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Fault tolerant algorithms for heat transfer problems

JOURNAL OF parallel AND DISTRIBUTED COMPUTING 2008年第5期68卷 663-677页

作者： Ltaief, Hatem Gabriel, Edgar Garbey, Marc Univ Houston Dept Comp Sci Houston TX 77204 USA

With the emergence of new massively parallel systems in the high performance computing area allowing scientific simulations to run on thousands of processors, the mean time between failures of large machines is decreasing from several weeks to a few minutes. The ability of hardware and software components to handle these singular events called process failures is therefore getting increasingly important. In order for a scientific code to continue despite a process failure, the application must be able to retrieve the lost data items. The recovery procedure after failures might be fairly straightforward for elliptic and linear hyperbolic problems. However, the reversibility in time for parabolic problems appears to be the most challenging part because it is an ill-posed problem. This paper focuses on new fault-tolerant numerical schemes for the time integration of parabolic problems. The new algorithm allows the application to recover from process failures and to reconstruct numerically the lost data of the failed process(es) avoiding the expensive roll-back operation required in most checkpoin/restart schemes. As a fault tolerant communication library, we use the fault tolerant message passing interface developed by the Innovative Computing Laboratory at the University of Tennessee. Experimental results show promising performances. Indeed, the three-dimensional parabolic benchmark code is able to recover and to keep on running after failures, adding only a very small penalty to the overall time of execution. (C) 2007 Elsevier Inc. All rights reserved.

关键词： parallel numerical algorithms process fault tolerance parabolic problems

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Algorithm-based fault location and recovery for matrix computations on multiprocessor systems

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IEEE TRANSACTIONS ON COMPUTERS 1996年第11期45卷 1239-1247页

作者： RoyChowdhury, A Banerjee, P NORTHWESTERN UNIV CTR PARALLEL & DISTRIBUTED COMPEVANSTONIL 60208 NORTHWESTERN UNIV DEPT ELECT & COMP ENGNEVANSTONIL 60208

Algorithm-based fault-tolerance (ABFT) is an inexpensive method of incorporating fault-tolerance into existing applications. Applications are modified to operate on encoded data and produce encoded results which may then be checked for correctness. An attractive feature of the scheme is that it requires little or no modification to the underlying hardware or system software. Previous algorithm-based methods for developing reliable versions of numerical programs for general-purpose multicomputers have mostly concerned themselves with error detection. A truly fault-tolerant algorithm, however, needs to locate errors and recover from them once they are located. In a parallel processing environment, this corresponds to locating the faulty processors and recovering the data corrupted by the faulty processors. In this paper, we first present a general scheme for performing fault-location and recovery under the ABFT framework. Our fault model assumes that a faulty processor can corrupt all the data it possesses. The fault-location scheme is an application of system-level diagnosis theory to the ABFT framework, while the fault-recovery scheme uses ideas from coding theory to maintain redundant data and uses this to recover corrupted data in the event of processor failures. Results are presented on implementations of three numerical algorithms on a 16-processor Intel iPSC/2 hypercube multicomputer, which demonstrate acceptably low overheads for the single and double fault location and recovery cases.

关键词： algorithm-based fault-tolerance parallel numerical algorithms fault location fault recovery system level diagnosis coding theory

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APPLICATION AND ACCURACY OF THE parallel DIAGONAL DOMINANT ALGORITHM

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parallel COMPUTING 1995年第8期21卷 1241-1267页

作者： SUN, XH Department of Computer Science Louisiana State University Baton Rouge LA 70803-4020 USA

The parallel Diagonal Dominant (PDD) algorithm is an efficient tridiagonal solver. In this paper, a detailed study of the PDD algorithm is given. First the PDD algorithm is extended to solve periodic tridiagonal systems and its scalability is studied. Then the reduced PDD algorithm, which has a smaller operation count than that of the conventional sequential algorithm for many applications, is proposed. Accuracy analysis is provided for a class of tridiagonal systems, the symmetric and skew-symmetric Toeplitz tridiagonal systems. Implementation results show that the analysis gives a good bound on the relative error, and the PDD and reduced PDD algorithms are good candidates for emerging massively parallel machines.

