M. T. Heath and P. Raghavan. Performance of a fully parallel sparse solver. Int. Journal of Supercomputer Applications, 11(1):49-64, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....maximize parallelism, precompute the nonzero structure of the Cholesky factor, and optimize the (2D) distributed data structures and communication pattern. Researchers have been quite successful in achieving scalable performance for sparse Cholesky factorization; available codes include CAPSS [38], MUMPS SYM [3] PaStix [40] PSLDLT [54] and PSPACES [36] In contrast, for nonsymmetric or inde nite systems, few distributed memory codes exist. They are more complicated than Choleksy for at least two reasons. First and foremost, some kind of numerical pivoting is necessary for stability. ....

M. T. Heath and P. Raghavan. Performance of a fully parallel sparse solver. Int. Journal of Supercomputer Applications, 11(1):49-64, 1997.

....in the future. In this section, we summarize the major characteristics of the parallel sparse direct codes of which we are aware. A clear description of the terms used in the tables is given by [19] Code Technique Scope Availability Ref CAPSS Multifrontal SPD www.netlib.org scalapack [20] MUMPS Multifrontal SYM UNS www.enseeiht.fr apo MUMPS [3] PaStiX Fan in SPD see caption ( 21] PSPASES Multifrontal SPD www.cs.umn.edu mjoshi pspases [18] SPOOLES Fan in SYM UNS www.netlib.org linalg spooles [8] SuperLU Fan out UNS www.nersc.gov xiaoye SuperLU [23] S Fan out y UNS ....

M. T. Heath and P. Raghavan. Performance of a fully parallel sparse solver. Int. Journal of Supercomputer Applications, 11(1):49--64, 1997. 60

....in the future. In the following tables, we summarize the major characteristics of the parallel sparse direct codes of which we are aware. A clear description of the terms used in the tables is given by [18] Code Technique Scope Availability Ref CAPSS Multifrontal SPD www.netlib.org scalapack [19] MUMPS Multifrontal SYM UNS www.enseeiht.fr apo MUMPS [3] PaStiX Fan in SPD see caption x [20] PSPASES Multifrontal SPD www.cs.umn.edu mjoshi pspases [17] SPOOLES Fan in SYM UNS www.netlib.org linalg spooles [8] SuperLU Fan out UNS www.nersc.gov xiaoye SuperLU [24] S Fan out y UNS ....

M. T. Heath and P. Raghavan. Performance of a fully parallel sparse solver. Int. Journal of Supercomputer Applications, 11(1):49-64, 1997.

....tables, we summarize the major characteristics of the parallel sparse direct codes of which we are aware. A clear description of the terms used in the tables is given by Heath, Ng and Peyton (1991) Code Technique Scope Availability Reference CAPSS Multifrontal SPD www.netlib.org scalapack (Heath and Raghavan 1997) MUMPS Multifrontal SYM UNS www.enseeiht.fr apo MUMPS (Amestoy et al. 1999) PaStiX Fan in SPD see caption x (Henon et al. 1999) PSPASES Multifrontal SPD www.cs.umn.edu mjoshi pspases (Gupta, Karypis and Kumar 1997) SPOOLES Fan in SYM UNS www.netlib.org linalg spooles (Ashcraft and Grimes ....

Heath, M. T. and Raghavan, P. (1997), `Performance of a fully parallel sparse solver', Int. J. Supercomputer Applications 11(1), 49--64.

....in the future. In this section, we summarize the major characteristics of the parallel sparse direct codes of which we are aware. A clear description of the terms used in the tables is given by [19] Code Technique Scope Availability Ref CAPSS Multifrontal SPD www.netlib.org scalapack [20] MUMPS Multifrontal SYM UNS www.enseeiht.fr apo MUMPS [3] PaStiX Fan in SPD see caption ( 21] PSPASES Multifrontal SPD www.cs.umn.edu mjoshi pspases [18] SPOOLES Fan in SYM UNS www.netlib.org linalg spooles [8] SuperLU Fan out UNS www.nersc.gov xiaoye SuperLU [23] S Fan out y UNS ....

