Solving PDE with relatively large mesh

mesh
1

I was solving a weak form problem from 1-dimensional ODE problem,

image
image1380×156 16.5 KB

The code are as follows:

from fenics import *

import math

import sys

sys.path.append('../..')    # change directory

from mshr import *

# Create mesh

mesh = IntervalMesh(10, 0, math.pi*2)

# Define function spaces

V = FunctionSpace(mesh, 'Lagrange', 1)

# Define boundaries

left = 'near(x[0], 0)'      # left boundary x = 0

# Define boundary conditions

bcu_fixed = DirichletBC(V, Constant(0), left)

bcs = [bcu_fixed]

# Define test functions

u = TrialFunction(V)

v = TestFunction(V)

# Define the weak form

a = u.dx(0)*v.dx(0)*dx

# inner(grad(u), grad(v))*dx

# Define the distributed load

f = Expression("sin(x[0])", degree = 4)

g = Expression("1", degree = 3)

# L = f*v*dx + g*v*dx      # second term is a natural B.C.

L = f*v*dx

# Compute solution

u = Function(V)

solve(a == L, u, bcs)

# Ouput results into a file in VTK format

vtkfile = File('result1.pvd')

vtkfile << u

file_write = open('test.txt', 'w')

target = u.vector().get_local()

result = []

for element in target:

    result = result + [float(element)]

print(result)

# print(mesh.coordinates())

However, the result fits like \pi sin(x-\pi)-\pi, instead of sin(x)
but if I change the mesh from
IntervalMesh(10, 0, math.pi*2)
to
IntervalMesh(10, 0, math.pi/2)
the solution will fit sin(x) perfectly
I don’t know why it is like that

2

Please format your code using 3x` encapsulation for code, such as

from dolfin import *
def test(a):
    return a

and $ encapsulation for math:
\pi \sin (x-\pi)