangle(20,
20,
d1=mpisize,
diracPoints=electrodes,
diracTags=["sl0", "sl1", "sr0", "sr1"])
loc = Locator(domain, electrodes[2:])
# this creates some reference Data:
x = domain.getX()
q = whereZero(x[0] - inf(x[0])) + whereZero(
x[0] - sup(x[0])) + whereZero(x[1] - inf(x[1]))
ppde = LinearPDE(domain, numEquations=1)
s = Scalar(0., DiracDeltaFunctions(domain))
s.setTaggedValue("sl0", 1.)
s.setTaggedValue("sl1", -1.)
ppde.setValue(A=kronecker(2) * sigma0, q=q, y_dirac=s)
pp = ppde.getSolution()
uu = loc(pp)
# arguments for DcRes
current = 10.
sourceInfo = ["sl0", "sl1"]
sampleTags = [("sr0", "sr1")]
sigmaPrimary = 7.
phiPrimary = pp * current * sigma0 / sigmaPrimary
uuscale = 1 - current * sigma0 / sigmaPrimary
delphi_in = [(uu[1] - uu[0]) * uuscale]
acw = DcRes(domain, loc, delphi_in, sampleTags, phiPrimary,
sigmaPrimary)
self.assertLess(Lsup(phiPrimary - acw.getPrimaryPotential()),
1.e-10 * Lsup(acw.getPrimaryPotential()))
SIGMA = 10. # matches current
args0 = acw.getArguments(SIGMA)
p = args0[0]
u = args0[1]
# true secondary potential
pps = pp - phiPrimary
self.assertLess(Lsup(p - pps), 1.e-6 * Lsup(pps))
# test return values at electrodes:
self.assertLess(abs(u[0] - uu[0] * uuscale),
1.e-6 * abs(uu[0] * uuscale))
self.assertLess(abs(u[1] - uu[1] * uuscale),
1.e-6 * abs(uu[1] * uuscale))
# this sould be zero
dd = acw.getDefect(SIGMA, *args0)
self.assertTrue(dd >= 0.)
self.assertTrue(dd <= 1e-7)
def __init__(self, domain):
super(SlippingFault, self).__init__(self)
self.domain = domain
self.__pde_u = LinearPDE(domain,
numEquations=self.domain.getDim(),
numSolutions=self.domain.getDim())
self.__pde_u.setSymmetryOn()
def doInitialization(self):
"""
initialize model
"""
if not self.displacement:
self.displacement = Vector(0., ContinuousFunction(self.domain))
if not self.velocity:
self.velocity = Vector(0., ContinuousFunction(self.domain))
if not self.stress:
self.stress = Tensor(0., ContinuousFunction(self.domain))
if not self.internal_force: self.internal_force = Data()
if not self.external_force: self.external_force = Data()
if not self.prescribed_velocity: self.prescribed_velocity = Data()
if not self.location_prescribed_velocity:
self.location_prescribed_velocity = Data()
# save the old values:
self.__stress_safe = self.stress
self.__temperature_safe = self.temperature
self.__displacement_safe = self.displacement
self.__velocity_safe = self.velocity
self.__velocity_old = None
self.__old_dt = None
self.__very_old_dt = None
# get node cooridnates and apply initial displacement
self.__x = self.domain.getX()
self.domain.setX(self.__x + self.displacement)
# open PDE:
self.__pde = LinearPDE(self.domain)
self.__pde.setSolverMethod(self.__pde.DIRECT)
self.__solver_options = self.__pde.getSolverOptions()
self.__solver_options.setSolverMethod(self.__solver_options.DIRECT)
self.__solver_options.setVerbosity(self.debug)
def wavePropagation(domain, h, tend, lam, mu, rho, xc, src_radius, U0):
# lists to collect displacement at point source
ts, u_pc0, u_pc1, u_pc2 = [], [], [], []
x = domain.getX()
# ... open new PDE ...
mypde = LinearPDE(domain)
mypde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
kron = kronecker(mypde.getDim())
dunit = numpy.array([1., 0., 0.]) # defines direction of point source
mypde.setValue(D=kron * rho,
q=whereNegative(length(x - xc) - src_radius) * dunit)
# ... set initial values ....
n = 0
# for first two time steps
u = Vector(0., Solution(domain))
u_last = Vector(0., Solution(domain))
t = 0
# define the location of the point source
L = Locator(domain, xc)
# find potential at point source
u_pc = L.getValue(u)
print("u at point charge = %s" % u_pc)
ts.append(t)
u_pc0.append(u_pc[0]), u_pc1.append(u_pc[1]), u_pc2.append(u_pc[2])
while t < tend:
t += h
# ... get current stress ....
g = grad(u)
stress = lam * trace(g) * kron + mu * (g + transpose(g))
# ... get new acceleration ....
amplitude = U0 * (4 * (t - t0)**3 / alpha**3 - 6 *
(t - t0) / alpha) * sqrt(2.) / alpha**2 * exp(
1. / 2. - (t - t0)**2 / alpha**2)
mypde.setValue(X=-stress, r=dunit * amplitude)
a = mypde.getSolution()
# ... get new displacement ...
u_new = 2 * u - u_last + h**2 * a
# ... shift displacements ....
u_last = u
u = u_new
n += 1
print("time step %d, t = %s" % (n, t))
u_pc = L.getValue(u)
print("u at point charge = %s" % u_pc)
ts.append(t)
u_pc0.append(u_pc[0]), u_pc1.append(u_pc[1]), u_pc2.append(u_pc[2])
# ... save current acceleration in units of gravity and displacements
if n == 1 or n % 10 == 0:
saveVTK("./data/usoln.%i.vtu" % (n / 10),
acceleration=length(a) / 9.81,
displacement=length(u),
tensor=stress,
Ux=u[0])
return ts, u_pc0, u_pc1, u_pc2
def getPotential(self):
"""
returns a list containing 3 lists one for each the primary, secondary
and total potential.
"""
primCon=self.primaryConductivity
coords=self.domain.getX()
pde=LinearPDE(self.domain, numEquations=1)
tol=1e-8
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
DIM=self.domain.getDim()
x=self.domain.getX()
q=whereZero(x[DIM-1]-inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=whereZero(xi-inf(xi))+whereZero(xi-sup(xi))
A = self.secondaryConductivity * kronecker(self.domain)
pde.setValue(A=A,q=q)
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
if(len(self.electrodes[0])==3):
for i in range(self.numElectrodes-1):
analyticRs=Data(0,(3,),ContinuousFunction(self.domain))
analyticRs[0]=(coords[0]-self.electrodes[i][0])
analyticRs[1]=(coords[1]-self.electrodes[i][1])
analyticRs[2]=(coords[2])
rsMag=(analyticRs[0]**2+analyticRs[1]**2+analyticRs[2]**2)**0.5
analyticPrimaryPot=(self.current*(1./primCon))/(2*pi*(rsMag+(whereZero(rsMag)*0.0000001))) #the magic number 0.0000001 is to avoid devide by 0
analyticRsPolePower=(analyticRs[0]**2+analyticRs[1]**2+analyticRs[2]**2)**1.5
analyticRsPolePower = analyticRsPolePower+(whereZero(analyticRsPolePower)*0.0000001)
gradUPrimary = Data(0,(3,),ContinuousFunction(self.domain))
gradUPrimary[0] =(self.current/(2*pi*primCon)) * (analyticRs[0]/analyticRsPolePower)
gradUPrimary[1] =(self.current/(2*pi*primCon)) * (analyticRs[1]/analyticRsPolePower)
gradUPrimary[2] =(self.current/(2*pi*primCon)) * (analyticRs[2]/analyticRsPolePower)
gradUPrimary=-gradUPrimary
X=(primCon-self.secondaryConductivity) * gradUPrimary
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,self.electrodes[i+1])
delPhiSecondary.append(loc.getValue(u))
delPhiPrimary.append(loc.getValue(analyticPrimaryPot))
else:
raise NotImplementedError("2d forward model is not yet implemented")
self.delPhiSecondary = delPhiSecondary
self.delPhiPrimary = delPhiPrimary
for i in range(len(delPhiPrimary)):
delPhiTotal.append(delPhiPrimary[i] + delPhiSecondary[i])
self.delPhiTotal=delPhiTotal
return [delPhiPrimary, delPhiSecondary, delPhiTotal]
def __init__(self,domain,dim,ng=1,useMPI=False,np=1,rho=2.35e3,mIds=False,\
FEDENodeMap=False,DE_ext=False,FEDEBoundMap=False,conf=False):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param ng: type integer, number of Gauss points
:param useMPI: type boolean, use MPI or not
:param np: type integer, number of processors
:param rho: type float, density of material
:param mIds: a list contains membrane node IDs
:param FEDENodeMap: a dictionary with FE and DE boundary node IDs in keys and values
:param DE_ext: name of file which saves initial state of exterior DE domain
:param FEDEBoundMap: a dictionary with FE and DE boundary element IDs in keys and values (deprecated)
:param conf: type float, conf pressure on membrane
"""
self.__domain = domain
self.__pde = LinearPDE(self.__domain,
numEquations=dim,
numSolutions=dim)
self.__pde.getSolverOptions().setSolverMethod(
SolverOptions.HRZ_LUMPING)
self.__pde.setSymmetryOn()
self.__numGaussPoints = ng
self.__rho = rho
self.__mIds = mIds
self.__FEDENodeMap = FEDENodeMap
self.__FEDEBoundMap = FEDEBoundMap
self.__conf = conf
self.__pool = get_pool(mpi=useMPI, threads=np)
self.__scenes = self.__pool.map(initLoad, range(ng))
self.__strain = escript.Tensor(0, escript.Function(self.__domain))
self.__stress = escript.Tensor(0, escript.Function(self.__domain))
self.__u = escript.Vector(0, escript.Solution(self.__domain))
self.__u_last = escript.Vector(0, escript.Solution(self.__domain))
self.__u_t = escript.Vector(0, escript.Solution(self.__domain))
self.__dt = 0
# ratio between timesteps in internal DE and FE domain
self.__nsOfDE_int = 1
# if FEDENodeMap is given, employ exterior DE domain
if self.__FEDENodeMap:
self.__sceneExt = self.__pool.apply(initLoadExt, (DE_ext, ))
# ratio between timesteps in external DE and FE domain
self.__nsOfDE_ext = 1
# get interface nodal forces as boundary condition
self.__FEf = self.__pool.apply(
initNbc, (self.__sceneExt, self.__conf, mIds, FEDENodeMap))
"""
# get interface nodal tractions as boundary condition (deprecated)
self.__Nbc=escript.Vector(0,escript.Solution(self.__domain))
FENbc = self.__pool.apply(initNbc,(self.__sceneExt,self.__conf,mIds,FEDENodeMap))
for FEid in FENbc.keys():
self.__Nbc.setValueOfDataPoint(FEid,FENbc[FEid])
"""
# get stress tensor at material points
s = self.__pool.map(getStress2D, self.__scenes)
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i, s[i])
def __init__(self,domain,debug=False):
super(StokesProblem, self).__init__(self,debug)
self.domain=domain
self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
self.__pde_u.setSymmetryOn()
self.__pde_p=LinearPDE(domain)
self.__pde_p.setReducedOrderOn()
self.__pde_p.setSymmetryOn()
def __init__(self, domain, phi_f=None, phi=None, L_g=None,
perm_f_0=None, perm_f_1=None, perm_f_2=None,
k_w =None, k_g=None, mu_w =None, mu_g =None,
rho_w =None, rho_g=None, sigma=0, A_mg=0, f_rg=1.,
wells=[], g=9.81*U.m/U.sec**2):
"""
set up
:param domain: domain
:type domain: `esys.escript.Domain`
:param phi_f: porosity of the fractured rock as function of the gas pressure
:type phi_f: `MaterialPropertyWithDifferential`
:param phi: total porosity if None phi=1.
