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,
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, reference=CartesianReferenceSystem()):
"""
set up the orthogonal coordinate transformation.
:param domain: domain in the domain of the coordinate transformation
:type domain: `esys.escript.AbstractDomain`
:param reference: the reference system
:type reference: `ReferenceSystem`
"""
self.__domain = domain
self.__reference_system = reference
self._volumefactor = esc.Scalar(1., esc.Function(domain))
self._scaling_factors = esc.Vector(1., esc.Function(domain))
def __init__(self, domain, reference=WGS84ReferenceSystem()):
"""
set up the orthogonal coordinate transformation.
:param domain: domain in the domain of the coordinate transformation
:type domain: `esys.escript.AbstractDomain`
:param reference: the reference system
:type reference: `ReferenceSystem`
"""
DIM = domain.getDim()
super(GeodeticCoordinateTransformation,
self).__init__(domain, reference)
a = reference.getSemiMajorAxis()
f = reference.getFlattening()
f_a = reference.getAngularUnit()
f_h = reference.getHeightUnit()
x = esc.Function(domain).getX()
if DIM == 2:
phi = 0.
else:
phi = x[1] * f_a
h = x[DIM - 1] * f_h
e = esc.sqrt(2 * f - f**2)
N = a / esc.sqrt(1 - e**2 * esc.sin(phi)**2)
M = (a * (1 - e**2)) / esc.sqrt(1 - e**2 * esc.sin(phi)**2)**3
v_phi = f_a * (M + h)
v_lam = f_a * (N + h) * esc.cos(phi)
v_h = f_h
s = esc.Vector(1., esc.Function(domain))
if DIM == 2:
v = v_phi * v_h
s[0] = 1 / v_lam
s[1] = 1 / v_h
else:
v = v_phi * v_lam * v_h
s[0] = 1 / v_lam
s[1] = 1 / v_phi
s[2] = 1 / v_h
self._volumefactor = v
self._scaling_factors = s
def __setOutput(self):
x = self.domain.getX()
self.__location_of_constraint = es.Vector(0, x.getFunctionSpace())
if self.domain.getDim() == 3:
vertex = [es.inf(x[0]), es.inf(x[1]), es.inf(x[2])]
msk = numpy.zeros((3, ))
if self.comp_mask[0]: msk[0] = 1
if self.comp_mask[1]: msk[1] = 1
if self.comp_mask[2]: msk[2] = 1
else:
vertex = [es.inf(x[0]), es.inf(x[1])]
msk = numpy.zeros((2, ))
if self.comp_mask[0]: msk[0] = 1
if self.comp_mask[1]: msk[1] = 1
self.__location_of_constraint = es.whereZero(
es.length(x - vertex), self.tol) * numpy.ones(shape)
if not self.value is None:
self.__value_of_constraint = self.__location_of_constraint * self.value
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 __init__(self,
domain,
v_p,
wavelet,
source_tag,
source_vector=[1., 0.],
eps=0.,
delta=0.,
azimuth=0.,
dt=None,
p0=None,
v0=None,
absorption_zone=300 * U.m,
absorption_cut=1e-2,
lumping=True):
"""
initialize the HTI wave solver
:param domain: domain of the problem
:type domain: `Doamin`
:param v_p: vertical p-velocity field
:type v_p: `escript.Scalar`
:param v_s: vertical s-velocity field
:type v_s: `escript.Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param azimuth: azimuth (rotation around verticle axis)
:param gamma: third Thompsen parameter
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param p0: initial solution (Q(t=0), P(t=0)). If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
"""
DIM = domain.getDim()
f = createAbsorptionLayerFunction(v_p.getFunctionSpace().getX(),
absorption_zone, absorption_cut)
self.v2_p = v_p**2
self.v2_t = self.v2_p * escript.sqrt(1 + 2 * delta)
self.v2_n = self.v2_p * (1 + 2 * eps)
if p0 == None:
p0 = escript.Data(0., (2, ), escript.Solution(domain))
else:
p0 = escript.interpolate(p0, escript.Solution(domain))
if v0 == None:
v0 = escript.Data(0., (2, ), escript.Solution(domain))
else:
v0 = escript.interpolate(v0, escript.Solution(domain))
if dt == None:
dt = min(
min(escript.inf(domain.getSize() / escript.sqrt(self.v2_p)),
escript.inf(domain.getSize() / escript.sqrt(self.v2_t)),
escript.inf(domain.getSize() / escript.sqrt(self.v2_n))),
wavelet.getTimeScale()) * 0.2
super(SonicHTIWave, self).__init__(dt, u0=p0, v0=v0, t0=0.)