关键词： parallel PROCESSING parallel numerical algorithms SCALABLE COMPUTING TRIDIAGONAL SYSTEMS TOEPLITZ SYSTEMS

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GENERALIZED NONLINEAR DIAGONAL DOMINANCE AND APPLICATIONS TO ASYNCHRONOUS ITERATIVE METHODS

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1991年第1-3期38卷 105-124页

作者： FROMMER, A UNIV KARLSRUHE INST APPL MATHW-7500 KARLSRUHEGERMANY

We introduce a concept of generalized diagonal dominance for nonlinear functions. As in the linear case, this brings together several, apparently different classes of nonlinear functions such as strictly diagonally dominant functions and certain M-functions. With our concept we easily obtain a quite far-reaching result on the global convergence of asynchronous iterative methods for finding zeros of nonlinear functions. Special cases include some known and several new convergence results for special iterative methods such as the nonlinear JOR-, SOR- and SSOR-method.

关键词： DIAGONAL DOMINANCE SYSTEMS OF NONLINEAR EQUATIONS M-FUNCTIONS ASYNCHRONOUS METHODS parallel numerical algorithms

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A Multi-GPU Aggregation-Based AMG Preconditioner for Iterative Linear Solvers

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IEEE TRANSACTIONS ON parallel AND DISTRIBUTED SYSTEMS 2023年第8期34卷 2365-2376页

作者： Bernaschi, Massimo Celestini, Alessandro Vella, Flavio D'Ambra, Pasqua Inst Appl Comp IAC CNR I-00185 Rome Italy Univ Trento I-38122 Trento Italy

We present and release in open source format a sparse linear solver which efficiently exploits heterogeneous parallel computers. The solver can be easily integrated into scientific applications that need to solve large and sparse linear systems on modern parallel computers made of hybrid nodes hosting Nvidia Graphics Processing Unit (GPU) accelerators. The work extends previous efforts of some of the authors in the exploitation of a single GPU accelerator and proposes an implementation, based on the hybrid MPI-CUDA software environment, of a Krylov-type linear solver relying on an efficient Algebraic MultiGrid (AMG) preconditioner already available in the BootCMatchG library. Our design for the hybrid implementation has been driven by the best practices for minimizing data communication overhead when multiple GPUs are employed, yet preserving the efficiency of the GPU kernels. Strong and weak scalability results of the new version of the library on well-known benchmark test cases are discussed. Comparisons with the Nvidia AmgX solution show a speedup, in the solve phase, up to 2.0x.

关键词： GPU accelerators heterogeneous computing iterative sparse linear solvers parallel numerical algorithms scalability

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parallel COMPUTATION OF THE FLOW OF INTEGRAL VISCOELASTIC FLUIDS ON A HETEROGENEOUS NETWORK OF WORKSTATIONS

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INTERNATIONAL JOURNAL FOR numerical METHODS IN FLUIDS 1994年第12期18卷 1167-1183页

作者： HENRIKSEN, P KEUNINGS, R Unité de Mécanique Appliquée Université Catholique de Louvain B-1348 Louvain-la-Neuve Belgium

We consider the parallel computation of flows of integral fluids on a heterogeneous network of workstations. The proposed methodology is relevant to computational mechanics problems which involve a compute-intensive treatment of internal variables (e.g. fibre suspension flow and deformation of viscoplastic solids). The main parallel computing issue in such applications is that of load balancing. Both static and dynamic allocation of work to processors are considered in the present paper. The proposed parallel algorithms have been implemented in an experimental, parallel version of the commercial POLYFLOW package developed in Louvain-la-Neuve. The implementation uses the public domain PVM software library (parallel Virtual Machine), which we have extended in order to ease porting to heterogeneous networks. We describe parallel efficiency results obtained with three PVM configurations, involving up to seven workstations with maximum relative processing speeds of five. The physical problems are the stick/slip and abrupt contraction flows of a K.B.K.Z. integral fluid. Using static allocation, parallel efficiencies in the range 67%-85% were obtained on a PVM network with four workstations having relative speeds of 2:1:1:1. parallel efficiencies higher than 90% were obtained on the three PVM configurations using the dynamic load-balancing schemes.

