Module `pytop.toolkit.dehomogenization`

Functions

def sh_stripe(mesh: fenics_adjoint.types.mesh.Mesh, source_vector: fenics_adjoint.types.function.Function, source_density: fenics_adjoint.types.function.Function, band_width: float, alpha=0.9, eps_0=1.0, g_0=0.0, absolute_tol=0.01, max_iter=1000) ‑> fenics_adjoint.types.function.Function

Solve the steady state Swift-Hohenberg equation with stripe pattern. see: https://doi.org/10.1038/s41598-023-41316-w https://doi.org/10.1016/j.compositesb.2022.109626

Args

mesh: the mesh
source_vector: the source vector
source_density: the source density
width: the width of the stripe
alpha: the coefficient of the source term
eps_0: the coefficient of the linear term
g_0: the coefficient of the cubic term
absolute_tol: the absolute tolerance
max_iter: the maximum iterations

Returns

stripe: the stripe pattern

def sh_stripe_tensor(mesh: fenics_adjoint.types.mesh.Mesh, source_tensor: fenics_adjoint.types.function.Function, source_density: fenics_adjoint.types.function.Function, band_width: float, perpendicular=True, alpha=0.9, eps_0=1.0, g_0=0.0, absolute_tol=0.01, max_iter=1000) ‑> fenics_adjoint.types.function.Function

Solve the steady state Swift-Hohenberg equation with stripe pattern. see: https://doi.org/10.1038/s41598-023-41316-w https://doi.org/10.1016/j.compositesb.2022.109626

Args

mesh: the mesh
source_tensor: the source tensor (Assuming 3-dim vector function. 1. a11, 2. a22, and 3. a12)
source_density: the source density
band_width: the width of the stripe
perpendicular: If True, the stripe is perpendicular to the source vector. Otherwise, the stripe is parallel to the source vector.
alpha: the coefficient of the source term
eps_0: the coefficient of the linear term
g_0: the coefficient of the cubic term
absolute_tol: the absolute tolerance
max_iter: the maximum iterations

Returns

stripe: the stripe pattern

Classes

class GaussianRandomField_2D (*args, **kwargs)

Base class for OverloadedType types.

The purpose of each OverloadedType is to extend a type such that it can be referenced by blocks as well as overload basic mathematical operations such as mul, add, where they are needed.

Expand source code

class GaussianRandomField_2D(UserExpression):
    def eval(self, val, x):
        val[0] = 10*np.random.randn()
        val[1] = 10*np.random.randn()
    def value_shape(self):
        return (2,)

Ancestors

fenics_adjoint.types.expression.UserExpression
fenics_adjoint.types.expression.BaseExpression
pyadjoint.overloaded_type.FloatingType
pyadjoint.overloaded_type.OverloadedType
dolfin.function.expression.UserExpression
dolfin.function.expression.BaseExpression
ufl.coefficient.Coefficient
ufl.core.terminal.FormArgument
ufl.core.terminal.Terminal
ufl.core.expr.Expr

Methods

def eval(self, val, x)
def value_shape(self)

class Problem (a, L)

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

Expand source code

class Problem(NonlinearProblem):
    def __init__(self, a, L):
        NonlinearProblem.__init__(self)
        self.L = L
        self.a = a
    def F(self, b, x):
        assemble(self.L, tensor=b)
    def J(self, A, x):
        assemble(self.a, tensor=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