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Timing models and local stopping criteria for asynchronous iterative algorithms

JOURNAL OF parallel AND DISTRIBUTED COMPUTING 1999年第3期58卷 446-465页

作者： Blathras, K Szyld, DB Shi, Y Temple Univ Philadelphia PA 19122 USA

Asynchronous iterative algorithms can reduce much of the data dependencies associated with synchronization barriers. The reported study investigates the potentials of asynchronous iterative algorithms by quantifying the critical parallel processing factors. Specifically, a time complexity-based analysis method is used to understand the inherent interdependencies between computing and communication overheads for the parallel asynchronous algorithm. The results show, not only that the computational experiments closely match the analytical results, but also that the use of asynchronous iterative algorithms can be beneficial for a vast number of parallel processing environments. The choice of local stopping criteria that is critically important to the overall system performance is investigated in depth. (C) 1999 Academic Press.

关键词： timing models asynchronous algorithms parallel iterative methods

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parallel multigrid preconditioning of the conjugate gradient method for systems of subsurface hydrology

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JOURNAL OF COMPUTATIONAL PHYSICS 1998年第1期142卷 148-162页

作者： Brieger, L Lecca, G Geophys Grp I-09123 Cagliari Italy Environm Grp I-09123 Cagliari Italy

parallel preconditioners are considered for improving the convergence rate of the conjugate gradient method for solving sparse symmetric positive definite systems generated by finite element models of subsurface flow The difficulties of adapting effective sequential preconditioners to the parallel environment are illustrated by our treatment of incomplete Cholesky preconditioning. These difficulties are avoided with multigrid preconditioning, which can be extended naturally to many processors so that the preconditioner remains global and effective. The coarse grid correction which defines the multigrid preconditioner is outlined and its parallel implementation with the distributed finite element data structure is presented, along with some examples of its use as a parallel preconditioner. (C) 1998 Academic Press.

关键词： multigrid preconditioning parallel preconditioners conjugate gradient method parallel iterative methods

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SOLVING NUMERICALLY THE NAVIER-STOKES EQUATIONS ON parallel SYSTEMS

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INTERNATIONAL JOURNAL FOR NUMERICAL methods IN FLUIDS 1990年第8期10卷 907-923页

作者： LIN, A Department of Mathematics Temple University Philadelphia PA 19122 U.S.A.

A new general approach for numerically computing flow fields on parallel computing environments is presented, discussed and analysed. The hierarchy presented here is based on a parallel split of operators. A portion of the theory is presented together with its application to two- and three-dimensional flows. This strategy is applied to a two-dimensional problem for which a specific parallel split, called a parabolized split, is given. The parallel algorithm that results from this split is analysed, leading to reasonably good parallel efficiency, which is close to 50%. Actual experiments lead to similar conclusions. This parallel strategy can also be used together with other parallel computing algorithms, such as domain decomposition, to give an optimal-type parallel algorithm for the Navier–Stokes equations.

关键词： parallel computing parallel iterative methods Numerical splitting techniques

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A new class of asynchronous iterative algorithms with order intervals

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MATHEMATICS OF COMPUTATION 1998年第221期67卷 237-255页

作者： Miellou, JC El Baz, D Spiteri, P Univ Franche Comte CNRS URA 040741 LCS F-25030 Besancon France CNRS LAAS LP 8001 F-31077 Toulouse France Inst Natl Polytech Toulouse LIMA CNRS UA 1399ENSEEIHT IRIT F-31071 Toulouse France

This paper deals with a new class of parallel asynchronous iterative algorithms for the solution of nonlinear systems of equations, The main feature of the new class of methods presented here is the possibility of flexible communication between processors. In particular partial updates can be exchanged. Approximation of the associated fixed point mapping is also considered. A detailed convergence study is presented, A connection with the Schwarz alternating method is made for the solution of nonlinear boundary value problems. Computational results on a shared memory multiprocessor IBM 3090 are briefly presented.

关键词： parallel iterative methods asynchronous iterations Schwarz alternating method domain decomposition methods boundary value problems

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Complexity and approximations for multimessage multicasting

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JOURNAL OF parallel AND DISTRIBUTED COMPUTING 1998年第2期55卷 215-235页

作者： Gonzalez, TF Univ Calif Santa Barbara Dept Comp Sci Santa Barbara CA 93106 USA

We consider multimessage multicasting over the n processor complete (or fully connected) static network (MM,). First we present a linear time algorithm that constructs for every degree d problem instance a communication schedule with total communication time at most d(2), where d is the maximum number of messages that each processor may send or receive. Then we present degree d problem instances such that all their communication schedules have total communication time at least d(2). We observe that our lower bound applies when the fan-out (maximum number of processors receiving any given message) is huge, and thus the number of processors is also huge. Since this environment is not likely to arise in the near future, we turn our attention to the study of important subproblems that are likely to arise in practice. We show that when each message has fan-out k = 1 the MM, problem corresponds to the makespan openshop preemptive scheduling problem which can be solved in polynomial time and show that for k greater than or equal to 2 our problem is NP-complete and remains NP-complete ev en when forwarding is allowed. We present an algorithm to generate a communication schedule with total communication time 2d-1 for any degree d problem instance with fan-out k = 2. Our main result is an O(q.d.e) time algorithm, where e less than or equal to nd (the input length), with an approximation bound of qd + k(1/q)(d-1), for any integer q such that k > q greater than or equal to 2. Our algorithms are centralized and require all the communication information ahead of time. Applications where all of this information is readily available include iterative algorithms for solving linear equations, and most dynamic programming procedures. The Meiko CS-2 machine and computer systems with processors communicating via dynamic permutation networks whose basic switches can act as data replicators (e.g., n by n Benes network with 2 by 2 switches that can also act as data replicators) will also b

