Designing OP2 for GPU architectures

OP2 is an “active” library framework for the solution of unstructured mesh applications. It aims to decouple the specification of a scientific application from its parallel implementation to achieve code longevity and near-optimal performance through re-targeting the back-end to different multi-core/many-core hardware. This paper presents the design of the current OP2 library for generating efficient code targeting contemporary GPU platforms. In this we focus on some of the software architecture design choices and low-level optimizations to maximize performance on NVIDIA’s Fermi architecture GPUs. The performance impact of these design choices is quantified on two NVIDIA GPUs (GTX560Ti, Tesla C2070) using the end-to-end performance of an industrial representative CFD application developed using the OP2 API. Results show that for each system, a number of key configuration parameters need to be set carefully in order to gain good performance. Utilizing a recently developed auto-tuning framework, we explore the effect of these parameters, their limitations and insights into optimizations for improved performance.     

Design and initial performance of a high-level unstructured mesh framework on heterogeneous parallel systems

OP2 is a high-level domain specific library framework for the solution of unstructured mesh-based applications. It utilizes source-to-source translation and compilation so that a single application code written using the OP2 API can be transformed into multiple parallel implementations for execution on a range of back-end hardware platforms. In this paper we present the design and performance of OP2’s recent developments facilitating code generation and execution on distributed memory heterogeneous systems. OP2 targets the solution of numerical problems based on static unstructured meshes. We discuss the main design issues in parallelizing this class of applications. These include handling data dependencies in accessing indirectly referenced data and design considerations in generating code for execution on a cluster of multi-threaded CPUs and GPUs. Two representative CFD applications, written using the OP2 framework, are utilized to provide a contrasting benchmarking and performance analysis study on a number of heterogeneous systems including a large scale Cray XE6 system and a large GPU cluster. A range of performance metrics are benchmarked including runtime, scalability, achieved compute and bandwidth performance, runtime bottlenecks and systems energy consumption. We demonstrate that an application written once at a high-level using OP2 is easily portable across a wide range of contrasting platforms and is capable of achieving near-optimal performance without the intervention of the domain application programmer.     

An edge-based unstructured mesh framework for atmospheric flows

This paper describes an unstructured/hybrid mesh framework providing a robust environment for multiscale atmospheric modeling. The framework builds on nonoscillatory forward-in-time MPDATA solvers using finite volume edge-based discretization, and admits meshes with arbitrarily shaped cells. The numerical formulation is equally applicable to global and limited area models. Theoretical considerations are supported with canonical examples of slab-symmetric, nonhydrostatic orographic problems in weakly and strongly stratified flow regimes and three-dimensional hydrostatic analogues of the strongly stratified case on a slowly and rapidly rotating sphere.     

A 2D unstructured multi-material Cell-Centered Arbitrary Lagrangian–Eulerian (CCALE) scheme using MOF interface reconstruction

We present an original Cell-Centered Arbitrary Lagrangian–Eulerian (CCALE) strategy using the Moment Of Fluid (MOF) interface reconstruction devoted to the numerical simulation of two-dimensional multi-material compressible fluid flows on general unstructured grids. Our methodology is assessed through several demanding two-dimensional tests and comparison with Volume Of Fluid (VOF) interface reconstruction. The corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme.     

A high-order one-step sub-cell force-based discretization for cell-centered Lagrangian hydrodynamics on polygonal grids

We present a one-step high-order cell-centered numerical scheme for solving Lagrangian hydrodynamics equations on unstructured grids. The underlying finite volume discretization is constructed through the use of the sub-cell force concept invoking conservation and thermodynamic consistency. The high-order extension is performed using a one-step discretization, wherein the fluxes are computed by means of a Taylor expansion. The time derivatives of the fluxes are obtained through the use of a node-centered solver which can be viewed as a two-dimensional extension of the Generalized Riemann Problem methodology introduced by Ben-Artzi and Falcovitz.     

非结构化离散型对等网络的枢纽副本复制机制

P2P网络使得网络中的数据传输更加方便和高效.当前大多数P2P相关研究集中在路由算法及结构化网络拓扑方面,忽略了非结构化离散型副本复制的研究.提出了一种基于非结构化离散型对等网络的枢纽节点副本复制机制(JRM).通过该机制,可以降低非结构化离散型对等网络中的数据流量并实现更好的负载平衡.给出了相关算法伪代码,并通过分析证明了该算法的优势.     

P2P环境中的skyline查询综述

随着数据规模的增长以及网络技术的发展,对等网络(P2P)作为一种分布式信息共享与搜索的平台引起了越来越广泛的关注。基于对等网络高度动态、高度分散、扩展性强等特点,P2P上的skyline计算方法不仅需要满足集中式skyline计算方法的各种要求,还需要考虑减小网络通讯量、减少平均节点访问数、保持负载平衡等。文中对这个发展领域的最新技术进行了研究,并且描述了分布式skyline方法的目的和主要原理,概括了适用于P2P环境中的现有方法,并进行了性能比较分析。最后,给出了P2P环境skyline计算的未来发展方向。     

An advertisement-based peer-to-peer search algorithm

Most of the existing search algorithms for unstructured peer-to-peer (P2P) systems share one common approach: the requesting node sends out a keyword search query and the query message is repeatedly routed and forwarded to other peers in the overlay network. Due to multiple hops involved in query forwarding, the search may result in a long delay before it is answered. Furthermore, some incapable nodes may be overloaded when the query traffic becomes intensive or bursty.     

Efficient nonlinear solvers for Laplace–Beltrami smoothing of three-dimensional unstructured grids

The Laplace–Beltrami system of nonlinear, elliptic, partial differential equations has utility in the generation of computational grids on complex and highly curved geometry. Discretization of this system using the finite-element method accommodates unstructured grids, but generates a large, sparse, ill-conditioned system of nonlinear discrete equations. The use of the Laplace–Beltrami approach, particularly in large-scale applications, has been limited by the scalability and efficiency of solvers. This paper addresses this limitation by developing two nonlinear solvers based on the Jacobian-Free Newton–Krylov (JFNK) methodology. A key feature of these methods is that the Jacobian is not formed explicitly for use by the underlying linear solver. Iterative linear solvers such as the Generalized Minimal RESidual (GMRES) method do not technically require the stand-alone Jacobian; instead its action on a vector is approximated through two nonlinear function evaluations. The preconditioning required by GMRES is also discussed. Two different preconditioners are developed, both of which employ existing Algebraic Multigrid (AMG) methods. Further, the most efficient preconditioner, overall, for the problems considered is based on a Picard linearization. Numerical examples demonstrate that these solvers are significantly faster than a standard Newton–Krylov approach; a speedup factor of approximately 26 was obtained for the Picard preconditioner on the largest grids studied here. In addition, these JFNK solvers exhibit good algorithmic scaling with increasing grid size.