Generalized finite differences

Electromagnetism

Scattering of electromagnetic waves

We have published solutions of scattering problems in following instances

Räbinä, J. (2014). On a Numerical Solution of the Maxwell Equations by Discrete Exterior Calculus. Jyväskylä Studies in Computing 200. University of Jyväskylä.
Räbinä, J., Mönkölä, S., Rossi, T., Penttilä, A. & Muinonen, K. (2014). Comparison of discrete exterior calculus and discrete-dipole approximation for electromagnetic scattering. Journal of Quantitative Spectroscopy & Radiative Transfer , 146, 417–423.
Räbinä, J., Mönkölä, S. & Rossi, T. (2015). Efficient time integration of Maxwell's equations with generalized finite differences. SIAM Journal of Scientific Computing, 37(6), B834–B854.
Lindqvist, H., Martikainen, J., Räbinä, J., Penttilä, A., & Muinonen, K. (2018). Ray optics for absorbing particles with application to ice crystals at near-infrared wavelengths. Journal of Quantitative Spectroscopy and Radiative Transfer, 217, 329-337.

Latest simulations consider scattering of clusters of up to million densely packed particles. Largest tasks include 10 billion unknowns and are solved using several thousand computing cores. Luckily, this method parallelizes well. Check out our scalability test.

Fig: A mesh for a particle cluster simulation. The outer layer include absorbing PML.

Fig: Averaged Muller matrices by number of particles in specific kind of particle cluster.

Electromagnetic scattering from meteor plasma

We combined the Maxwell equations with the Drude model to model scattering from meteor plasma. By using domain decomposition and MPI parallelization, our software proved to be highly competitive in efficiency. Results can be found in

Räbinä, J., Mönkölä, S., Rossi, T., Markkanen, J., Gritsevich, M. & Muinonen, K. (2016). Controlled time integration for the numerical simulation of meteor radar reflections. Journal of Quantitative Spectroscopy & Radiative Transfer, 178, 295-305.

Fig: Distribution of normalized meteor plasma frequency.

Fig: Cross section of electric fields for different peak plasma frequency. The incident wave comes from top of the figure.

Heating process in microwave oven

Purpose of this numerical experiment was to study structured grid refinement procedure. Relative permittivity of water for microwave is about 70. This requires heavy refinement. For details, see our presentation or

Räbinä, J., Mönkölä, S., & Rossi, T. (2016). High-quality discretizations for microwave simulations. In Proceedings of 2016 URSI International Symposium on Electromagnetic Theory (EMTS), Espoo, Finland, 14-18 Aug 2016, 129-132.

Fig: Meshing of a microwave oven with high level refinement of the grid.

animation_microwaveoven.avi

Fig: Electric and magnetic fields during first 8 nanoseconds of operation.