Magnetodynamics with cohomology conditions

Here we represent and induction heating eddy current problem that utilizes the homology and cohomology solver of Gmsh.

Contents

Problem definition

$T-\Omega$ potential formulation

$A-V$ potential formulation

Implementation

Indheat.geo: problem geometry and cohomology computation in Gmsh

Indheat.pro: weak formulation in GetDP

How to use

All the files (.geo and .pro) must be located in the same directory.

Meshing the domain and computing the cohomology

Go to the directory and then type:

gmsh indheat.geo -algo frontal3d -3

After the mesh is built, a file indheat.msh should have been created in the directory.

Solving the problem with GetDP

In a Terminal, type (in the right directory)

getdp indheat.pro -solve MagDynAVComplex -pos MagDynAV

Showing the result

Open the file "jTO.pos" with Gmsh by typing "gmsh jTO.pos" in a terminal in the right directory.

Result

Boundary mesh of the conducting regions. Current density in the conducting regions.