Module pytop.physics.utils

Functions

def inner_e(x, y, restrict_to_one_side=False, quadrature_degree=1)

The inner product of the tangential component of a vector field on all of the facets of the mesh (Measure objects dS and ds). By default, restrict_to_one_side is False. In this case, the function will return an integral that is restricted to both sides ('+') and ('-') of a shared facet between elements. You should use this in the case that you want to use the 'projected' version of DuranLibermanSpace. If restrict_to_one_side is True, then this will return an integral that is restricted ('+') to one side of a shared facet between elements. You should use this in the case that you want to use the multipliers version of DuranLibermanSpace.

Args

x
DOLFIN or UFL Function of rank (2,) (vector).
y
DOLFIN or UFL Function of rank (2,) (vector).
restrict_to_one_side (Optional[bool]: Default is False.
quadrature_degree : Optional[int]
Default is 1.

Returns

UFL Form.

def isoparametric_2D(z: fenics_adjoint.types.function.Function, e: fenics_adjoint.types.function.Function, u: fenics_adjoint.types.function.Function, v: fenics_adjoint.types.function.Function) ‑> fenics_adjoint.types.function.Function

Apply 2D isoparametric projection onto orientation vector.

Args

z : dolfin_adjoint.Function
0-component of the orientation vector (on natural setting).
e : dolfin_adjoint.Function
1-component of the orientation vector (on natural setting)
u : dolfin_adjoint.Function
0-component of the orientation vector (on real setting).
v : dolfin_adjoint.Function
1-component of the orientation vector (on real setting).

Returns

dolfin_adjoint.Vector
Orientation vector with unit circle boundary condition on real setting.
def isoparametric_2D_box_to_circle(z: fenics_adjoint.types.function.Function, e: fenics_adjoint.types.function.Function) ‑> fenics_adjoint.types.function.Function

Apply 2D isoparametric projection onto orientation vector.

Args

z : dolfin_adjoint.Function
0-component of the orientation vector (on natural setting).
e : dolfin_adjoint.Function
1-component of the orientation vector (on natural setting)

Returns

dolfin_adjoint.Vector
Orientation vector with unit circle boundary condition on real setting.
def isoparametric_2D_box_to_triangle(z: fenics_adjoint.types.function.Function, e: fenics_adjoint.types.function.Function, tolerance=1e-06) ‑> fenics_adjoint.types.function.Function

Apply 2D isoparametric projection onto orientation vector.

Args

z : dolfin_adjoint.Function
0-component of the orientation vector (on natural setting).
e : dolfin_adjoint.Function
1-component of the orientation vector (on natural setting).
tolerance : float
tolerance value. This is used to avoid square root of negative values.

Returns

dolfin_adjoint.Vector
Orientation vector with unit circle boundary condition on real setting.
def penalized_weight(rho, p=3, eps=0.001)

Penalized weight function.

Args: (float, float) rho: density. p: penalization parameter. eps: penalization parameter.

Returns: (float) penalized weight.

def sgn(x, k=10)

Classes

class Custom_nonlinear_problem (J, F, bcs)

Custom nonlinear problem class for FEniCS.

init(self: dolfin.cpp.nls.NonlinearProblem) -> None

Expand source code 
class Custom_nonlinear_problem(NonlinearProblem):
    """Custom nonlinear problem class for FEniCS.
    """
    def __init__(self, J, F, bcs):
        self.bilinear_form = J
        self.linear_form = F
        self.bcs = bcs
        NonlinearProblem.__init__(self)

    def F(self, b, x):
        assemble(self.linear_form, tensor=b)
        for bc in self.bcs:
            bc.apply(b, x)

    def J(self, A, x):
        assemble(self.bilinear_form, tensor=A)
        for bc in self.bcs:
            bc.apply(A)

Ancestors

  • dolfin.cpp.nls.NonlinearProblem
  • pybind11_builtins.pybind11_object

Methods

def F(self, b, x)

F(self: dolfin.cpp.nls.NonlinearProblem, arg0: dolfin.cpp.la.GenericVector, arg1: dolfin.cpp.la.GenericVector) -> None

def J(self, A, x)

J(self: dolfin.cpp.nls.NonlinearProblem, arg0: dolfin.cpp.la.GenericMatrix, arg1: dolfin.cpp.la.GenericVector) -> None