[Libmesh-users] Solving Poisson's equation in a fixed 2-d grid

[Paul H. <pph...@gm...>]

Dear libmesh users,

I would like to use libmesh to solve Poisson's equation which was
previously done using the Fourier Method.
I made myself familiar with this issue using the libmesh examples ex3.C and
ex4.C. Unfortunately
these are of limited help to me, because I need to solve for a 2-d array
rho(x,y), with already fixed values for
x_1, x_2, ...., x_n; y_1, .....y_n.  [ I need to calculate the electric
potential from a charge density for further using the potential
in a Vlasov solver.  ]

Example ex3 uses MeshTools::Generation::build_square & QGauss for the mesh
which uses somewhat arbitrary points in (x,y), which
I cannot map onto my 2-d array rho(x,y). I guess I need to construct my
"own" mesh for this case but as I am very new to FEM
and libmesh I don't know exactly how. Could somebody provide my a reference
how to do this or some clues ?
I looked up the class documentation but couldn't find anything.

Thank you very much for your help !!

Paul Hilscher