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Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost…

[Abridged] We present the results of a highly parallel Kepler equation solver using the Graphics Processing Unit (GPU) on a commercial nVidia GeForce 280GTX and the "Compute Unified Device Architecture" programming environment. We apply…

Astrophysics · Physics 2008-12-17 Eric B. Ford

We present a detailed comparison between two adaptive numerical approaches to solve partial differential equations (PDEs), adaptive multiresolution (MR) and adaptive mesh refinement (AMR). Both discretizations are based on finite volumes in…

Numerical Analysis · Mathematics 2016-03-17 Ralf Deiterding , Margarete O. Domingues , Sonia M. Gomes , Kai Schneider

This dissertation presents the design, implementation and evaluation of GPU-accelerated simulation frameworks for Evolutionary Spatial Cyclic Games (ESCGs), a class of agent-based models used to study ecological and evolutionary dynamics.…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-26 Louie Sinadjan

We describe a grid-based numerical method for 3D hydrodynamic cosmological simulations which is adaptive in space and time and combines the best features of higher order--accurate Godunov schemes for Eulerian hydrodynamics with adaptive…

Astrophysics · Physics 2016-01-27 Michael L. Norman , Greg L. Bryan

Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper…

Numerical Analysis · Mathematics 2025-11-26 Alexandre Epalle , Isabelle Ramière , Guillaume Latu , Frédéric Lebon

Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Yet despite their efficiency, computations remain expensive…

Numerical Analysis · Mathematics 2025-12-23 Manuel Liebchen , Robert Jendersie , Utku Kaya , Christian Lessig , Thomas Richter

A new N-body and hydrodynamical code, called RAMSES, is presented. It has been designed to study structure formation in the universe with high spatial resolution. The code is based on Adaptive Mesh Refinement (AMR) technique, with a tree…

Astrophysics · Physics 2014-10-13 Romain Teyssier

We study the performance behaviour of a seismic simulation using the ExaHyPE engine with a specific focus on memory characteristics and energy needs. ExaHyPE combines dynamically adaptive mesh refinement (AMR) with ADER-DG. It is…

Accurate simulation to dynamics of axial piston pump (APP) is essential for its design, manufacture and maintenance. However, limited by computation capacity of CPU device and traditional solvers, conventional iteration methods are…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-11 Xin Yao , Yang Liu , Jin Jiang , Yesen Chen , Zhilong Chen , Hongkang Dong , Xiaofeng Wei , Teng Zhang , Dongyun Wang

Computational studies that use block-structured adaptive mesh refinement (AMR) approaches suffer from unnecessarily high mesh resolution in regions adjacent to important solution features. This deficiency limits the performance of AMR…

Computational Physics · Physics 2022-03-02 Brandon Gusto , Tomasz Plewa

When numerically solving partial differential equations, for a given problem and operating condition, adaptive mesh refinement (AMR) has proven its efficiency to automatically build a discretization achieving a prescribed accuracy at low…

High-resolution simulations often rely on the Adaptive Mesh Resolution (AMR) technique to optimize memory consumption versus attainable precision. While this technique allows for dramatic improvements in terms of computing performance, the…

Data Structures and Algorithms · Computer Science 2013-01-03 Marc Labadens , Daniel Pomarède , Damien Chapon , Romain Teyssier , Frédéric Bournaud , Florent Renaud , Nicolas Grandjouan

We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic Multigrid (AMG) preconditioner previously proposed by one of the…

Numerical Analysis · Mathematics 2018-10-11 Massimo Bernaschi , Pasqua D'Ambra , Dario Pasquini

In this paper, we present a new method to perform numerical simulations of astrophysical MHD flows using the Adaptive Mesh Refinement framework and Constrained Transport. The algorithm is based on a previous work in which the MUSCL--Hancock…

Astrophysics · Physics 2009-11-11 S. Fromang , P. Hennebelle , R. Teyssier

In this work, we introduce the novel application of the adaptive mesh refinement (AMR) technique in the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial. Indeed, an…

Numerical Analysis · Mathematics 2026-02-17 Daniele Massaro , Valerio Lupi , Adam Peplinski , Philipp Schlatter

Purpose: We presented a GPU-based MC framework, ARCHER-EPID, specifically designed for EPID transit dosimetry, with improving accuracy and efficiency. Methods: A comprehensive MC framework was developed to perform full radiation transport…

Medical Physics · Physics 2025-10-29 Ning Gao , Didi Li , Na Liu , Yankui Chang , Qiang Ren , Xi Pei , Zhi Wang , Xie George Xu

Clawpack is a library for solving nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. It supports Adaptive Mesh Refinement (AMR), which is essential in…

Mathematical Software · Computer Science 2018-08-09 Xinsheng Qin , Randall J. LeVeque , Michael R. Motley

In response to the unique challenges of Mixed Reality (MR) game development, we developed GAMR, an analytics tool specifically designed for MR games. GAMR aims to assist developers in identifying and resolving gameplay issues effectively.…

Human-Computer Interaction · Computer Science 2024-08-06 Parisa Sargolzaei , Mudit Rastogi , Loutfouz Zaman

The solver module of the Astrometric Verification Unit - Global Sphere Reconstruction (AVU-GSR) pipeline aims to find the astrometric parameters of $\sim$$10^8$ stars in the Milky Way, besides the attitude and instrumental settings of the…

Instrumentation and Methods for Astrophysics · Physics 2025-04-01 Valentina Cesare , Ugo Becciani , Alberto Vecchiato , Mario Gilberto Lattanzi , Marco Aldinucci , Beatrice Bucciarelli