Alejandro Hernández-Cano, Alexander Hägele, Allen Hao Huang, Angelika Romanou, Antoni-Joan Solergibert, Barna Pásztor, Bettina Messmer, Dhia Garbaya, Eduard Frank Ďurech, Ido Hakimi, Juan Garcia Giraldo, Mete Ismayilzada, Negar Foroutan, Skander Moalla, Tiancheng Chen, Vinko Sabolčec, Yixuan Xu, Michael Aerni, Badr AlKhamissi, Inés Altemir Marinas, Mohammad Hossein Amani, Matin Ansaripour, Ilia Badanin, Harold Benoit, Emanuela Boros, Nicholas John Browning, Fabian Bösch, Maximilian Böther, Niklas Canova, Camille Challier, Clément Charmillot, Jonathan Coles, Jan Milan Deriu, Arnout Devos, Lukas Drescher, Daniil Dzenhaliou, Maud Ehrmann, Dongyang Fan, Simin Fan, Silin Gao, Miguel Gila, María Grandury, Diba Hashemi, Alexander Miserlis Hoyle, Jiaming Jiang, Mark Klein, Andrei Kucharavy, Anastasiia Kucherenko, Frederike Lübeck, Roman Machacek, Theofilos Ioannis Manitaras, Andreas Marfurt, Kyle Matoba, Simon Matrenok, Henrique Mendonça, Fawzi Roberto Mohamed, Syrielle Montariol, Luca Mouchel, Sven Najem-Meyer, Jingwei Ni, Gennaro Oliva, Matteo Pagliardini, Elia Palme, Andrei Panferov, Léo Paoletti, Marco Passerini, Ivan Pavlov, Auguste Poiroux, Kaustubh Ponkshe, Nathan Ranchin, Javier Rando, Mathieu Sauser, Jakhongir Saydaliev, Mukhammadali Sayfiddinov, Marian Schneider, Stefano Schuppli, Marco Scialanga, Andrei Semenov, Kumar Shridhar, Raghav Singhal, Anna Sotnikova, Alexander Sternfeld, Ayush Kumar Tarun, Paul Teiletche, Jannis Vamvas, Xiaozhe Yao, Hao Zhao, Alexander Ilic, Ana Klimovic, Andreas Krause, Caglar Gulcehre, David Rosenthal, Elliott Ash, Florian Tramèr, Joost VandeVondele, Livio Veraldi, Martin Rajman, Thomas C. Schulthess, Torsten Hoefler, Antoine Bosselut, Martin Jaggi, Imanol Schlag. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Non-linear phase field models are increasingly used for the simulation of fracture propagation problems. The numerical simulation of fracture networks of realistic size requires the efficient parallel solution of large coupled non-linear systems. Although in principle efficient iterative multi-level methods for these types of problems are available, they are not widely used in practice due to the complexity of their parallel implementation. Here, we present Utopia, which is an open-source C++ library for parallel non-linear multilevel solution strategies. Utopia provides the advantages of high-level programming interfaces while at the same time a framework to access low-level data-structures without breaking code encapsulation. Complex numerical procedures can be expressed with few lines of code, and evaluated by different implementations, libraries, or computing hardware. In this paper, we investigate the parallel performance of our implementation of the recursive multilevel trust-region (RMTR) method based on the Utopia library. RMTR is a globally convergent multilevel solution strategy designed to solve non-convex constrained minimization problems. In particular, we solve pressure-induced phase-field fracture propagation in large and complex fracture networks. Solving such problems is deemed challenging even for a few fractures, however, here we are considering networks of realistic size with up to 1000 fractures.

We propose COSMA: a parallel matrix-matrix multiplication algorithm that is near communication-optimal for all combinations of matrix dimensions, processor counts, and memory sizes. The key idea behind COSMA is to derive an optimal (up to a factor of 0.03% for 10MB of fast memory) sequential schedule and then parallelize it, preserving I/O optimality. To achieve this, we use the red-blue pebble game to precisely model MMM dependencies and derive a constructive and tight sequential and parallel I/O lower bound proofs. Compared to 2D or 3D algorithms, which fix processor decomposition upfront and then map it to the matrix dimensions, it reduces communication volume by up to √ times. COSMA outperforms the established ScaLAPACK, CARMA, and CTF algorithms in all scenarios up to 12.8x (2.2x on average), achieving up to 88% of Piz Daint's peak performance. Our work does not require any hand tuning and is maintained as an open source implementation.

The capabilities of CP2K, a density-functional theory package and OMEN, a nano-device simulator, are combined to study transport phenomena from first-principles in unprecedentedly large nanostructures. Based on the Hamiltonian and overlap matrices generated by CP2K for a given system, OMEN solves the Schrödinger equation with open boundary conditions (OBCs) for all possible electron momenta and energies. To accelerate this core operation a robust algorithm called SplitSolve has been developed. It allows to simultaneously treat the OBCs on CPUs and the Schrödinger equation on GPUs, taking advantage of hybrid nodes. Our key achievements on the Cray-XK7 Titan are (i) a reduction in time-to-solution by more than one order of magnitude as compared to standard methods, enabling the simulation of structures with more than 50000 atoms, (ii) a parallel efficiency of 97% when scaling from 756 up to 18564 nodes, and (iii) a sustained performance of 15 DP-PFlop/s.