Related papers: A user-guide to Gridap -- grid-based approximation…
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means…
We describe the design and early implementation of an extensible, component-based software architecture for natural language engineering applications which interfaces with high performance distributed computing services. The architecture…
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…
Traditional solvers for delay differential equations (DDEs) are designed around only a single method and do not effectively use the infrastructure of their more-developed ordinary differential equation (ODE) counterparts. In this work we…
This year marks the consolidation of Julia (https://julialang.org/), a programming language designed for scientific computing, as the first stable version (1.0) has been released, in August 2018. Among its main features, expressiveness and…
PowerDynamics.jl is a Julia package for time-domain modeling of power grids that is specifically designed for the stability analysis of systems with high shares of renewable energies. It makes use of Julia's state-of-the-art differential…
Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…
We present QuantumToolbox$.$jl, an open-source Julia package for simulating open quantum systems. Designed with a syntax familiar to users of QuTiP (Quantum Toolbox in Python), it harnesses Julia's high-performance ecosystem to deliver fast…
In this paper, we provide an affirmative answer to the long-standing question: Are GPUs useful in solving linear programming? We present cuPDLP.jl, a GPU implementation of restarted primal-dual hybrid gradient (PDHG) for solving linear…
Elliptic partial differential equations (PDEs) arise in many areas of computational sciences such as computational fluid dynamics, biophysics, engineering, geophysics and more. They are difficult to solve due to their global nature and…
Grid diagrams are a combinatorial version of classical link diagrams, widely used in theoretical, computational and applied knot theory. Motivated by questions from (bio)-physical knot theory, we introduce GridPyM, a Sage compatible Python…
This paper proposes integrating Aspect-oriented Programming (AOP) into Julia, a language widely used in scientific and High-Performance Computing (HPC). AOP enhances software modularity by encapsulating cross-cutting concerns, such as…
We present QUBO.jl, an end-to-end Julia package for working with QUBO (Quadratic Unconstrained Binary Optimization) instances. This tool aims to convert a broad range of JuMP problems for straightforward application in many physics and…
The Julia programming language was designed to fill the needs of scientific computing by combining the benefits of productivity and performance languages. Julia allows users to write untyped scripts easily without needing to worry about…
Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of physical processes relevant to science and engineering. Multilevel preconditioners represent a family of scalable techniques for solving discrete…
Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…
The GRAPE$.$jl package (https://github.com/JuliaQuantumControl/GRAPE.jl) implements Gradient Ascent Pulse Engineering, a widely used method of quantum optimal control. Its purpose is to find controls that steer a quantum system in a…