##
## The 3D displacement vector is (u, v, w),
## where
## u lies along the x-direction,
## v, along the y-direction,
## and w, out-of-the-plane, or along
## the z-direction
u = fieldindex.VectorFieldIndex(0)
v = fieldindex.VectorFieldIndex(1)
fx = fieldindex.VectorFieldIndex(0)
fy = fieldindex.VectorFieldIndex(1)
if config.dimension() == 2:
# fx is conjugate to u and fy is conjugate to v for Elasticity
conjugate.conjugatePair("Elasticity", ForceBalanceEquation, [fx, fy],
Displacement, [u, v])
## out-of-plane compoments
## The available out-of-plane components of stress are $\sigma_{zz},
## \sigma_{zy}, \sigma_{zx}$, in *that* order, (0, 1, 2). The
## out-of-plane displacement is (\frac{\partial u}{\partial z},
## \frac{\partial v}{partial z}, \frac{\partial w}{\partial z}.
u_xz = fieldindex.VectorFieldIndex(0)
u_yz = fieldindex.VectorFieldIndex(1)
u_zz = fieldindex.VectorFieldIndex(2)
sigma_xz = fieldindex.OutOfPlaneSymTensorIndex(2, 0)
sigma_yz = fieldindex.OutOfPlaneSymTensorIndex(2, 1)
sigma_zz = fieldindex.OutOfPlaneSymTensorIndex(2, 2)
# If the conjugatePair information is omitted, OOF2 will still run
# properly, but it will not use the more efficient symmetric matrix
# solvers because it will not know how to symmetrize the matrix.
from ooflib.engine import conjugate
from ooflib.SWIG.engine import fieldindex
# Field and Equation components are both specified by instances of
# FieldIndex classes. A ScalarFieldIndex has only one value. It's
# only purpose is to make it possible to treat scalar fields the same
# way as other more complicated fields.
fx = fieldindex.ScalarFieldIndex()
conjugate.conjugatePair(
"Frivolous", # the property type
JamEqn, fx, # the equation, and its component
Strawberry, fx) # the field, and its component
fz = fieldindex.OutOfPlaneVectorFieldIndex(2)
conjugate.conjugatePair("Frivolous",
OutOfPlaneJam, fz,
Strawberry.out_of_plane(), fz)
# A material Property is what connects a Field to a Flux. Properties
# are almost always defined in C++ code, but their Registrations are
# in Python.
# Load the module containing the Property subclass code.
import fruitSWIG.fruitproperty
if config.dimension() == 2:
AtomOutOfPlane = problem.advertise(equation.PlaneFluxEquation(
'Plane_Atom_Flux', Atom_Flux, 1))
ChargeOutOfPlane = problem.advertise(equation.PlaneFluxEquation(
'Plane_Charge_Flux', Charge_Flux, 1))
##
## Atom flux equation
##
## In-plane components, C
##
C = fieldindex.ScalarFieldIndex()
DivJd = fieldindex.ScalarFieldIndex()
conjugate.conjugatePair("Diffusivity", AtomBalanceEquation, DivJd,
Concentration, C)
conjugate.conjugatePair("Current", ChargeBalanceEquation, DivJd,
problem.Voltage, C)
## $\nabla \cdot \vec{Jd}$ is conjugate to C
## out-of-plane components, $\frac{\partial C}{\partial z}$
if config.dimension() == 2:
C_z = fieldindex.OutOfPlaneVectorFieldIndex(2)
Jd_z = fieldindex.OutOfPlaneVectorFieldIndex(2)
conjugate.conjugatePair("Diffusivity", AtomOutOfPlane, Jd_z,
Concentration.out_of_plane(), C_z)
conjugate.conjugatePair("Current", ChargeOutOfPlane, Jd_z,
problem.Voltage.out_of_plane(), C_z)
if config.dimension() == 2:
AtomOutOfPlane = problem.advertise(
equation.PlaneFluxEquation('Plane_Atom_Flux', Atom_Flux, 1))
ChargeOutOfPlane = problem.advertise(
equation.PlaneFluxEquation('Plane_Charge_Flux', Charge_Flux, 1))
##
## Atom flux equation
##
## In-plane components, C
##
C = fieldindex.ScalarFieldIndex()
DivJd = fieldindex.ScalarFieldIndex()
conjugate.conjugatePair("Diffusivity", AtomBalanceEquation, DivJd,
Concentration, C)
conjugate.conjugatePair("Current", ChargeBalanceEquation, DivJd,
problem.Voltage, C)
## $\nabla \cdot \vec{Jd}$ is conjugate to C
## out-of-plane components, $\frac{\partial C}{\partial z}$
if config.dimension() == 2:
C_z = fieldindex.OutOfPlaneVectorFieldIndex(2)
Jd_z = fieldindex.OutOfPlaneVectorFieldIndex(2)
conjugate.conjugatePair("Diffusivity", AtomOutOfPlane, Jd_z,
Concentration.out_of_plane(), C_z)
conjugate.conjugatePair("Current", ChargeOutOfPlane, Jd_z,
problem.Voltage.out_of_plane(), C_z)
##
## The 3D displacement vector is (u, v, w),
## where
## u lies along the x-direction,
## v, along the y-direction,
## and w, out-of-the-plane, or along
## the z-direction
u = fieldindex.VectorFieldIndex(0)
v = fieldindex.VectorFieldIndex(1)
fx = fieldindex.VectorFieldIndex(0)
fy = fieldindex.VectorFieldIndex(1)
if config.dimension() == 2:
# fx is conjugate to u and fy is conjugate to v for Elasticity
conjugate.conjugatePair("Elasticity", ForceBalanceEquation, [fx, fy],
Displacement, [u, v])
## out-of-plane compoments
## The available out-of-plane components of stress are $\sigma_{zz},
## \sigma_{zy}, \sigma_{zx}$, in *that* order, (0, 1, 2). The
## out-of-plane displacement is (\frac{\partial u}{\partial z},
## \frac{\partial v}{partial z}, \frac{\partial w}{\partial z}.
u_xz = fieldindex.VectorFieldIndex(0)
u_yz = fieldindex.VectorFieldIndex(1)
u_zz = fieldindex.VectorFieldIndex(2)
sigma_xz = fieldindex.OutOfPlaneSymTensorIndex(2,0)
sigma_yz = fieldindex.OutOfPlaneSymTensorIndex(2,1)
sigma_zz = fieldindex.OutOfPlaneSymTensorIndex(2,2)
