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Nowadays, numerous component models are used for various purposes: to build applications, middleware or even operating systems. Those models commonly support structure reconfiguration, that is modification of application's architecture at…

Networking and Internet Architecture · Computer Science 2007-05-23 Jakub Kornas , Matthieu Leclercq , Vivien Quema , Jean-Bernard Stefani

Numerical solutions of partial differential equations enable a broad range of scientific research. The Dedalus Project is a flexible, open-source, parallelized computational framework for solving general partial differential equations using…

Instrumentation and Methods for Astrophysics · Physics 2020-04-29 Keaton J. Burns , Geoffrey M. Vasil , Jeffrey S. Oishi , Daniel Lecoanet , Benjamin P. Brown

We introduce ACEpotentials.jl, a Julia-language software package that constructs interatomic potentials from quantum mechanical reference data using the Atomic Cluster Expansion (Drautz, 2019). As the latter provides a complete description…

We present ForwardDiff, a Julia package for forward-mode automatic differentiation (AD) featuring performance competitive with low-level languages like C++. Unlike recently developed AD tools in other popular high-level languages such as…

Mathematical Software · Computer Science 2016-07-28 Jarrett Revels , Miles Lubin , Theodore Papamarkou

Approximating partial differential equations for extensive industrial and scientific applications requires leveraging the power of modern high-performance computing. In large-scale parallel computations, the geometrical discretisation…

Numerical Analysis · Mathematics 2024-12-30 Pere A. Martorell , Santiago Badia

Geometric computing with chain complexes allows for the computation of the whole chain of linear spaces and (co)boundary operators generated by a space decomposition into a cell complex. The space decomposition is stored and handled with…

Computational Geometry · Computer Science 2017-11-07 Francesco Furiani , Giulio Martella , Alberto Paoluzzi

Performant numerical solving of differential equations is required for large-scale scientific modeling. In this manuscript we focus on two questions: (1) how can researchers empirically verify theoretical advances and consistently compare…

Software Engineering · Computer Science 2018-07-18 Christopher Rackauckas , Qing Nie

In this paper we present \texttt{SymOrb.jl}, a software which combines group representation theory and variational methods to provide numerical solutions of singular dynamical systems of paramount relevance in Celestial Mechanics and other…

We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems. JuliaReach consists of two main packages: Reachability, containing implementations of reachability algorithms for continuous and hybrid systems, and…

Systems and Control · Electrical Eng. & Systems 2024-12-20 Sergiy Bogomolov , Marcelo Forets , Goran Frehse , Kostiantyn Potomkin , Christian Schilling

Rimu.jl is a Julia package for solving many-body quantum problems. The core of the package is a matrix-free implementation of Hamiltonians and other operators and compact representation of Fock states, which together allow for efficient…

Computational Physics · Physics 2026-01-28 Matija Čufar , C. J. Bradly , Ray Yang , Elke Pahl , Joachim Brand

Scientific computing is increasingly incorporating the advancements in machine learning and the ability to work with large amounts of data. At the same time, machine learning models are becoming increasingly sophisticated and exhibit many…

Programming Languages · Computer Science 2019-07-19 Mike Innes , Alan Edelman , Keno Fischer , Chris Rackauckas , Elliot Saba , Viral B Shah , Will Tebbutt

We discuss computability and computational complexity of conformal mappings and their boundary extensions. As applications, we review the state of the art regarding computability and complexity of Julia sets, their invariant measures and…

Complex Variables · Mathematics 2017-03-21 Cristobal Rojas , Michael Yampolsky

In this paper we settle most of the open questions on algorithmic computability of Julia sets. In particular, we present an algorithm for constructing quadratics whose Julia sets are uncomputable. We also show that a filled Julia set of a…

Dynamical Systems · Mathematics 2007-09-30 Mark Braverman , Michael Yampolsky

We describe the user interface, governing equations, and numerical methods underpinning the community ocean modeling software called "Oceananigans". Oceananigans development has been lead by the Climate Modeling Alliance to build a…

We present the software design of Gridap, a novel finite element library written exclusively in the Julia programming language, which is being used by several research groups world-wide to simulate complex physical phenomena such as…

Mathematical Software · Computer Science 2022-04-13 Francesc Verdugo , Santiago Badia

Ai4EComponentLib.jl(Ai4EComponentLib) is a component-base model library based on Julia language, which relies on the differential equation solver DifferentialEquations.jl and the symbolic modeling tool Modelingtoolkit.jl. To handle problems…

Software Engineering · Computer Science 2022-08-25 Yuebao Yang , Jingyi Yang , Mingtao Li

In the field of computational fluid dynamics, direct numerical simulations generate highly detailed data for the analysis of turbulent flows by resolving all relevant physical scales. Yet their large size, complexity, and heterogeneity make…

Fluid Dynamics · Physics 2026-03-26 Lorenzo Piu , Heinz Pitsch , Alessandro Parente

No single Automatic Differentiation (AD) system is the optimal choice for all problems. This means informed selection of an AD system and combinations can be a problem-specific variable that can greatly impact performance. In the Julia…

Mathematical Software · Computer Science 2022-02-08 Frank Schäfer , Mohamed Tarek , Lyndon White , Chris Rackauckas

SymBoltz is a new Julia package for solving the linear Einstein-Boltzmann equations in cosmology. It features a symbolic-numeric interface for specifying equations, is free of approximation switching schemes, and is compatible with…

Cosmology and Nongalactic Astrophysics · Physics 2026-03-11 Herman Sletmoen

We introduce JuliVQC: a light-weight, yet extremely efficient variational quantum circuit simulator. JuliVQC is part of an effort for classical simulation of the \textit{Zuchongzhi} quantum processors, where it is extensively used to…

Quantum Physics · Physics 2024-06-28 Wei-You Liao , Xiang Wang , Xiao-Yue Xu , Chen Ding , Shuo Zhang , He-Liang Huang , Chu Guo