Towards the scalability and hybrid parallelization of a spatially variant lattice algorithm

The purpose of this research is to design a faster implementation of the spatially variant algorithm that improves its performance when it is running on a parallel computer system. The spatially variant algorithm is used to synthesize a spatially variant lattice for a periodic electromagnetic structure. The algorithm has the ability to spatially vary the unit cell orientation and exploit its directional dependencies. The algorithm produces a lattice that is smooth, continuous and free of defects. The lattice spacing remains strikingly uniform when the unit cell orientation, lattice spacing, fill fraction and more are spatially varied. This is important for maintaining consistent properties throughout the lattice. Periodic structures like a photonic crystal or metamaterial devices can be enhanced using the spatially variant algorithm and unlocked new physics applications. Our current effort is to write a portable spatially variant code for parallel architectures. To develop and write the code, we pick a general purpose programming language that supports structured programming. We start our work by writing an optimized sequential code that uses FFTW (Fastest Fourier Transform in the West) for handling the Fourier Transform of the unit cell device and CSparse (Concise Sparse Matrix Package in C) for handling the numerical linear algebra operations. For the parallel code we use FFTW for handling the Fourier Transform of the unit cell device and PETSc (Portable, Extensible Toolkit for Scientific Computation) for handling the numerical linear algebra operations. Using Message Passing Interface (MPI) for distributed memory helps us to improve the performance of the spatially variant code when it is executed on a parallel system