关键词： parallel numerical algorithms LOAD-BALANCING SCHEMES NETWORK OF WORKSTATIONS parallel SOFTWARE TOOLS PVM VISCOELASTIC FLUIDS

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Block row projection method based on M-matrix splitting

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2018年 340卷 731-744页

作者： Zhang, Zhengyi Sameh, Ahmed H. Purdue Univ Dept Comp Sci 305 N Univ St W Lafayette IN 47907 USA

We propose a hybrid sparse linear system solver based on M-matrix splitting and block-row projection (BRP). We split the sparse coefficient matrix A into two (nonsingular) M-matrices, and construct an augmented larger linear system which we solve using a BRP method. The robustness of BRP is compared with those of ILUT-preconditioned GMRES, and the sparse direct solver Pardiso. We also demonstrate the parallel scalability of BRP on a cluster of multicore nodes. (C) 2017 Elsevier B.V. All rights reserved.

关键词： numerical linear algebra Krylov subspace methods Preconditioners Block row projection M-matrix splitting parallel numerical algorithms

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A parallel sparse linear system solver based on Hermitian/skew-Hermitian splitting

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2016年第8期72卷 2000-2007页

作者： Zhang, Zhengyi Sameh, Ahmed H. Purdue Univ Dept Comp Sci 305 N Univ St W Lafayette IN 47907 USA

In this paper we describe a parallel algorithm for solving large sparse nonsingular linear systems Ax = f, of order n, using the Hermitian Skew-Hermitian splitting approach for handling the augmented linear system, of order 2n, that arises from the linear least problem of minimizing the 2-norm of (f-Ax). We use the restarted GMRES as the outer iteration with the Hermitian Skew-Hermitian Splitting (HSS) preconditioner. In solving systems involving this preconditioner, the most time consuming part deals with handling shifted skew-symmetric systems. We solve such systems using the successive overrelaxation (SOR). Theoretical analysis shows that our solver always converges to the unique solution of Ax = f. We present several numerical experiments that demonstrate the robustness of our solver compared to other schemes, and show its parallel scalability on a single multicore node. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： numerical linear algebra Krylov subspace methods Preconditioners Hermitian/Skew-Hermitian splitting parallel numerical algorithms

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SCALABLE HETEROGENEOUS CPU-GPU COMPUTATIONS FOR UNSTRUCTURED TETRAHEDRAL MESHES

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IEEE MICRO 2015年第4期35卷 6-15页

作者： Langguth, Johannes Sourouri, Mohammed Lines, Glenn Terje Baden, Scott B. Cai, Xing Univ Calif San Diego Dept Comp Sci & Engn San Diego CA 92103 USA

Multicore CPUs can be combined with GPUs to perform computations over 3D unstructured meshes on heterogeneous CPU-GPU clusters. The authors explain how to unlock the CPUs' computing power without slowing down other tasks related to data movement. By solving the representative diffusion equation using the cell-centered finite volume method, the authors demonstrate that combining the computing capacity of CPUs and GPUs delivers a performance advantage over the GPU-only approach.

关键词： Computer programs emerging technologies GPUs Graphics processing units Instruction sets irregular meshes Mathematical model multicore processors parallel numerical algorithms Particle separators Performance evaluation performance optimization sparse linear algebra Three-dimensional displays

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parallel versions of Stone's strongly implicit algorithm

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CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE 2001年第12期13卷 1049-1062页

作者： Reeve, JS Scurr, AD Merlin, JH Univ Southampton Dept Elect & Comp Sci Southampton SO17 1BJ Hants England

In this paper, we describe various methods of deriving a parallel version of Stone's Strongly Implicit Procedure (SIP) for solving sparse linear equations arising from finite difference approximation to partial differential equations (PDEs). Sequential versions of this algorithm have been very successful in solving semi-conductor, heat conduction and flow simulation problems and an efficient parallel version would enable much larger simulations to be run. An initial investigation of various parallelizing strategies was undertaken using a version of high performance Fortran (HPF) and the best methods were reprogrammed using the MPI message passing libraries for increased efficiency. Early attempts concentrated on developing a parallel version of the characteristic wavefront computation pattern of the existing sequential SIP code. However, a red-black ordering of grid points, similar to that used in parallel versions of the Gauss-Seidel algorithm, is shown to be far more efficient. The results of both the wavefront and red-black MPI based algorithms are reported for various size problems and number of processors on a sixteen node IBM SP2. Copyright (C) 2001 John Wiley & Sons, Ltd.

关键词： strongly implicit methods Stones algorithm parallel numerical algorithms

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