Computer Physics Communications

We are launching FindBounce, a Mathematica package for the evaluation of the Euclidean bounce action that enters the decay rate of metastable states in quantum and thermal field theories. It is based on the idea of polygonal bounces, which is a semi-analytical approach to solving the bounce equation by discretizing the potential into piecewise linear segments. This allows for a fast and robust evaluation of arbitrary potentials with specified precision and any number of scalar fields. Time cost grows linearly with the number of fields and/or the number of segments. Computation with 20 fields takes ~2s with 0.5% accuracy of the action. The FindBounce function is simple to use with the native Mathematica look and feel, it is easy to install, and comes with detailed documentation and physical examples, such as the calculation of the nucleation temperature. We also provide timing benchmarks with comparisons to existing tools, where applicable.

We present a framework to solve non-linear eigenvalue problems suitable for a Finite Element discretization. The implementation is based on the open-source finite element software GetDP and the open-source library SLEPc. As template examples, we propose and compare in detail different ways to address the numerical computation of the electromagnetic modes of frequency-dispersive objects. This is a non-linear eigenvalue problem involving a non-Hermitian operator. A classical finite element formulation is derived for five different solutions and solved using algorithms adapted to the large size of the resulting discrete problem. The proposed solutions are applied to the computation of the dispersion relation of a diffraction grating made of a Drude material. The important numerical consequences linked to the presence of sharp corners and sign-changing coefficients are carefully examined. For each method, the convergence of the eigenvalues with respect to the mesh refinement and the shape function order, as well as computation time and memory requirements are investigated. The open-source template model used to obtain the numerical results is provided. Details of the implementation of polynomial and rational eigenvalue problems in GetDP are given in the appendix.

A radiating electric dipole is located near the interface with a layer of material. The electric and magnetic fields reflect off the interface and transmit through the material. The exact solution of Maxwell’s equations can be found in terms of Sommerfeld-type integrals. These integrals have in general a singularity on the integration axis, and the integrands are extremely complicated functions of the parameters in the problem. We present a method for the computation of these integrals, and the corresponding electric and magnetic fields. Key to the solution is the splitting of the incident field in its traveling and evanescent contributions. With a change of variables, the singularities can be transformed away, and the method also greatly improves the accuracy and efficiency of the integration. We illustrate the feasibility of our approach with the computation of the flow lines of electromagnetic energy in the system. For such flow diagrams, a large number of integrals needs to be computed with reasonable accuracy. We show that in our approach even the smallest details in flow diagrams can be revealed.

The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump-probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green’s functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. We present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green’s functions on the L-shaped Kadanoff-Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green’s functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green’s functions. The library employs a discretization of the Kadanoff-Baym contour into time N points and a high-order implementation of integration routines. The total integrated error scales up to O(N^-7), which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers.

STGF is a community code employed for outer-region R-matrix calculations, describing electron-impact collisional processes. It is widely recognised that the original version of STGF was written by M.J. Seaton in 1983, but through constant refinement over the next decades by worldwide contributors has evolved into its current form that more reflects modern coding practice and current computer architectures. Despite its current wide acceptance, it was never formally published. Therefore, we present an updated high-performance parallel version of PSTGF, that balances the requirements of small university clusters, yet can exploit the computational power of cutting edge supercomputers. There are many improvements over the original STGF, but most noticeably, the full introduction of MQDT options that provide subsequent integration with ICFT (Intermediate Coupling Frame Transformation) codes, and for either Breit–Pauli/DARC (Dirac Atomic R-matrix Codes), better load balancing, high levels of vectorisation and simplified output. Semantically, the program is full Fortran 90 in conjunction with MPI (Message Passing Interface) though has CUDA Fortran options for the most numerically intensive code sections.

varRhoTurbVOF contains a set of OpenFOAM volume of fluid (VOF) solvers for turbulent isothermal multiphase flows, which are variable-density incompressible. Unlike their official counterparts, where Favre-averaged and Reynolds-averaged velocities coexist in different equations, new solvers use Favre-averaged velocities consistently in all equations. This major update introduces three main improvements to the previous version of varRhoTurbVOF. First, the implementation is extended to VOF solvers for isothermal and non-isothermal phase change two-phase flows, where the flow is no longer incompressible. Second, in order to introduce backward compatibility and to avoid code duplication, the turbulence model construction procedure is redesigned such that solvers can determine whether the variable-density effect is considered or not in the turbulence modeling part based on the input file at run time. Third, the Egorov turbulence damping model for ω-based turbulence models is implemented with its most recent developments. Plus, an extension to ϵ-based turbulence models is developed and implemented.

We present and make available novel implementations of the two-dimensional Ising model that is used as a benchmark to show the computational capabilities of modern Graphic Processing Units (GPUs). The rich programming environment now available on GPUs and flexible hardware capabilities allowed us to quickly experiment with several implementation ideas: a simple stencil-based algorithm, recasting the stencil operations into matrix multiplies to take advantage of Tensor Cores available on NVIDIA GPUs, and a highly optimized multi-spin coding approach. Using the managed memory API available in CUDA allows for simple and efficient distribution of these implementations across a multi-GPU NVIDIA DGX-2 server. We show that even a basic GPU implementation can outperform current results published on TPUs (Yang et al., 2019) and that the optimized multi-GPU implementation can simulate very large lattices faster than custom FPGA solutions (Ortega-Zamorano et al., 2016).

We present FeynCalc 9.3, a new stable version of a powerful and versatile Mathematica package for symbolic quantum field theory (QFT) calculations. Some interesting new features such as highly improved interoperability with other packages, automatic extraction of the ultraviolet divergent parts of 1-loop integrals, support for amplitudes with Majorana fermions and γ-matrices with explicit Dirac indices are explained in detail. Furthermore, we discuss some common problems and misunderstandings that may arise in the daily usage of the package, providing explanations and workarounds.

Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn–Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. Finally, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets.

A new version of PETOOL (Parabolic Equation Toolbox) is introduced with various additional capabilities. PETOOL is an open-source and MATLAB-based software tool with a user-friendly graphical user interface (GUI) for the analysis and visualization of electromagnetic wave propagation over variable terrain and through arbitrary atmosphere. Four novel features of the second version are as follows: (i) Several evaporation duct models have been developed. (ii) Real atmosphere data have been included in the form of “Binary Universal Form for Representation (BUFR)” data developed by “World Meteorological Organization (WMO)”. (iii) Real terrain data have been incorporated into the toolbox in the form of “Digital Terrain Elevation Data (DTED)” developed by “National Imagery and Mapping Agency (NIMA)”. (iv) A special add-on has been developed to generate a 3D coverage map of propagation factor/loss on real terrain data. The toolbox can be used for research and/or educational purposes to analyze more realistic propagation scenarios in an easier and flexible manner. The previous version of this program (AEJS_v1_0) may be found at https://doi.org/10.1016/j.cpc.2011.07.017.