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In this thesis we develop techniques to efficiently solve numerical Partial Differential Equations (PDEs) using Graphical Processing Units (GPUs). Focus is put on both performance and re--usability of the methods developed, to this end a…

Numerical Analysis · Mathematics 2021-01-19 Andrew Gloster

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

We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-11-20 Utkarsh Utkarsh , Valentin Churavy , Yingbo Ma , Tim Besard , Prakitr Srisuma , Tim Gymnich , Adam R. Gerlach , Alan Edelman , George Barbastathis , Richard D. Braatz , Christopher Rackauckas

Graphics Processing Units (GPUs) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Once, researchers and practitioners noticed the potential of using GPU for general…

Numerical Analysis · Computer Science 2016-07-12 K. Parand , Saeed Zafarvahedian , Sayyed A. Hossayni

Discontinuous Galerkin (dG) methods on meshes consisting of polygonal/polyhedral (henceforth, collectively termed as \emph{polytopic}) elements have received considerable attention in recent years. Due to the physical frame basis functions…

Numerical Analysis · Mathematics 2021-02-16 Zhaonan Dong , Emmanuil H. Georgoulis , Thomas Kappas

The vision of super computer at every desk can be realized by powerful and highly parallel CPUs or GPUs or APUs. Graphics processors once specialized for the graphics applications only, are now used for the highly computational intensive…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-04-16 Chittampally Vasanth Raja , Srinivas Balasubramanian , Prakash S Raghavendra

In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…

Numerical Analysis · Mathematics 2021-09-01 Santiago Badia , Manuel Caicedo , Alberto F. Martín , Javier Principe

We describe a method for parallelizing the lexicographic enumeration algorithm for the factorization set of an element in a numerical semigroup via bounds. This enables the use of GPU and distributed computing methods. We provide a CUDA…

Commutative Algebra · Mathematics 2024-05-14 Thomas Barron

The prediction of a dielectric breakdown in a high-voltage device is based on criteria that evaluate the electric field along field lines. Therefore it is necessary to efficiently compute the electric field at arbitrary points in space. A…

Numerical Analysis · Mathematics 2020-11-03 Cedric Münger , Steffen Börm , Jörg Ostrowski

A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…

Numerical Analysis · Mathematics 2020-05-13 Jun Hu , Hua Wang

The edge computing paradigm has emerged to handle cloud computing issues such as scalability, security and low response time among others. This new computing trend heavily relies on ubiquitous embedded systems on the edge. Performance and…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-01-28 Mohammad Hosseinabady , Mohd Amiruddin Bin Zainol , Jose Nunez-Yanez

Memory bound applications such as solvers for large sparse systems of equations remain a challenge for GPUs. Fast solvers should be based on numerically efficient algorithms and implemented such that global memory access is minimised. To…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-06-01 Eike Hermann Müller , Robert Scheichl , Eero Vainikko

Elliptic partial differential equations arise in many fields of science and engineering such as steady state distribution of heat, fluid dynamics, structural/mechanical engineering, aerospace engineering and seismology etc. In three…

Numerical Analysis · Mathematics 2011-10-12 Akhlaq Husain

Applications that exploit the architectural details of high-performance computing (HPC) systems have become increasingly invaluable in academia and industry over the past two decades. The most important hardware development of the last…

Mathematical Software · Computer Science 2020-05-15 Daniel J. Magee , Anthony S. Walker , Kyle E. Niemeyer

We present a matrix-free multigrid method for high-order discontinuous Galerkin (DG) finite element methods with GPU acceleration. A performance analysis is conducted, comparing various data and compute layouts. Smoother implementations are…

Numerical Analysis · Mathematics 2025-11-03 Cu Cui , Guido Kanschat

The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower…

Numerical Analysis · Mathematics 2019-05-01 Denis Davydov , Jean-Paul Pelteret , Daniel Arndt , Paul Steinmann

The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems…

Electro-quasistatic field problems involving nonlinear materials are commonly discretized in space using finite elements. In this paper, it is proposed to solve the resulting system of ordinary differential equations by an explicit…

Computational Engineering, Finance, and Science · Computer Science 2017-09-26 Christian Richter , Sebastian Schöps , Markus Clemens

The simplex algorithm has been successfully used for many years in solving linear programming (LP) problems. Due to the intensive computations required (especially for the solution of large LP problems), parallel approaches have also…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-11-22 Basilis Mamalis , Marios Perlitis

We present a hardware-accelerated computation of Hasse-Weil invariants of all hyperelliptic curves of given genus over a fixed finite field. Our main motivation is the determination of traces of Frobenius on cohomology corresponding moduli…

Number Theory · Mathematics 2018-05-31 Martin Raum