I tried to solved 2D Poisson equation. -\Delta u = sin(\pi x) sin(\pi y) on \Gamma =[-1,1] \times [-1,1]
and u=0 on \partial \Gamma . I want to read the solution, but don’t know how to read vtu file? Can anyone give me some suggestions?
<?xml version="1.0"?>
<VTKFile type="UnstructuredGrid" version="0.1" >
<UnstructuredGrid>
<Piece NumberOfPoints="121" NumberOfCells="200">
<Points>
<DataArray type="Float64" NumberOfComponents="3" format="ascii">-1 -1 0 -0.$
</Points>
<Cells>
<DataArray type="UInt32" Name="connectivity" format="ascii">0 1 12 0 11 12 $
<DataArray type="UInt32" Name="offsets" format="ascii">3 6 9 12 15 18 21 24 $
<DataArray type="UInt8" Name="types" format="ascii">5 5 5 5 5 5 5 5 5 5 5 5 $
</Cells>
<PointData Scalars="f_8">
<DataArray type="Float64" Name="f_8" format="ascii">0.0000000000000000e+00 $
</PointData>
</Piece>
</UnstructuredGrid>
</VTKFile>
bmf
March 28, 2021, 9:11am
2
Hi,
I am not quite certain what do you mean by reading vtu file. If you want to visualize the solution, I would suggest to import your vtu file into Paraview , visit or to use vedo . However, if you want to re-read your solution from file for further calculations, you should initially save them in XDMF format instead and load them back in as explained here .
1 Like
Thanks for your answer. I visualized the solution by using Paraview. I want to print the value of solution u. Can you please tell me how do I get ?
dokken
March 28, 2021, 8:47pm
4
Thanks for your help. I get the following output. Could you please suggest me what the first, second , third and fourth column represent?
I believe third column represent the solution u.
dokken
March 29, 2021, 6:00am
6
You need to supply the script you used to obtain this print for anyone to help interpret the result
I wrote the following scripts.
u_D = 0
f = sin(pi*x)*sin(pi*y)
"""
from __future__ import print_function
from fenics import *
from dolfin import *
import matplotlib.pyplot as plt
import numpy as np
# Create mesh and define function space
nx = ny = 10
mesh = RectangleMesh(Point(-1, -1), Point(1, 1), nx, ny)
V = FunctionSpace(mesh, 'P', 1)
# Define boundary condition
u_D = Constant(0.0)
def boundary(x, on_boundary):
return on_boundary
bc = DirichletBC(V, u_D, boundary)
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
f= Expression('sin(pi*x[0])*sin(pi*x[1])', degree=2)
a = dot(grad(u), grad(v))*dx
L = f*v*dx
# Compute solution
u = Function(V)
solve(a == L, u, bc)
#print('Solution=',u)
print(u.vector().get_local())
# Plot solution and mesh
plot(u)
plot(mesh, title="Solution to Poisson Equation")
# Save solution to file in VTK format
vtkfile = File('poisson/solution.pvd')
vtkfile << u
# Compute error in L2 norm
error_L2 = errornorm(u_D, u, 'L2')
# Compute maximum error at vertices
vertex_values_u_D = u_D.compute_vertex_values(mesh)
vertex_values_u = u.compute_vertex_values(mesh)
import numpy as np
error_max = np.max(np.abs(vertex_values_u_D - vertex_values_u))
# Print errors
print('error_L2 =', error_L2)
print('error_max =', error_max)
#print(print(error_max.vector().get_local()))
# Hold plot
#interactive()
# Plot solution
#import matplotlib.pyplot as plt
plt.show()
The output I got:
Could you please tell me what’s the column represent?
dokken
March 29, 2021, 4:20pm
8
As explained in the post I referred to, the i-th value in the vector you are printing corresponds to the function value at the coordinate from the i-th row of V.tabulate_dof_coordinates().