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We introduce an efficient algorithm for the computation of the $W_3$ invariant of general unitary maps, which converges rapidly even on coarse discretization grids. The algorithm does not require extensive manipulation of the unitary maps,…

Quantum Physics · Physics 2017-07-05 B. Höckendorf , A. Alvermann , H. Fehske

We consider Monte Carlo simulations of classical spin models of statistical mechanics using the massively parallel architecture provided by graphics processing units (GPUs). We discuss simulations of models with discrete and continuous…

Computational Physics · Physics 2012-07-20 Martin Weigel , Taras Yavors'kii

One of the main challenges in Heavy Energy Physics is to make fast analysis of high amount of experimental and simulated data. At LHC-CERN one p-p event is approximate 1 Mb in size. The time taken to analyze the data and obtain fast results…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-07-01 Mihai Niculescu , Sorin-Ion Zgura

In this work, we consider the reformulation of hierarchical ($\mathcal{H}$) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). $\mathcal{H}$ matrices approximate specific dense…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-09-04 Peter Zaspel

In this paper, we explore three combinatorial descriptions of semistable types of hyperelliptic curves over local fields: dual graphs, their quotient trees by the hyperelliptic involution, and configurations of the roots of the defining…

Number Theory · Mathematics 2026-01-13 Tim Dokchitser , Vladimir Dokchitser , Celine Maistret , Adam Morgan

The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…

Numerical Analysis · Mathematics 2013-01-14 Chunsheng Feng , Shi Shu , Jinchao Xu , Chen-Song Zhang

General-purpose Computing on Graphics Processing Units (GPGPU) has been introduced to many areas of scientific research such as bioinformatics, cryptography, computer vision, and deep learning. However, computing models in the High-energy…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-07-23 Max Isacson , Mattias Ellert , Richard Brenner

We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing methods for sufficiently large genus or residue field. The…

Number Theory · Mathematics 2026-02-20 Maarten Derickx , Kenji Terao

We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…

Numerical Analysis · Mathematics 2026-02-26 Vladimír Lukeš , Eduard Rohan

In this paper, we give improved bounds for the computational complexity of computing with planar algebraic curves. More specifically, for arbitrary coprime polynomials $f$, $g \in \mathbb{Z}[x,y]$ and an arbitrary polynomial $h \in…

Symbolic Computation · Computer Science 2014-08-01 Alexander Kobel , Michael Sagraloff

In many Multimedia content analytics frameworks feature likelihood maps represented as histograms play a critical role in the overall algorithm. Integral histograms provide an efficient computational framework for extracting multi-scale…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-11-07 Mahdieh Poostchi , Kannappan Palaniappan , Da Li , Michela Becchi , Filiz Bunyak , Guna Seetharaman

The Hilbert-space Gaussian Process (HGP) approach offers a hyperparameter-independent basis function approximation for speeding up Gaussian Process (GP) inference by projecting the GP onto M basis functions. These properties result in a…

Machine Learning · Computer Science 2024-08-06 Frida Viset , Anton Kullberg , Frederiek Wesel , Arno Solin

Strong gravitational lensing is a powerful probe of cosmology and the dark matter distribution. Efficient lensing software is already a necessity to fully use its potential and the performance demands will only increase with the upcoming…

Instrumentation and Methods for Astrophysics · Physics 2019-02-12 Markus Rexroth , Christoph Schäfer , Gilles Fourestey , Jean-Paul Kneib

Given a sextic CM field $K$, we give an explicit method for finding all genus 3 hyperelliptic curves defined over $\mathbb{C}$ whose Jacobians are simple and have complex multiplication by the maximal order of this field, via an…

Number Theory · Mathematics 2019-02-20 Jennifer S. Balakrishnan , Sorina Ionica , Kristin Lauter , Christelle Vincent

We define and study the subspace of cuspidal functions for $G$-bundles on a class of nilpotent extensions $C$ of curves over a finite field. We show that this subspace is preserved by the action of a certain noncommutative Hecke algebra…

Number Theory · Mathematics 2023-03-30 Alexander Braverman , David Kazhdan , Alexander Polishchuk

We present an efficient and scalable algorithm for performing matrix-vector multiplications ("matvecs") for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving…

Numerical Analysis · Mathematics 2025-07-25 Sreeram Venkat , Milinda Fernando , Stefan Henneking , Omar Ghattas

The exponential growth of floating point power in graphics processing units (GPUs), together with their low cost, has given rise to an attractive platform upon which to deploy lattice QCD calculations. GPUs are essentially many (O(100))…

High Energy Physics - Lattice · Physics 2010-11-05 M. A. Clark

Adaptive mesh refinement (AMR) reduces computational costs in CFD by concentrating resolution where needed, but efficiently embedding complex, non-aligned geometries on GPUs remains challenging. We present a GPU-native algorithm for…

Computational Engineering, Finance, and Science · Computer Science 2026-04-28 Khodr Jaber , Ebenezer E. Essel , Pierre E. Sullivan

We survey recent contributions to finite element exterior calculus on manifolds and surfaces within a comprehensive formalism for the error analysis of vector-valued partial differential equations on manifolds. Our primary focus is on…

Numerical Analysis · Mathematics 2024-01-02 Martin W. Licht

The HPEC Graph Challenge is a collection of benchmarks representing complex workloads that test the hardware and software components of HPC systems, which traditional benchmarks, such as LINPACK, do not. The first benchmark, Subgraph…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-09-05 Siddharth Samsi , Dan Campbell , Emanuel Scoullos , Oded Green