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Parallel solutions of compressible flows using overlapping and non-overlapping mesh partitioning strategies

PARALLEL COMPUTING 1996年第7期22卷 943-968页

作者： Lanteri, S INRIA 2004 Route des Lucioles B.P. 93 06902 Sophia-Antipolis Cedex France

Defining a good strategy for the parallelisation of an unstructured mesh based solver is a challenge, particularly when one aims at reaching a high level of performance while maintaining portability of the source code between scalar, vector and parallel machines. In this paper, we present parallel solutions of realistic three-dimensional flows obtained on the Intel Paragon, the Cray T3D and the IBM SP2 MPPs (Massively Parallel Processors). The solver under consideration is a representative subset of an existing industrial code, N3S-MUSCL which implements a mixed finite element/finite volume formulation on unstructured tetrahedral meshes. The adopted parallelisation strategy combines mesh partitioning techniques and a message-passing programming model. We compare in details performance results obtained with parallel solution strategies based on overlapping and non-overlapping mesh partitions.

关键词： Computational Fluid Dynamics Euler/Navier-Stokes equations unstructured meshes mesh partitioning distributed memory computers

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Parallel algorithms for adaptive mesh refinement

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 1997年第3期18卷 686-708页

作者： Jones, MT Plassmann, PE ARGONNE NATL LAB DIV MATH & COMP SCIARGONNEIL 60439

Computational methods based on the use of adaptively constructed nonuniform meshes reduce the amount of computation and storage necessary to perform many scientific calculations. The adaptive construction of such nonuniform meshes is an important part of these methods. In this paper, we present a parallel algorithm for adaptive mesh refinement that is suitable for implementation on distributed-memory parallel computers. Experimental results obtained on the Intel DELTA are presented to demonstrate that for scientific computations involving the finite element method, the algorithm exhibits scalable performance and has a small run time in comparison with other aspects of the scientific computations examined. It is also shown that the algorithm has a fast expected running time under the parallel random access machine (PRAM) computation model.

关键词： adaptive mesh refinement distributed memory computers parallel algorithms sparse matrices unstructured mesh computation

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Delaunay decoupling method for parallel guaranteed quality planar mesh refinement

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2006年第4期27卷 1394-1423页

作者： Linardakis, L Chrisochoides, N Coll William & Mary Dept Comp Sci Williamsburg VA 23187 USA

Creating in parallel guaranteed quality large unstructured meshes is a challenging problem. Parallel mesh generation procedures decompose the original mesh generation problem into smaller subproblems that can be solved in parallel. The subproblems can be treated as either completely or partially coupled, or they can be treated as completely decoupled. In this paper we present a parallel guaranteed quality Delaunay method for 2-dimensional domains which is based on the complete decoupling of the subproblems. As a result the method eliminates the communication and the synchronization during the meshing of the subproblems. Moreover, it achieves 100% code reuse of existing,fine-tuned, and well-tested sequential mesh generators. The approach we describe in this paper presents for the first time an effective way to create in parallel guaranteed quality meshes with billions of elements in a few hundreds of seconds, and at the same time demonstrates that these meshes can be generated in an efficient and scalable way. Our performance data indicate superlinear speedups.

关键词： mesh generation domain decomposition Delaunay triangulation parallel algorithms distributed memory computers

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Structure-adaptive parallel solution of sparse triangular linear systems

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PARALLEL COMPUTING 2014年第9期40卷 454-470页

作者： Totoni, Ehsan Heath, Michael T. Kale, Laxmikant V. Univ Illinois Dept Comp Sci Urbana IL 61801 USA

Solving sparse triangular systems of linear equations is a performance bottleneck in many methods for solving more general sparse systems. Both for direct methods and for many iterative preconditioners, it is used to solve the system or improve an approximate solution, often across many iterations. Solving triangular systems is notoriously resistant to parallelism, however, and existing parallel linear algebra packages appear to be ineffective in exploiting significant parallelism for this problem. We develop a novel parallel algorithm based on various heuristics that adapt to the structure of the matrix and extract parallelism that is unexploited by conventional methods. By analyzing and reordering operations, our algorithm can often extract parallelism even for cases where most of the nonzero matrix entries are near the diagonal. Our main parallelism strategies are: (1) identify independent rows, (2) send data earlier to achieve greater overlap, and (3) process dense off-diagonal regions in parallel. We describe the implementation of our algorithm in Charm(++) and MPI and present promising experimental results on up to 512 cores of BlueGene/P, using numerous sparse matrices from real applications. Published by Elsevier B.V.