:type phi: scalar or None
:param L_g: gas adsorption as function of gas pressure
:type L_g: `MaterialPropertyWithDifferential`
:param S_fg: gas saturation in the fractured rock as function of the capillary pressure p_fc=S_fg- p_f
:type S_fg: `MaterialPropertyWithDifferential`
:param perm_f_0: permeability in the x_0 direction in the fractured media
:type perm_f_0: scalar
:param perm_f_1: permeability in the x_1 direction in the fractured media
:type perm_f_1: scalar
:param perm_f_2: permeability in the x_2 direction in the fractured media
:type perm_f_2: scalar
:param k_w: relative permeability of water as function of water saturation
:type k_w: `MaterialProperty`
:param k_g: relative permeability of gas as function of gas saturation
:type k_g: `MaterialProperty`
:param mu_w: viscosity of water as function of water pressure
:type mu_w: `MaterialProperty`
:param mu_g: viscosity of gas as function of gas pressure
:type mu_g: `MaterialProperty`
:param rho_w: density of water as function of water pressure
:type rho_w: `MaterialPropertyWithDifferential`
:param rho_g: density of gas as function of gas pressure
:type rho_g: `MaterialPropertyWithDifferential`
:param wells : list of wells
:type wells: list of `Well`
:param sigma: shape factor for gas matrix diffusion
:param A_mg: diffusion constant for gas adsorption
:param f_rg: gas re-adsorption factor
"""
DualPorosity.__init__(self, domain,
phi_f=phi_f, phi_m=None, phi=phi,
S_fg=None, S_mg=None,
perm_f_0=perm_f_0, perm_f_1=perm_f_1, perm_f_2=perm_f_2,
perm_m_0=None , perm_m_1=None, perm_m_2=None,
k_w =k_w, k_g=k_g, mu_w =mu_w, mu_g =mu_g,
rho_w =rho_w, rho_g=rho_g,
wells=wells, g=g)
self.L_g=L_g
self.sigma = sigma
self.A_mg = A_mg
self.f_rg = f_rg
self.__pde=LinearPDE(self.domain, numEquations=3, numSolutions =3)
def __update(self, tag, tag_value, value):
if self.__pde == None:
self.__pde = LinearPDE(self.domain, numSolutions=1)
mask = Scalar(0., Function(self.domain))
mask.setTaggedValue(tag, 1.)
self.__pde.setValue(Y=mask)
mask = wherePositive(abs(self.__pde.getRightHandSide()))
value *= (1. - mask)
value += tag_value * mask
return value
def __init__(self, domain, debug=False):
super(StokesProblem, self).__init__(self, debug)
self.domain = domain
self.__pde_u = LinearPDE(domain,
numEquations=self.domain.getDim(),
numSolutions=self.domain.getDim())
self.__pde_u.setSymmetryOn()
self.__pde_p = LinearPDE(domain)
self.__pde_p.setReducedOrderOn()
self.__pde_p.setSymmetryOn()
def __init__(self,domain):
super(SimpleStokesProblem, self).__init__(self)
self.__pde_u=LinearPDE(domain)
self.__pde_u.setSymmetryOn()
self.__pde_u.setValue(A=identityTensor4(dom))
self.__pde_p=LinearPDE(domain)
self.__pde_p.setReducedOrderOn()
self.__pde_p.setSymmetryOn()
self.__pde_p.setValue(D=1.)
def __init__(self,
domain,
pore0=0.,
perm=1.e-5,
kf=2.2e9,
dt=0.001,
ng=1,
useMPI=False,
np=1,
rtol=1.e-2):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param pore0: type float, initial pore pressure
:param perm: type float, d^2/(150 mu_f) in KC equation
:param kf: type float, bulk modulus of the fluid
:param dt: type float, time step for calculation
:param ng: type integer, number of Gauss points
:param useMPI: type boolean, use MPI or not
:param np: type integer, number of processors
:param rtol: type float, relevative tolerance for global convergence
"""
self.__domain = domain
self.__upde = LinearPDE(domain,
numEquations=domain.getDim(),
numSolutions=domain.getDim())
self.__ppde = LinearPDE(domain, numEquations=1, numSolutions=1)
# use reduced interpolation for pore pressure
self.__ppde.setReducedOrderOn()
self.__upde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
self.__ppde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
self.__upde.setSymmetryOn()
self.__ppde.setSymmetryOn()
self.__dt = dt
self.__bulkFluid = kf
self.__numGaussPoints = ng
self.__rtol = rtol
self.__stress = escript.Tensor(0, escript.Function(domain))
self.__S = escript.Tensor4(0, escript.Function(domain))
self.__pool = get_pool(mpi=useMPI, threads=np)
self.__scenes = self.__pool.map(initLoad, range(ng))
st = self.__pool.map(getStressAndTangent2D, self.__scenes)
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i, st[i][0])
self.__S.setValueOfDataPoint(i, st[i][1])
self.__strain = escript.Tensor(0, escript.Function(domain))
self.__pore = escript.Scalar(pore0, escript.ReducedSolution(domain))
self.__pgauss = util.interpolate(pore0, escript.Function(domain))
self.__permeability = perm
self.__meanStressRate = escript.Scalar(0, escript.Function(domain))
self.__r = escript.Vector(
0, escript.Solution(domain)) #Dirichlet BC for u
def __init__(self, domain):
super(SimpleStokesProblem, self).__init__(self)
self.__pde_u = LinearPDE(domain)
self.__pde_u.setSymmetryOn()
self.__pde_u.setValue(A=identityTensor4(dom))
self.__pde_p = LinearPDE(domain)
self.__pde_p.setReducedOrderOn()
self.__pde_p.setSymmetryOn()
self.__pde_p.setValue(D=1.)
def __init__(self,
domain,
ng=1,
useMPI=False,
np=1,
random=False,
rtol=1.e-2,
verbose=False):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param ng: type integer, number of Gauss points
:param useMPI: type boolean, use MPI or not
:param np: type integer, number of processors
:param random: type boolean, if or not use random density field
:param rtol: type float, relevant tolerance for global convergence
:param verbose: type boolean, if or not print messages during calculation
"""
self.__domain = domain
self.__pde = LinearPDE(domain,
numEquations=self.__domain.getDim(),
numSolutions=self.__domain.getDim())
try:
self.__pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
except:
#import time
print(
"======================================================================="
)
print(
"For better performance compile python-escript with direct solver method"
)
print(
"======================================================================="
)
input("Press Enter to continue...")
#time.sleep(5)
self.__pde.setSymmetryOn()
#self.__pde.getSolverOptions().setTolerance(rtol**2)
#self.__pde.getSolverOptions().setPackage(SolverOptions.UMFPACK)
self.__numGaussPoints = ng
self.__rtol = rtol
self.__verbose = verbose
self.__pool = get_pool(mpi=useMPI, threads=np)
self.__scenes = self.__pool.map(initLoad, list(range(ng)))
self.__strain = escript.Tensor(0, escript.Function(self.__domain))
self.__stress = escript.Tensor(0, escript.Function(self.__domain))
self.__S = escript.Tensor4(0, escript.Function(self.__domain))
st = self.__pool.map(getStressAndTangent, self.__scenes)
for i in range(ng):
self.__stress.setValueOfDataPoint(i, st[i][0])
self.__S.setValueOfDataPoint(i, st[i][1])
def __init__(self,
domain,
ng=1,
useMPI=False,
np=1,
random=False,
rtol=1.e-2,
usePert=False,
pert=-2.e-6,
verbose=False):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param ng: type integer, number of Gauss points
:param useMPI: type boolean, use MPI or not
:param np: type integer, number of processors
:param random: type boolean, if or not use random density field
:param rtol: type float, relevative tolerance for global convergence
:param usePert: type boolean, if or not use perturbation method
:param pert: type float, perturbated strain applied to DEM to obtain tangent operator
:param verbose: type boolean, if or not print messages during calculation
"""
self.__domain = domain
self.__pde = LinearPDE(domain,
numEquations=self.__domain.getDim(),
numSolutions=self.__domain.getDim())
self.__pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
self.__pde.setSymmetryOn()
#self.__pde.getSolverOptions().setTolerance(rtol**2)
#self.__pde.getSolverOptions().setPackage(SolverOptions.UMFPACK)
self.__numGaussPoints = ng
self.__rtol = rtol
self.__usepert = usePert
self.__pert = pert
self.__verbose = verbose
self.__pool = get_pool(mpi=useMPI, threads=np)
self.__scenes = self.__pool.map(initLoad, range(ng))
self.__strain = escript.Tensor(0, escript.Function(self.__domain))
self.__stress = escript.Tensor(0, escript.Function(self.__domain))
self.__S = escript.Tensor4(0, escript.Function(self.__domain))
if self.__usepert:
s = self.__pool.map(getStressTensor, self.__scenes)
t = self.__pool.map(getTangentOperator,
zip(self.__scenes, repeat(pert)))
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i, s[i])
self.__S.setValueOfDataPoint(i, t[i])
else:
st = self.__pool.map(getStressAndTangent2D, self.__scenes)
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i, st[i][0])
self.__S.setValueOfDataPoint(i, st[i][1])
def test_PDE2D(self):
dx_tests=0.1
sigma0=1.
electrodes=[(0.5-2*dx_tests,1.), (0.5-dx_tests,1.), (0.5+dx_tests,1.), (0.5+2*dx_tests,1.)]
domain=finRectangle(20,20, d1=mpisize, diracPoints=electrodes, diracTags=["sl0", "sl1", "sr0", "sr1"] )
loc=Locator(domain,electrodes[2:])
# this creates some reference Data:
x=domain.getX()
q=whereZero(x[0]-inf(x[0]))+whereZero(x[0]-sup(x[0]))+whereZero(x[1]-inf(x[1]))
ppde=LinearPDE(domain, numEquations=1)
s=Scalar(0.,DiracDeltaFunctions(domain))
s.setTaggedValue("sl0" ,1.)
s.setTaggedValue("sl1",-1.)
ppde.setValue(A=kronecker(2)*sigma0, q=q, y_dirac=s)
pp=ppde.getSolution()
uu=loc(pp)
# arguments for DcRes
current = 10.
sourceInfo = [ "sl0", "sl1" ]
sampleTags = [ ("sr0", "sr1") ]
sigmaPrimary=7.
phiPrimary=pp*current*sigma0/sigmaPrimary
uuscale=1-current*sigma0/sigmaPrimary
delphi_in = [ (uu[1]-uu[0]) * uuscale]
acw=DcRes(domain, loc, delphi_in, sampleTags, phiPrimary, sigmaPrimary)
self.assertLess(Lsup(phiPrimary-acw.getPrimaryPotential()), 1.e-10 * Lsup(acw.getPrimaryPotential()))
SIGMA=10. # matches current
args0=acw.getArguments(SIGMA)
p=args0[0]
u=args0[1]
# true secondary potential
pps=pp-phiPrimary
self.assertLess(Lsup(p-pps), 1.e-6*Lsup(pps))
# test return values at electrodes:
self.assertLess(abs(u[0]-uu[0]*uuscale), 1.e-6 * abs(uu[0]*uuscale))
self.assertLess(abs(u[1]-uu[1]*uuscale), 1.e-6 * abs(uu[1]*uuscale))
# this sould be zero
dd=acw.getDefect(SIGMA, *args0)
self.assertTrue( dd >= 0.)
self.assertTrue( dd <= 1e-7 )
def getMaxEigenvalue(self):
"""
return the max eigenvalue of the model
type: float
"""
dom = self.getDomain()
dim = dom.getDim()
pdeKu_P = LinearPDE(dom,numEquations=dim,numSolutions=dim)
T = self.getCurrentTangent()
pdeKu_P.setValue(A=T)
pdeKu_P.getOperator().saveMM('tempMTX.mtx')
mtx = mmread('tempMTX.mtx')
maxEigVal = max(eigs(mtx,k=1,return_eigenvectors=False,which='LR'))
return maxEigVal.real
def __init__(self,domain,pore0=0.,perm=1.e-5,kf=2.2e9,dt=0.001,ng=1,useMPI=False,np=1,rtol=1.e-2):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param pore0: type float, initial pore pressure
:param perm: type float, d^2/(150 mu_f) in KC equation
:param kf: type float, bulk modulus of the fluid
:param dt: type float, time step for calculation
:param ng: type integer, number of Gauss points
:param useMPI: type boolean, use MPI or not
:param np: type integer, number of processors
:param rtol: type float, relevative tolerance for global convergence
"""
self.__domain=domain
self.__upde=LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim())
self.__ppde=LinearPDE(domain,numEquations=1,numSolutions=1)
# use reduced interpolation for pore pressure
self.__ppde.setReducedOrderOn()
try:
self.__upde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
self.__ppde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
except:
#import time
print("=======================================================================")
print("For better performance compile python-escript with direct solver method")
print("=======================================================================")
input("Press Enter to continue...")