关键词： approximation algorithms multimessage multicasting dynamic networks parallel iterative methods communication schedules

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Normalized explicit finite element approximate inverse preconditioning

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COMPUTERS & STRUCTURES 2004年第28期82卷 2377-2388页

作者： Gravvanis, GA Giannoutakis, KM Hellen Open Univ Dept Comp Sci GR-11362 Athens Greece Univ Athens Dept Informat & Telecommun GR-15784 Athens Greece

Normalized explicit approximate inverse matrix techniques for computing explicitly various families of normalized approximate inverses based on normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference and finite element discretization of partial differential equations are presented. Normalized explicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of linear and non-linear systems. Theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also presented. Applications of the proposed methods on characteristic linear and non-linear problems are discussed and numerical results are given. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： initial/boundary value problems finite element method finite difference method non-linear systems sparse linear systems normalized approximate factorization procedures normalized approximate inverse finite element matrix techniques preconditioning conjugate gradient schemes rate of convergence and computational complexity parallel iterative methods parallel computations

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Some convergence results of PD relaxation methods

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APPLIED MATHEMATICS AND COMPUTATION 2000年第2-3期107卷 103-112页

作者： Cvetkovic, L Obrovski, J Fac Sci Novi Sad Inst Math YU-21000 Novi Sad Yugoslavia

In the recent paper of Bai and Su a class of parallel decomposition-type accelerated overrelaxation (PDAOR) methods suitable to the SIMD-systems is established and convergence conditions are concluded when the coefficient matrices of the linear systems are L-matrices, H-matrices dr symmetric positive-definite matrices. In the case of H-matrices we improve the convergence area fbr relaxation parameters. (C) 2000 Elsevier Science Inc. All rights reserved.

关键词： linear systems parallel iterative methods H-matrices convergence

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A parallel iterative Galerkin method based on nonconforming quadrilateral elements for second-order partial differential equations

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APPLIED MATHEMATICS AND COMPUTATION 2002年第2-3期127卷 387-404页

作者： Kim, Y Lee, S Kim, LS Korea Adv Inst Sci & Technol Dept Math Taejon 305701 South Korea

A parallel iterative Galerkin method based on domain decomposition technique with nonconforming quadrilateral finite elements will be analyzed for second-order elliptic equations subject to the Robin boundary condition, Optimal order error estimates are derived with respect to a broken H-1-norm and L-2-norm. Applications to time-dependent problems skill be considered. Some numerical experiments supporting the theoretical results will be given. This paper is to extend the work in [J. Douglas Jr., J.E. Santos. D. Sheen. X. Ye. Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems. Mathematical Modelling and Numerical Analysis, RAIRO, Model. Math. Anal, Numer. 33 (4) (1999) 747] to the non-self-adjoint case of second-order equations including the term b . delu. We suppose that uniformly ellipticity holds, Hence the arguments in (loc. cit.) may be applied, word for word. So some proofs will be omitted. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： parallel iterative methods nonconforming methods elliptic problems domain decomposition methods

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Explicit preconditioned domain decomposition schemes for solving nonlinear boundary value problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2003年第1-3期45卷 263-272页

作者： Gravvanis, GA Athens Univ Econ & Business Dept Informat GR-10434 Athens Greece Univ Aegean Dept Math GR-83200 Karlovassi Samos Greece

A new class of inner-outer iterative procedures in conjunction with Picard-Newton methods based on explicit preconditioning iterative methods for solving nonlinear systems is presented. Explicit preconditioned iterative schemes, based on the explicit computation of a class of domain decomposition generalized approximate inverse matrix techniques are presented for the efficient solution of nonlinear boundary value problems on multiprocessor systems. Applications of the new composite scheme on characteristic nonlinear boundary value problems are discussed and numerical results are given. (C) 2003 Elsevier Science Ltd. All rights reserved.

关键词： arrow-type matrix domain decomposition approximate factorization procedures approximate inverse matrix techniques preconditioning parallel iterative methods

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Computing all-pairs shortest paths on a linear systolic array and hardware realization on a reprogrammable FPGA platform

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JOURNAL OF SUPERCOMPUTING 2007年第1期40卷 49-66页

作者： Milovanovic, E. I. Milovanovic, I. Z. Bekakos, M. P. Tselepis, I. N. Domocritus Univ Thrace Dept Elect & Comp Engn Sch Engn Hellas Greece Fac Elect Engn Nish 18000 Serbia

In this paper a regular bidirectional linear systolic array (RBLSA) for computing all-pairs shortest paths of a given directed graph is designed. The obtained array is optimal with respect to a number of processing elements (PE) for a given problem size. The execution time of the array has been minimized. To obtain RBLSA with optimal number of PEs, the accommodation of the inner computation space of the systolic algorithm to the projection direction vector is performed. Finally, FPGA-based reprogrammable systems are revolutionizing certain types of computation and digital logic, since as logic emulation systems they offer some orders of magnitude speedup over software simulation;herein, a FPGA realization of the RBLSA is investigated and the performance evaluation results are discussed.

关键词： systolic arrays all-pairs shortest paths parallel computations parallel iterative methods FPGA

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