import sys, os
sys.path.insert(0, os.path.join(os.pardir, 'src'))
from u_xx_f_sympy import model2, x
import sympy as sym
import numpy as np
from fe1D import finite_element1D, mesh_uniform, u_glob
import matplotlib.pyplot as plt
C = 5
D = 2
L = 4
m_values = [0, 1, 2, 3, 4]
d_values = [1, 2, 3, 4]
for m in m_values:
u = model2(x**m, L, C, D)
print('\nm=%d, u: %s' % (m, u))
u_exact = sym.lambdify([x], u)
for d in d_values:
vertices, cells, dof_map = mesh_uniform(
N_e=2, d=d, Omega=[0,L], symbolic=False)
vertices[1] = 3 # displace vertex
essbc = {}
essbc[dof_map[-1][-1]] = D
c, A, b, timing = finite_element1D(
vertices, cells, dof_map,
essbc,
ilhs=lambda e, phi, r, s, X, x, h:
phi[1][r](X, h)*phi[1][s](X, h),
integrand = (i+1)*(j+1)*(1-x)**(i+j)
A_ij = sym.integrate(integrand, (x, 0, 1))
A_ij = sym.simplify(A_ij)
print A_ij
psi_i = (1-x)**(i+1)
integrand = 2*psi_i - D*(i+1)*(1-x)**i
b_i = sym.integrate(integrand, (x, 0, 1)) - C*psi_i.subs(x, 0)
b_i = sym.factor(sym.simplify(b_i))
print b_i
print sym.expand(2 - (2+i)*(D+C))
# Solving model2 problem with f(x) and fe1D.py
from u_xx_f_sympy import model2, x, C, D, L
m = 2
u = model2(x**m, L, C, D)
print u
#u_exact = lambda x: D + C*(x-L) + (1./6)*(L**3 - x**3)
u_exact = sym.lambdify([x, C, D, L], u)
import numpy as np
from fe1D import finite_element1D_naive, mesh_uniform
# Override C, D and L with numeric values
C = 5
D = 2
L = 4
d = 1
vertices, cells, dof_map = mesh_uniform(
N_e=2, d=d, Omega=[0,L], symbolic=False)