#time.sleep(5)
self.__upde.setSymmetryOn()
self.__ppde.setSymmetryOn()
self.__dt=dt
self.__bulkFluid=kf
self.__numGaussPoints=ng
self.__rtol=rtol
self.__stress=escript.Tensor(0,escript.Function(domain))
self.__S=escript.Tensor4(0,escript.Function(domain))
self.__pool=get_pool(mpi=useMPI,threads=np)
self.__scenes=self.__pool.map(initLoad,list(range(ng)))
st = self.__pool.map(getStressAndTangent2D,self.__scenes)
for i in range(ng):
self.__stress.setValueOfDataPoint(i,st[i][0])
self.__S.setValueOfDataPoint(i,st[i][1])
self.__strain=escript.Tensor(0,escript.Function(domain))
self.__pore=escript.Scalar(pore0,escript.ReducedSolution(domain))
self.__pgauss=util.interpolate(pore0,escript.Function(domain))
self.__permeability=perm
self.__meanStressRate=escript.Scalar(0,escript.Function(domain))
self.__r=escript.Vector(0,escript.Solution(domain)) #Dirichlet BC for u
def doInitialization(self):
"""
initialize model
"""
if not self.displacement: self.displacement=Vector(0.,ContinuousFunction(self.domain))
if not self.velocity: self.velocity=Vector(0.,ContinuousFunction(self.domain))
if not self.stress: self.stress=Tensor(0.,ContinuousFunction(self.domain))
if not self.internal_force: self.internal_force = Data()
if not self.external_force: self.external_force = Data()
if not self.prescribed_velocity: self.prescribed_velocity = Data()
if not self.location_prescribed_velocity: self.location_prescribed_velocity =Data()
# save the old values:
self.__stress_safe=self.stress
self.__temperature_safe=self.temperature
self.__displacement_safe=self.displacement
self.__velocity_safe=self.velocity
self.__velocity_old=None
self.__old_dt=None
self.__very_old_dt=None
# get node cooridnates and apply initial displacement
self.__x=self.domain.getX()
self.domain.setX(self.__x+self.displacement)
# open PDE:
self.__pde=LinearPDE(self.domain)
self.__pde.setSolverMethod(self.__pde.DIRECT)
self.__solver_options=self.__pde.getSolverOptions()
self.__solver_options.setSolverMethod(self.__solver_options.DIRECT)
self.__solver_options.setVerbosity(self.debug)
def getPDE(self, system):
dim = self.domain.getDim()
if system:
pde=LinearPDE(self.domain, numEquations=dim)
else:
pde=LinearPDE(self.domain, numEquations=1)
self._setCoefficients(pde, system)
so = pde.getSolverOptions()
so.setPackage(self.package)
so.setSolverMethod(self.method)
so.setPreconditioner(self.preconditioner)
so.setTolerance(self.SOLVER_TOL)
so.setVerbosity(self.SOLVER_VERBOSE)
self._setSolverOptions(so)
return pde, self._getSolution(system), self._getGrad(system)
def __init__(self,domain,ng=1,useMPI=False,np=1,random=False,rtol=1.e-2,verbose=False):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param ng: type integer, number of Gauss points
:param useMPI: type boolean, use MPI or not
:param np: type integer, number of processors
:param random: type boolean, if or not use random density field
:param rtol: type float, relevant tolerance for global convergence
:param verbose: type boolean, if or not print messages during calculation
"""
self.__domain=domain
self.__pde=LinearPDE(domain,numEquations=self.__domain.getDim(),numSolutions=self.__domain.getDim())
self.__pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
self.__pde.setSymmetryOn()
#self.__pde.getSolverOptions().setTolerance(rtol**2)
#self.__pde.getSolverOptions().setPackage(SolverOptions.UMFPACK)
self.__numGaussPoints=ng
self.__rtol=rtol
self.__verbose=verbose
self.__pool=get_pool(mpi=useMPI,threads=np)
self.__scenes=self.__pool.map(initLoad,range(ng))
self.__strain=escript.Tensor(0,escript.Function(self.__domain))
self.__stress=escript.Tensor(0,escript.Function(self.__domain))
self.__S=escript.Tensor4(0,escript.Function(self.__domain))
st = self.__pool.map(getStressAndTangent,self.__scenes)
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i,st[i][0])
self.__S.setValueOfDataPoint(i,st[i][1])
def getPDE(self, system):
dim = self.domain.getDim()
if system:
pde = LinearPDE(self.domain, numEquations=dim)
else:
pde = LinearPDE(self.domain, numEquations=1)
self._setCoefficients(pde, system)
so = pde.getSolverOptions()
so.setPackage(self.package)
so.setSolverMethod(self.method)
so.setPreconditioner(self.preconditioner)
so.setTolerance(self.SOLVER_TOL)
so.setVerbosity(self.SOLVER_VERBOSE)
self._setSolverOptions(so)
return pde, self._getSolution(system), self._getGrad(system)
def __init__(self, domain, phi_f=None, phi=None, L_g=None,
perm_f_0=None, perm_f_1=None, perm_f_2=None,
k_w =None, k_g=None, mu_w =None, mu_g =None,
rho_w =None, rho_g=None, sigma=0, A_mg=0, f_rg=1.,
wells=[], g=9.81*U.m/U.sec**2):
"""
set up
:param domain: domain
:type domain: `esys.escript.Domain`
:param phi_f: porosity of the fractured rock as function of the gas pressure
:type phi_f: `MaterialPropertyWithDifferential`
:param phi: total porosity if None phi=1.
:type phi: scalar or None
:param L_g: gas adsorption as function of gas pressure
:type L_g: `MaterialPropertyWithDifferential`
:param S_fg: gas saturation in the fractured rock as function of the capillary pressure p_fc=S_fg- p_f
:type S_fg: `MaterialPropertyWithDifferential`
:param perm_f_0: permeability in the x_0 direction in the fractured media
:type perm_f_0: scalar
:param perm_f_1: permeability in the x_1 direction in the fractured media
:type perm_f_1: scalar
:param perm_f_2: permeability in the x_2 direction in the fractured media
:type perm_f_2: scalar
:param k_w: relative permeability of water as function of water saturation
:type k_w: `MaterialProperty`
:param k_g: relative permeability of gas as function of gas saturation
:type k_g: `MaterialProperty`
:param mu_w: viscosity of water as function of water pressure
:type mu_w: `MaterialProperty`
:param mu_g: viscosity of gas as function of gas pressure
:type mu_g: `MaterialProperty`
:param rho_w: density of water as function of water pressure
:type rho_w: `MaterialPropertyWithDifferential`
:param rho_g: density of gas as function of gas pressure
:type rho_g: `MaterialPropertyWithDifferential`
:param wells : list of wells
:type wells: list of `Well`
:param sigma: shape factor for gas matrix diffusion
:param A_mg: diffusion constant for gas adsorption
:param f_rg: gas re-adsorption factor
"""
DualPorosity.__init__(self, domain,
phi_f=phi_f, phi_m=None, phi=phi,
S_fg=None, S_mg=None,
perm_f_0=perm_f_0, perm_f_1=perm_f_1, perm_f_2=perm_f_2,
perm_m_0=None , perm_m_1=None, perm_m_2=None,
k_w =k_w, k_g=k_g, mu_w =mu_w, mu_g =mu_g,
rho_w =rho_w, rho_g=rho_g,
wells=wells, g=g)
self.L_g=L_g
self.sigma = sigma
self.A_mg = A_mg
self.f_rg = f_rg
self.__pde=LinearPDE(self.domain, numEquations=3, numSolutions =3)
def __update(self,tag,tag_value,value):
if self.__pde==None:
self.__pde=LinearPDE(self.domain,numSolutions=1)
mask=Scalar(0.,Function(self.domain))
mask.setTaggedValue(tag,1.)
self.__pde.setValue(Y=mask)
mask=wherePositive(abs(self.__pde.getRightHandSide()))
value*=(1.-mask)
value+=tag_value*mask
return value
def __init__(self,domain,ng=1,np=1,random=False,rtol=1.e-2,usePert=False,pert=-2.e-6,verbose=False):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param ng: type integer, number of Gauss points
:param np: type integer, number of processors
:param random: type boolean, if or not use random density field
:param rtol: type float, relevative tolerance for global convergence
:param usePert: type boolean, if or not use perturbation method
:param pert: type float, perturbated strain applied to DEM to obtain tangent operator
:param verbose: type boolean, if or not print messages during calculation
"""
self.__domain=domain
self.__pde=LinearPDE(domain,numEquations=self.__domain.getDim(),numSolutions=self.__domain.getDim())
self.__pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
#self.__pde.getSolverOptions().setTolerance(rtol**2)
#self.__pde.getSolverOptions().setPackage(SolverOptions.UMFPACK)
self.__numGaussPoints=ng
self.__rtol=rtol
self.__usepert=usePert
self.__pert=pert
self.__verbose=verbose
self.__pool=Pool(processes=np)
self.__scenes=self.__pool.map(initLoad,range(ng))#where is initLoad???from simDEM.py,to load RVEs; map(function, iterable)
self.__strain=escript.Tensor(0,escript.Function(self.__domain))
'''Tensor(value=0., what=FunctionSpace(), expanded=False) returns a Data object of shape (d,d) in the FunctionSpace what, where d is the spatial dimension of the Domain of what. Values are initialized with value, a double precision quantity(here is 0). If expanded is True the Data object is represented in expanded form.
'''
self.__stress=escript.Tensor(0,escript.Function(self.__domain))
#Function(domain): returns the general FunctionSpace on the Domain domain. Data objects in this type of general FunctionSpace are defined over the whole geometric region defined by domain.
self.__S=escript.Tensor4(0,escript.Function(self.__domain))
#Tensor4 is similar to Tensor, which returns a Data object of shape (d,d,d,d)
#simDEM part
if self.__usepert: #here usepert=false, so this is not invoked.
s = self.__pool.map(getStressTensor,self.__scenes) #getstresstensor is defined in simDEM, but here it is not invoked.
