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We present a finite element toolbox for the computation of Bogoliubov-de Gennes modes used to assess the linear stability of stationary solutions of the Gross-Pitaevskii (GP) equation. Applications concern one (single GP equation) or two-component (a system of coupled GP equations) Bose-Einstein condensates in one, two and three dimensions of space. An implementation using the free software ▪is distributed with this paper. For the computation of the GP stationary (complex or real) solutions we use a Newton algorithm coupled with a continuation method exploring the parameter space (the chemical potential or the interaction constant). Bogoliubov-de Gennes equations are then solved using dedicated libraries for the associated eigenvalue problem. Mesh adaptivity is proved to considerably reduce the computational time for cases implying complex vortex states. Programs are validated through comparisons with known theoretical results for simple cases and numerical results reported in the literature. Program Title: FFEM_BdG_toolbox.zip CPC Library link to program files: https://doi.org/10.17632/dgypyc34gb.1 Licensing provisions: Apache 2.0 Programming language: ▪(v 4.12) free software (www.freefem.org) Nature of problem: The software computes Bogoliubov-de Gennes (BdG) complex modes of Bose-Einstein condensates described by the Gross-Pitaevskii (GP) equation. BdG equations are obtained by linearizing the GP equation (or the system of coupled GP equations) around a stationary solution. Obtained BdG modes are used to assess on the stability of stationary states. Solution method: Stationary states of the GP equation are obtained by a Newton algorithm. Parameter space is explored using a continuation on the chemical potential. Once the stationary (complex or real) state is captured accurately, BdG modes are computed by solving the associated eigenvalue problem with the ARPACK library. Complex eigenvalues and eigenvectors are computed and stored. The wave function is discretized by P2 (piece-wise quadratic) Galerkin triangular (in 2D) or tetrahedral (in 3D) finite elements. Mesh adaptation is implemented to reduce the computational time. Examples are given for stationary states in one- and two-component Bose-Einstein condensates. [ABSTRACT FROM AUTHOR]

UnDiFi-2D , an open source (free software) Un structured-grid, Di scontinuity Fi tting code, is presented. The aim of UnDiFi-2D is to model gas-dynamic discontinuities in two-dimensional (2D) flows as if they were true discontinuities of null thickness that bound regions of the flow-field where a smooth solution to the governing PDEs exists. UnDiFi-2D therefore needs to be coupled with an unstructured CFD solver that is used to discretize the governing PDEs within the smooth regions of the flow-field. Two different, in-house developed, CFD solvers are also included in the current distribution. The main features of the UnDiFi-2D software can be summarized as follows: Programming language UnDiFi-2D is written in standard Fortran 77/95; its design is highly modular in order to enhance simplicity of use, maintenance and allow coupling with virtually any existing CFD solver; Usability, maintenance and enhancement In order to improve the usability, maintenance and enhancement of the code also the documentation has been carefully taken into account. The git distributed versioning system has been adopted to facilitate collaborative maintenance and code development; Copyrights UnDiFi-2D is a free software that anyone can use, copy, distribute, change and improve under the GNU Public License version 3. The present paper is a manifesto of the first public release of the UnDiFi-2D code. It describes the currently implemented features, which are the result of more than a decade of still ongoing CFD developments. This work is focused on the computational techniques adopted and a detailed description of the main characteristics is reported. UnDiFi-2D capabilities are demonstrated by means of examples test cases. The design of the code allows to easily include existing CFD codes and is aimed at ease code reuse and readability. Program title: UnDiFi-2D CPC Library link to program files: https://doi.org/10.17632/5hwssmc2mx.1 Licensing provisions: GNU General Public License, version 3 Programming language: Fortran; developed and tested with Intel Fortran Compiler v. 18.0.3 and GNU gfortran. External routines: The code depends on several libraries and third-party packages which are detailed in the corpus of the text. Nature of problem: Numerical computation of flows with discontinuities. Solution method: Shock-fitting technique. Additional comments including restrictions and unusual features: • At present, UnDiFi-2D is validated for inviscid steady and unsteady two-dimensional flows without changes in the number of discontinuity lines and interaction points. • UnDiFi-2D implements a shock-fitting algorithm and can be coupled with unstructured cell-vertex solvers, with an Arbitrary Lagrangian-Eulerian (ALE) formulation. • UnDiFi-2D project adopts git [1], a free and open source distributed version control system. A public repository dedicated to UnDiFi-2D project [2] has been created on github [3], a web-based hosting service for software development projects using git versioning system. Finally, a comprehensive documentation is provided in the form of user manual developed in Pandoc [4]. [1] Git, a free and open source distributed version control system, http://git-scm.com. [2] UnDiFi-2D documentation, https://github.com/UnDiFi/UnDiFi-2D. [3] Github, a web-based hosting service for software development projects using git versioning system, https://github.com. [4] M. Dominici, TUGboat 35(1) (2014) 44-50. [ABSTRACT FROM AUTHOR]

• High-precision computation capabilities implemented in open-source framework YADE. • Full python support for all arbitrary precision types implemented in the C++ backend. • Benchmark of GNU gcc, Intel icpc and clang compilers for all precision types. • Importance of high precision is shown by simulations of an elastic triple pendulum. • The influence of high precision on damping, time step and energy is presented. This paper deals with the implementation of arbitrary precision calculations into the open-source discrete element framework YADE published under the GPL-2+ free software license. This new capability paves the way for the simulation framework to be used in many new fields such as quantum mechanics. The implementation details and associated gains in the accuracy of the results are discussed. Besides the "standard" double (64 bits) type, support for the following high-precision types is added: long double (80 bits), float128 (128 bits), mpfr_float_backend (arbitrary precision) and cpp_bin_float (arbitrary precision). Benchmarks are performed to quantify the additional computational cost involved with the new supported precisions. Finally, a simple calculation of a chaotic triple pendulum is performed to demonstrate the new capabilities and the effect of different precisions on the simulation result. [ABSTRACT FROM AUTHOR]

Abstract: Computational physics as a mode of studying the mathematical and physical sciences has grown world-wide over the past two decades, but this trend is yet to fully develop in Africa. The essential ingredients are there for this to happen: increasing internet connectivity, cheaper computing resources and the widespread availability of open source and freeware. The missing ingredients centre on intellectual isolation and the low levels of quality international collaborations. Low level of funding for research from local governments remains a critical issue. This paper gives a motivation for the importance of developing computational physics at the university undergraduate level, graduate level and research levels and gives suggestions on how this may be achieved within the African context. It is argued that students develop a more intuitive feel for the mathematical and physical sciences, that they learn useful, transferable skills that make our graduates well-sought after in the industrial and commercial environments, and that such graduates are better prepared to tackle research problems at the masters and doctoral levels. At the research level, the case of the African School Series on Electronic Structure Methods and Applications (ASESMA) is presented as a new multi-national modality for engaging with African scientists. There are many novel aspects to this School series, which are discussed. [Copyright &y& Elsevier]