Research on the single-host parallel computing with the local time step scheme for modeling of hydro-sediment-morphodynamic processes

2021 ◽  
Author(s):  
Zixiong Zhao ◽  
Peng Hu ◽  
Wei Li ◽  
Zhixian Cao ◽  
Zhiguo He
Keyword(s):  
Parallel Computing ◽  
Local Time ◽  
High Performance ◽  
Water Model ◽  
Time Step ◽  
Time Stepping ◽  
Computational Performance ◽  
Cuda Programming ◽  
Single Host ◽  
Algorithmic Acceleration

<p>In recent decades, computational hydraulics and sediment modelling have a great development due to compute technology. Applying a finite-volume Godunov-type hydrodynamic shallow water model with hydro-sediment-morphodynamic processes, this work demonstrates and analysis the ability of single-host parallel computing technology with algorithmic acceleration technology. This model is implemented for high-performance computing using the NVIDIA’s Compute Unified Device Architecture (CUDA) programming framework, using a domain decomposition technique and across multiple cores through an efficient implementation of the Open Multi-Processing (Open MP) architecture, and using an algorithmic acceleration technology named local time stepping scheme (LTS), which is capable of obtain much efficiency improvement via different time step sizes for different grid sizes. The model is applied for three cases, through which we compare the effectiveness of CPU, Open MP, Open MP+LTS, CUDA, and CUDA+LTS, demonstrating high computational performance across CUDA+LTS which can lead to speedups of 40 times with respect to CPU and high-precision results across CUDA +LTS.</p><p>KEY WORDS: Hydro-sediment-morphological modeling; local time step; Open MP; CUDA.</p>

scholarly journals Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. T67-T77 ◽  
Author(s):  
Sara Minisini ◽  
Elena Zhebel ◽  
Alexey Kononov ◽  
Wim A. Mulder
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Local Time ◽  
Heterogeneous Media ◽  
Small Scale ◽  
Time Step ◽  
Element Discretization ◽  
Time Stepping ◽  
Local Time Stepping

Modeling and imaging techniques for geophysics are extremely demanding in terms of computational resources. Seismic data attempt to resolve smaller scales and deeper targets in increasingly more complex geologic settings. Finite elements enable accurate simulation of time-dependent wave propagation in heterogeneous media. They are more costly than finite-difference methods, but this is compensated by their superior accuracy if the finite-element mesh follows the sharp impedance contrasts and by their improved efficiency if the element size scales with wavelength, hence with the local wave velocity. However, 3D complex geologic settings often contain details on a very small scale compared to the dominant wavelength, requiring the mesh to contain elements that are smaller than dictated by the wavelength. Also, limitations of the mesh generation software may produce regions where the elements are much smaller than desired. In both cases, this leads to a reduction of the time step required to solve the wave propagation and significantly increases the computational cost. Local time stepping (LTS) can improve the computational efficiency and speed up the simulation. We evaluated a local formulation of an LTS scheme with second-order accuracy for the discontinuous Galerkin finite-element discretization of the wave equation. We tested the benefits of the scheme by considering a geologic model for a North-Sea-type example.

scholarly journals Local time stepping with adaptive time step control for a two-phase fluid system

2009 ◽  
Vol 29 ◽  
pp. 73-88 ◽  
Author(s):  
Frédéric Coquel ◽  
Quang Long Nguyen ◽  
Marie Postel ◽  
Quang Huy Tran
Keyword(s):  
Local Time ◽  
Time Step ◽  
Fluid System ◽  
Two Phase ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Adaptive Time Step ◽  
Adaptive Time ◽  
Step Control ◽  
Phase Fluid

scholarly journals Newmark local time stepping on high-performance computing architectures

2017 ◽  
Vol 334 ◽  
pp. 308-326 ◽  
Author(s):  
Max Rietmann ◽  
Marcus Grote ◽  
Daniel Peter ◽  
Olaf Schenk
Keyword(s):  
High Performance Computing ◽  
Local Time ◽  
High Performance ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Performance Computing

scholarly journals Construction and convergence analysis of conservative second order local time discretisation for linear wave equations

2021 ◽  
Author(s):  
Juliette Chabassier ◽  
Sébastien Imperiale
Keyword(s):  
Local Time ◽  
Wave Equations ◽  
Second Order ◽  
Linear Wave ◽  
Time Step ◽  
Time Stepping ◽  
Time Discretisation ◽  
Regularity Properties ◽  
Local Time Stepping ◽  
Linear Wave Equations

In this work we present and analyse a time discretisation strategy for linear wave equations that aims at using locally in space the most adapted time discretisation among a family of implicit or explicit centered second order schemes. The proposed family of schemes is adapted to domain decomposition methods such as the mortar element method. They correspond in that case to local implicit schemes and to local time stepping. We show that, if some regularity properties of the solution are satisfied and if the time step verifies a stability condition, then the family of proposed time discretisations provides, in a strong norm, second order space-time convergence. Finally, we provide 1D and 2D numerical illustrations that confirm the obtained theoretical results and we compare our approach on 1D test cases to other existing local time stepping strategies for wave equations.

scholarly journals Machine-Learned Preconditioners for Linear Solvers in Geophysical Fluid Flows