t = self.__pool.map(getTangentOperator,zip(self.__scenes,repeat(pert)))#to get initial D and sigma
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i,s[i])
self.__S.setValueOfDataPoint(i,t[i])
else:
st = self.__pool.map(getStressAndTangent2D,self.__scenes)
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i,st[i][0])
self.__S.setValueOfDataPoint(i,st[i][1])
def __init__(self,domain,dim,ng=1,useMPI=False,np=1,rho=2.35e3,mIds=False,\
FEDENodeMap=False,DE_ext=False,FEDEBoundMap=False,conf=False):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param ng: type integer, number of Gauss points
:param useMPI: type boolean, use MPI or not
:param np: type integer, number of processors
:param rho: type float, density of material
:param mIds: a list contains membrane node IDs
:param FEDENodeMap: a dictionary with FE and DE boundary node IDs in keys and values
:param DE_ext: name of file which saves initial state of exterior DE domain
:param FEDEBoundMap: a dictionary with FE and DE boundary element IDs in keys and values (deprecated)
:param conf: type float, conf pressure on membrane
"""
self.__domain=domain
self.__pde=LinearPDE(self.__domain,numEquations=dim,numSolutions=dim)
self.__pde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
self.__pde.setSymmetryOn()
self.__numGaussPoints=ng
self.__rho=rho
self.__mIds=mIds
self.__FEDENodeMap=FEDENodeMap
self.__FEDEBoundMap=FEDEBoundMap
self.__conf=conf
self.__pool=get_pool(mpi=useMPI,threads=np)
self.__scenes=self.__pool.map(initLoad,range(ng))
self.__strain=escript.Tensor(0,escript.Function(self.__domain))
self.__stress=escript.Tensor(0,escript.Function(self.__domain))
self.__u=escript.Vector(0,escript.Solution(self.__domain))
self.__u_last=escript.Vector(0,escript.Solution(self.__domain))
self.__u_t=escript.Vector(0,escript.Solution(self.__domain))
self.__dt=0
# ratio between timesteps in internal DE and FE domain
self.__nsOfDE_int=1
# if FEDENodeMap is given, employ exterior DE domain
if self.__FEDENodeMap:
self.__sceneExt=self.__pool.apply(initLoadExt,(DE_ext,))
# ratio between timesteps in external DE and FE domain
self.__nsOfDE_ext=1
# get interface nodal forces as boundary condition
self.__FEf = self.__pool.apply(initNbc,(self.__sceneExt,self.__conf,mIds,FEDENodeMap))
"""
# get interface nodal tractions as boundary condition (deprecated)
self.__Nbc=escript.Vector(0,escript.Solution(self.__domain))
FENbc = self.__pool.apply(initNbc,(self.__sceneExt,self.__conf,mIds,FEDENodeMap))
for FEid in FENbc.keys():
self.__Nbc.setValueOfDataPoint(FEid,FENbc[FEid])
"""
# get stress tensor at material points
s = self.__pool.map(getStress2D,self.__scenes)
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i,s[i])
def __init__(self,domain,ng=1,useMPI=False,np=1,random=False,rtol=1.e-2,usePert=False,pert=-2.e-6,verbose=False):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param ng: type integer, number of Gauss points
:param useMPI: type boolean, use MPI or not
:param np: type integer, number of processors
:param random: type boolean, if or not use random density field
:param rtol: type float, relevative tolerance for global convergence
:param usePert: type boolean, if or not use perturbation method
:param pert: type float, perturbated strain applied to DEM to obtain tangent operator
:param verbose: type boolean, if or not print messages during calculation
"""
self.__domain=domain
self.__pde=LinearPDE(domain,numEquations=self.__domain.getDim(),numSolutions=self.__domain.getDim())
try:
self.__pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
except:
#import time
print("=======================================================================")
print("For better performance compile python-escript with direct solver method")
print("=======================================================================")
input("Press Enter to continue...")
#time.sleep(5)
self.__pde.setSymmetryOn()
#self.__pde.getSolverOptions().setTolerance(rtol**2)
#self.__pde.getSolverOptions().setPackage(SolverOptions.UMFPACK)
self.__numGaussPoints=ng
self.__rtol=rtol
self.__usepert=usePert
self.__pert=pert
self.__verbose=verbose
self.__pool=get_pool(mpi=useMPI,threads=np)
self.__scenes=self.__pool.map(initLoad,list(range(ng)))
self.__strain=escript.Tensor(0,escript.Function(self.__domain))
self.__stress=escript.Tensor(0,escript.Function(self.__domain))
self.__S=escript.Tensor4(0,escript.Function(self.__domain))
if self.__usepert:
s = self.__pool.map(getStressTensor,self.__scenes)
t = self.__pool.map(getTangentOperator,list(zip(self.__scenes,repeat(pert))))
for i in range(ng):
self.__stress.setValueOfDataPoint(i,s[i])
self.__S.setValueOfDataPoint(i,t[i])
else:
st = self.__pool.map(getStressAndTangent2D,self.__scenes)
for i in range(ng):
self.__stress.setValueOfDataPoint(i,st[i][0])
self.__S.setValueOfDataPoint(i,st[i][1])
def getMaxEigenvalue(self):
"""
return the max eigenvalue of the model
type: float
"""
dom = self.getDomain()
dim = dom.getDim()
pdeKu_P = LinearPDE(dom, numEquations=dim, numSolutions=dim)
T = self.getCurrentTangent()
pdeKu_P.setValue(A=T)
pdeKu_P.getOperator().saveMM('tempMTX.mtx')
mtx = mmread('tempMTX.mtx')
maxEigVal = max(eigs(mtx, k=1, return_eigenvectors=False, which='LR'))
return maxEigVal.real
def gzpot(p, y, x, *args):
#rho, rhox, rhoy, R = p
rhox = args[0] / 2.
rhoy = args[1] / 2.
rho, R, z = p
#Domain related.
mx = args[0]
my = args[1]
#PDE related
G = 6.67300 * 10E-11
#DOMAIN CONSTRUCTION
domain = ReadGmsh('data/example10m/example10m.msh', 2)
domx = Solution(domain).getX()
mask = wherePositive(R - length(domx - rholoc))
rhoe = rho * mask
kro = kronecker(domain)
q = whereZero(domx[1] - my) + whereZero(domx[1]) + whereZero(
domx[0]) + whereZero(domx[0] - mx)
#ESCRIPT PDE CONSTRUCTION
mypde = LinearPDE(domain)
mypde.setValue(A=kro, Y=4. * np.pi * G * rhoe, q=q, r=0.0)
mypde.setSymmetryOn()
sol = mypde.getSolution()
g_field = grad(sol) #The graviational accelleration g.
g_fieldz = g_field * [0, 1] #The vertical component of the g field.
gz = length(g_fieldz) #The magnitude of the vertical component.
#MODEL SIZE SAMPLING
sol_escgz = []
sol_escx = []
for i in range(0, len(x)):
sol_escgz.append([x[i], rhoy + z])
sample = [] # array to hold values
rec = Locator(gz.getFunctionSpace(), sol_escgz) #location to record
psol = rec.getValue(gz)
err = np.sum((np.array(y) - np.array(psol))**2.)
print("Lsup= ",
Lsup(np.array(psol) - np.array(sol_angz)) / Lsup(np.array(psol)))
return err
def gzpot(p, y, x, *args):
#rho, rhox, rhoy, R = p
rhox=args[0]/2.; rhoy=args[1]/2.
rho, R, z =p
#Domain related.
mx = args[0]; my = args[1];
#PDE related
G=6.67300*10E-11
#DOMAIN CONSTRUCTION
domain=ReadGmsh('data/example10m/example10m.msh',2)
domx=Solution(domain).getX()
mask=wherePositive(R-length(domx-rholoc))
rhoe=rho*mask
kro=kronecker(domain)
q=whereZero(domx[1]-my)+whereZero(domx[1])+whereZero(domx[0])+whereZero(domx[0]-mx)
#ESCRIPT PDE CONSTRUCTION
mypde=LinearPDE(domain)
mypde.setValue(A=kro,Y=4.*np.pi*G*rhoe,q=q,r=0.0)
mypde.setSymmetryOn()
sol=mypde.getSolution()
g_field=grad(sol) #The graviational accelleration g.
g_fieldz=g_field*[0,1] #The vertical component of the g field.
gz=length(g_fieldz) #The magnitude of the vertical component.
#MODEL SIZE SAMPLING
sol_escgz=[]
sol_escx=[]
for i in range(0,len(x)):
sol_escgz.append([x[i],rhoy+z])
sample=[] # array to hold values
rec=Locator(gz.getFunctionSpace(),sol_escgz) #location to record
psol=rec.getValue(gz)
err = np.sum((np.array(y) - np.array(psol))**2.)
print("Lsup= ",Lsup(np.array(psol)-np.array(sol_angz))/Lsup(np.array(psol)))
return err
class SlippingFault(SaddlePointProblem):
"""
simple example of saddle point problem
"""
def __init__(self,domain):
super(SlippingFault, self).__init__(self)
self.domain=domain
self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
self.__pde_u.setSymmetryOn()
def initialize(self,density=1.,lmbd=1., mu=1., traction=Data(),fixed_u_mask=Data(), slip=0.):
d=self.domain.getDim()
self.slip=slip
A =self.__pde_u.createCoefficientOfGeneralPDE("A")
for i in range(self.domain.getDim()):
for j in range(self.domain.getDim()):
A[i,j,j,i] += mu
A[i,j,i,j] += mu
A[i,i,j,j] += lmbd
self.__pde_u.setValue(A=A,q=fixed_u_mask,Y=-kronecker(Function(self.domain))[d-1]*g*density,y=traction)
def inner(self,p0,p1):
return integrate(inner(p0,p1),FunctionOnContactZero(self.domain))
def solve_f(self,u,p,tol=1.e-8):
self.__pde_u.setTolerance(tol)
self.__pde_u.setValue(y_contact=-p)
# print "p:",inf(p),sup(p)
# print "u:",inf(u),sup(u)
self.__pde_u.setValue(y_contact=-p)
return self.__pde_u.getSolution()
def solve_g(self,u,tol=1.e-8):
dp=Vector(0.,FunctionOnContactZero(self.domain))
h=FunctionOnContactZero(self.domain).getSize()
# print jump(u)-self.slip
dp[0]=(self.slip[0]-jump(u[0]))*lam_mu/h
dp[1]=(self.slip[1]-jump(u[1]))*lam_mu/h
dp[2]=(self.slip[2]-jump(u[2]))*lam_mu/h
return dp
res=1000.0
con=1/res
cur=10.
################################################ESTABLISHING PARAMETERS
#the folder to put our outputs in, leave blank "" for script path
save_path= os.path.join("data","example11")
#ensure the dir exists
mkDir(save_path)
####################################################DOMAIN CONSTRUCTION
domain = Rectangle(l0=mx,l1=my,n0=ndx, n1=ndy)
x=Solution(domain).getX()
kro=kronecker(domain)
source1=[mx/4.,0]; source2=[3.*mx/4.,0]
sourceg=length(exp(-length(x-source1)/(100.)))+length(exp(-length(x-source2)/(100.)))
sourceg=sourceg/integrate(sourceg)
q=whereZero(x[1]-my)+whereZero(x[0])+whereZero(x[0]-mx)
###############################################ESCRIPT PDE CONSTRUCTION
mypde=LinearPDE(domain)
mypde.setValue(A=kro*con,Y=sourceg,q=q,r=0)
mypde.setSymmetryOn()
sol=mypde.getSolution()
# Save the output to file.
saveVTK(os.path.join(save_path,"ex11a.vtu"),source=sourceg,res_pot=sol)
class Mechanics(Model):
"""
base class for mechanics models in updated lagrangean framework
:note: Instance variable domain - domain (in)
:note: Instance variable internal_force - =Data()
:note: Instance variable external_force - =Data()
:note: Instance variable prescribed_velocity - =Data()
:note: Instance variable location_prescribed_velocity - =Data()
:note: Instance variable temperature - = None
:note: Instance variable expansion_coefficient - = 0.
:note: Instance variable bulk_modulus - =1.
:note: Instance variable shear_modulus - =1.
:note: Instance variable rel_tol - =1.e-3
:note: Instance variable abs_tol - =1.e-15
:note: Instance variable max_iter - =10
:note: Instance variable displacement - =None
:note: Instance variable stress - =None
"""
SAFTY_FACTOR_ITERATION = 1. / 100.
def __init__(self, **kwargs):
"""
set up the model
:keyword debug: debug flag
:type debug: ``bool``
"""
super(Mechanics, self).__init__(self, **kwargs)
self.declareParameter(domain=None, \
displacement=None, \
stress=None, \
velocity=None, \
internal_force=None, \
external_force=None, \
prescribed_velocity=None, \
location_prescribed_velocity=None, \
temperature = None, \
expansion_coefficient = 0., \
bulk_modulus=2., \
shear_modulus=1., \
rel_tol=1.e-3,abs_tol=1.e-15,max_iter=10)
self.__iter = 0
def doInitialization(self):
"""
initialize model
"""
if not self.displacement:
self.displacement = Vector(0., ContinuousFunction(self.domain))
if not self.velocity:
self.velocity = Vector(0., ContinuousFunction(self.domain))
if not self.stress:
self.stress = Tensor(0., ContinuousFunction(self.domain))
if not self.internal_force: self.internal_force = Data()
if not self.external_force: self.external_force = Data()
if not self.prescribed_velocity: self.prescribed_velocity = Data()
if not self.location_prescribed_velocity:
self.location_prescribed_velocity = Data()
# save the old values:
self.__stress_safe = self.stress
self.__temperature_safe = self.temperature
self.__displacement_safe = self.displacement
self.__velocity_safe = self.velocity
self.__velocity_old = None
self.__old_dt = None
self.__very_old_dt = None
# get node cooridnates and apply initial displacement
self.__x = self.domain.getX()
self.domain.setX(self.__x + self.displacement)
# open PDE:
self.__pde = LinearPDE(self.domain)
self.__pde.setSolverMethod(self.__pde.DIRECT)
self.__solver_options = self.__pde.getSolverOptions()
self.__solver_options.setSolverMethod(self.__solver_options.DIRECT)
self.__solver_options.setVerbosity(self.debug)
# self.__pde.setSymmetryOn()
def doStepPreprocessing(self, dt):
"""
step up pressure iteration
if run within a time dependend problem extrapolation of pressure from previous time steps is used to
get an initial guess (that needs some work!!!!!!!)
