## 1 Description

This code solves for (quasi-)stationary electromagnetic fields produced by steady or alternating currents with a given frequency. For this purpose, the vector potential formulation of Maxwell's equations is used, which is solved in the frequency domain using a block coupled matrix solver so that even high-frequency electromagnetic phenomena can be treated well. The theory and implementation are described in [1, pp. 14-19, 73-74].

## 2 Installation

Download from https://github.com/cbusse1/electromagnetic-solver-foam-extend

## 3 Usage examples

Two test cases are provided in the repository above. The first one simulates the electromagnetic (EM) field of a coil in air, where the coil is modeled by three parallel current loops. In the second test case, the EM field is induced into an electrically conductive material leading to Joule heating and Lorentz-forces acting on the conductor. The test cases are described in [1, pp. 27-31].

To use the solver the following inputs need to be specified

in "../case/0":

- Source current density Jcoil in A/m^2 - Electrical conductivity sigma in A/Vm

in "../case/constant/physicalProperties":

- Magnetic permeability muMag (default muMag=mu0) in Vs/Am - Current frequency w in 1/s

The output quantities are:

- Magnetic vector potential A in Vs/m - Magnetic flux density B in Vs/m^2 - Magnetic field strength H in A/m - Induced current density Jind in A/m^2 - (Time-averaged) Joule heat density in W/m^3 - (Time-averaged) Lorentz-force density fL in N/m^3

## 4 Documentation

This implementation is based on the master thesis by Busse (2019).

## 5 References

[1] Busse, Christian: Numerical Modeling of an Inductively Coupled Plasma (ICP). Ilmenau 2019. https://doi.org/10.22032/dbt.40314

## 6 History

02 Apr 2020: First upload