self.__wavelet = wavelet
self.__mypde = lpde.LinearPDESystem(domain)
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(
lpde.SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=escript.kronecker(2),
X=self.__mypde.createCoefficient('X'))
self.__source_tag = source_tag
self.__r = escript.Vector(
0, escript.DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
def __init__(self,
domain,
v_p,
v_s,
wavelet,
source_tag,
source_vector=[0., 1.],
eps=0.,
delta=0.,
theta=0.,
rho=1.,
dt=None,
u0=None,
v0=None,
absorption_zone=300 * U.m,
absorption_cut=1e-2,
lumping=True):
"""
initialize the TTI wave solver
:param domain: domain of the problem
:type domain: `Domain`
:param v_p: vertical p-velocity field
:type v_p: `escript.Scalar`
:param v_s: vertical s-velocity field
:type v_s: `escript.Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param delta: second Thompsen parameter
:param theta: tilting (in Rad)
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param u0: initial solution. If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
"""
cos = escript.cos
sin = escript.sin
DIM = domain.getDim()
if not DIM == 2:
raise ValueError("Only 2D is supported.")
f = createAbsorptionLayerFunction(
escript.Function(domain).getX(), absorption_zone, absorption_cut)
v_p = v_p * f
v_s = v_s * f
if u0 == None:
u0 = escript.Vector(0., escript.Solution(domain))
else:
u0 = escript.interpolate(p0, escript.Solution(domain))
if v0 == None:
v0 = escript.Vector(0., escript.Solution(domain))
else:
v0 = escript.interpolate(v0, escript.Solution(domain))
if dt == None:
dt = min((1. / 5.) * min(escript.inf(domain.getSize() / v_p),
escript.inf(domain.getSize() / v_s)),
wavelet.getTimeScale())
super(TTIWave, self).__init__(dt, u0=u0, v0=v0, t0=0.)
self.__wavelet = wavelet
self.__mypde = lpde.LinearPDESystem(domain)
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(
lpde.SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=rho * escript.kronecker(DIM),
X=self.__mypde.createCoefficient('X'))
self.__source_tag = source_tag
self.__r = escript.Vector(
0, escript.DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
c0_33 = v_p**2 * rho
c0_66 = v_s**2 * rho
c0_11 = (1 + 2 * eps) * c0_33
c0_13 = escript.sqrt(2 * c0_33 * (c0_33 - c0_66) * delta +
(c0_33 - c0_66)**2) - c0_66
self.c11 = c0_11 * cos(theta)**4 - 2 * c0_13 * cos(
theta)**4 + 2 * c0_13 * cos(theta)**2 + c0_33 * sin(
theta)**4 - 4 * c0_66 * cos(theta)**4 + 4 * c0_66 * cos(
theta)**2
self.c13 = -c0_11 * cos(theta)**4 + c0_11 * cos(
theta)**2 + c0_13 * sin(theta)**4 + c0_13 * cos(
theta)**4 - c0_33 * cos(theta)**4 + c0_33 * cos(
theta)**2 + 4 * c0_66 * cos(theta)**4 - 4 * c0_66 * cos(
theta)**2
self.c16 = (-2 * c0_11 * cos(theta)**2 - 4 * c0_13 * sin(theta)**2 +
2 * c0_13 + 2 * c0_33 * sin(theta)**2 - 8 * c0_66 *
sin(theta)**2 + 4 * c0_66) * sin(theta) * cos(theta) / 2
self.c33 = c0_11 * sin(theta)**4 - 2 * c0_13 * cos(
theta)**4 + 2 * c0_13 * cos(theta)**2 + c0_33 * cos(
theta)**4 - 4 * c0_66 * cos(theta)**4 + 4 * c0_66 * cos(
theta)**2
self.c36 = (2 * c0_11 * cos(theta)**2 - 2 * c0_11 +
4 * c0_13 * sin(theta)**2 - 2 * c0_13 +
2 * c0_33 * cos(theta)**2 + 8 * c0_66 * sin(theta)**2 -
4 * c0_66) * sin(theta) * cos(theta) / 2