"""
# reset iteration counters:
self.__iter = 0
self.__diff = self.UNDEF_DT
# set initial guesses for the iteration:
self.displacement = self.__displacement_safe
self.stress = self.__stress_safe
self.velocity = self.__velocity_safe
# update geometry
self.domain.setX(self.__x + self.displacement)
def doStep(self, dt):
"""
"""
self.__iter += 1
k3 = kronecker(self.domain)
# set new thermal stress increment
if self.temperature == None:
self.deps_th = 0.
else:
self.deps_th = self.expansion_coefficient * (
self.temperature - self.__temperature_safe)
# set PDE coefficients:
self.__pde.setValue(A=self.S)
self.__pde.setValue(X=-self.stress -
self.bulk_modulus * self.deps_th * k3)
if self.internal_force: self.__pde.setValue(Y=self.internal_force)
if self.external_force: self.__pde.setValue(y=self.external_force)
self.__pde.setValue(q=self.location_prescribed_velocity, \
r=Data())
if not self.prescribed_velocity.isEmpty() and self.__iter == 1:
self.__pde.setValue(r=dt * self.prescribed_velocity)
# solve the PDE:
self.__solver_options.setTolerance(self.rel_tol**2)
self.du = self.__pde.getSolution()
# update geometry
self.displacement = self.displacement + self.du
self.domain.setX(self.__x + self.displacement)
self.velocity = (self.displacement - self.__displacement_safe) / dt
if self.debug:
for i in range(self.domain.getDim()):
self.trace("du %d range %e:%e" %
(i, inf(self.du[i]), sup(self.du[i])))
for i in range(self.domain.getDim()):
self.trace(
"displacement %d range %e:%e" %
(i, inf(self.displacement[i]), sup(self.displacement[i])))
for i in range(self.domain.getDim()):
self.trace("velocity %d range %e:%e" %
(i, inf(self.velocity[i]), sup(self.velocity[i])))
self.__stress_last = self.stress
def terminateIteration(self):
"""iteration is terminateIterationd if relative pressure change is less than rel_tol"""
if self.__iter > self.max_iter:
raise IterationDivergenceError(
"Maximum number of iterations steps reached")
if self.__iter == 0:
self.__diff = self.UNDEF_DT
else:
self.__diff, diff_safe = Lsup(self.stress -
self.__stress_last), self.__diff
s_sup = Lsup(self.stress)
self.trace("stress max and increment :%e, %e" %
(s_sup, self.__diff))
if self.__iter > 2 and diff_safe < self.__diff:
raise IterationDivergenceError(
"no improvement in stress iteration")
return self.__diff <= self.rel_tol * self.SAFTY_FACTOR_ITERATION * s_sup + self.abs_tol
def doStepPostprocessing(self, dt):
"""
accept all the values:
"""
self.__displacement_safe = self.displacement
self.__temperature_safe = self.temperature
self.__stress_safe = self.stress
self.__velocity_safe = self.velocity
def getSafeTimeStepSize(self, dt):
"""
returns new step size
"""
a = sup(length(self.velocity) / self.domain.getSize())
if a > 0:
return 1. / a
else:
return self.UNDEF_DT
# surface
bblock = PlaneSurface(bblockloop)
################################################CREATE MESH FOR ESCRIPT
# Create a Design which can make the mesh
d=Design(dim=2, element_size=200)
# Add the subdomains and flux boundaries.
d.addItems(PropertySet("top",tblock),PropertySet("bottom",bblock),\
PropertySet("linebottom",l12))
# Create the geometry, mesh and Escript domain
d.setScriptFileName(os.path.join(save_path,"example05.geo"))
d.setMeshFileName(os.path.join(save_path,"example05.msh"))
domain=MakeDomain(d, optimizeLabeling=True)
print("Domain has been generated ...")
##############################################################SOLVE PDE
mypde=LinearPDE(domain)
mypde.getSolverOptions().setVerbosityOn()
mypde.setSymmetryOn()
kappa=Scalar(0,Function(domain))
kappa.setTaggedValue("top",2.0*W/m/K)
kappa.setTaggedValue("bottom",4.0*W/m/K)
mypde.setValue(A=kappa*kronecker(domain))
x=Solution(domain).getX()
mypde.setValue(q=whereZero(x[1]-sup(x[1])),r=Ttop)
qS=Scalar(0,FunctionOnBoundary(domain))
qS.setTaggedValue("linebottom",qin)
mypde.setValue(y=qS)
print("PDE has been generated ...")
###########################################################GET SOLUTION
T=mypde.getSolution()
print("PDE has been solved ...")
tend = 0.5 * day # - time to end simulation
outputs = 200 # number of time steps required.
h = (tend - t) / outputs #size of time step
#user warning statement
print("Expected Number of time outputs is: ", (tend - t) / h)
i = 0 #loop counter
#the folder to put our outputs in, leave blank "" for script path
save_path = os.path.join("data", "example02")
#ensure the dir exists
mkDir(save_path, os.path.join(save_path, "tempT"))
####################################################DOMAIN CONSTRUCTION
rod = Rectangle(l0=mx, l1=my, n0=ndx, n1=ndy)
x = Solution(rod).getX()
###############################################ESCRIPT PDE CONSTRUCTION
mypde = LinearPDE(rod)
A = zeros((2, 2))
A[0, 0] = kappa
q = whereZero(x[0])
mypde.setValue(A=A, D=rhocp / h, q=q, r=T0)
# ... set initial temperature ....
T = T0 * whereZero(x[0]) + Tref * (1 - whereZero(x[0]))
# ... open a collector for the time marks and corresponding total energy
t_list = []
E_list = []
# ... convert solution points for plotting
plx = x.toListOfTuples()
plx = np.array(plx) #convert to tuple to numpy array
plx = plx[:, 0] #extract x locations
########################################################START ITERATION
from esys.escript.linearPDEs import LinearPDE
try:
from esys.finley import Rectangle
HAVE_FINLEY = True
except ImportError:
HAVE_FINLEY = False
from esys.weipa import saveVTK
if not HAVE_FINLEY:
print("Finley module not available")
else:
#... set some parameters ...
kappa=1.
omega=0.1
eta=10.
#... generate domain ...
mydomain = Rectangle(l0=5.,l1=1.,n0=50, n1=10)
#... open PDE and set coefficients ...
mypde=LinearPDE(mydomain)
mypde.setSymmetryOn()
n=mydomain.getNormal()
x=mydomain.getX()
mypde.setValue(A=kappa*kronecker(mydomain),D=omega,Y=omega*x[0], \
d=eta,y=kappa*n[0]+eta*x[0])
#... calculate error of the PDE solution ...
u=mypde.getSolution()
print("error is ",Lsup(u-x[0]))
# output should be similar to "error is 1.e-7"
saveVTK("x0.vtu",sol=u)
#~ tester=tester.toListOfTuples()
#~ tester=np.reshape(tester,(ndx+1,ndy+1))
#~ pl.clf()
#~ pl.imshow(tester)
#~ pl.colorbar()
#~ pl.savefig("tester3.png")
abcT = abc.toListOfTuples()
abcT = np.reshape(abcT, (ndx + 1, ndy + 1))
pl.clf()
pl.imshow(abcT)
pl.colorbar()
pl.savefig("abc.png")
# ... open new PDE ...
mypde = LinearPDE(domain)
#mypde.setSolverMethod(LinearPDE.LUMPING)
mypde.setSymmetryOn()
kmat = kronecker(domain)
mypde.setValue(D=kmat * rho)
# define small radius around point xc
# Lsup(x) returns the maximum value of the argument x
src_radius = 50 #2*Lsup(domain.getSize())
print("src_radius = ", src_radius)
#dunit=numpy.array([0.,1.]) # defines direction of point source
dunit = (x - xc)
absrc = length(dunit)
dunit = dunit / maximum(absrc, 1e-10)
pl.clf()
pl.plot(source)
#pl.plot(time,decay1);pl.plot(time,decay2);
#pl.plot(time,tdecay)
pl.savefig(os.path.join(savepath, 'source.png'))
# will introduce a spherical source at middle left of bottom face
xc = [mx / 2, 0]
####################################################DOMAIN CONSTRUCTION
domain = Rectangle(l0=mx, l1=my, n0=ndx, n1=ndy,
order=2) # create the domain
x = domain.getX() # get the locations of the nodes in the domani
##########################################################ESTABLISH PDE
mypde = LinearPDE(domain) # create pde
mypde.setSymmetryOn() # turn symmetry on
# turn lumping on for more efficient solving
mypde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
kmat = kronecker(
domain) # create the kronecker delta function of the domain
mypde.setValue(D=kmat * rho) #set the general form value D
##########################################################ESTABLISH ABC
# Define where the boundary decay will be applied.
bn = 50.
bleft = xstep * bn
bright = mx - (xstep * bn)
bbot = my - (ystep * bn)
# btop=ystep*bn # don't apply to force boundary!!!
# Join line segments to create domain boundary.
c = CurveLoop(l01, l12, l23, l30)
# surface
rec = PlaneSurface(c)
#############################################EXPORTING MESH FOR ESCRIPT
# Create a Design which can make the mesh
d = Design(dim=2, element_size=200 * m)
# Add the subdomains and flux boundaries.
d.addItems(rec, PropertySet("linebottom", l12))
d.addItems(l01, l23, l30) # just in case we need them
#############################################MAKE THE DOMAIN
domain = MakeDomain(d, optimizeLabeling=True)
print("Domain has been generated ...")
##############################################################SOLVE PDE
mypde = LinearPDE(domain)
mypde.getSolverOptions().setVerbosityOn()
mypde.setSymmetryOn()
mypde.setValue(A=kappa * kronecker(domain))
x = Solution(domain).getX()
mypde.setValue(q=whereZero(x[1] - sup(x[1])), r=Ttop)
qS = Scalar(0, FunctionOnBoundary(domain))
qS.setTaggedValue("linebottom", qin)
mypde.setValue(y=-qS)
print("PDE has been generated ...")
###########################################################GET SOLUTION
T = mypde.getSolution()
print("PDE has been solved ...")
