Efficient numerical methods for the analysis of electromagnetic fields

The large-size problem of electromagnetic fields synthesis (containing $10^8$ and more radiating objects) for holographic lithography needs is considered. The performance and scalability analysis carried out for some numerical methods on MVS-100K JSCC RAS and MIIT T4700 clusters showed that these methods cannot be used when creating a real-size chip on the state-of-the-art HPC systems. The specially designed Big Pixel method was implemented as a part of a parallel software package. This method allows calculating the Gabor hologram for the real-size chip topology on the existing clusters. An example of Gabor hologram synthesis for the topology consisting of $1.6\times 10^9$ elements is discussed.