ACM Transactions on Mathematical Software (TOMS)

Besançon, Mathieu; Designolle, Sébastien; Halbey, Jannis; Hendrych, Deborah; Kuzinowicz, Dominik; Pokutta, Sebastian; Troppens, Hannah; Viladrich Herrmannsdoerfer, Daniel; Wirth, Elias

doi: 10.1145/3765626pmid: N/A

Frank-Wolfe (FW) algorithms have emerged as an essential class of methods for constrained optimization, especially on large-scale problems. In this article, we summarize the algorithmic design choices and progress made in the last years of the development of FrankWolfe.jl, a Julia package gathering high-performance implementations of state-of-the-art FW variants. We review key use cases of the library in the recent literature, which match its original dual purpose: first, becoming the de-facto toolbox for practitioners applying FW methods to their problem, and second, offering a modular ecosystem to algorithm designers who experiment with their own variants and implementations of algorithmic blocks. Finally, we demonstrate the performance of several FW variants on important problem classes in several experiments, which we curated in a separate repository for continuous benchmarking.

Bucelli, Michele

doi: 10.1145/3748817pmid: N/A

This article presents updates to lifex [Africa, SoftwareX (2022)], a C++ library for high-performance finite element simulations of multiphysics, multiscale, and multidomain problems. In this release, we introduce an additional intergrid transfer method for non-matching multiphysics coupling on the same domain, significantly optimize nearest-neighbor point searches and interface coupling utilities, extend the support for 2D and mixed-dimensional problems, and provide improved facilities for input/output and simulation serialization and restart. These advancements also propagate to the previously released modules of lifex specifically designed for cardiac modeling and simulation, namely lifex-fiber [Africa et al., BMC Bioinformatics (2023)], lifex-ep [Africa et al., BMC Bioinformatics (2023)], and lifex-cfd [Africa et al., Computer Physics Communications (2024)]. The changes introduced in this release aim at consolidating lifex’s position as a valuable and versatile tool for the simulation of multiphysics systems.

Kinnewig, Sebastian; Heinlein, Alexander; Wick, Thomas

doi: 10.1145/3766906pmid: N/A

In this work, restricted additive Schwarz (RAS) and optimized restricted additive Schwarz (ORAS) preconditioners from the Trilinos package FROSch (Fast and Robust Overlapping Schwarz) are employed to solve model problems implemented using deal.II (differential equations analysis library). Therefore, a Tpetra-based interface for coupling deal.II and FROSch is implemented. While RAS preconditioners have been available before, ORAS preconditioners have been newly added to FROSch. The deal.II–FROSch interface works for both Lagrange-based and Nédélec finite elements. Here, as model problems, nonstationary, nonlinear, variational-monolithic fluid-structure interaction and the indefinite time-harmonic Maxwell’s equations are considered. Several numerical experiments in two and three spatial dimensions confirm the performance of the preconditioners as well as the FROSch-deal.II interface. In conclusion, the overall software interface is straightforward and easy to use while giving satisfactory solver performances for challenging PDE systems.

San-José, Rodrigo

doi: 10.1145/3773284pmid: N/A

We generalize the Brouwer-Zimmermann algorithm, which is the most efficient general algorithm for computing the minimum distance of a random linear code, to the case of generalized Hamming weights. We also adapt this algorithm to compute the relative generalized Hamming weights of a nested pair of linear codes. In the package GHWs, we provide an implementation of this algorithm in Sage, as well as several other utilities for working with generalized Hamming weights. With this implementation, we show that the proposed algorithm is faster than the naive approach of computing the generalized Hamming weights using the definition.

Pashinska-Gadzheva, Maria; Bouyukliev, Iliya

doi: 10.1145/3777479pmid: N/A

We present the Linear Codes Weight Invariant Library (LinCodeWeightInv) for optimized computing of the weight distribution and other weight characteristics of a random linear code (minimum distance, number of codewords with a given weight, etc.). The presented library is developed for linear codes over finite fields with up to 64 elements. We use two main methods for optimizations—efficient algorithms for generating the codewords and integration of extended vector registers with SSE4.1, AVX2, and AVX512 instruction sets for x86 architectures and NEON instructions set for ARM. The LinCodeWeightInv is compared to other software systems for linear codes over finite fields. Comparing our library to the Magma software, we get between 1.3 and 4 times faster execution times for \(\mathbb{F}_{2}\) and \(\mathbb{F}_{5}\) and up to 49 depending on the field and the code length. Comparing the LinCodeWeightInv library to the open source software GAP, we observe a reduction in computation time by factors between 5 and 7 for \(\mathbb{F}_{2}\) . For other finite fields, we observe more than 100 times faster execution times.

Prokopenko, Andrey; Arndt, Daniel; Lebrun-Grandié, Damien; Turcksin, Bruno

doi: 10.1145/3772288pmid: N/A

This article provides an overview of the 2.0 release of the ArborX library, a performance portable geometric search library based on Kokkos. We describe the major changes in ArborX 2.0 including a new interface for the library to support a wider range of user problems, new search data structures (brute force and distributed), support for user functions to be executed on the results (callbacks), and an expanded set of the supported algorithms (ray tracing and clustering).

McCoid, Conor

doi: 10.1145/3766904pmid: N/A

Intersection algorithms are crucial in many applications, but they may not be robust. Without robustness, these algorithms may fail to correctly identify large intersections. To prevent that, this article develops a parsimonious algorithm for the intersection of simplices. This generalizes earlier algorithms on triangle and tetrahedral intersections. This article outlines the algorithm and its parsimony and proves its consistency. Numerical experiments confirm its applicability.