M. T. Heath and P. Raghavan. Performance of a fully parallel sparse solver. Int. Journal of Supercomputer Applications, 11(1):49-64, 1997. 60

....code [10] developed within the EU PARASOL Project, also targets message passing architectures. Partly because of the success of fast and parallel methods for performing the numerical factorization, other phases of the solution are now becoming more critical on parallel computers. The package [61] executes all phases in parallel, and there has been much recent work in finding parallel methods for performing the reordering. This has been another reason for the growth in dissection approaches (for example, see [65, 77] Parallelism in the triangular solve can be obtained either using the ....

M. T. Heath and P. Raghavan. Performance of a fully parallel sparse solver. In Proceedings of SHPCC '94, Scalable High-Performance Computing Conference. May 23-25, 1994, Knoxville, Tennessee, pages 334--341, Los Alamitos, California, 1994. IEEE Computer Society Press.

....Pub Stanford Distributed Memory Algorithms sym. van der Stappen [18] RL, Markowitz, Scalar Res Author sym Lucas et al. 15] MF, no pivoting, BLAS 1 Res Author pattern s.p.d. Rothberg et al. 17] RL, 2 D block, BLAS 3 Res Author s.p.d. Gupta [10] MF, 2 D block, BLAS 3 Res Author s.p.d. CAPSS [12] MF, full parallel, BLAS 1 Pub NETLIB (require coordinates) Abbreviations used in the table: nonsym. nonsymmetric. sym pattern symmetric nonzero structure, nonsymmetric values. sym. symmetric and may be indefinite. s.p.d symmetric and positive definite. MF, LL and RL ....

M. T. Heath and P. Raghavan. Performance of a fully parallel sparse solver. In Proc. Scalable High-Performance Computing Conf., pages 334--341, Los Alamitos, CA, 1994. IEEE.

....shared memory parallel computers, SuperLU MT, is available from the Berkeley and the MA41 code from HSL that we have discussed in this paper, also has a version for shared memory computers. The only public domain software for distributed memory machines that we are aware of is the CAPSS code by Heath and Raghavan (1995,1997), which is included in the SCALAPACK package. Gupta is freely distributing a non machine specific source code version of the WSSMP code (Gupta, Joshi and Kumar 1997) that is available under license for the IBM SP2. Koster and Bisseling (1994) plan a public release of their parallel ....

Heath, M. T. and Raghavan, P. (1997), `Performance of a fully parallel sparse solver', Int J. Supercomputer Applications 11(1), 49--64.

.... environment, it is very beneficial if some memory is available as shared memory to hold information such as mapping vectors [99] The first work to exploit parallelism at all phases of the sparse solution process was by [212] later developed by [104] and [213] More recently, the work of [118] also exploits parallelism in all phases, although the matrix must be held in Cartesian form; that is, in a two or three dimensional coordinate system. While this is quite natural in the context of discretized PDEs, it is not a convenient interface in general. Schreiber [180] presents a clear ....

....is also targeting message passing architectures. Parallelism of other phases than factorization Partly because of the success of fast and parallel methods for performing the numerical factorization, other phases of the solution are now becoming more critical on parallel computers. The package [118] executes all phases in parallel, and there has been much recent work in finding parallel methods for performing the reordering. This has been another reason for the growth in dissection approaches (for example, see [130, 168] Parallelism in the triangular solve can be obtained either using the ....

M. T. Heath and P. Raghavan. Performance of a fully parallel sparse solver. In IEEE, editor, Proceedings of SHPCC '94, Scalable High-Performance Computing Conference. May 23-25, 1994, Knoxville, Tennessee, pages 334-- 341, Los Alamitos, California, 1994. IEEE Computer Society Press.

....memory is available as shared memory to hold information such as mapping vectors. The first work to exploit parallelism at all phases of the sparse solution process was by Zmijewski (1987) later developed by Gilbert and Zmijewski (1987) and Zmijewski and Gilbert (1988) More recently, the work of Heath and Raghavan (1994) also exploits parallelism in all phases, although they require that the matrix be held in Cartesian form; that is, in a two or three dimensional coordinate system. While this is quite natural in the context of discretized PDEs, it is not a convenient interface in general. Schreiber (1993) ....

