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Enabling scalable parallel implementations of structured adaptive mesh refinement applications

JOURNAL OF SUPERCOMPUTING 2007年第2期39卷 177-203页

作者： Chandra, Sumir Li, Xiaolin Saif, Taher Parashar, Manish State Univ New Jersey Organizat Rutgers Appl Software Syst Lab Dept Elect & Comp Engn Piscataway NJ 08854 USA Oklahoma State Univ Scalable Software Syst Lab Stillwater OK 74078 USA

Parallel implementations of dynamic structured adaptive mesh refinement (SAMR) methods lead to significant runtime management challenges that can limit their scalability on large systems. This paper presents a runtime engine that addresses the scalability of SAMR applications with localized refinements and high SAMR efficiencies on large numbers of processors (upto 1024 processors). The SAMR runtime engine augments hierarchical partitioning with bin-packing based load-balancing to manage the space-time heterogeneity of the SAMR grid hierarchy, and includes a communication substrate that optimizes the use of MPI non-blocking communication primitives. An experimental evaluation on the IBM SP2 supercomputer using the 3-D Richtmyer-meshkov compressible turbulence kernel demonstrates the effectiveness of the runtime engine in improving SAMR scalability.

关键词： structured adaptive mesh refinement SAMR scalability hierarchical partitioning bin-packing based load-balancing MPI non-blocking communication optimization 3-D Richtmyer-meshkov application

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Data structures and algorithms for high-dimensional structured adaptive mesh refinement

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ADVANCES IN ENGINEERING SOFTWARE 2015年 82卷 75-86页

作者： Grandin, Magnus Uppsala Univ Div Comp Sci Dept Informat Technol SE-75105 Uppsala Sweden

Spatial discretization of high-dimensional partial differential equations requires data representations that are of low overhead in terms of memory and complexity. Uniform discretization of computational domains quickly grows out of reach due to an exponential increase in problem size with dimensionality. Even with spatial adaptivity, the number of mesh data points can be unnecessarily large if care is not taken as to where refinement is done. This paper proposes an adaptive scheme that generates the mesh by recursive bisection, allowing mesh blocks to be arbitrarily anisotropic to allow for fine structures in some directions without over-refining in those directions that suffice with less refinement. Within this framework, the mesh blocks are organized in a linear kd-tree with an explicit node index map corresponding to the hierarchical splitting of internal nodes. Algorithms for refinement, coarsening and 2:1 balancing of a mesh hierarchy are derived. To demonstrate the capabilities of the framework, examples of generated meshes are presented and the algorithmic scalability is evaluated on a suite of test problems. In conclusion, although the worst-case complexity of sorting the nodes and building the node map index is n(2), the average runtime scaling in the studied examples is no worse than n log n. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： structured adaptive mesh refinement Anisotropic mesh High-dimensional Hierarchical data structure kd-tree Morton order 2:1 balancing

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Addressing spatiotemporal and computational heterogeneity in structured adaptive mesh refinement

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COMPUTING AND VISUALIZATION IN SCIENCE 2006年第3期9卷 145-163页

作者： Chandra, Sumir Parashar, Manish Rutgers State Univ Dept Elect & Comp Engn 94 Brett Rd Piscataway NJ 08854 USA

structured adaptive mesh refinement (SAMR) techniques can provide accurate and cost-effective solutions to realistic scientific and engineering simulations modeling complex physical phenomena. However, the adaptive nature and inherent space-time heterogeneity of SAMR applications result in significant runtime management challenges. Moreover, certain SAMR applications involving reactive flows exhibit pointwise varying workloads and cannot be addressed by traditional parallelization approaches, which assume homogeneous loads. This paper presents hierarchical partitioning, bin-packing based load balancing, and Dispatch structured partitioning strategies to manage the spatiotemporal and computational heterogeneity in SAMR applications. Experimental evaluation of these schemes using 3-D Richtmyer-meshkov compressible turbulence and 2-D reactive-diffusion kernels demonstrates the improvement in overall performance.

关键词： Spatiotemporal and computational heterogeneity structured adaptive mesh refinement

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Hierarchical partitioning techniques for structured adaptive mesh refinement applications

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JOURNAL OF SUPERCOMPUTING 2004年第3期28卷 265-278页

作者： Li, XL Parashar, M Rutgers State Univ Dept Elect & Comp Engn Piscataway NJ 08854 USA

This paper presents the design and preliminary evaluation of hierarchical partitioning and load-balancing techniques for distributed structured adaptive mesh refinement (SAMR) applications. The overall goal of these techniques is to enable the load distribution to reflect the state of the adaptive grid hierarchy and exploit it to reduce synchronization requirements, improve load-balance, and enable concurrent communications and incremental redistribution. The hierarchical partitioning algorithm (HPA) partitions the computational domain into subdomains and assigns them to hierarchical processor groups. Two variants of HPA are presented in this paper. The static hierarchical partitioning algorithm (SHPA) assigns portions of overall load to processor groups. In SHPA, the group size and the number of processors in each group is setup during initialization and remains unchanged during application execution. It is experimentally shown that SHPA reduces communication costs as compared to the Non-HPA scheme, and reduces overall application execution time by up to 59%. The adaptive hierarchical partitioning algorithm (AHPA) dynamically partitions the processor pool into hierarchical groups that match the structure of the adaptive grid hierarchy. Initial evaluations of AHPA show that it can reduce communication costs by up to 70%.

关键词： dynamic load balancing hierarchical partitioning algorithm distributed computing structured adaptive mesh refinement

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Hierarchical partitioning techniques for structured adaptive mesh refinement (SAMR) applications

Hierarchical partitioning techniques for Structured Adaptive...

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31st International Conference on Parallel Processing (ICPP 2002)

作者： Li, XL Ramanathan, S Parashar, M Rutgers State Univ Appl Software Syst Lab Dept Elect & Comp Engn Piscataway NJ 08854 USA

ISBN: (纸本)0769516807

This paper presents the design and preliminary evaluation of hierarchical partitioning and load-balancing techniques for distributed structured adaptive mesh refinement (SAMR) applications. The overall goal of these techniques is to enable the load distribution to reflect the state of the adaptive grid hierarchy and exploit it to reduce synchronization requirements, improve load-balance, and enable concurrent communications and incremental redistribution. The hierarchical partitioning algorithm (HPA) partitions the computational domain into subdomains and assigns them to hierarchical processor groups. Two variants of HPA are presented in this paper. The Static Hierarchical Partitioning Algorithm (SHPA) assigns portions of overall load to processor groups. In SHPA, the group size and the number of processors in each group is setup during initialization and remains unchanged during application execution. It is experimentally shown that SHRA reduces communication costs as compared to the Non-HPA scheme, and reduces overall application execution time by up to 41%. The adaptive Hierarchical Partitioning Algorithm (AHPA) dynamically partitions the processor pool into hierarchical groups that match the structure of the adaptive grid hierarchy. Initial evaluations of AHRA show that it can reduce communication costs by up to 70%.

关键词： dynamic load balancing hierarchical partitioning algorithm distributed computing structured adaptive mesh refinement

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Hierarchical partitioning techniques for structured adaptive mesh refinement applications

Hierarchical partitioning techniques for structured adaptive...

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4th International Workshop on High Performance Scientific and Engineering Computing with Applications

作者： Li, XL Parashar, M Rutgers State Univ Dept Elect & Comp Engn Piscataway NJ 08854 USA

关键词： dynamic load balancing hierarchical partitioning algorithm distributed computing structured adaptive mesh refinement

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A two-dimensional geometric multigrid model for Poisson equation with interface on structured adaptive mesh refinement grid

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APPLIED OCEAN RESEARCH 2021年 111卷 102655-102655页

作者： Zhang, Yunxing Ma, Shan Liao, Kangping Duan, Wenyang Harbin Engn Univ Coll Shipbldg Engn Inst Fluid Mech Harbin 150001 Peoples R China

In this study, a two-dimensional Geometric Multigrid (GMG) model for Poisson equation with interface on structured adaptive mesh refinement (SAMR) grid is developed. The model is designed to be combined with Navier-Stokes solvers with staggered arrangements of variables, although solvers with collocated arrangement are also applicable. Based on a general GMG method, special attention for flux conservation is taken on the coarse-fine interface. As large density ratios commonly exist in interface flows such as free surface flows, Galerkin Coarse grid Approximation (GCA) method is adopted to generate coefficients on coarse grids to enhance the robustness and efficiency of the model. Benchmark case is carried out for the validation of the model, and it is demonstrated to obtain 2nd-order accuracy and acceptable efficiency for even the density ratio reaches 104. Point iteration and line relaxation iteration of Gauss-Seidel methods are compared to obtain a better performance. Furthermore, the model is implemented in a developed Navier-Stokes solver to validate its performance in simulating interface problems. The numerical results are compared with theoretical solution or experimental data from reliable sources.

关键词： Poisson equation Interface flows structured adaptive mesh refinement Geometric multigrid method Galerkin coarse grid approximation

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A DYNAMIC MPI-OPENMP MODEL FOR structured adaptive mesh refinement

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PARALLEL PROCESSING LETTERS 2005年第1-2期15卷 37-47页

作者： Rantakokko, Jarmo Uppsala Univ Dept Informat Technol Sci Comp Box 337 S-75105 Uppsala Sweden

We compare experimentally different parallelization models using MPI and OpenMP for structured adaptive mesh refinement on a shared-memory parallel computer, a Sun-Fire 15K. Due to the dynamic properties of the mesh no static parallelization model with fixed number of processes and threads performs best in all stages. Different combinations of MPI and OpenMP are preferable in different settings of the application and grid hierarchy. We suggest a new dynamic approach using a mixed MPI-OpenMP model that adapts the number of threads during run time and gives good performance in all stages throughout the whole run as the solution state changes, i.e. the resolution in the computational grid changes.

关键词： OpenMP PDE structured adaptive mesh refinement

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Computation of airfoil-vortex interaction using a vorticity-preserving scheme

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AIAA JOURNAL 2008年第7期46卷 1614-1623页

作者： Falissard, Fabrice Lerat, Alain Sides, Jacques Ecole Natl Super Arts & Metiers Lab Simulat Numer & Mecan Fluides F-75013 Paris France Off Natl Etud & Rech Aerosp F-92322 Chatillon France

We recently proved that a dissipative residual-based scheme of second-order accuracy is vorticity-preserving for the compressible Enter equations. In the present paper, this scheme is extended to curvilinear grids and applied to the computation of the interaction between a Scully vortex and a NACA0012 airfoil at a Mach number of 0.5. A grid convergence study and a comparison with a conventional scheme and with experimental measurements are presented. The new scheme shows a faster grid convergence, especially for the vortex trajectories and deformations during the interaction.

关键词： Pressure Coefficient Airfoil Vortex Modeling Euler Equations Freestream Mach Number Courant Friedrichs Lewy Velocity Profiles Advection structured adaptive mesh refinement Blade Vortex Interaction

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Hybrid runtime management of space-time heterogeneity for parallel structured adaptive applications

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2007年第9期18卷 1202-1214页

作者： Li, Xiaolin Parashar, Manish Oklahoma State Univ Dept Comp Sci Stillwater OK 74078 USA Rutgers State Univ Dept Elect & Comp Engn Piscataway NJ 08854 USA

structured adaptive mesh refinement (SAMR) techniques provide an effective means for dynamically concentrating computational effort and resources to appropriate regions in the application domain. However, due to their dynamism and space-time heterogeneity, scalable parallel implementation of SAMR applications remains a challenge. This paper investigates hybrid runtime management strategies and presents an adaptive hierarchical multipartitioner (AHMP) framework. AHMP dynamically applies multiple partitioners to different regions of the domain, in a hierarchical manner, to match the local requirements of the regions. Key components of the AHMP framework include a segmentation-based clustering algorithm (SBC) that can efficiently identify regions in the domain with relatively homogeneous partitioning requirements, mechanisms for characterizing the partitioning requirements of these regions, and a runtime system for selecting, configuring, and applying the most appropriate partitioner to each region. Further, to address dynamic resource situations for long-running applications, AHMP provides a hybrid partitioning strategy (HPS) that involves application-level pipelining, trading space for time when resources are sufficiently large and underutilized, and an application-level out-of-core strategy (ALOC), trading time for space when resources are scarce in order to enhance the survivability of applications. The AHMP framework has been implemented and experimentally evaluated on up to 1,280 processors of the IBM SP4 cluster at the San Diego Supercomputer Center.

关键词： parallel computing structured adaptive mesh refinement dynamic load balancing hierarchical multipartitioner high-performance computing

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