@article{60298, abstract = {{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.}}, author = {{Wingenbach, Jan and Bauch, David and Ma, Xuekai and Schade, Robert and Plessl, Christian and Schumacher, Stefan}}, issn = {{0010-4655}}, journal = {{Computer Physics Communications}}, publisher = {{Elsevier BV}}, title = {{{PHOENIX – Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger equations with integrated extensions}}}, doi = {{10.1016/j.cpc.2025.109689}}, volume = {{315}}, year = {{2025}}, } @article{23597, author = {{Kapil, Venkat and Rossi, Mariana and Marsalek, Ondrej and Petraglia, Riccardo and Litman, Yair and Spura, Thomas and Cheng, Bingqing and Cuzzocrea, Alice and Meißner, Robert H. and Wilkins, David M. and Helfrecht, Benjamin A. and Juda, Przemysław and Bienvenue, Sébastien P. and Fang, Wei and Kessler, Jan and Poltavsky, Igor and Vandenbrande, Steven and Wieme, Jelle and Corminboeuf, Clemence and Kühne, Thomas D. and Manolopoulos, David E. and Markland, Thomas E. and Richardson, Jeremy O. and Tkatchenko, Alexandre and Tribello, Gareth A. and Van Speybroeck, Veronique and Ceriotti, Michele}}, issn = {{0010-4655}}, journal = {{Computer Physics Communications}}, pages = {{214--223}}, title = {{{i-PI 2.0: A universal force engine for advanced molecular simulations}}}, doi = {{10.1016/j.cpc.2018.09.020}}, year = {{2018}}, } @article{13276, author = {{Rutkai, Gábor and Köster, Andreas and Guevara-Carrion, Gabriela and Janzen, Tatjana and Schappals, Michael and Glass, Colin W. and Bernreuther, Martin and Wafai, Amer and Stephan, Simon and Kohns, Maximilian and Reiser, Steffen and Deublein, Stephan and Horsch, Martin and Hasse, Hans and Vrabec, Jadran}}, issn = {{0010-4655}}, journal = {{Computer Physics Communications}}, pages = {{343--351}}, title = {{{ms2: A Molecular Simulation Tool for Thermodynamic Properties, Release 3.0}}}, doi = {{10.1016/j.cpc.2017.07.025}}, volume = {{221}}, year = {{2017}}, } @article{18636, abstract = {{We derive formulas for the Coulomb matrix within the full-potential linearized augmented-plane-wave (FLAPW) method. The Coulomb matrix is a central ingredient in implementations of many-body perturbation theory, such as the Hartree–Fock and GW approximations for the electronic self-energy or the random-phase approximation for the dielectric function. It is represented in the mixed product basis, which combines numerical muffin-tin functions and interstitial plane waves constructed from products of FLAPW basis functions. The interstitial plane waves are here expanded with the Rayleigh formula. The resulting algorithm is very efficient in terms of both computational cost and accuracy and is superior to an implementation with the Fourier transform of the step function. In order to allow an analytic treatment of the divergence at k=0 in reciprocal space, we expand the Coulomb matrix analytically around this point without resorting to a projection onto plane waves. Without additional approximations, we then apply a basis transformation that diagonalizes the Coulomb matrix and confines the divergence to a single eigenvalue. At the same time, response matrices like the dielectric function separate into head, wings, and body with the same mathematical properties as in a plane-wave basis. As an illustration we apply the formulas to electron-energy-loss spectra (EELS) for nickel at different k vectors including k=0. The convergence of the spectra towards the result at k=0 is clearly seen. Our all-electron treatment also allows to include transitions from 3s and 3p core states in the EELS spectrum that give rise to a shallow peak at high energies and lead to good agreement with experiment.}}, author = {{Friedrich, Christoph and Schindlmayr, Arno and Blügel, Stefan}}, issn = {{0010-4655}}, journal = {{Computer Physics Communications}}, number = {{3}}, pages = {{347--359}}, publisher = {{Elsevier}}, title = {{{Efficient calculation of the Coulomb matrix and its expansion around k=0 within the FLAPW method}}}, doi = {{10.1016/j.cpc.2008.10.009}}, volume = {{180}}, year = {{2009}}, } @article{18595, abstract = {{Excited-state calculations, notably for quasiparticle band structures, are nowadays routinely performed within the GW approximation for the electronic self-energy. Nevertheless, certain numerical approximations and simplifications are still employed in practice to make the computations feasible. An important aspect for periodic systems is the proper treatment of the singularity of the screened Coulomb interaction in reciprocal space, which results from the slow 1/r decay in real space. This must be done without introducing artificial interactions between the quasiparticles and their periodic images in repeated cells, which occur when integrals of the screened Coulomb interaction are discretised in reciprocal space. An adequate treatment of both aspects is crucial for a numerically stable computation of the self-energy. In this article we build on existing schemes for isotropic screening and present an extension for anisotropic systems. We also show how the contributions to the dielectric function arising from the non-local part of the pseudopotentials can be computed efficiently. These improvements are crucial for obtaining a fast convergence with respect to the number of points used for the Brillouin zone integration and prove to be essential to make GW calculations for strongly anisotropic systems, such as slabs or multilayers, efficient.}}, author = {{Freysoldt, Christoph and Eggert, Philipp and Rinke, Patrick and Schindlmayr, Arno and Godby, Rex W. and Scheffler, Matthias}}, issn = {{0010-4655}}, journal = {{Computer Physics Communications}}, number = {{1}}, pages = {{1--13}}, publisher = {{Elsevier}}, title = {{{Dielectric anisotropy in the GW space–time method}}}, doi = {{10.1016/j.cpc.2006.07.018}}, volume = {{176}}, year = {{2007}}, }