....Cholesky factorizations to speed up this computation (see also Shanno and Simantiraki 1996) Partly because of the success of fast and parallel methods for performing the numerical factorization, other phases of the solution are now becoming more critical on parallel computers. The package of Heath and Raghavan (1994) executes all phases in parallel, and there has been much recent work in finding parallel methods for performing the reordering. This has been another reason for the growth in dissection approaches (for example, see Karypis and Kumar 1995c, and Raghavan 1995c) It is possible to parallelize the ....

Heath, M. T. and Raghavan, P. (1994), Performance of a fully parallel sparse solver, in IEEE, ed., `Proceedings of SHPCC '94, Scalable High-Performance Computing Conference. May 23-25, 1994, Knoxville, Tennessee', IEEE Computer Society Press, Los Alamitos, California, pp. 334--341.

....BLAS 3 Pub Stanford Distributed Memory Algorithms unsym. van der Stappen [108] RL, Markowitz Scalar Res Author sym Lucas et al. 85] MF, no pivoting BLAS 1 Res Author pattern s.p.d. Rothberg et al. 98] RL, 2 D block BLAS 3 Res Author s.p.d. Gupta [72] MF, 2 D block BLAS 3 Res Author s.p.d. CAPSS [74] MF, full parallel BLAS 1 Pub netlib (require coordinates) Table 6.1: Software to solve sparse linear systems using direct methods. Abbreviations used in the table: unsym. fully unsymmetric matrices sym pattern unsymmetric matrices with symmetric nonzero patterns sym. symmetric but ....

M. T. Heath and P. Raghavan. Performance of a fully parallel sparse solver. In Proc. Scalable High-Performance Computing Conf., pages 334--341, Los Alamitos,CA, 1994. IEEE.

....are solved using forward and back substitution. The cost of this step is of lower order, and on serial machines it is quite negligible compared to the cost of factorization. Parallel sparse matrix factorization on message passing multiprocessors has been the subject of much recent research [11, 13, 19, 22]. Numeric factorization can be performed very effectively on multiprocessors using either parallel multifrontal or columnblock methods. The parallel numeric factorization step leaves the factors distributed across the processors, ready for the next solution step. In broad terms, the parallel ....

....limit the discussion to schemes where the dense matrix is wrap mapped by columns to processors; this is a natural mapping for the factorization step and also works well for substitution schemes. Such wrap mapping can also be accomplished during the factorization without explicit redistribution [13, 18]. Each algorithm has a row mapped analog for back substitution. We now use the terminology in [9, 12] for a brief overview of the schemes we consider; detailed descriptions can be found in [9, 12, 16] Substitution schemes are formulated as two loops, one nested within the other. The terms ....

[Article contains additional citation context not shown here]

M. T. Heath and P. Raghavan, Performance of a fully parallel sparse solver, Internat. J. Supercomput. Appl. High Perf. Comput., 11 (1997), pp. 46--61.

....that of CND. For the latter, we again use two versions, one with CND all through and the other (CND MMD) with CND for a distributed phase and MMD for the local. The version of CND and CNDMMD we use for fair comparison is not the code available in public domain as part of a fully parallel solver [13]. The redistribution step after distributed CND has been modified to redistribute only the graph information while the version in the solver redistributes the numeric values as well as the right hand side vector for later numeric factorization. Recall that MMD is applied in a local phase for both ....

M. T. Heath and P. Raghavan, Performance of a fully parallel sparse solver, in Scalable High Performance Computing Conference, Los Alamitos, CA, 1994, IEEE Computer Society Press. submitted to International Journal of Supercomputer Applications.

....of PCO against that of CND. Once again, we use two versions, one with CND all through and the other (CNDM) with CND for a distributed phase and MMD for the local. The version of CND and CNDM we use for fair comparison is not the code available in public domain as part of a fully parallel solver [18]. The redistribution step after distributed CND has been modified to redistribute only the graph information while the version in the solver redistributes the numeric values as well as the right hand side vector for later numeric factorization. Recall that MMD is applied in a local phase for both ....

M. T. Heath and P. Raghavan, Performance of a fully parallel sparse solver, in Scalable High Performance Computing Conference, Los Alamitos, CA, 1994, IEEE Computer Society Press. To appear in the International Journal of Supercomputer Applications.

No context found.

Heath, M., and Raghavan, P., 1994b. "Performance of a fully parallel sparse solver," Proc. Scalable High-Performance Computing Conf., IEEE Computer Society Press, Los Alamitos, CA, pp.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC