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Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple gpus

JOURNAL OF COMPUTATIONAL PHYSICS 2012年第21期231卷 7133-7151页

作者： Bollig, Evan F. Flyer, Natasha Erlebacher, Gordon Florida State Univ Dept Comp Sci Tallahassee FL 32306 USA Natl Ctr Atmospher Res Inst Math Appl Geosci Boulder CO 80305 USA

This paper presents parallelization strategies for the radial basis function-finite difference (RBF-FD) method. As a generalized finite differencing scheme, the RBF-FD method functions without the need for underlying meshes to structure nodes. It offers high-order accuracy approximation and scales as O(N) per time step, with N being with the total number of nodes. To our knowledge, this is the first implementation of the RBF-FD method to leverage gpu accelerators for the solution of PDEs. Additionally, this implementation is the first to span both multiple CPUs and multiple gpus. OpenCL kernels target the gpus and inter-processor communication and synchronization is managed by the Message Passing Interface (MPI). We verify our implementation of the RBF-FD method with two hyperbolic PDEs on the sphere, and demonstrate up to 9x speedup on a commodity gpu with unoptimized kernel implementations. On a high performance cluster, the method achieves up to 7x speedup for the maximum problem size of 27,556 nodes. (C) 2012 Elsevier Inc. All rights reserved.

关键词： multi-gpu computing Radial basis functions RBF-FD High-order finite differencing Parallel computing OpenCL

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Large-scale robust topology optimization using multi-gpu systems

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2016年 311卷 393-414页

作者： Martinez-Frutos, Jesus Herrero-Perez, David Tech Univ Cartagena Dept Struct & Construct Campus Muralla Mar Murcia 30202 Spain

Robust topology optimization of continuum structures is an intensive computational task due to the use of uncertainty propagation methods to estimate the statistical metrics within the topology optimization process. Such a computational problem is exacerbated for large finite element (FE) models in terms of memory consumption and processing time. For these reasons, the efficient resolution of robust topology optimization with large models remains an important computational challenge. This work aims to alleviate these computational constraints proposing a well-suited strategy for Graphics Processing Unit (gpu) computing. Such a proposal exploits the multilevel parallelism provided by multi-gpu systems for the parallel execution both within FE models and through uncertainty propagation methods. Task-level parallelism is used to concurrently evaluate the independent simulation models arising from a sparse grid stochastic collocation method. Data-level parallelism with different granularities is then exploited for the efficient resolution of each simulation model and the computation required by the topology optimization process. The resolution of the different calculations of robust topology optimization pipeline using multi-CPU systems are compared to the classically used multi-CPU implementation achieving significant speedups. (C) 2016 Elsevier B.V. All rights reserved,

关键词： Topology optimization Robust design Large-scale multi-gpu computing Stochastic collocation Random fields

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multi-agent simulation on multiple gpus

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SIMULATION MODELLING PRACTICE AND THEORY 2015年 57卷 118-132页

作者： Ho, N. M. Thoai, N. Wong, W. F. Ho Chi Minh City Univ Technol Fac Comp Sci & Engn Ho Chi Minh Vietnam Natl Univ Singapore Sch Comp Singapore 117548 Singapore

multi-agent simulation is widely used in many areas including biology, economic, political, and environmental science to study complex systems. Unfortunately, it is computationally expensive. In this paper, we shall explore the implementation of a general multi-agent simulation system on a system with multiple gpus acting as accelerators. In particular, we have ported the popular Java multi-agent simulation framework MASON to a nVidia CUDA-based multi-gpu setting. We evaluated our implementation over different numbers and types of nVidia gpus. For our evaluation, we ported three models in the original version of MASON. On the well-known Boids model, we achieved a speedup of 187x. Using a fictional model, we showed that speedup of up to 468x is possible. In the paper, we shall also describe the detailed internals of our system, and the various issues we encountered and how they were solved. (C) 2015 Elsevier B.V. All rights reserved.

关键词： multi-agent simulation MASON Simulation framework CUDA multi-gpu computing

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multiscale Hemodynamics Using gpu Clusters

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Communications in Computational Physics 2012年第1期11卷 48-64页

作者： Mauro Bisson Massimo Bernaschi Simone Melchionna Sauro Succi Efthimios Kaxiras Department of Computer Science University of Rome“Sapienza”Italy Istituto Applicazioni Calcolo Consiglio Nazionale delle RicercheRomeItaly Istituto Processi Chimico-Fisici Consiglio Nazionale delle RicercheRomeItaly Institute of Material Sciences and Engineering ´Ecole Polytechnique F´ed´erale de LausanneSwitzerland Freiburg Institute for Advanced Studies School of Soft Matter ResearchAlbertstr.1979104 FreiburgGermany Department of Physics and School of Engineering and Applied Sciences Harvard UniversityCambridgeMAUSA

The parallel implementation of MUPHY,a concurrent multiscale code for large-scale hemodynamic simulations in anatomically realistic geometries,for multi-gpu platforms is *** tests show excellent results,with a nearly linear parallel speed-up on up to 32gpus and a more than tenfold gpu/CPU acceleration,all across the range of *** basic MUPHY scheme combines a hydrokinetic(Lattice Boltzmann)representation of the blood plasma,with a Particle Dynamics treatment of suspended biological bodies,such as red blood *** the best of our knowledge,this represents the first effort in the direction of laying down general design principles for multiscale/physics parallel Particle Dynamics applications in non-ideal *** configures the present multi-gpu version of MUPHY as one of the first examples of a high-performance parallel code for multiscale/physics biofluidic applications in realistically complex geometries.

关键词： multi-gpu computing hemodynamics molecular dynamics irregular domain

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An Adaptative multi-gpu based Branch-and-Bound. A Case Study: the Flow-Shop Scheduling Problem

An Adaptative Multi-GPU based Branch-and-Bound. A Case Study...

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14th IEEE International Conference on High Performance computing and Communications (HPCC) / IEEE 9th International Conference on Embedded Software and Systems (ICESS)

作者： Chakroun, I. Melab, N. Univ Lille 1 CNRS UMR 8022 LIFLINRIA Lille Nord Europe F-59655 Villeneuve Dascq France

ISBN: (纸本)9780769547497

Solving exactly Combinatorial Optimization Problems (COPs) using a Branch-and-Bound (B&B) algorithm requires a huge amount of computational resources. Therefore, we recently investigated designing B&B algorithms on top of graphics processing units (gpus) using a parallel bounding model. The proposed model assumes parallelizing the evaluation of the lower bounds on pools of sub-problems. The results demonstrated that the size of the evaluated pool has a significant impact on the performance of B&B and that it depends strongly on the problem instance being solved. In this paper, we design an adaptative parallel B&B algorithm for solving permutation-based combinatorial optimization problems such as FSP (Flow-shop Scheduling Problem) on gpu accelerators. To do so, we propose a dynamic heuristic for parameter auto-tuning at runtime. Another challenge of this pioneering work 1 is to exploit larger degrees of parallelism by using the combined computational power of multiple gpu devices. The approach has been applied to the permutation flow-shop problem. Extensive experiments have been carried out on well-known FSP benchmarks using an Nvidia Tesla S1070 computing System equipped with two Tesla T10 gpus. Compared to a CPU-based execution, accelerations up to x105 are achieved for large problem instances.

关键词： Branch-and-Bound Algorithms multi-gpu computing Parallel Bounding Flow-Shop Scheduling Problem

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Cellular Automata on a multi-gpu Architecture: A Technical Overview 32

Cellular Automata on a Multi-GPU Architecture: A Technical O...

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32nd Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP)

作者： Giordano, Andrea De Rango, Alessio D'Ambrosio, Donato Gil, Marisa Macri, Davide Martorell, Xavier Rongo, Rocco Utrera, Gladys Mendicino, Giuseppe Spataro, William ICAR CNR Arcavacata Di Rende Italy Univ Calabria Dept Environm Engn Calabria Italy Univ Calabria Dept Math & Comp Sci Calabria Italy Univ Politecnica Catalunya BarcelonaTECH Barcelona Spain

ISBN: (纸本)9798350363074;9798350363081

This work is focused on the transparent execution of Cellular Automata models on amulti-gpu architecture. Although Cellular Automata models can be easily parallelized on a single gpu, the domain size and transition function complexity may require the use of multiple gpus. Our goal is to allow modellers to be completely unaware of the parallel execution context, i.e., the code implementing the Cellular Automata model remains the same regardless if the execution is performed on CPU, single gpu, or multi-gpu systems. This paper supplies meaningful technical insights on how to ensure both transparency and efficiency in multi-gpu execution of Cellular Automata models. In particular, an object-oriented approach is exploited in which a transparent layer is devised that abstracts the parallelization details and allows a strong "separation of concerns" between the execution parallelism issues and the model implementation. Preliminary experiments have been carried out on the multi-gpu cluster CTE-POWER available at the Barcelona Supercomputing Center (BSC), witnessing good speedups notwithstanding the transparency feature supplied by our approach.

关键词： multi-gpu computing Cellular Automata Modelling and Simulation

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SIGmA: gpu Accelerated Simplification of SAT Formulas 15th

SIGmA: GPU Accelerated Simplification of SAT Formulas

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15th International Conference on integrated Formal Methods (IFM)

作者： Osama, Muhammad Wijs, Anton Eindhoven Univ Technol NL-5600 MB Eindhoven Netherlands

ISBN: (纸本)9783030349684;9783030349677

We present SIGmA (SAT sImplification on gpu Architectures), a preprocessor to accelerate SAT solving that runs on NVIDIA gpus. We discuss the tool, focussing on its full functionality and how it can be used in combination with state-of-the-art SAT solvers. SIGmA performs various types of simplification, such as variable elimination, subsumption elimination, blocked clause elimination and hidden redundancy elimination. We study the effectiveness of our tool when applied prior to SAT solving. Overall, for our large benchmark set of problems, SIGmA enables MiniSat and Lingeling to solve many problems in less time compared to applying the SatElite preprocessor.

关键词： Boolean satisfiability SAT decomposition Parallel SAT preprocessing multi-gpu computing

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Implementation of a Lattice Boltzmann Method for Large Eddy Simulation on multiple gpus

Implementation of a Lattice Boltzmann Method for Large Eddy ...

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14th IEEE International Conference on High Performance computing and Communications (HPCC) / IEEE 9th International Conference on Embedded Software and Systems (ICESS)

作者： Li, Qinjian Zhong, Chengwen Li, Kai Zhang, Guangyong Lu, Xiaowei Zhang, Qing Zhao, Kaiyong Chu, Xiaowen Northwestern Polytech Univ Ctr High Performance Comp Xian 710072 Peoples R China Northwestern Polytech Univ Natl Key Lab Sci & Technol Aerodynam Design & Res Xian 710072 Peoples R China Natl Key Lab High efficient Server Storage Techno Jian Jiangxi Peoples R China Hong Kong Baptist Univ Dept Comp Sci Inspur HKBU Joint Lab Heterogeneous Comp Hong Kong Peoples R China

ISBN: (纸本)9780769547497

Recently, the Graphic Processor Unit (gpu) has evolved into a highly parallel, multithreaded, many-core processor with tremendous computational horsepower and very high memory bandwidth. To improve the simulation efficiency of complex flow phenomena in the field of computational fluid dynamics, a CUDA-based simulation algorithm of large eddy simulation using multiple gpus is proposed. Our implementation adopted the "collision after propagation" scheme and performed the propagation process by global memory reading transactions. The working set is split up into equal sub-domains and assigned to each gpu for simplicity. Using recently released hardware, up to four gpus can be controlled by a single CPU thread and run in parallel. The results show that our multi-gpu implementation could perform simulations on a rather large scale (meshes: 10240 x 10240) even using double-precision floating point calculation and achieved 190X speedup over the sequential implementation on CPU.

关键词： CUDA Lattice Boltzmann method multi-gpu computing Large eddy simulation Parellel computing

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multi-gpu Load Balancing for Simulation and Rendering

Multi-GPU Load Balancing for Simulation and Rendering

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作者： Hagan, Robert Douglas Virginia Tech | University

gpu computing can significantly improve performance by taking advantage of massive parallelism of gpus for data parallel applications. Computation in visualization applications is suitable for parallelization on the gpu, which can improve performance and interactivity in these applications. If used effectively, multiple gpus can lead to a significant speedup over a single gpu. However, the use of multiple gpus requires memory management, scheduling, and load balancing to ensure that a program takes full advantage of available processors. This work presents methods for data-driven and dynamic multi-gpu load balancing using a pipelined approach and a framework for use with different applications. Data-driven load balancing can improve utilization for applications by taking into account past performance for different combinations of input parameters. The dynamic load balancing method based on buffer fullness can adjust to workload changes at runtime to gain an additional performance improvement. This work provides a framework for load balancing to account for differing characteristics of applications. Implementation of a multi-gpu data structure allows for use of these load balancing methods in the framework. The effectiveness of the framework is demonstrated with performance results from interactive visualization that shows a significant speedup due to load balancing.

关键词： Load Balancing multi-gpu computing Rendering Simulation Thesis

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Parallel physics-informed neural networks via domain decomposition

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JOURNAL OF COMPUTATIONAL PHYSICS 2021年 447卷 110683-110683页

作者： Shukla, Khemraj Jagtap, Ameya D. Karniadakis, George Em Brown Univ Div Appl Math 182 George St Annapolis RI 02912 USA

We develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively. This domain decomposition endows cPINNs and XPINNs with several advantages over the vanilla PINNs, such as parallelization capacity, large representation capacity, efficient hyperparameter tuning, and is particularly effective for multi-scale and multi-physics problems. Here, we present a parallel algorithm for cPINNs and XPINNs constructed with a hybrid programming model described by MPI + X, where X is an element of {CPUs, gpus}. The main advantage of cPINN and XPINN over the more classical data and model parallel approaches is the flexibility of optimizing all hyperparameters of each neural network separately in each subdomain. We compare the performance of distributed cPINNs and XPINNs for various forward problems, using both weak and strong scalings. Our results indicate that for space domain decomposition, cPINNs are more efficient in terms of communication cost but XPINNs provide greater flexibility as they can also handle time-domain decomposition for any differential equations, and can deal with any arbitrarily shaped complex subdomains. To this end, we also present an application of the parallel XPINN method for solving an inverse diffusion problem with variable conductivity on the United States map, using ten regions as subdomains. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Scientific machine learning Distributed machine learning Domain decomposition PINNs multi-gpu computing

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