### EM wave scattering with the VectorHelmholtz module

Posted:

**08 Jun 2018, 02:28**I have been exploring the level of capability of electromagnetic wave propagation in Elmer. I successfully ran the tutorial example on pp. 80-84 of the Elmer Models Manual (http://www.nic.funet.fi/index/elmer/doc ... Manual.pdf), so the basics are in place.

Public domain Comsol documentation discusses a classic benchmark problem in EM wave scattering

(https://www.comsol.com/model/download/4 ... sphere.pdf) and demonstrates a successful solution with their RF module. I have briefly looked into attempting replication of this calculation with the Elmer VectorHelmholtz module. There appear to be a few issues in carrying out this comparison from what I have found so far. Some of the issues are perhaps minor, but a few may be more substantial.

I have used GMSH to construct a geometry and mesh resembling the Comsol case. Problem symmetry is wisely used to reduce the modeled volume to one-fourth the full geometry. Some manual renumbering of the model boundary indices may be necessary to assign the PEC and PMC boundary conditions, but this seems straightforward. The items that look more challenging are:

1. Comsol separates the total vector electric field Et into and incident plane wave Ei and the field scattered by the conducting sphere Esc. That is, Et = Ei + Esc. Thus when Et is substituted into the wave equation (from Maxwell's equations), the only unknown to solve for is Esc. (Comsol seems to have a built-in means to specify Ei. This is conveniently done in Cartesian coordinates, even though the problem geometry is spherical.)

2. After solving for Esc, Comsol identifies a valid near-field solution adjacent to the scatterer, and then transforms that to a far-field solution using the Stratton-Chu equation.

3. An essential ingredient in obtaining a proper Esc is to use a perfectly matched layer [PML] as the outer shell on the model. Presumably, the above far-field solution for Esc is then coupled into the PML to eliminate unwanted reflections from the model outer boundaries. (PML technology is evidently well-established since it's first publication in the 1990s. But just how to integrate it with the Elmer VectorHelmholtz module is not clear to me, a relatively new user.)

The items 1-3 above are the issues that seem to be preventing an immediate direct comparison of Elmer with Comsol in this application. Perhaps there are workarounds that are evident to the community. If so, I am very interested in learning about them. Thank you.

Public domain Comsol documentation discusses a classic benchmark problem in EM wave scattering

(https://www.comsol.com/model/download/4 ... sphere.pdf) and demonstrates a successful solution with their RF module. I have briefly looked into attempting replication of this calculation with the Elmer VectorHelmholtz module. There appear to be a few issues in carrying out this comparison from what I have found so far. Some of the issues are perhaps minor, but a few may be more substantial.

I have used GMSH to construct a geometry and mesh resembling the Comsol case. Problem symmetry is wisely used to reduce the modeled volume to one-fourth the full geometry. Some manual renumbering of the model boundary indices may be necessary to assign the PEC and PMC boundary conditions, but this seems straightforward. The items that look more challenging are:

1. Comsol separates the total vector electric field Et into and incident plane wave Ei and the field scattered by the conducting sphere Esc. That is, Et = Ei + Esc. Thus when Et is substituted into the wave equation (from Maxwell's equations), the only unknown to solve for is Esc. (Comsol seems to have a built-in means to specify Ei. This is conveniently done in Cartesian coordinates, even though the problem geometry is spherical.)

2. After solving for Esc, Comsol identifies a valid near-field solution adjacent to the scatterer, and then transforms that to a far-field solution using the Stratton-Chu equation.

3. An essential ingredient in obtaining a proper Esc is to use a perfectly matched layer [PML] as the outer shell on the model. Presumably, the above far-field solution for Esc is then coupled into the PML to eliminate unwanted reflections from the model outer boundaries. (PML technology is evidently well-established since it's first publication in the 1990s. But just how to integrate it with the Elmer VectorHelmholtz module is not clear to me, a relatively new user.)

The items 1-3 above are the issues that seem to be preventing an immediate direct comparison of Elmer with Comsol in this application. Perhaps there are workarounds that are evident to the community. If so, I am very interested in learning about them. Thank you.