self.c66 = -c0_11 * cos(theta)**4 + c0_11 * cos(
theta)**2 + 2 * c0_13 * cos(theta)**4 - 2 * c0_13 * cos(
theta)**2 - c0_33 * cos(theta)**4 + c0_33 * cos(
theta)**2 + c0_66 * sin(theta)**4 + 3 * c0_66 * cos(
theta)**4 - 2 * c0_66 * cos(theta)**2
def __init__(self,
domain,
v_p,
v_s,
wavelet,
source_tag,
source_vector=[1., 0., 0.],
eps=0.,
gamma=0.,
delta=0.,
rho=1.,
dt=None,
u0=None,
v0=None,
absorption_zone=None,
absorption_cut=1e-2,
lumping=True,
disable_fast_assemblers=False):
"""
initialize the VTI wave solver
:param domain: domain of the problem
:type domain: `Domain`
:param v_p: vertical p-velocity field
:type v_p: `escript.Scalar`
:param v_s: vertical s-velocity field
:type v_s: `escript.Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param delta: second Thompsen parameter
:param gamma: third Thompsen parameter
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param u0: initial solution. If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
:param disable_fast_assemblers: if True, forces use of slower and more general PDE assemblers
"""
DIM = domain.getDim()
self.fastAssembler = hasattr(
domain, "createAssembler") and not disable_fast_assemblers
f = createAbsorptionLayerFunction(v_p.getFunctionSpace().getX(),
absorption_zone, absorption_cut)
v_p = v_p * f
v_s = v_s * f
if u0 == None:
u0 = escript.Vector(0., escript.Solution(domain))
else:
u0 = escript.interpolate(p0, escript.Solution(domain))
if v0 == None:
v0 = escript.Vector(0., escript.Solution(domain))
else:
v0 = escript.interpolate(v0, escript.Solution(domain))
if dt == None:
dt = min((1. / 5.) * min(escript.inf(domain.getSize() / v_p),
escript.inf(domain.getSize() / v_s)),
wavelet.getTimeScale())
super(HTIWave, self).__init__(dt, u0=u0, v0=v0, t0=0.)
self.__wavelet = wavelet
self.c33 = v_p**2 * rho
self.c44 = v_s**2 * rho
self.c11 = (1 + 2 * eps) * self.c33
self.c66 = (1 + 2 * gamma) * self.c44
self.c13 = escript.sqrt(2 * self.c33 * (self.c33 - self.c44) * delta +
(self.c33 - self.c44)**2) - self.c44
self.c23 = self.c33 - 2 * self.c66
if self.fastAssembler:
C = [("c11", self.c11), ("c23", self.c23), ("c13", self.c13),
("c33", self.c33), ("c44", self.c44), ("c66", self.c66)]
if "speckley" in domain.getDescription().lower():
C = [(n, escript.interpolate(d,
escript.ReducedFunction(domain)))
for n, d in C]
self.__mypde = lpde.WavePDE(domain, C)
else:
self.__mypde = lpde.LinearPDESystem(domain)
self.__mypde.setValue(X=self.__mypde.createCoefficient('X'))
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(
lpde.SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=rho * escript.kronecker(DIM))
self.__source_tag = source_tag
if DIM == 2:
source_vector = [source_vector[0], source_vector[2]]
self.__r = escript.Vector(
0, escript.DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
def __setOutput(self):
x = self.domain.getX()
self.__location_of_constraint = es.Vector(0, x.getFunctionSpace())
if self.domain.getDim() == 3:
x0, x1, x2 = x[0], x[1], x[2]
d = max(
es.sup(x0) - es.inf(x0),
es.sup(x1) - es.inf(x1),
es.sup(x2) - es.inf(x2))
left_mask = es.whereZero(x0 - es.inf(x0), self.tol * d)
if self.left[0]:
self.__location_of_constraint += left_mask * [1., 0., 0.]
