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The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
We report on the latest additions to our open-source, block-grid adaptive framework MPI-AMRVAC, which is a general toolkit for especially hyperbolic/parabolic partial differential equations (PDEs). Applications traditionally focused on…
Like many groups considering the new programming language Julia, we faced the challenge of accessing the algorithms that we develop in Julia from R. Therefore, we developed the R package JuliaConnectoR, available from the CRAN repository…
LazySets.jl is a Julia library that provides ways to symbolically represent sets of points as geometric shapes, with a special focus on convex sets and polyhedral approximations. LazySets provides methods to apply common set operations,…
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for…
We use a space-time discretization based on physics informed deep learning (PIDL) to approximate solutions of a class of rate-dependent strain gradient plasticity models. The differential equation governing the plastic flow, the so-called…
We present a general purpose method for solving partial differential equations on a closed surface, based on a technique for discretizing the surface introduced by Wenjun Ying and Wei-Cheng Wang [J. Comput. Phys. 252 (2013), pp. 606-624]…
Graphical Business Process Modelling Languages (BPML) like Role Activity Diagrams (RAD) provide ease and flexibility for modelling business behaviour. However, these languages show limited applicability in terms of enactment over…
Simulation of non-adiabatic dynamics of a quantum system coupled to dissipative environments poses significant challenges. New sophisticated methods are regularly being developed with an eye towards moving to larger systems and more…
Efficient accelerator modeling and particle tracking are key for the design and configuration of modern particle accelerators. In this work, we present JuTrack, a nested accelerator modeling package developed in the Julia programming…
High level domain specific languages for the finite element method underpin high productivity programming environments for simulations based on partial differential equations (PDE) while employing automatic code generation to achieve high…
Advanced ultrasound computed tomography techniques like full-waveform inversion are mathematically challenging and orders of magnitude more computationally expensive than conventional ultrasound imaging methods. This computational and…
Reliable predictions of critical phenomena, such as weather, wildfires and epidemics often rely on models described by Partial Differential Equations (PDEs). However, simulations that capture the full range of spatio-temporal scales…
In the realm of scientific computing, both Julia and Python have established themselves as powerful tools. Within the context of High Energy Physics (HEP) data analysis, Python has been traditionally favored, yet there exists a compelling…
Technical computing is a challenging application area for programming languages to address. This is evinced by the unusually large number of specialized languages in the area (e.g. MATLAB, R), and the complexity of common software stacks,…
Ordinary Differential Equations (ODE) are used throughout science where the capture of rates of change in states is sought. While both pieces of commercial and open software exist to study such systems, their efficient and accurate usage…
Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although…
We present \texttt{MathOptAI.jl}, an open-source Julia library for embedding trained machine learning predictors into a JuMP model. \texttt{MathOptAI.jl} can embed a wide variety of neural networks, decision trees, and Gaussian Processes…
We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core…
We present a straightforward approach for distributed parallelization of stencil-based xPU applications on a regular staggered grid, which is instantiated in the package ImplicitGlobalGrid.jl. The approach allows to leverage remote direct…