Considerable work went into the teaching section. Every course offering now has its own page with details on the structure and content, and a link to Digicampus. While Digicampus remains our central hub for communication and day-to-day updates during the semester, the new pages give you an overview without having to log in.

The interactive Pluto.jl notebooks that contain our lecture notes for Höhere Mathematik (in German) are now reachable directly from the site. You can run them in the browser, read them as static pages, or download the source files and work with them on your own machine.

The publication list is considerably more complete than it used to be, and each entry now links to the preprint, the DOI and, where we have one, the repository to reproduce the results.

If you find something broken or missing, please let us know.

Computational Science and Engineering is an important enabler for more sustainable technologies, yet the sustainability dimension of CSE itself is rarely discussed. With rapid advances in computational methods, including AI and increasingly autonomous workflows, this question has only become more pressing: growing computational capabilities do not automatically translate into greater resource efficiency. Our conclusion then and now is that sustainability in CSE should not be an afterthought, but embedded as a core design principle in the methods we develop.

Abstract. Computational Science and Engineering (CSE) combines expertise at the intersection of engineering, applied mathematics, and computer science to form powerful methods for model-based design and model-based decision support across disciplines. Today, CSE methods and tools have an impact as an enabling technology in the development of increasingly sustainable products, processes, and operations. However, sustainability is rarely considered holistically in the context of CSE itself. This paper develops a perspective on sustainability in CSE by distinguishing CSE as an enabler of sustainability in application domains from sustainability within CSE itself, which rests on two complementary pillars: sustainable computing and sustainable software. We present illustrative examples for these pillars and derive recommendations and best practices for CSE stakeholders. Developing an understanding of how sustainability can create added value in CSE is an important future direction for the field. This calls for a concerted effort within the CSE community to define measurable outcomes and best practices that embed sustainability as a core design principle rather than an afterthought.

The format put the emphasis on working rather than listening. A keynote by Chris Rackauckas, VP at JuliaHub and co-PI of the Julia Lab at MIT, and a number of short talks set the stage, but most of the two days went into breakout sessions along four tracks: the numerical foundations of SciML, going beyond prediction towards control and optimization, automation and scalability from prototype to production scale, and domain awareness and interpretability. The discussions were lively throughout, and their results will feed into a joint article on the current state and the future directions of the field.

Thank you to everyone who joined for the many excellent contributions and for the open and collaborative atmosphere - it was exactly what we had hoped for when bringing together people from such different corners of SciML. The workshop was organized by Andreas Hofmann and Lars Mikelsons of the Chair for Mechatronics jointly with the HPSC Lab.

TrixiParticles.jl is written in Julia and designed for solving multiphysics problems with particle-based methods, from free-surface flows to fluid-structure interaction, with GPU support across vendors. It is developed by our PhD student Niklas Neher (HLRS), Erik Faulhaber (University of Cologne), and Sven Berger (Helmholtz-Zentrum Hereon).

Congratulations to the team for this awesome achievement! 🎉🙌

He will work on the project KIPATCH, funded by the Centre for Future Production, which is concerned with optimizing the manufacturing process of fibre patch placement with the help of AI-based surrogate models. Lukas holds Bachelor’s and Master’s degrees in mechanical engineering from TU Munich, where he was particularly interested in numerical approaches to application-oriented problems. Before joining our lab, he spent two years working for Everllence SE in Augsburg. The experience gained there will be very helpful in the industry-focused KIPATCH project.

Welcome to the HPSC Lab, Lukas 👋! We are looking forward to working with you!

Abstract Making use of the partial differential equations solver Trixi.jl, written in Julia, we develop adaptive multiphysics interface coupling for arbitrary equations. The physics of the coupling can be freely chosen by the user and can be designed to conserve quantities, like momentum and energy. Using the quadtree p4est we are able to arbitrarily partition the domain into subdomains on which we solve different equations. These domains can be non-simply connected domains. Our coupling can be dynamic in time. If the criteria for the domain decomposition for the different models change, we can adapt these domains automatically through our implementation of Adaptive Model Selection (AMS). Furthermore, AMS works together with Adaptive Mesh Refinement (AMR), which makes our implementation particularly versatile and efficient.

