Perfectly Matched Layers in a Divergence Preserving ADI Scheme for Electromagnetics

TL;DR

This paper develops and compares a divergence-preserving ADI scheme with PML boundary conditions for efficient electromagnetic simulations involving relativistic particles and radiation.

Contribution

It formulates a divergence-preserving ADI scheme with PML for electromagnetic simulations and evaluates its performance in various scenarios.

Findings

The scheme effectively absorbs radiation at boundaries.

It maintains divergence preservation in the ADI method.

Performance varies with different simulation setups.

Abstract

For numerical simulations of highly relativistic and transversely accelerated charged particles including radiation fast algorithms are needed. While the radiation in particle accelerators has wavelengths in the order of 100 um the computational domain has dimensions roughly 5 orders of magnitude larger resulting in very large mesh sizes. The particles are confined to a small area of this domain only. To resolve the smallest scales close to the particles subgrids are envisioned. For reasons of stability the alternating direction implicit (ADI) scheme by D. N. Smithe et al. (J. Comput. Phys. 228 (2009) pp.7289-7299) for Maxwell equations has been adopted. At the boundary of the domain absorbing boundary conditions have to be employed to prevent reflection of the radiation. In this paper we show how the divergence preserving ADI scheme has to be formulated in perfectly matched layers (PML) and compare the performance in several scenarios.