Bruno Lang

Electronic-structure theory is the foundation of the description of materials including multiscale modeling of their properties and functions. Obviously, without sufficient accuracy at the base, reliable predictions are unlikely at any level that follows. The software package FHI-aims has proven to be a game changer for accurate free-energy calculations because of its scalability, numerical precision, and its efficient handling of density functional theory (DFT) with hybrid functionals and van der Waals interactions. It treats molecules, clusters, and extended systems (solids and liquids) on an equal footing. Besides DFT, FHI-aims also includes quantum-chemistry methods, descriptions for excited states and vibrations, and calculations of various types of transport. Recent advancements address the integration of FHI-aims into an increasing number of workflows and various artificial intelligence (AI) methods. This Roadmap describes the state-of-the-art of FHI-aims and advancements that are currently ongoing or planned.

We present techniques for improving the efficiency of s in the solution of the dynamic problem, i.e., for building and maintaining a Pareto archive. We propose algorithms for (re)building a tree from a set of points, either as a or by a clustering approach. Numerical experiments confirm that rebuilding the tree at intervals, combined with modified strategies for updating the lower and upper bounds in each node and for computing the distances of points to whole subtrees in between the rebuilds, can lead to significant speedups over using plain -based updates throughout, in particular for higher dimensions.

Molflow+ is a Monte Carlo (MC) simulation software for ultra-high vacuum, mainly used to simulate pressure in particle accelerators. In this article, we present and discuss the design choices arising in a new implementation of its ray-tracing–based simulation unit for Nvidia RTX Graphics Processing Units (GPUs). The GPU simulation kernel was designed with Nvidia’s OptiX 7 API to make use of modern hardware-accelerated ray-tracing units, found in recent RTX series GPUs based on the Turing and Ampere architectures. Even with the challenges posed by switching to 32 bit computations, our kernel runs much faster than on comparable CPUs at the expense of a marginal drop in calculation precision.

It is customary to identify sparse matrices with the corresponding adjacency or incidence graph. For the solution of linear systems of equations using Gaussian elimination, the representation by its adjacency graph allows a symbolic computation that can be used to predict memory footprints and enables the determination of near-optimal elimination orderings based on heuristics. The Hermitian eigenvalue problem on the other hand seems to evade such treatment at first glance due to its inherent iterative nature. In this paper we prove this assertion wrong by showing the equivalence of the Hermitian eigenvalue problem with a symbolic edge elimination procedure. A symbolic calculation based on the incidence graph of the matrix can be used in analogy to the symbolic phase of Gaussian elimination to develop heuristics which reduce memory footprint and computations. Yet, we also show that the question of an optimal elimination strategy remains NP-hard, in analogy to the linear systems case.

Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.