Abstract. Multiphysics simulations cover a range of scenarios in which multiple models interact in nontrivial ways. In some cases, fundamentally different physical descriptions are coupled across interfaces, as in fluid-structure interaction. In others, alternative models of the same physical process, differing in resolution or fidelity, must be combined within a single simulation, e.g., when combining compressible Euler and magnetohydrodynamics formulations. Yet another class involves the interaction of processes with different characteristic scales or governing equations that coexist within the same physical domain, for example in coupled flow-aeroacoustics or flow-gravity problems. Despite their different physical interpretations, these scenarios pose similar challenges from a computational and algorithmic perspective. The interacting models are typically heterogeneous in their mathematical structure, numerical discretization, and computational requirements, and must be coordinated consistently in space and time. These challenges are further exacerbated by the use of mesh or model adaptivity and when targeting heterogeneous computing architectures. Against this background, this talk discusses the development and implementation of multiphysics coupling techniques for such heterogeneous settings. The presented concepts are illustrated using examples from Trixi.jl and TrixiParticles.jl, two open-source software packages for high-performance simulations in Julia. Trixi.jl is a high-order numerical solver for hyperbolic partial differential equations that enables the exploration of mesh and model adaptivity in grid-based coupled simulations. TrixiParticles.jl is a particle-based solver for multiphysics simulations on complex geometries, with a focus on robustness and versatility. Using selected representative application scenarios, we discuss practical challenges and design choices arising from adaptivity, heterogeneous models, and heterogeneous computing architectures.

Valentin joined our lab in August 2024 and has worked on high-performance computing — especially GPU acceleration — within our Trixi framework packages Trixi.jl and TrixiParticles.jl. Alongside this, he continued his work on automatic differentiation in Julia and on improving the Julia language from the compiler side.

We wish Valentin all the best for his new position and the next chapter of his scientific journey!

Abstract. We introduce the concept of volume term adaptivity for high-order discontinuous Galerkin (DG) schemes solving time-dependent partial differential equations. Termed v-adaptivity, we present a novel general approach that exchanges the discretization of the volume contribution of the DG scheme at every Runge-Kutta stage based on suitable indicators. Depending on whether robustness or efficiency is the main concern, different adaptation strategies can be chosen. Precisely, the weak form volume term discretization is used instead of the entropy-conserving flux-differencing volume integral whenever the former produces more entropy than the latter, resulting in an entropy-stable scheme. Conversely, if increasing the efficiency is the main objective, the weak form volume integral may be employed as long as it does not increase entropy beyond a certain threshold or cause instabilities. Thus, depending on the choice of the indicator, the v-adaptive DG scheme improves robustness, efficiency and approximation quality compared to schemes with a uniform volume term discretization. We thoroughly verify the accuracy, linear stability, and entropy-admissibility of the v-adaptive DG scheme before applying it to various compressible flow problems in two and three dimensions.

Abstract. Lax-Wendroff methods combined with discontinuous Galerkin/flux reconstruction spatial discretization provide a high-order, single-stage, quadrature-free method for solving hyperbolic conservation laws. In this work, we introduce automatic differentiation (AD) for performing the Cauchy-Kowalewski procedure used in the element-local time average flux computation step (the predictor step) of Lax-Wendroff methods. The application of AD is similar for methods of any order and does not need positivity corrections during the predictor step. This contrasts with the approximate Lax-Wendroff procedure, which requires different finite difference formulas for different orders of the method and positivity corrections in the predictor step for fluxes that can only be computed on admissible states. The method is Jacobian-free and problem-independent, allowing direct application to any physical flux function. Numerical experiments demonstrate the order and positivity preservation of the method. Additionally, performance comparisons indicate that the wall-clock time of automatic differentiation is always on par with the approximate Lax-Wendroff method.

