Time out of the Solver

variational formulation
1

Hello,

I’m new to FeniCS and I so might do some basic mistakes, so please forgive for those.
So I tried to use FeniCS in order to solve a differential equation in one dimension. I’m currently using this code:

     from dolfin import *
     from __future__ import print_function
     from fenics import *
     import matplotlib.pyplot as plt

    #Definition of parameters
     Rint = 300
     Rext = 1000
     Rratio = Rint/Rext
     Omega = 60000
     
    #Definition of the mesh
    nx1 = 100
    mesh1 = UnitIntervalMesh(nx1)
    Hh1 = FunctionSpace(mesh1, 'P', 1)
    
  #Definition of the boundaries
   class DirichletBoundary1(SubDomain):
       def inside(self, x, on_boundary):
           return on_boundary and (abs(x[0] - Rratio) < tol) or (x[0] < Rratio ) #Here I'm not quiet sure of the x[0] < Rratio, i just want to say that between 0 and Rratio on the x 
abscissa I'm on the boundary..

    class DirichletBoundary2(SubDomain):
       def inside(self, x, on_boundary):
           return on_boundary and (abs(x[0] - 1) < tol)

    bcD1 = DirichletBC(Hh1, Omega, DirichletBoundary1())
    bcD2 = DirichletBC(Hh1, 0, DirichletBoundary2())

    boundaries1 = MeshFunction("size_t", mesh1, mesh1.topology().dim()-1, 0)
    ds1 = Measure("ds", domain=mesh1, subdomain_data=boundaries1)

    #Definition of particular functions
    ksi = Expression('exp(1/(Re*x[0]))', degree = 1, Re = Rext)
    x2 = Expression('pow(x[0]*Re, 2), degree = 1, Re = Rext)

    #Variational Form
    u1 = TrialFunction(Hh1)
    v1 = TrialFunction(Hh1)
    l1 = 0
    a1 = (-x2 * ksi * dot( grad(u1), grad(v1)) + ksi * dot(u1, v1))*dx

   u1 = Function(Hh1)
   bcs = [bcD1, bcD2]
   solve(a1 == l1, u1, bcs)

So on the last line, i get an error :
image
(i cannot uppload more than one image, so i put the last lines, but at the begining it started to create a Non linear Problem from what i saw with the comments)

So I assumed that I should use NonlinearVariationnalSolver instead, but when I used it, it showed me a different error with a wrong type of argument…

Please can you help me in order to complete my numerical resolution ?

Thanks for taking the time to read me !

2

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