Hello FEniCS community
I am trying to solve the Poisson equation for an azimuthal symmetric problem.
1 / r (du / dr) + (d² u / dr²) + (d² u / dz²) = 0
For complex geometries.
I translated it to
a = inner( grad(u), grad(v))* dx + Expression("1.0/(x[0])")* grad(u)[0]*v* dx
it gives no proper result (most certainly because of the 1/0 condition. (All I get shown is an empty plot). So i tried to "regularize" the problem
a = inner( grad(u), grad(v))* dx + Expression("1.0/(x[0] + 0.000001)")* grad(u)[0]*v* dx
but now the result is very sensitive to the mesh arround x[0] = 0 and i get insane results. (negative u values with only not negative boundary conditions and no sources)
So i tried to solve the problem using an adaptive mesh. With
problem = LinearVariationalProblem(a, L, u, bc)
solver = AdaptiveLinearVariationalSolver(problem, M)
But all i get
*** -------------------------------------------------------------------------
*** Error: Unable to solve linear system using PETSc Krylov solver.
*** Reason: Solution failed to converge in 4 iterations (PETSc reason DIVERGED_INDEFINITE_MAT, residual norm ||r|| = 1.863995e-02).
*** Where: This error was encountered inside PETScKrylovSolver.cpp.
*** Process: 0
*** DOLFIN version: 1.6.0
*** Git changeset: unknown
*** -------------------------------------------------------------------------
And I do not know how to tackle that problem. What worked for a simple test geometry was to go all the way to
a = inner( grad(u), grad(v))* dx + Expression("1.0/(x[0] + 0.7)")* grad(u)[0]*v* dx
but that is not useful since I am specially interested in the region around x[0] = 0.
The only solution i see right now is switching to a 3d simulation but i would like to avoid that.
I there a practical way to solve the azimuthal symmetric Poisson equation in FEniCS?