if self.left[1]:
self.__location_of_constraint += left_mask * [0., 1., 0.]
if self.left[2]:
self.__location_of_constraint += left_mask * [0., 0., 1.]
right_mask = es.whereZero(x0 - es.sup(x0), self.tol * d)
if self.right[0]:
self.__location_of_constraint += right_mask * [1., 0., 0.]
if self.right[1]:
self.__location_of_constraint += right_mask * [0., 1., 0.]
if self.right[2]:
self.__location_of_constraint += right_mask * [0., 0., 1.]
front_mask = es.whereZero(x1 - es.inf(x1), self.tol * d)
if self.front[0]:
self.__location_of_constraint += front_mask * [1., 0., 0.]
if self.front[1]:
self.__location_of_constraint += front_mask * [0., 1., 0.]
if self.front[2]:
self.__location_of_constraint += front_mask * [0., 0., 1.]
back_mask = es.whereZero(x1 - es.sup(x1), self.tol * d)
if self.back[0]:
self.__location_of_constraint += back_mask * [1., 0., 0.]
if self.back[1]:
self.__location_of_constraint += back_mask * [0., 1., 0.]
if self.back[2]:
self.__location_of_constraint += back_mask * [0., 0., 1.]
bottom_mask = es.whereZero(x2 - es.inf(x2), self.tol * d)
if self.bottom[0]:
self.__location_of_constraint += bottom_mask * [1., 0., 0.]
if self.bottom[1]:
self.__location_of_constraint += bottom_mask * [0., 1., 0.]
if self.bottom[2]:
self.__location_of_constraint += bottom_mask * [0., 0., 1.]
top_mask = es.whereZero(x2 - es.sup(x2), self.tol * d)
if self.top[0]:
self.__location_of_constraint += top_mask * [1., 0., 0.]
if self.top[1]:
self.__location_of_constraint += top_mask * [0., 1., 0.]
if self.top[2]:
self.__location_of_constraint += top_mask * [0., 0., 1.]
if not self.value is None:
self.__value_of_constraint = self.__location_of_constraint * self.value
else:
x0, x1 = x[0], x[1]
d = max(es.sup(x0) - es.inf(x0), es.sup(x1) - es.inf(x1))
left_mask = es.whereZero(x0 - es.inf(x0), self.tol * d)
if self.left[0]:
self.__location_of_constraint += left_mask * [1., 0.]
if self.left[1]:
self.__location_of_constraint += left_mask * [0., 1.]
right_mask = es.whereZero(x0 - es.sup(x0), self.tol * d)
if self.right[0]:
self.__location_of_constraint += right_mask * [1., 0.]
if self.right[1]:
self.__location_of_constraint += right_mask * [0., 1.]
bottom_mask = es.whereZero(x1 - es.inf(x1), self.tol * d)
if self.bottom[0]:
self.__location_of_constraint += bottom_mask * [1., 0.]
if self.bottom[1]:
self.__location_of_constraint += bottom_mask * [0., 1.]
top_mask = es.whereZero(x1 - es.sup(x1), self.tol * d)
if self.top[0]:
self.__location_of_constraint += top_mask * [1., 0.]
if self.top[1]:
self.__location_of_constraint += top_mask * [0., 1.]
if not self.value is None:
self.__value_of_constraint = self.__location_of_constraint * self.value[:
2]
