PHOENIX – Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger equations with integrated extensions

In this work, we introduce PHOENIX, a highly optimized explicit open-source solver for two-dimensional nonlinear Schrödinger equations with extensions. The nonlinear Schrödinger equation and its extensions (Gross-Pitaevskii equation) are widely studied to model and analyze complex phenomena in fields such as optics, condensed matter physics, fluid dynamics, and plasma physics. It serves as a powerful tool for understanding nonlinear wave dynamics, soliton formation, and the interplay between nonlinearity, dispersion, and diffraction. By extending the nonlinear Schrödinger equation, various physical effects such as non-Hermiticity, spin-orbit interaction, and quantum optical aspects can be incorporated. PHOENIX is designed to accommodate a wide range of applications by a straightforward extendability without the need for user knowledge of computing architectures or performance optimization. The high performance and power efficiency of PHOENIX are demonstrated on a wide range of entry-class to high-end consumer and high-performance computing GPUs and CPUs. Compared to a more conventional MATLAB implementation, a speedup of up to three orders of magnitude and energy savings of up to 99.8% are achieved. The performance is compared to a performance model showing that PHOENIX performs close to the relevant performance bounds in many situations. The possibilities of PHOENIX are demonstrated with a range of practical examples from the realm of nonlinear (quantum) photonics in planar microresonators with active media including exciton-polariton condensates. Examples range from solutions on very large grids, the use of local optimization algorithms, to Monte Carlo ensemble evolutions with quantum noise enabling the tomography of the system's quantum state. Program Title: PHOENIX CPC Library link to program files: https://doi.org/10.17632/kthy8wj3n5.1 Developer's repository link: https://github.com/Schumacher-Group-UPB/PHOENIX/ Licensing provision: MIT Programming language: C++, CUDA Nature of problem: Time evolution of two-dimensional nonlinear systems such as Bose-Einstein condensates, nonlinear optical systems or hybrid light-matter systems (e.g., exciton-polariton condensates). Solution method: Solving the extended two-dimensional nonlinear Schrödinger equation (Gross-Pitaevskii equation) on uniformly discretized grids in real-space with a fourth-order Runge-Kutta scheme. The use of CPU and GPU and the precision used (fp32/fp64) can be set when compiling the code. Sub-grid decomposition is possible for optimal cache efficiency. The solver provides a framework that allows users unfamiliar with the details of GPU and CPU parallelization to extend the set of equations with additional terms.