The speaker, Prof. Dr. Michael Resch, is Director of the High-Performance Computing Center Stuttgart (HLRS) and Professor of High-Performance Computing at the University of Stuttgart. He has led the HLRS since 2003 and is widely recognized for his work on large-scale simulation, HPC infrastructures, and the broader role of digital technologies in science and society.

In his talk, Michael Resch addressed the rapid rise of artificial intelligence and its implications for computing infrastructures and energy demand. He discussed concerns ranging from increasing hardware costs to the growing power consumption of modern AI systems, and questioned whether current trends toward ever larger and more energy-intensive HPC systems are always the right strategic choice. While highlighting the undeniable usefulness of AI tools, he also pointed out that their current energy footprint is often disproportionate to their productive output, offering several impulses for a more critical and differentiated view on future developments.

The event was attended by more than 60 participants and concluded with an engaged Q&A session, including lively discussion with the audience. A small reception afterwards provided further opportunities for exchange. Thanks to the support of Ioana Lupu, Ursula Weiß, and Vivienne Ehlert, the event ran smoothly, and we would like to thank Michael Resch once again for coming to Augsburg and contributing to a very successful Public Climate School event.

With our two external participants Martin Obergaulinger from the University of Valencia and Philippe Bourdin from the University of Graz we engaged in discussions about potential sources of numerical dissipation and how to best quantify it. Finally, we had a day-long hackathon session where we started to look into numerical codes and their dissipation rate in dependence of the spatial resolution by using the Taylor-Green vortex as test case.

This event was organized by Michael Schlottke-Lakemper (HPSC), Christoph Knote (Model-based Environmental Exposure Science) and Simon Candelaresi (HPSC)

Our external speakers are Martin Obergaulinger from the University of Valencia and Philippe Bourdin from the University of Graz. From the HPSC Lab, Simon Candelaresi will be speaking. Apart from talks, we will have plenty of time for discussions and hands-on activities.

This event is organized by Michael Schlottke-Lakemper (HPSC), Christoph Knote (Model-based Environmental Exposure Science) and Simon Candelaresi (HPSC)

Participants can register here.

In his lecture on Wissenschaftliches Rechnen im KI-Zeitalter: Zwischen Rechen- und Denkmaschine, which roughly translates to “Scientific Computing in the AI Age: From Number Crunchers to Thinking Machines”, Michael discussed how scientific computing is changing in the era of artificial intelligence, using the contrast between “calculating machines” and “thinking machines” as a guiding theme. He outlined the continued importance of classical high-performance computing for large-scale simulations in areas such as aerospace, climate and weather modeling, and biomedicine, and contrasted this with recent advances of AI methods, for example in protein structure prediction and data-driven weather forecasting. At the same time, he highlighted key challenges for the use of AI in scientific computing, including issues of reliability, explainability, and reproducibility. The lecture concluded with examples from current research in numerical methods, GPU-based computing, and secure machine learning, emphasizing the complementary roles of simulation-based and data-driven approaches in future scientific computing.

Abstract. Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for smoothed particle hydrodynamics (SPH) and other particle-based methods. Our pipeline begins with the generation of a resolution-adaptive point cloud near the geometry’s surface employing a face-based neighborhood search. This point cloud forms the basis for a signed distance field, enabling efficient, localized computations near surface regions. To create an initial particle configuration, we apply a hierarchical winding number method for fast and accurate inside-outside segmentation. Particle positions are then relaxed using an SPH-inspired scheme, which also serves to pack boundary particles. This ensures full kernel support and promotes isotropic distributions while preserving the geometry interface. By leveraging the meshless nature of particle-based methods, our approach does not require connectivity information and is thus straightforward to integrate into existing particle-based frameworks. It is robust to imperfect input geometries and memory-efficient without compromising performance. Moreover, our experiments demonstrate that with increasingly higher resolution, the resulting particle distribution converges to the exact geometry.