I am going to find a way to solve the eigenvalues by FEniCSx, and I want to show all the eigenvalues and the parameters. I got some code from this link (A known analytical solution — FEniCSx tutorial) which seems to solve the eigenvector and find the error. Can anyone teach me how to revise it to solve the eigenvalue, and show the parameters? I really appreciate any help you can provide.
t = 0 # Start time
T = 2 # End time
num_steps = 20 # Number of time steps
dt = (T-t)/num_steps # Time step size
alpha = 3
beta = 1.2
import numpy
from dolfinx import mesh, fem
import ufl
from mpi4py import MPI
from petsc4py import PETSc
nx, ny = 5, 5
domain = mesh.create_unit_square(MPI.COMM_WORLD, nx, ny, mesh.CellType.triangle)
V = fem.FunctionSpace(domain, ("CG", 1))
class exact_solution():
def __init__(self, alpha, beta, t):
self.alpha = alpha
self.beta = beta
self.t = t
def __call__(self, x):
return 1 + x[0]**2 + self.alpha * x[1]**2 + self.beta * self.t
u_exact = exact_solution(alpha, beta, t)
u_D = fem.Function(V)
u_D.interpolate(u_exact)
tdim = domain.topology.dim
fdim = tdim - 1
domain.topology.create_connectivity(fdim, tdim)
boundary_facets = mesh.exterior_facet_indices(domain.topology)
bc = fem.dirichletbc(u_D, fem.locate_dofs_topological(V, fdim, boundary_facets))
u_n = fem.Function(V)
u_n.interpolate(u_exact)
f = fem.Constant(domain, beta - 2 - 2 * alpha)
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
F = u*v*ufl.dx + dt*ufl.dot(ufl.grad(u), ufl.grad(v))*ufl.dx - (u_n + dt*f)*v*ufl.dx
a = fem.form(ufl.lhs(F))
L = fem.form(ufl.rhs(F))
A = fem.petsc.assemble_matrix(a, bcs=[bc])
A.assemble()
b = fem.petsc.create_vector(L)
uh = fem.Function(V)
solver = PETSc.KSP().create(domain.comm)
solver.setOperators(A)
solver.setType(PETSc.KSP.Type.PREONLY)
solver.getPC().setType(PETSc.PC.Type.LU)
for n in range(num_steps):
# Update Diriclet boundary condition
u_exact.t+=dt
u_D.interpolate(u_exact)
# Update the right hand side reusing the initial vector
with b.localForm() as loc_b:
loc_b.set(0)
fem.petsc.assemble_vector(b, L)
# Apply Dirichlet boundary condition to the vector
fem.petsc.apply_lifting(b, [a], [[bc]])
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(b, [bc])
# Solve linear problem
solver.solve(b, uh.vector)
uh.x.scatter_forward()
# Update solution at previous time step (u_n)
u_n.x.array[:] = uh.x.array
# Compute L2 error and error at nodes
V_ex = fem.FunctionSpace(domain, ("CG", 2))
u_ex = fem.Function(V_ex)
u_ex.interpolate(u_exact)
error_L2 = numpy.sqrt(domain.comm.allreduce(fem.assemble_scalar(fem.form((uh - u_ex)**2 * ufl.dx)), op=MPI.SUM))
if domain.comm.rank == 0:
print(f"L2-error: {error_L2:.2e}")
# Compute values at mesh vertices
error_max = domain.comm.allreduce(numpy.max(numpy.abs(uh.x.array-u_D.x.array)), op=MPI.MAX)
if domain.comm.rank == 0:
print(f"Error_max: {error_max:.2e}")
When I copy the code from the link you provided and test whether the code works in my computer, I found that the following error appear. How can I solve it? Thanks.
Traceback (most recent call last):
File "/Users/victoriachan/Documents/CityU Doc/FYP/python_files/eigen_3.21.6.py", line 4, in <module>
from analytical_modes import verify_mode
ModuleNotFoundError: No module named 'analytical_modes'
I upgraded and the error happens again. I am using VScode. This error only appeared after I closed the images generated from the program. Not sure if it matters.
Thank you for your explanation, I understand what you mean. However, I’m afraid that the problem still persists and cannot be solved at the moment. Do you have any other suggestions that we can try?
I am not entirely certain if the list of dependencies I am providing is what you need, but I have included the versions of the installed packages that I am using along with the Conda version, since I am using Conda. I hope this information is helpful to you.