###########################################################
xi, yi, zi = toRegGrid(T, nx=50, ny=50)
pl.matplotlib.pyplot.autumn()
#~ tester=np.reshape(tester,(ndx+1,ndy+1))
#~ pl.clf()
#~ pl.imshow(tester)
#~ pl.colorbar()
#~ pl.savefig("tester2.png")
#~
#~ tester=fbottom*wherePositive(bottom)
#~ tester=tester.toListOfTuples()
#~ tester=np.reshape(tester,(ndx+1,ndy+1))
#~ pl.clf()
#~ pl.imshow(tester)
#~ pl.colorbar()
#~ pl.savefig("tester3.png")
# ... open new PDE ...
mypde = LinearPDE(domain)
print(mypde.isUsingLumping())
print(mypde.getSolverOptions())
#mypde.getSolverOptions().setSolverMethod(SolverOptions.LUMPING)
mypde.setSymmetryOn()
kmat = kronecker(domain)
mypde.setValue(D=kmat * rho)
# define small radius around point xc
# Lsup(x) returns the maximum value of the argument x
src_radius = 50 #2*Lsup(domain.getSize())
print("src_radius = ", src_radius)
dunit = numpy.array([0., 1.]) # defines direction of point source
#~ dunit=(x-xc)
#~ absrc=length(dunit)
def wavePropagation(dom, rho, mu, lmbd, eta):
x = Function(dom).getX()
# ... open new PDE ...
mypde = LinearPDE(dom)
mypde.setSolverMethod(LinearPDE.LUMPING)
k = kronecker(Function(dom))
mypde.setValue(D=k * rho)
dt = (1. / 5.) * inf(dom.getSize() / sqrt((2 * mu + lmbd) / rho))
if output: print("time step size = ", dt)
# ... set initial values ....
n = 0
t = 0
t_write = 0.
n_write = 0
# initial value of displacement at point source is constant (U0=0.01)
# for first two time steps
u = Vector(0., Solution(dom))
v = Vector(0., Solution(dom))
a = Vector(0., Solution(dom))
a2 = Vector(0., Solution(dom))
v = Vector(0., Solution(dom))
if not os.path.isdir(WORKDIR): os.mkdir(WORKDIR)
starttime = time.clock()
while t < t_end and n < n_end:
if output:
print(n + 1,
"-th time step t ",
t + dt,
" max u and F: ",
Lsup(u),
end=' ')
# prediction:
u_pr = u + dt * v + (dt**2 / 2) * a + (dt**3 / 6) * a2
v_pr = v + dt * a + (dt**2 / 2) * a2
a_pr = a + dt * a2
# ... get current stress ....
eps = symmetric(grad(u_pr))
stress = lmbd * trace(eps) * k + 2 * mu * eps
# ... force due to event:
if abs(t - tc) < 5 * tc_length:
F = exp(-((t - tc) / tc_length)**2) * exp(-(length(x - xc) /
src_radius)**2) * event
if output: print(Lsup(F))
else:
if output: print(0.)
# ... get new acceleration ....
mypde.setValue(X=-stress, Y=F - eta * v_pr)
a = mypde.getSolution()
# ... get new displacement ...
da = a - a_pr
u = u_pr + (dt**2 / 12.) * da
v = v_pr + (5 * dt / 12.) * da
a2 += da / dt
# ... save current acceleration in units of gravity and displacements
if output:
if t >= t_write:
saveVTK(os.path.join(WORKDIR, "disp.%i.vtu" % n_write),
displacement=u,
amplitude=length(u))
t_write += dt_write
n_write += 1
t += dt
n += 1
endtime = time.clock()
totaltime = endtime - starttime
global netotal
print(">>number of elements: %s, total time: %s, per time step: %s <<" %
(netotal, totaltime, totaltime / n))
class StokesProblem(SaddlePointProblem):
"""
simple example of saddle point problem
"""
def __init__(self,domain,debug=False):
super(StokesProblem, self).__init__(self,debug)
self.domain=domain
self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
self.__pde_u.setSymmetryOn()
self.__pde_p=LinearPDE(domain)
self.__pde_p.setReducedOrderOn()
self.__pde_p.setSymmetryOn()
def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1):
self.eta=eta
A =self.__pde_u.createCoefficientOfGeneralPDE("A")
for i in range(self.domain.getDim()):
for j in range(self.domain.getDim()):
A[i,j,j,i] += self.eta
A[i,j,i,j] += self.eta
self.__pde_p.setValue(D=1/self.eta)
self.__pde_u.setValue(A=A,q=fixed_u_mask,Y=f)
def inner(self,p0,p1):
return integrate(p0*p1,Function(self.__pde_p.getDomain()))
def solve_f(self,u,p,tol=1.e-8):
self.__pde_u.setTolerance(tol)
g=grad(u)
self.__pde_u.setValue(X=self.eta*symmetric(g)+p*kronecker(self.__pde_u.getDomain()))
return self.__pde_u.getSolution()
def solve_g(self,u,tol=1.e-8):
self.__pde_p.setTolerance(tol)
self.__pde_p.setValue(X=-u)
dp=self.__pde_p.getSolution()
return dp
def __init__(self,domain):
super(SlippingFault, self).__init__(self)
self.domain=domain
self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
self.__pde_u.setSymmetryOn()
class MultiScale(object):
"""
problem description:
-(A_{ijkl} u_{k,l})_{,j} = -X_{ij,j} + Y_i
Neumann boundary: n_j A_{ijkl} u_{k,l} = n_j X_{ij} + y_i
Dirichlet boundary: u_i = r_i where q_i > 0
:var u: unknown vector, displacement
:var A: elastic tensor / tangent operator
:var X: old/current stress tensor
:var Y: vector, body force
:var y: vector, Neumann bc traction
:var q: vector, Dirichlet bc mask
:var r: vector, Dirichlet bc value
"""
def __init__(self,
domain,
ng=1,
useMPI=False,
np=1,
random=False,
rtol=1.e-2,
verbose=False):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param ng: type integer, number of Gauss points
:param useMPI: type boolean, use MPI or not
:param np: type integer, number of processors
:param random: type boolean, if or not use random density field
:param rtol: type float, relevant tolerance for global convergence
:param verbose: type boolean, if or not print messages during calculation
"""
self.__domain = domain
self.__pde = LinearPDE(domain,
numEquations=self.__domain.getDim(),
numSolutions=self.__domain.getDim())
self.__pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
self.__pde.setSymmetryOn()
#self.__pde.getSolverOptions().setTolerance(rtol**2)
#self.__pde.getSolverOptions().setPackage(SolverOptions.UMFPACK)
self.__numGaussPoints = ng
self.__rtol = rtol
self.__verbose = verbose
self.__pool = get_pool(mpi=useMPI, threads=np)
self.__scenes = self.__pool.map(initLoad, range(ng))
self.__strain = escript.Tensor(0, escript.Function(self.__domain))
self.__stress = escript.Tensor(0, escript.Function(self.__domain))
self.__S = escript.Tensor4(0, escript.Function(self.__domain))
st = self.__pool.map(getStressAndTangent, self.__scenes)
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i, st[i][0])
self.__S.setValueOfDataPoint(i, st[i][1])
def initialize(self,
b=escript.Data(),
f=escript.Data(),
specified_u_mask=escript.Data(),
specified_u_val=escript.Data()):
"""
initialize the model for each time step, e.g. assign parameters
:param b: type vector, body force on FunctionSpace, e.g. gravity
:param f: type vector, boundary traction on FunctionSpace (FunctionOnBoundary)
:param specified_u_mask: type vector, mask of location for Dirichlet boundary
:param specified_u_val: type vector, specified displacement for Dirichlet boundary
"""
self.__pde.setValue(Y=b, y=f, q=specified_u_mask, r=specified_u_val)
def getDomain(self):
"""
return model domain
"""
return self.__domain
def getRelTolerance(self):
"""
return relative tolerance for convergence
type float
"""
return self.__rtol
def getCurrentPacking(self, pos=(), time=0, prefix=''):
if len(pos) == 0:
# output all Gauss points packings
self.__pool.map(outputPack,
zip(self.__scenes, repeat(time), repeat(prefix)))
else:
# output selected Gauss points packings
scene = [self.__scenes[i] for i in pos]
self.__pool.map(outputPack, zip(scene, repeat(time),
repeat(prefix)))
def getLocalVoidRatio(self):
void = escript.Scalar(0, escript.Function(self.__domain))
e = self.__pool.map(getVoidRatio, self.__scenes)
for i in xrange(self.__numGaussPoints):
void.setValueOfDataPoint(i, e[i])
return void
def getLocalAvgRotation(self):
rot = escript.Vector(0, escript.Function(self.__domain))
r = self.__pool.map(avgRotation, self.__scenes)
for i in xrange(self.__numGaussPoints):
rot.setValueOfDataPoint(i, r[i])
return rot
def getLocalFabric(self):
fabric = escript.Tensor(0, escript.Function(self.__domain))
f = self.__pool.map(getFabric, self.__scenes)
for i in xrange(self.__numGaussPoints):
fabric.setValueOfDataPoint(i, f[i])
return fabric
def getCurrentTangent(self):
"""
return current tangent operator
type Tensor4 on FunctionSpace
"""
return self.__S
def getCurrentStress(self):
"""
return current stress
type: Tensor on FunctionSpace
"""
return self.__stress
def getCurrentStrain(self):
"""
return current strain
type: Tensor on FunctionSpace
"""
return self.__strain
def exitSimulation(self):
"""finish the whole simulation, exit"""
self.__pool.close()
def solve(self, iter_max=100):
"""
solve the equation using Newton-Ralphson scheme
"""
iterate = 0
rtol = self.getRelTolerance()
stress = self.getCurrentStress()
s = self.getCurrentTangent()
x_safe = self.__domain.getX()
self.__pde.setValue(A=s, X=-stress)
#residual0=util.L2(self.__pde.getRightHandSide()) # using force error
u = self.__pde.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 = 1.0 # initial error before iteration
converged = (err < rtol)
while (not converged) and (iterate < iter_max):
if self.__verbose:
print "Not converged after %d iteration(s)! Relative error: %e" % (
iterate, err)
iterate += 1
self.__domain.setX(x_safe + u)
self.__pde.setValue(A=update_s, X=-update_stress, r=escript.Data())
#residual=util.L2(self.__pde.getRightHandSide())
du = self.__pde.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 * 0.001: # 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)
#if err>err_safe: # to ensure consistent convergence, however this may not be achieved due to fluctuation!
# raise RuntimeError,"No improvement of convergence with iterations! Relative error: %e"%err
"""
update 'domain geometry', 'stress', 'tangent operator',
'accumulated strain' and 'simulation scenes'.
"""
self.__domain.setX(x_safe + u)
self.__stress = update_stress
self.__S = update_s
self.__strain += D
self.__scenes = update_scenes
if self.__verbose:
print "Convergence reached after %d iteration(s)! Relative error: %e" % (
iterate, err)
return u
"""
apply strain to DEM packing,
get stress and tangent operator (including two methods)
"""
def applyStrain_getStressTangentDEM(self, st=escript.Data()):
st = st.toListOfTuples()
st = numpy.array(st).reshape(-1, 9)
stress = escript.Tensor(0, escript.Function(self.__domain))
S = escript.Tensor4(0, escript.Function(self.__domain))
scenes = self.__pool.map(shear, zip(self.__scenes, st))
st = self.__pool.map(getStressAndTangent, scenes)
for i in xrange(self.__numGaussPoints):
stress.setValueOfDataPoint(i, st[i][0])
S.setValueOfDataPoint(i, st[i][1])
return stress, S, scenes
class MultiScale(object):
"""
problem description:
-(A_{ijkl} u_{k,l})_{,j} = -X_{ij,j} + Y_i
Neumann boundary: n_j A_{ijkl} u_{k,l} = n_j X_{ij} + y_i
Dirichlet boundary: u_i = r_i where q_i > 0
:var u: unknown vector, displacement
:var A: elastic tensor / tangent operator
:var X: old/current stress tensor
:var Y: vector, body force
:var y: vector, Neumann bc traction
:var q: vector, Dirichlet bc mask
:var r: vector, Dirichlet bc value
"""
def __init__(self,domain,ng=1,useMPI=False,np=1,random=False,rtol=1.e-2,usePert=False,pert=-2.e-6,verbose=False):
"""
initialization of the problem, i.e. model constructor
:param domain: type Domain, domain of the problem
:param ng: type integer, number of Gauss points
:param useMPI: type boolean, use MPI or not
:param np: type integer, number of processors
:param random: type boolean, if or not use random density field
:param rtol: type float, relevative tolerance for global convergence
:param usePert: type boolean, if or not use perturbation method
:param pert: type float, perturbated strain applied to DEM to obtain tangent operator
:param verbose: type boolean, if or not print messages during calculation
"""
self.__domain=domain
self.__pde=LinearPDE(domain,numEquations=self.__domain.getDim(),numSolutions=self.__domain.getDim())
self.__pde.getSolverOptions().setSolverMethod(SolverOptions.DIRECT)
self.__pde.setSymmetryOn()
#self.__pde.getSolverOptions().setTolerance(rtol**2)
#self.__pde.getSolverOptions().setPackage(SolverOptions.UMFPACK)
self.__numGaussPoints=ng
self.__rtol=rtol
self.__usepert=usePert
self.__pert=pert
self.__verbose=verbose
self.__pool=get_pool(mpi=useMPI,threads=np)
self.__scenes=self.__pool.map(initLoad,range(ng))
self.__strain=escript.Tensor(0,escript.Function(self.__domain))
self.__stress=escript.Tensor(0,escript.Function(self.__domain))
self.__S=escript.Tensor4(0,escript.Function(self.__domain))
if self.__usepert:
s = self.__pool.map(getStressTensor,self.__scenes)
t = self.__pool.map(getTangentOperator,zip(self.__scenes,repeat(pert)))
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i,s[i])
self.__S.setValueOfDataPoint(i,t[i])
else:
st = self.__pool.map(getStressAndTangent2D,self.__scenes)
for i in xrange(ng):
self.__stress.setValueOfDataPoint(i,st[i][0])
self.__S.setValueOfDataPoint(i,st[i][1])
def initialize(self, b=escript.Data(), f=escript.Data(), specified_u_mask=escript.Data(), specified_u_val=escript.Data()):
"""
initialize the model for each time step, e.g. assign parameters
:param b: type vector, body force on FunctionSpace, e.g. gravity
:param f: type vector, boundary traction on FunctionSpace (FunctionOnBoundary)
:param specified_u_mask: type vector, mask of location for Dirichlet boundary
:param specified_u_val: type vector, specified displacement for Dirichlet boundary
"""
self.__pde.setValue(Y=b,y=f,q=specified_u_mask,r=specified_u_val)
def getDomain(self):
"""
return model domain
"""
return self.__domain
def getRelTolerance(self):
"""
return relative tolerance for convergence
type float
"""
return self.__rtol
def getCurrentPacking(self,pos=(),time=0,prefix=''):
if len(pos) == 0:
# output all Gauss points packings
self.__pool.map(outputPack,zip(self.__scenes,repeat(time),repeat(prefix)))
else:
# output selected Gauss points packings
scene = [self.__scenes[i] for i in pos]
self.__pool.map(outputPack,zip(scene,repeat(time),repeat(prefix)))
def getLocalVoidRatio(self):
void=escript.Scalar(0,escript.Function(self.__domain))
e = self.__pool.map(getVoidRatio2D,self.__scenes)
for i in xrange(self.__numGaussPoints):
void.setValueOfDataPoint(i,e[i])
return void
def getLocalAvgRotation(self):
rot=escript.Scalar(0,escript.Function(self.__domain))
r = self.__pool.map(avgRotation2D,self.__scenes)
for i in xrange(self.__numGaussPoints):
rot.setValueOfDataPoint(i,r[i])
return rot
def getLocalFabric(self):
fabric=escript.Tensor(0,escript.Function(self.__domain))
f = self.__pool.map(getFabric2D,self.__scenes)
for i in xrange(self.__numGaussPoints):
fabric.setValueOfDataPoint(i,f[i])
return fabric
""" used for clumped particle model only
def getLocalParOriFab(self):
fabric=escript.Tensor(0,escript.Function(self.__domain))
f = self.__pool.map(getParOriFabric,self.__scenes)
for i in xrange(self.__numGaussPoints):
fabric.setValueOfDataPoint(i,f[i])
return fabric
"""
""" used for cohesive particle model only
def getLocalBondBreakage(self,oriIntr=[]):
debond = escript.Scalar(0,escript.Function(self.__domain))
num = self.__pool.map(getDebondingNumber,zip(self.__scenes,repeat(oriIntr)))
for i in xrange(self.__numGaussPoints):
debond.setValueOfDataPoint(i,num[i])
return debond
"""
def getCurrentTangent(self):
"""
return current tangent operator
type Tensor4 on FunctionSpace
"""
return self.__S
def getCurrentStress(self):
"""
return current stress
type: Tensor on FunctionSpace
"""
return self.__stress
def getCurrentStrain(self):
"""
return current strain
type: Tensor on FunctionSpace
"""
return self.__strain
def exitSimulation(self):
"""finish the whole simulation, exit"""
self.__pool.close()
def solve(self, iter_max=100):
"""
solve the equation using Newton-Ralphson scheme
"""
iterate=0
rtol=self.getRelTolerance()
stress=self.getCurrentStress()
s=self.getCurrentTangent()
x_safe=self.__domain.getX()
self.__pde.setValue(A=s, X=-stress)
#residual0=util.L2(self.__pde.getRightHandSide()) # using force error
u=self.__pde.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=1.0 # initial error before iteration
converged=(err<rtol)
while (not converged) and (iterate<iter_max):
if self.__verbose:
print "Not converged after %d iteration(s)! Relative error: %e"%(iterate,err)
iterate+=1
self.__domain.setX(x_safe+u)
self.__pde.setValue(A=update_s,X=-update_stress,r=escript.Data())
#residual=util.L2(self.__pde.getRightHandSide())
du=self.__pde.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*0.001: # 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)
#if err>err_safe: # to ensure consistent convergence, however this may not be achieved due to fluctuation!
# raise RuntimeError,"No improvement of convergence with iterations! Relative error: %e"%err
"""
update 'domain geometry', 'stress', 'tangent operator',
'accumulated strain' and 'simulation scenes'.
"""
self.__domain.setX(x_safe+u)
self.__stress=update_stress
self.__S=update_s
self.__strain+=D
self.__scenes=update_scenes
if self.__verbose:
print "Convergence reached after %d iteration(s)! Relative error: %e"%(iterate,err)
return u
"""
apply strain to DEM packing,
get stress and tangent operator (including two methods)
"""
def applyStrain_getStressTangentDEM(self,st=escript.Data()):
st = st.toListOfTuples()
st = numpy.array(st).reshape(-1,4)
stress = escript.Tensor(0,escript.Function(self.__domain))
S = escript.Tensor4(0,escript.Function(self.__domain))
scenes = self.__pool.map(shear2D,zip(self.__scenes,st))
if self.__usepert:
s = self.__pool.map(getStressTensor,scenes)
t = self.__pool.map(getTangentOperator,zip(scenes,repeat(self.__pert)))
for i in xrange(self.__numGaussPoints):
stress.setValueOfDataPoint(i,s[i])
S.setValueOfDataPoint(i,t[i])
else:
ST = self.__pool.map(getStressAndTangent2D,scenes)
for i in xrange(self.__numGaussPoints):
stress.setValueOfDataPoint(i,ST[i][0])
S.setValueOfDataPoint(i,ST[i][1])
return stress,S,scenes
domain = Brick(l0=mx,l1=my,n0=ndx, n1=ndy,l2=mz,n2=ndz)
x=Solution(domain).getX()
x=x-[mx/2,my/2,mz/2]
domain.setX(interpolate(x, ContinuousFunction(domain)))
mask=wherePositive(100-length(x-rholoc))
rho=rho*mask
kro=kronecker(domain)
mass=rho*vol(domain)
ipot=FunctionOnBoundary(domain)
xb=ipot.getX()
q=whereZero(x[2]-inf(x[2]))
###############################################ESCRIPT PDE CONSTRUCTION
mypde=LinearPDE(domain)
mypde.setValue(A=kro,Y=4.*3.1415*G*rho,q=q,r=0)
mypde.setSymmetryOn()
sol=mypde.getSolution()
saveVTK(os.path.join(save_path,"ex10b.vtu"),\
grav_pot=sol,\
g_field=-grad(sol),\
g_fieldz=-grad(sol)*[0,0,1],\
gz=length(-grad(sol)*[0,0,1]))
################################################MODEL SIZE SAMPLING
sampler=[]
for i in range(-250,250,1):
sampler.append([i,0,250])
sample=[] # array to hold values
# data recording times
rtime = 0.0 # first time to record
rtime_inc = tend / 20.0 # time increment to record
#Check to make sure number of time steps is not too large.
print("Time step size= ", h, "Expected number of outputs= ", tend / h)
U0 = 0.005 # amplitude of point source
# want a spherical source in the middle of area
xc = [500, 500] # with reference to mx,my this is the source location
####################################################DOMAIN CONSTRUCTION
mydomain = Rectangle(l0=mx, l1=my, n0=ndx, n1=ndy) # create the domain
x = mydomain.getX() # get the node locations of the domain
##########################################################ESTABLISH PDE
mypde = LinearPDE(mydomain) # create pde
mypde.setSymmetryOn() # turn symmetry on
mypde.setValue(D=1.) # set the value of D in the general form to 1.
############################################FIRST TIME STEPS AND SOURCE
# define small radius around point xc
src_radius = 30
print("src_radius = ", src_radius)
# set initial values for first two time steps with source terms
u = U0 * (cos(length(x - xc) * 3.1415 / src_radius) +
1) * whereNegative(length(x - xc) - src_radius)
u_m1 = u
#plot source shape
cut_loc = [] #where the cross section of the source along x will be
src_cut = [] #where the cross section of the source will be
# create locations for source cross section
slip_max=1.
mydomain = Rectangle(l0=1.,l1=1.,n0=16, n1=16) # n1 need to be multiple of 4!!!
# .. create the fault system
fs=FaultSystem(dim=2)
fs.addFault(V0=[0.5,0.25], strikes=90*DEG, ls=0.5, tag=1)
# ... create a slip distribution on the fault:
p, m=fs.getParametrization(mydomain.getX(),tag=1)
p0,p1= fs.getW0Range(tag=1)
s=m*(p-p0)*(p1-p)/((p1-p0)/2)**2*slip_max*[0.,1.]
# ... calculate stress according to slip:
D=symmetric(grad(s))
chi, d=fs.getSideAndDistance(D.getFunctionSpace().getX(),tag=1)
sigma_s=(mu*D+lam*trace(D)*kronecker(mydomain))*chi
#... open symmetric PDE ...
mypde=LinearPDE(mydomain)
mypde.setSymmetryOn()
#... set coefficients ...
C=Tensor4(0.,Function(mydomain))
for i in range(mydomain.getDim()):
for j in range(mydomain.getDim()):
C[i,i,j,j]+=lam
C[j,i,j,i]+=mu
C[j,i,i,j]+=mu
# ... fix displacement in normal direction
x=mydomain.getX()
msk=whereZero(x[0])*[1.,0.] + whereZero(x[0]-1.)*[1.,0.] \
+whereZero(x[1])*[0.,1.] + whereZero(x[1]-1.)*[0.,1.]
mypde.setValue(A=C,X=-0.5*sigma_s,q=msk)
#... solve pde ...
mypde.getSolverOptions().setVerbosityOn()
x = domain.getX() # get the locations of the nodes in the domain
lam = Scalar(0, Function(domain))
mu = Scalar(0, Function(domain))
rho = Scalar(0, Function(domain))
#Setting parameters for each layer in the model.
for i in range(0, nlayers):
rho.setTaggedValue("volume_%d" % i, rhoc + i * 100.)
lamc = (vel + i * 100.)**2. * (rhoc + i * 100.) / 2.
muc = (vel + i * 100.)**2. * (rhoc + i * 100.) / 4.
lam.setTaggedValue("volume_%d" % i, lamc)
mu.setTaggedValue("volume_%d" % i, muc)
##########################################################ESTABLISH PDE
mypde = LinearPDE(domain) # create pde
mypde.setSymmetryOn() # turn symmetry on
# turn lumping on for more efficient solving
#mypde.getSolverOptions().setSolverMethod(SolverOptions.HRZ_LUMPING)
kmat = kronecker(
domain) # create the kronecker delta function of the domain
mypde.setValue(D=rho * kmat) #set the general form value D
############################################FIRST TIME STEPS AND SOURCE
# define small radius around point xc
src_rad = 20
print("src radius= ", src_rad)
# set initial values for first two time steps with source terms
xb = FunctionOnBoundary(domain).getX()
yx = (cos(length(xb - xc) * 3.1415 / src_rad) +
1) * whereNegative(length(xb - xc) - src_rad)
mydomain = Rectangle(l0=1., l1=1., n0=16,
n1=16) # n1 need to be multiple of 4!!!