关键词： Triangular solver Parallel algorithms Sparse linear systems distributed memory computers

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On runtime parallel scheduling for processor load balancing

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IEEE TRANSACTIONS ON PARALLEL AND distributed SYSTEMS 1997年第2期8卷 173-186页

作者： Wu, MY IEEE

Parallel scheduling is a new approach for load balancing. In parallel scheduling, all processors cooperate to schedule work. Parallel scheduling is able to accurately balance the load by using global load information at compile-time or runtime. It provides high-quality load balancing. This paper presents an overview of the parallel scheduling technique. Scheduling algorithms for tree, hypercube, and mesh networks are presented. These algorithms can fully balance the load and maximize locality at runtime. Communication costs are significantly reduced compared to other existing algorithms.

关键词： distributed memory computers load balancing runtime parallel scheduling scheduling algorithms trees hypercubes meshes

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AN IMPROVED SPECTRAL BISECTION ALGORITHM AND ITS APPLICATION TO DYNAMIC LOAD BALANCING

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PARALLEL COMPUTING 1995年第1期21卷 29-48页

作者： VANDRIESSCHE, R ROOSE, D Department of Computer Science Katholieke Uniuersiteit Leuven Celestijnenlaan 200 A B-3001 Leuven Belgium

The efficient parallel execution of grid-oriented scientific calculations requires a partitioning of the grid that minimises both load imbalance and interprocessor communication. For unstructured static grids, good partitions are obtained with the recursive spectral bisection heuristic, applied to the interdependency graph of the grid. We will describe an alternative spectral bisection algorithm that yields better partitions than the standard algorithm, especially for interdependency graphs with a large variation in the weights of the edges. We will further describe how even in case of dynamically changing grids, grid-oriented problems can be formulated as graph partitioning problems for the purpose of load balancing. We will then partition these dynamically changing grids with the alternative spectral algorithm.

关键词： distributed memory computers DYNAMIC LOAD BALANCING GRAPH PARTITIONING (RECURSIVE) SPECTRAL BISECTION

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High-level programming of massively parallel computers based on shared virtual memory

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PARALLEL COMPUTING 1998年第3-4期24卷 383-400页

作者： Gerndt, M Res Ctr Julich Cent Inst Appl Math D-52425 Julich Germany

Highly parallel machines needed to solve compute-intensive scientific applications are based on the distribution of physical memory across the compute nodes. The drawback of such systems is, the necessity to write applications in the message passing programming model. Therefore, a lot of research is going on in higher-level programming models and supportive hardware, operating system techniques, languages. The research direction outlined in this article is based on shared virtual memory systems, i.e., scalable parallel systems with a global address space which support an adaptive mapping of global addresses to physical memories. We introduce programming concepts and program optimizations for SVM systems in the context of the SVM-Fortran programming environment which is based on a shared virtual memory system implemented on Intel Paragon. The performance results for real applications proved that this environment enables users to obtain a similar or better performance than by progamming in HPF. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： distributed memory computers scientific computing shared virtual memory parallel programming models language constructs for data locality optimization performance analysis tools

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A repartitioning hypergraph model for dynamic load balancing

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JOURNAL OF PARALLEL AND distributed COMPUTING 2009年第8期69卷 711-724页

作者： Catalyurek, Umit V. Boman, Erik G. Devine, Karen D. Bozdag, Doruk Heaphy, Robert T. Riesen, Lee Ann Ohio State Univ Dept Biomed Informat Columbus OH 43210 USA Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA Sandia Natl Labs Dept Scalable Algorithms Albuquerque NM 87185 USA

In parallel adaptive applications, the computational structure of the applications changes over time, leading to load imbalances even though the initial load distributions were balanced. To restore balance and to keep communication volume low in further iterations of the applications, dynamic load balancing (repartitioning) of the changed computational structure is required. Repartitioning differs from static load balancing (partitioning) due to the additional requirement of minimizing migration cost to move data from an existing partition to a new partition. In this paper, we present a novel repartitioning hypergraph model for dynamic load balancing that accounts for both communication volume in the application and migration cost to move data, in order to minimize the overall cost. The use of a hypergraph-based model allows us to accurately model communication costs rather than approximate them with graph-based models. We show that the new model can be realized using hypergraph partitioning with fixed vertices and describe our parallel multilevel implementation within the Zoltan load balancing toolkit. To the best of our knowledge, this is the first implementation for dynamic load balancing based on hypergraph partitioning. To demonstrate the effectiveness of our approach, we conducted experiments on a Linux cluster with 1024 processors. The results show that, in terms of reducing total cost, our new model compares favorably to the graph-based dynamic load balancing approaches, and multilevel approaches improve the repartitioning quality significantly. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Dynamic load balancing Hypergraph partitioning Parallel algorithms Scientific computing distributed memory computers

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Graded Delaunay decoupling method for parallel guaranteed quality planar mesh generation

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2008年第4期30卷 1875-1891页

作者： Linardakis, Leonidas Chrisochoides, Nikos Virginia Inst Marine Sci Dept Phys Sci Gloucester Point VA 23062 USA Coll William & Mary Dept Comp Sci Williamsburg VA 23187 USA

We present a method for creating large two-dimensional graded Delaunay meshes on parallel machines. The method decouples the mesh generation procedure for each subdomain and thus eliminates the communication between processors, while the final mesh is of the same guaranteed quality as in the sequential case. This work extends our previous result on the uniform Delaunay decoupling method [L. Linardakis and N. Chrisochoides, SIAM J. Sci. Comput., 27 (2006), pp. 1394 1423], by allowing the element size to be governed by a sizing function, or a background mesh. The graded Delaunay decoupling method can produce in parallel very large graded meshes efficiently, demonstrating high speedup and scalability. Ten billion elements can be created in five minutes with small overrefinement (about 2%). The decoupling parallelization approach is effective, using off-the-shelf, well-tested, and fine-tuned sequential mesh generation libraries without modification.

关键词： mesh generation parallel mesh generation Delaunay mesh domain decomposition parallel algorithms distributed memory computers

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Computational challenges in the numerical treatment of large air pollution models

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ECOLOGICAL MODELLING 2004年第2期179卷 187-203页

作者： Dimov, I Georgiev, K Ostromsky, T Zlatev, Z Bulgarian Acad Sci Inst Parallel Proc BU-1113 Sofia Bulgaria Natl Environm Res Inst DK-4000 Roskilde Denmark

Air pollution, especially the reduction of the air pollution to some acceptable levels, is an important environmental problem, which will become even more important in the next 10-20 years. This problem can successfully be studied when high-resolution comprehensive models are developed and used on a routine basis. However, such models are very time-consuming, even when modem high-speed computers are available. Indeed, if an air pollution model is to be applied on a large space domain by using fine grids, then its discretization will always lead to huge computational problems. Assume, for example, that the space domain is discretized by using a (480 x 480) grid and that the number of chemical species studied by the model is 35. Then several systems of ordinary differential equations containing 8 064 000 equations have to be treated at every time-step (the number of time-steps being typically several thousand). If a three-dimensional version of the same air pollution model is to be used, then the figure above must be multiplied by the number of layers. It is extremely difficult to treat such large computational problems, even when the fastest computers that are available at present are used. There is an additional great difficulty, which is very often underestimated (or even neglected) when large application packages are moved from sequential computers to modem parallel machines. The high-speed computers have normally a very complicated memory architecture and, therefore, the task of producing an efficient code for the particular high-speed computer that is available is both extremely hard and time consuming. The use of standard parallelization tools in the solution of the problems sketched above is discussed in this paper. Numerical results obtained on different types of parallel computers are presented. (C) 2004 Elsevier B.V. All rights reserved.

关键词： air pollution modelling partial differential equations finite element method ordinary differential equations predictor-corrector methods parallel computations shared memory computers distributed memory computers

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