norm.py

利用C

"""This module provides a simple way to compute various norms of
Functions, including the standard L2 norm and other norms"""

__author__ = "Anders Logg ([e-mail])"
__date__ = "2008-03-19 -- 2008-03-19"
__copyright__ = "Copyright (C) 2008 Anders Logg"
__license__  = "GNU LGPL Version 2.1"

__all__ = ['norm']

from assemble import assemble
from ffc import dot, grad, div, curl, dx
from math import sqrt
from constants import DOLFIN_EPS 

def norm(v, mesh, type="l2"):

    """Return norm of given function. Example usage includes:

        norm(v, mesh)
        norm(u0 - u1, mesh)
        norm(v, mesh, 'Hdiv')
        
    If the type is not specified, the standard L_2 norm is
    computed. Possible norm types include:

      L_2:     norm(v, mesh, 'L2')
      H^1:     norm(v, mesh, 'H1')
      H^1_0:   norm(v, mesh, 'H10')
      H(div):  norm(v, mesh, 'Hdiv')
      H(curl): norm(v, mesh, 'Hcurl')
    """

    if type.lower() == "l2":
        M = dot(v, v)*dx
    elif type.lower() == "h1":
        M = dot(v, v)*dx + dot(grad(v), grad(v))*dx
    elif type.lower() == "h10":
        M = dot(grad(v), grad(v))*dx
    elif type.lower() == "hdiv":
        M = div(v)*div(v)*dx
    elif type.lower() == "hcurl":
        M = dot(curl(v), curl(v))*dx

    r = assemble(M, mesh) 
    if r < DOLFIN_EPS: return 0.0 
    else: return sqrt(r)