2021 ◽  
Author(s):  
Jan Ackmann ◽  
Peter Düben ◽  
Tim Palmer ◽  
Piotr Smolarkiewicz
Keyword(s):  
Machine Learning ◽  
Shallow Water ◽  
Water Model ◽  
Implicit Time ◽  
Learning Approaches ◽  
Shallow Water Model ◽  
Time Step ◽  
Linear Solvers ◽  
Linear Solver ◽  
Time Stepping

<p>Semi-implicit grid-point models for the atmosphere and the ocean require linear solvers that are working efficiently on modern supercomputers. The huge advantage of the semi-implicit time-stepping approach is that it enables large model time-steps. This however comes at the cost of having to solve a computationally demanding linear problem each model time-step to obtain an update to the model’s pressure/fluid-thickness field. In this study, we investigate whether machine learning approaches can be used to increase the efficiency of the linear solver.</p><p>Our machine learning approach aims at replacing a key component of the linear solver—the preconditioner. In the preconditioner an approximate matrix inversion is performed whose quality largely defines the linear solver’s performance. Embedding the machine-learning method within the framework of a linear solver circumvents potential robustness issues that machine learning approaches are often criticized for, as the linear solver ensures that a sufficient, pre-set level of accuracy is reached. The approach does not require prior availability of a conventional preconditioner and is highly flexible regarding complexity and machine learning design choices.</p><p>Several machine learning methods of different complexity from simple linear regression to deep feed-forward neural networks are used to learn the optimal preconditioner for a shallow-water model with semi-implicit time-stepping. The shallow-water model is specifically designed to be conceptually similar to more complex atmosphere models. The machine-learning preconditioner is competitive with a conventional preconditioner and provides good results even if it is used outside of the dynamical range of the training dataset.</p>

Numerical Local Time Stepping Solutions for Transient Statistical Energy Analysis

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Oriol Guasch ◽  
Carlos García
Keyword(s):  
Finite Difference ◽  
Local Time ◽  
Energy Analysis ◽  
Blow Up ◽  
Statistical Energy Analysis ◽  
Time Step ◽  
Time Step Size ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Forward Euler

Subsystem energies evolve in transient statistical energy analysis (TSEA) according to a linear system of ordinary differential equations (ODEs), which is usually numerically solved by means of the forward Euler finite difference scheme. Stability requirements pose limits on the maximum time step size to be used. However, it has been recently pointed out that one should also consider a minimum time step limit, if time independent loss factors are to be assumed. This limit is based on the subsystem internal time scales, which rely on their characteristic mean free paths and group velocities. In some cases, these maximum and minimum limits become incompatible, leading to a blow up of the forward Euler solution. It is proposed to partially mitigate this problem by resorting to a local time-stepping finite difference strategy. Subsystems are grouped into sets characterized by different time step sizes and evolve according to them.

Toward a neuroscope: An application of high-performance computing for real-time evaluation of brain function using MRI

1994 ◽  
Vol 52 ◽  
pp. 922-923
Author(s):  
C. S. Potter ◽  
C. D. Gregory ◽  
H. D. Morris ◽  
Z.-P. Liang ◽  
P. C. Lauterbur
Keyword(s):  
Human Brain ◽  
Brain Function ◽  
High Performance ◽  
Complex Signal ◽  
Time Step ◽  
Brain Organization ◽  
Cognitive Studies ◽  
Positron Emission ◽  
Imaging And Spectroscopy ◽  
3D Anatomy

Over the past few years, several laboratories have demonstrated that changes in local neuronal activity associated with human brain function can be detected by magnetic resonance imaging and spectroscopy. Using these methods, the effects of sensory and motor stimulation have been observed and cognitive studies have begun. These new methods promise to make possible even more rapid and extensive studies of brain organization and responses than those now in use, such as positron emission tomography.Human brain studies are enormously complex. Signal changes on the order of a few percent must be detected against the background of the complex 3D anatomy of the human brain. Today, most functional MR experiments are performed using several 2D slice images acquired at each time step or stimulation condition of the experimental protocol. It is generally believed that true 3D experiments must be performed for many cognitive experiments. To provide adequate resolution, this requires that data must be acquired faster and/or more efficiently to support 3D functional analysis.

Matlab and Parallel Computing

2012 ◽  
Vol 17 (4) ◽  
pp. 207-216 ◽  
Author(s):  
Magdalena Szymczyk ◽  
Piotr Szymczyk
Keyword(s):  
Image Processing ◽  
Signal Processing ◽  
Parallel Computing ◽  
Distributed Computing ◽  
Control Systems ◽  
High Performance ◽  
Parallel Applications ◽  
Process Simulations ◽  
Key Features ◽  
Financial Process

Abstract The MATLAB is a technical computing language used in a variety of fields, such as control systems, image and signal processing, visualization, financial process simulations in an easy-to-use environment. MATLAB offers "toolboxes" which are specialized libraries for variety scientific domains, and a simplified interface to high-performance libraries (LAPACK, BLAS, FFTW too). Now MATLAB is enriched by the possibility of parallel computing with the Parallel Computing ToolboxTM and MATLAB Distributed Computing ServerTM. In this article we present some of the key features of MATLAB parallel applications focused on using GPU processors for image processing.

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