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In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell…

Numerical Analysis · Mathematics 2026-01-09 Harald Garcke , Robert Nürnberg

Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/$hp$ element method. In particular,…

Non-equilibrium electronic quantum transport is crucial for the operation of existing and envisioned electronic, optoelectronic, and spintronic devices. The ultimate goal of encompassing atomistic to mesoscopic length scales in the same…

Computational Physics · Physics 2024-10-08 Saurabh Sawant , François Léonard , Zhi Yao , Andrew Nonaka

We present a novel parallelization strategy for evaluating Finite Element Method (FEM) variational forms on GPUs, focusing on those that are expressible through the Unified Form Language (UFL) on simplex meshes. We base our approach on code…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-06-24 Kaushik Kulkarni , Andreas Klöckner

Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult…

Computational Physics · Physics 2023-04-10 Ayoub Farkane , Mounir Ghogho , Mustapha Oudani , Mohamed Boutayeb

We implemented the pressure-implicit with splitting of operators (PISO) and semi-implicit method for pressure-linked equations (SIMPLE) solvers of the Navier-Stokes equations on Fermi-class graphics processing units (GPUs) using the CUDA…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-10-01 Tadeusz Tomczak , Katarzyna Zadarnowska , Zbigniew Koza , Maciej Matyka , Łukasz Mirosław

We present the components of a high-order accurate Navier-Stokes solver designed to simulate high-Reynolds-number stratified flows. The proposed numerical model addresses some of the numerical and computational challenges that…

Fluid Dynamics · Physics 2025-10-01 Nidia Reyes-Gil , Greg Thomsen , Kristopher Rowe , Peter Diamessis

We present a spectral element model for general-purpose simulation of non-overturning nonlinear water waves using the incompressible Navier-Stokes equations (INSE) with a free surface. The numerical implementation of the spectral element…

Numerical Analysis · Mathematics 2024-11-25 Anders Melander , Wojciech Laskowski , Spencer J. Sherwin , Allan P. Engsig-Karup

The present work is targeted at performing a strong scaling study of the high-order spectral element fluid dynamics solver Nek5000. Prior studies indicated a recommendable metric for strong scalability from a theoretical viewpoint, which we…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-06-12 Nicolas Offermans , Oana Marin , Michel Schanen , Jing Gong , Paul Fischer , Philipp Schlatter , Aleks Obabko , Adam Peplinksi , Maxwell Hutchinson , Elia Merzari

We present a parallelized geometric multigrid (GMG) method, based on the cell-based Vanka smoother, for higher order space-time finite element methods (STFEM) to the incompressible Navier--Stokes equations. The STFEM is implemented as a…

Numerical Analysis · Mathematics 2022-07-13 Mathias Anselmann , Markus Bause

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain…

Machine Learning · Computer Science 2024-10-16 Khemraj Shukla , Zongren Zou , Chi Hin Chan , Additi Pandey , Zhicheng Wang , George Em Karniadakis

We present IncompressibleNavierStokes.jl, an open-source Julia package for solving the incompressible Navier--Stokes equations on staggered Cartesian grids. The package features matrix-free, hardware-agnostic kernels that are compiled from…

Numerical Analysis · Mathematics 2026-04-21 Syver Døving Agdestein , Benjamin Sanderse

We present a GPU based openACC fortran program named HeTDSE, which provides an efficient way to investigate the non-perturbative electronic dynamics of helium subjected to a strong laser pulse by solving full-dimensional two-electron time…

Computational Physics · Physics 2020-10-06 Changli Wei , Xi Zhao

We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…

Numerical Analysis · Mathematics 2025-12-11 Nils Margenberg , Carolin Mehlmann

The present paper addresses the numerical solution of turbulent flows with high-order discontinuous Galerkin methods for discretizing the incompressible Navier-Stokes equations. The efficiency of high-order methods when applied to…

Fluid Dynamics · Physics 2018-08-29 Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

This paper presents a porting of {DG-SWEM}, a first-order discontinuous Galerkin solver for storm surge based on the Advanced Circulation Model (ADCIRC), to NVIDIA GPUs. Time-explicit discontinuous Galerkin methods contain a large number of…

Computational Physics · Physics 2025-09-23 Chayanon Wichitrnithed , Eirik Valseth , Ethan J. Kubatko , Shintaro Bunya , Clint Dawson

BATSRUS, our state-of-the-art extended magnetohydrodynamic code, is the most used and one of the most resource-consuming models in the Space Weather Modeling Framework. It has always been our objective to improve its efficiency and speed…

Instrumentation and Methods for Astrophysics · Physics 2025-01-14 Yifu An , Yuxi Chen , Hongyang Zhou , Alexander Gaenko , Gábor Tóth

Next generation High-Energy Physics (HEP) experiments are presented with significant computational challenges, both in terms of data volume and processing power. Using compute accelerators, such as GPUs, is one of the promising ways to…

We present a pseudo-spectal Navier-Stokes solver for plane parallel flows (Couette/Poiseuille), that has been developed on the MATLAB programming language. The code performs direct numerical simulations (DNSs) of turbulence in 3 dimensions…

Fluid Dynamics · Physics 2024-05-28 Marios-Andreas Nikolaidis

This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An…

Computational Engineering, Finance, and Science · Computer Science 2016-09-21 J. -F. Remacle , R. Gandham , T. Warburton