Module `optfx.filters`

Some filters for topology optimization.

Expand source code

#! /usr/bin/python3
# -*- coding: utf-8 -*-
''' Some filters for topology optimization.
'''
from dolfin import *
from dolfin_adjoint import *
import numpy as np
from ufl import tanh
from .optimizer import optimize
from .core import Module

def helmholtzFilter(u, U, R=0.025):
    ''' Apply the helmholtz filter.

    Args:
        u (dolfin_adjoint.Function): Target function
        U (dolfin_adjoint.FunctionSpace): Functionspace of target function
        R (float, optional): Filter radius. Defaults to 0.025.

    Returns:
        (dolfin_adjoint.Function): Filtered function
    '''
    v = TrialFunction(U)
    dv = TestFunction(U)
    vh = Function(U)
    r = R/(2*np.sqrt(3))
    a = r**2*inner(grad(v), grad(dv))*dx + dot(v, dv)*dx
    L = inner(u, dv)*dx
    solve(a == L, vh,
            solver_parameters={"linear_solver": "lu"},
            form_compiler_parameters={"optimize": True}) 
    return vh

def hevisideFilter(u, U, beta=10.0, eta=0.5):
    ''' Apply the heviside function (approximate with hyperbolic tangent function).

    Args:
        u (dolfin_adjoint.Function): Target function.
        U (dolfin_adjoint.FunctionSpace): Function space for function.
        beta (float): Coefficient for the smoothness. Defaults to 10.
        eta (float, optional): Cutoff value. Defaults to 0.5.

    Returns:
        dolfin_adjoint.Form: Filtered function.
    '''
    return project((tanh(beta*eta)+tanh(beta*(u-eta)))/(tanh(beta*eta)+tanh(beta*(1.0-eta))), U)

def b2c(z, e):
    ''' 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.
    '''    
    u = as_vector([-1/np.sqrt(2), 0, 1/np.sqrt(2), 1, 1/np.sqrt(2), 0, -1/np.sqrt(2), -1])
    v = as_vector([-1/np.sqrt(2), -1, -1/np.sqrt(2), 0, 1/np.sqrt(2), 1, 1/np.sqrt(2), 0])
    N1 = -(1-z)*(1-e)*(1+z+e)/4
    N2 =  (1-z**2)*(1-e)/2
    N3 = -(1+z)*(1-e)*(1-z+e)/4
    N4 =  (1+z)*(1-e**2)/2
    N5 = -(1+z)*(1+e)*(1-z-e)/4
    N6 =  (1-z**2)*(1+e)/2
    N7 = -(1-z)*(1+e)*(1+z-e)/4
    N8 =  (1-z)*(1-e**2)/2
    N = as_vector([N1, N2, N3, N4, N5, N6, N7, N8])
    Nx = inner(u, N)
    Ny = inner(v, N)
    return as_vector((Nx, Ny))

Functions

def b2c(z, e)

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.

Expand source code

def b2c(z, e):
    ''' 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.
    '''    
    u = as_vector([-1/np.sqrt(2), 0, 1/np.sqrt(2), 1, 1/np.sqrt(2), 0, -1/np.sqrt(2), -1])
    v = as_vector([-1/np.sqrt(2), -1, -1/np.sqrt(2), 0, 1/np.sqrt(2), 1, 1/np.sqrt(2), 0])
    N1 = -(1-z)*(1-e)*(1+z+e)/4
    N2 =  (1-z**2)*(1-e)/2
    N3 = -(1+z)*(1-e)*(1-z+e)/4
    N4 =  (1+z)*(1-e**2)/2
    N5 = -(1+z)*(1+e)*(1-z-e)/4
    N6 =  (1-z**2)*(1+e)/2
    N7 = -(1-z)*(1+e)*(1+z-e)/4
    N8 =  (1-z)*(1-e**2)/2
    N = as_vector([N1, N2, N3, N4, N5, N6, N7, N8])
    Nx = inner(u, N)
    Ny = inner(v, N)
    return as_vector((Nx, Ny))

def helmholtzFilter(u, U, R=0.025)

Apply the helmholtz filter.

Args

u : dolfin_adjoint.Function: Target function
U : dolfin_adjoint.FunctionSpace: Functionspace of target function
R : float, optional: Filter radius. Defaults to 0.025.

Returns

(dolfin_adjoint.Function): Filtered function

Expand source code

def helmholtzFilter(u, U, R=0.025):
    ''' Apply the helmholtz filter.

    Args:
        u (dolfin_adjoint.Function): Target function
        U (dolfin_adjoint.FunctionSpace): Functionspace of target function
        R (float, optional): Filter radius. Defaults to 0.025.

    Returns:
        (dolfin_adjoint.Function): Filtered function
    '''
    v = TrialFunction(U)
    dv = TestFunction(U)
    vh = Function(U)
    r = R/(2*np.sqrt(3))
    a = r**2*inner(grad(v), grad(dv))*dx + dot(v, dv)*dx
    L = inner(u, dv)*dx
    solve(a == L, vh,
            solver_parameters={"linear_solver": "lu"},
            form_compiler_parameters={"optimize": True}) 
    return vh

def hevisideFilter(u, U, beta=10.0, eta=0.5)

Apply the heviside function (approximate with hyperbolic tangent function).

Args

u : dolfin_adjoint.Function: Target function.
U : dolfin_adjoint.FunctionSpace: Function space for function.
beta : float: Coefficient for the smoothness. Defaults to 10.
eta : float, optional: Cutoff value. Defaults to 0.5.

Returns

dolfin_adjoint.Form: Filtered function.

Expand source code

def hevisideFilter(u, U, beta=10.0, eta=0.5):
    ''' Apply the heviside function (approximate with hyperbolic tangent function).

    Args:
        u (dolfin_adjoint.Function): Target function.
        U (dolfin_adjoint.FunctionSpace): Function space for function.
        beta (float): Coefficient for the smoothness. Defaults to 10.
        eta (float, optional): Cutoff value. Defaults to 0.5.

    Returns:
        dolfin_adjoint.Form: Filtered function.
    '''
    return project((tanh(beta*eta)+tanh(beta*(u-eta)))/(tanh(beta*eta)+tanh(beta*(1.0-eta))), U)