examples/fem_test.py

   1 #!/usr/bin/env python
   2 import iam_sympy_example
   3
   4 """
   5 Go to the sympy root directory and execute:
   6
   7 $ python examples/fem_test.py
   8 [  1/60,     0, -1/360,     0, -1/90, -1/360]
   9 [     0,  4/45,      0,  2/45,  2/45,  -1/90]
  10 [-1/360,     0,   1/60, -1/90,     0, -1/360]
  11 [     0,  2/45,  -1/90,  4/45,  2/45,      0]
  12 [ -1/90,  2/45,      0,  2/45,  4/45,      0]
  13 [-1/360, -1/90, -1/360,     0,     0,   1/60]
  14 """
  15
  16 from fem import *
  17
  18 t = ReferenceSimplex(2)
  19 fe = Lagrange(2,2)
  20
  21 u = 0
  22 #compute u = sum_i u_i N_i
  23 us = []
  24 for i in range(0, fe.nbf()):
  25    ui = Symbol("u_%d" % i)
  26    us.append(ui)
  27    u += ui*fe.N[i]
  28
  29
  30 J = zeros(fe.nbf())
  31 for i in range(0, fe.nbf()):
  32    Fi = u*fe.N[i]
  33    for j in range(0, fe.nbf()):
  34        uj = us[j]
  35        integrands = diff(Fi, uj)
  36        J[j,i] = t.integrate(integrands)
  37
  38
  39 pprint(J)