# .. create the fault system
fs = FaultSystem(dim=2)
fs.addFault(V0=[0.5, 0.25], strikes=90 * DEG, ls=0.5, tag=1)
# ... create a slip distribution on the fault:
p, m = fs.getParametrization(mydomain.getX(), tag=1)
p0, p1 = fs.getW0Range(tag=1)
s = m * (p - p0) * (p1 - p) / ((p1 - p0) / 2)**2 * slip_max * [0., 1.]
# ... calculate stress according to slip:
D = symmetric(grad(s))
chi, d = fs.getSideAndDistance(D.getFunctionSpace().getX(), tag=1)
sigma_s = (mu * D + lam * trace(D) * kronecker(mydomain)) * chi
#... open symmetric PDE ...
mypde = LinearPDE(mydomain)
mypde.setSymmetryOn()
#... set coefficients ...
C = Tensor4(0., Function(mydomain))
for i in range(mydomain.getDim()):
for j in range(mydomain.getDim()):
C[i, i, j, j] += lam
C[j, i, j, i] += mu
C[j, i, i, j] += mu
# ... fix displacement in normal direction
x = mydomain.getX()
msk=whereZero(x[0])*[1.,0.] + whereZero(x[0]-1.)*[1.,0.] \
+whereZero(x[1])*[0.,1.] + whereZero(x[1]-1.)*[0.,1.]
mypde.setValue(A=C, X=-0.5 * sigma_s, q=msk)
#... solve pde ...
mypde.getSolverOptions().setVerbosityOn()
res.setTaggedValue("volume_2",res3)
res.setTaggedValue("volume_3",res4)
con=1/res
x=Solution(domain).getX()
kro=kronecker(domain)
source1=[3.*mx/8.,my/2,0]; source2=[5.*mx/8.,my/2,0]
c1=length(exp(-length(x-source1)/(10.))); c1=c1/integrate(c1)
c2=-length(exp(-length(x-source2)/(10.))); c2=c2/integrate(c2)
sourceg=cur*(c1-c2)
q=whereZero(x[1]-my)+whereZero(x[1])+whereZero(x[0])+whereZero(x[0]-mx)+whereZero(x[2]-mz)
###############################################ESCRIPT PDE CONSTRUCTION
mypde=LinearPDE(domain)
mypde.setValue(A=con*kro,Y=sourceg,q=q,r=0)
#mypde.setSymmetryOn()
sol=mypde.getSolution()
res.expand()
# Save the output to file.
saveVTK(os.path.join(save_path,"ex11c.vtu"),\
source=sourceg,\
res_pot=sol,\
res=res,\
curden=-con*grad(sol),\
abscd=length(-con*grad(sol)),\
efield=-grad(sol))
L0=1.;L1=1.
# location, size and value of heat source
xc=[0.3,0.4]; r=0.1; Qc=3000
# material parameter
k=1; rhocp=100;
# bottom temperature:
T_bot=100
# generate domain:
mydomain=Rectangle(l0=L0,l1=L1,n0=20,n1=20)
x=mydomain.getX()
# set boundray temperature:
T_D=T_bot/L1*(L1-x[1])
# set heat source:
Q=Qc*whereNegative(length(x-xc)-r)
# generate domain:
mypde=LinearPDE(mydomain)
mypde.setSymmetryOn()
# set PDE coefficients:
mypde.setValue(A=dt*k*kronecker(mydomain), D=dt*rhocp,
r=T_D, q=whereZero(x[1])+whereZero(x[1]-L1))
# initial temperature
T=T_D
# step counter and time marker:
N=0; t=0
# stop when t_end is reached:
while t<t_end:
print("time step %d, t=%s"%(N,t))
# update PDE coefficient:
mypde.setValue(Y=dt*rhocp*T+dt*Q)
# new temperature:
T=mypde.getSolution()
def runTest(dom, n=1, a=0, b=0):
print("================== TEST : n= %s a=%s b=%s ================" %
(n, a, b))
DIM = dom.getDim()
normal = dom.getNormal()
mypde = LinearPDE(dom, numEquations=n, numSolutions=n)
x = dom.getX()
A = mypde.createCoefficient("A")
D = mypde.createCoefficient("D")
Y = mypde.createCoefficient("Y")
y = mypde.createCoefficient("y")
q = mypde.createCoefficient("q")
if n == 1:
u_ref = Scalar(0., Solution(dom))
for j in range(DIM):
q += whereZero(x[j])
A[j, j] = 1
y += sin(sqrt(2.)) * normal[0]
Y += b * x[0] * sin(sqrt(2.))
D += b
u_ref = x[0] * sin(sqrt(2.))
else:
u_ref = Data(0., (n, ), Solution(dom))
for i in range(n):
for j in range(DIM):
q[i] += whereZero(x[j])
A[i, j, i, j] = 1
if j == i % DIM: y[i] += sin(i + sqrt(2.)) * normal[j]
for j in range(n):
if i == j:
D[i, i] = b + (n - 1) * a
Y[i] += b * x[i % DIM] * sin(i + sqrt(2.))
else:
D[i, j] = -a
Y[i] += a * (x[i % DIM] * sin(i + sqrt(2.)) -
x[j % DIM] * sin(j + sqrt(2.)))
u_ref[i] = x[i % DIM] * sin(i + sqrt(2.))
# - u_{j,ii} + b*u_i+ a*sum_{k<>j} (u_i-u_k) = F_j
mypde.setValue(A=A, D=D, y=y, q=q, r=u_ref, Y=Y)
mypde.getSolverOptions().setVerbosityOn()
mypde.getSolverOptions().setTolerance(TOL)
mypde.setSymmetryOn()
u = mypde.getSolution()
error = Lsup(u - u_ref) / Lsup(u_ref)
print("error = ", error)
if error > 10 * TOL:
print(
"XXXXXXXXXX Error to large ! XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX")
save_path = os.path.join("data", "example10")
#ensure the dir exists
mkDir(save_path)
####################################################DOMAIN CONSTRUCTION
domain = Rectangle(l0=mx, l1=my, n0=ndx, n1=ndy)
x = Solution(domain).getX()
mask = wherePositive(10 - length(x - rholoc))
rho = rho * mask
kro = kronecker(domain)
q = whereZero(x[1] - my) + whereZero(x[1]) + whereZero(
x[0]) + whereZero(x[0] - mx)
###############################################ESCRIPT PDE CONSTRUCTION
mypde = LinearPDE(domain)
mypde.setValue(A=kro, Y=4. * 3.1415 * G * rho)
mypde.setValue(q=q, r=0)
mypde.setSymmetryOn()
sol = mypde.getSolution()
g_field = grad(sol) #The gravitational acceleration g.
g_fieldz = g_field * [0, 1] #The vertical component of the g field.
gz = length(g_fieldz) #The magnitude of the vertical component.
# Save the output to file.
saveVTK(os.path.join(save_path,"ex10a.vtu"),\
grav_pot=sol,g_field=g_field,g_fieldz=g_fieldz,gz=gz)
##################################################REGRIDDING & PLOTTING
xi, yi, zi = toRegGrid(sol, nx=50, ny=50)
domain = MakeDomain(d, optimizeLabeling=True)
x = domain.getX()
print("Domain has been generated ...")
lam = Scalar(0, Function(domain))
lam.setTaggedValue("top", lam1)
lam.setTaggedValue("bottom", lam2)
mu = Scalar(0, Function(domain))
mu.setTaggedValue("top", mu1)
mu.setTaggedValue("bottom", mu2)
rho = Scalar(0, Function(domain))
rho.setTaggedValue("top", rho1)
rho.setTaggedValue("bottom", rho2)
##########################################################ESTABLISH PDE
mypde = LinearPDE(domain) # create pde
mypde.setSymmetryOn() # turn symmetry on
# turn lumping on for more efficient solving
# mypde.getSolverOptions().setSolverMethod(SolverOptions.LUMPING)
kmat = kronecker(domain) # create the kronecker delta function of the domain
mypde.setValue(D=rho * kmat) # set the general form value D
##########################################################ESTABLISH ABC
# Define where the boundary decay will be applied.
bn = 20.0
bleft = xstep * bn
bright = width - (xstep * bn)
bbot = depth - (ystep * bn)
# btop=ystep*bn # don't apply to force boundary!!!
# locate these points in the domain
class TemperatureAdvection(Model):
"""
The conservation of internal heat energy is given by
*rho c_p ( dT/dt+v[j] * grad(T)[j])-grad(\kappa grad(T)_{,i}=Q*
*n_i \kappa T_{,i}=0*
it is assummed that *\rho c_p* is constant in time.
solved by Taylor Galerkin method
"""
def __init__(self,**kwargs):
super(TemperatureAdvection, self).__init__(**kwargs)
self.declareParameter(domain=None, \
temperature=1., \
velocity=numpy.zeros([3]),
density=1., \
heat_capacity=1., \
thermal_permabilty=1., \
# reference_temperature=0., \
# radiation_coefficient=0., \
thermal_source=0., \
fixed_temperature=0.,
location_fixed_temperature=Data(),
safety_factor=0.1)
def doInitialization(self):
self.__pde=LinearPDE(self.domain)
self.__pde.setSymmetryOn()
self.__pde.setReducedOrderOn()
self.__pde.getSolverOptions().setSolverMethod(SolverOptions.LUMPING)
self.__pde.setValue(D=self.heat_capacity*self.density)
def getSafeTimeStepSize(self,dt):
"""
returns new step size
"""
h=self.domain.getSize()
return self.safety_factor*inf(h**2/(h*abs(self.heat_capacity*self.density)*length(self.velocity)+self.thermal_permabilty))
def G(self,T,alpha):
"""
tangential operator for taylor galerikin
"""
g=grad(T)
self.__pde.setValue(X=-self.thermal_permabilty*g, \
Y=self.thermal_source-self.__rhocp*inner(self.velocity,g), \
r=(self.__fixed_T-self.temperature)*alpha,\
q=self.location_fixed_temperature)
return self.__pde.getSolution()
def doStepPostprocessing(self,dt):
"""
perform taylor galerkin step
"""
T=self.temperature
self.__rhocp=self.heat_capacity*self.density
self.__fixed_T=self.fixed_temperature
self.temperature=dt*self.G(dt/2*self.G(T,1./dt)+T,1./dt)+T
self.trace("Temperature range is %e %e"%(inf(self.temperature),sup(self.temperature)))
#~ pl.clf()
#~ pl.imshow(tester)
#~ pl.colorbar()
#~ pl.savefig("tester2.png")
#~
#~ tester=fbottom*wherePositive(bottom)
#~ tester=tester.toListOfTuples()
#~ tester=np.reshape(tester,(ndx+1,ndy+1))
#~ pl.clf()
#~ pl.imshow(tester)
#~ pl.colorbar()
#~ pl.savefig("tester3.png")
# ... open new PDE ...
mypde=LinearPDE(domain)
print(mypde.isUsingLumping())
print(mypde.getSolverOptions())
#mypde.getSolverOptions().setSolverMethod(SolverOptions.LUMPING)
mypde.setSymmetryOn()
kmat = kronecker(domain)
mypde.setValue(D=kmat*rho)
# define small radius around point xc
# Lsup(x) returns the maximum value of the argument x
src_radius = 50#2*Lsup(domain.getSize())
print("src_radius = ",src_radius)
dunit=numpy.array([0.,1.]) # defines direction of point source
#~ dunit=(x-xc)
#~ absrc=length(dunit)
def doInitialization(self):
self.__pde=LinearPDE(self.domain)
self.__pde.setSymmetryOn()
self.__pde.setReducedOrderOn()
self.__pde.getSolverOptions().setSolverMethod(SolverOptions.LUMPING)
self.__pde.setValue(D=self.heat_capacity*self.density)
