Universität Paderborn

In this work, we introduce PHOENIX, a highly optimized explicit open-source solver for two-dimensional nonlinear Schrodinger equations with extensions.The nonlinear Schrodinger 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 Schrodinger equation, various phys. 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 tomog. of the system′s quantum state.Program Title: PHOENIXCPC Library link to program files:https://doi.org/10.17632/kthy8wj3n5.1Developer′s repository link:https://github.com/Schumacher-Group-UPB/PHOENIX/Licensing provision: MITProgramming language: C++, CUDANature 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 Schrodinger equation (Gross-Pitaevskii equation) on uniformly discretized grids in real-space with a wide range of Runge-Kutta schemes.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 addnl. terms.

The macroscopic material properties of steels are affected by microstructure evolution during hot-forming.Phase transformations, carbide precipitation, and recrystallization are examples of the relevant phenomena.Most engineering components require high strength and sufficient residual ductility to withstand mech. loads and to provide favorable manufacturing conditions.One way to achieve this state is a microstructure composed of bimodal grains.The key contribution of the present manuscript is the proposition of a prototype model for an existing thermodn. framework, combining two phase-field approaches for the numerical investigation of recrystallization effects.The developed prototype model captures phase transformations, carbon diffusion, and carbide precipitation during static recrystallizationA combined phase-field approach models the microstructure evolution driven by temperature, curvature effects and stored energy effects.The corresponding order parameters are fractions of ferrite, martensite, and carbide phases as well as grain orientation and microstructure crystallinity describing grain boundary movement.The grain boundary evolution is captured by a Kobayashi-Warren-Carter approach.The prototype model builds upon a generalized framework on thermodn. and captures grain boundary motion in multi-phase continua.This yields a novel constitutive framework capable of describing the complex material behavior of metals during recrystallization annealing.To demonstrate the evolution of phase fractions and carbide precipitation, conclusive two-dimensional phase-field simulations are solved with the finite-element method.

Electron-energy-loss-spectroscopy (EELS) spectra in the scanning transmission electron microscope (STEM) are affected by various types of noise. Additionally, they are convolved with the detector point spread function and the energy distribution of the electron source. Often, iterative deconvolution is employed to sharpen peaks and improve the data. However, since the Richardson-Lucy algorithm (RLA) has become the standard deconvolution algorithm in EELS, little progress has been made in terms of technique. In this paper, the authors aim to provide an update to STEM-EELS deconvolution and demonstrate how to significantly improve results compared to those achievable with the RLA. The major limitation of the RLA is that it does not guarantee convergence. Furthermore, the RLA is restricted to pure Poisson noise and lacks adaptability due to limitations in its general structure, particularly when compared to more modern algorithms. A new and versatile approach is the Alternating Direction Method of Multipliers (ADMM), which is based on Lagrangian methods and enables to overcome these restrictions. The generality of ADMM allows us to develop a deconvolution algorithm tailored to EELS maps and incorporate a recent noise model. We extend the standard Bayesian maximum likelihood of the RLA to a maximum a-posteriori approach in ADMM, which enables us to leverage the principles of total general variation (TGV) to enforce convergence. Furthermore, we define the algorithm such that it operates unbiased of the user. To demonstrate the superiority of the ADMM, it is tested against the RLA using simulated data. Eventually, our algorithm is successfully applied to experimental data as well.