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Multigrid solvers are among the most efficient methods for solving the Poisson equation, which is ubiquitous in computational physics. For example, in the context of incompressible flows, it is typically the costliest operation. The present…

Numerical Analysis · Mathematics 2025-12-10 Gilles Poncelet , Jonathan Lambrechts , Thomas Gillis , Philippe Chatelain

We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz…

Fluid Dynamics · Physics 2025-08-07 Rafael Diez Sanhueza , Jurriaan Peeters , Pedro Costa

We present a MATLAB-based framework for two- and three-dimensional fast Fourier transforms on multiple GPUs for large-scale numerical simulations using the pseudo-spectral Fourier method. The software implements two complementary multi-GPU…

Mathematical Software · Computer Science 2026-03-31 Maik Punke , Marco Salvalaglio

Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad…

Materials Science · Physics 2023-06-23 A. D. Boccardo , M. Tong , S. B. Leen , D. Tourret , J. Segurado

We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are…

Materials Science · Physics 2009-11-13 Luigi Genovese , Thierry Deutsch , Stefan Goedecker

We present an efficient implementation for running three-dimensional numerical simulations of fluid-structure interaction problems on single GPUs, based on Nvidia CUDA through Numba and Python. The incompressible flow around moving bodies…

Fluid Dynamics · Physics 2024-12-05 M. Guerrero-Hurtado , J. M. Catalán , M. Moriche , A. Gonzalo , O. Flores

With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…

Mathematical Software · Computer Science 2020-07-16 Kyaw L. Oo , Andreas Vogel

Eulerian nonlinear uncertainty propagation methods often suffer from finite domain limitations and computational inefficiencies. A recent approach to this class of algorithm, Grid-based Bayesian Estimation Exploiting Sparsity, addresses the…

Chaotic Dynamics · Physics 2025-08-20 Benjamin L. Hanson , Carlos Rubio , Adrián García-Gutiérrez , Thomas Bewley

We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a method of solution which combines a finite difference…

Computational Physics · Physics 2011-08-18 Aldo Frezzotti , Gian Pietro Ghiroldi , Livio Gibelli

Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few…

Machine Learning · Statistics 2018-04-04 S. T. John , James Hensman

This work presents the development, performance analysis and subsequent optimization of a GPU-based spectral hyperviscosity solver for turbulent flows described by the three dimensional incompressible Navier-Stokes equations. The method…

Fluid Dynamics · Physics 2024-04-23 Tobias Rohner , Siddhartha Mishra

Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…

Numerical Analysis · Mathematics 2024-09-19 Fredrik Fryklund , Leslie Greengard , Shidong Jiang , Samuel Potter

We present a polynomial multigrid method for the nodal interior penalty formulation of the Poisson equation on three-dimensional Cartesian grids. Its key ingredient is a weighted overlapping Schwarz smoother operating on element-centered…

Numerical Analysis · Computer Science 2016-12-19 Joerg Stiller

Immersed boundary methods (IBMs) facilitate the simulation of flows around stationary, moving, and deforming bodies on Cartesian grids. However, extending these simulations to the large grid sizes required for realistic flow problems…

Fluid Dynamics · Physics 2026-03-16 Sushrut Kumar , Joshua Romero , Jung-Hee Seo , Massimiliano Fatica , Rajat Mittal

We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of…

Numerical Analysis · Mathematics 2018-05-08 Ali Karakus , Noel Chalmers , Kasia Swirydowicz , Timothy Warburton

We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our…

Astrophysics · Physics 2009-11-07 Tomoaki Matsumoto , Tomoyuki Hanawa

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

Machine Learning · Computer Science 2020-06-16 Armin Lederer , Markus Kessler , Sandra Hirche

A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…

Numerical Analysis · Mathematics 2016-04-05 Alex Townsend , Heather Wilber , Grady B. Wright

Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in physical space. The…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-10-17 Andrew Ho , Genia Vogman

This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is…

Robotics · Computer Science 2024-06-12 Zeming Wu , Zhuping Wang , Hao Zhang