Anshul Gupta. Analysis and Design of Scalable Parallel Algorithms for Scientific Computing. PhD thesis, University of Minnesota, Minneapolis, MN, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in Appendices A E) can be obtained from the site http: www.cs.umn.edu agupta wsmp.html. For solving symmetric systems, WSMP uses a modified version of the multifrontal algorithm [3, 10] for sparse Cholesky factorization and a highly scalable parallel sparse Cholesky factorization algorithm [8, 4]. The package also uses scalable parallel sparse triangular solvers [9] and an improved and parallelized version of a multilevel nesteddissection algorithm [5] for computing fill reducing orderings. For details on the implementation and performance of WSMP for solving symmetric sparse systems, ....

Anshul Gupta. Analysis and Design of Scalable Parallel Algorithms for Scientific Computing. PhD thesis, University of Minnesota, Minneapolis, MN, 1995.

....research neglected it. Tasks that can be executed on more than one processors and whose computation time decreases as more processors are allocated to them are called scalable tasks. As the number of processors allocated to a scalable task increases, its computation time decreases monotonously [14 18]. However the workload of a task, the sum of computation amount of each processor executing it, increases due to the parallel execution overhead. Numerous attempts have been made on utilizing the scalability of tasks effectively. The goal of these scheduling algorithms is to minimize the total ....

....H(n)s against n values are relatively small and f is near to 1 [14] Each scalable real time task (T i ) is characterized with D i and C i , where D i is its deadline and C i is an array of worst case computation times for various numbers of processors. Many parallel algorithms are prevalent [13, 18] and thus we assume that C i of each task is given to a scheduler. 2.2 Scheduling Problem Formulation The concern of on line scheduler is to find a schedule in which tasks newly arriving and remaining in the waiting queue can be scheduled so that deadlines of all tasks are met 1 . This ....

A. Gupta, "Analysis and Design of Scalable Parallel Algorithms for Scientific Computing," PhD thesis, Univ. of Minnesota, Minneapolis, Minn., 1995.

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Anshul Gupta. Analysis and Design of Scalable Parallel Algorithms for Scientific Computing. PhD thesis, University of Minnesota, Minneapolis, MN, 1995.

....(also in Appendices A E) can be obtained from the site http: www.cs.umn.edu agupta wsmp.html. For solving symmetric systems, WSMP uses a modified version of the multifrontal algorithm [10] for sparse Cholesky factorization and a highly scalable parallel sparse Cholesky factorization algorithm [8, 3]. The package also uses scalable parallel sparse triangular solvers [9] and an improved and parallelized version of the previously released package WGPP [4, 5] for computing fill reducing orderings. Sparse symmetric factorization in WSMP has been clocked at up to 3.6 GFLOPS on an RS6000 ....

Anshul Gupta. Analysis and Design of Scalable Parallel Algorithms for Scientific Computing. PhD thesis, University of Minnesota, Minneapolis, MN, 1995.

....matrices. This algorithm, while performing the ordering in parallel, also distributes the data among the processors in way that the remaining steps can be carried out with minimum data movement. At the end of the parallel ordering step, the parallel symbolic factorization algorithm described in [19] can proceed without any redistribution. In [19, 25] we present efficient parallel algorithms for solving the upper and lower triangular systems. The experimental results in [19, 25] show that the data mapping scheme described in Section 3 works well for triangular solutions. We hope that the ....

....ordering in parallel, also distributes the data among the processors in way that the remaining steps can be carried out with minimum data movement. At the end of the parallel ordering step, the parallel symbolic factorization algorithm described in [19] can proceed without any redistribution. In [19, 25], we present efficient parallel algorithms for solving the upper and lower triangular systems. The experimental results in [19, 25] show that the data mapping scheme described in Section 3 works well for triangular solutions. We hope that the work presented in this paper, along with [19, 25, 32] ....

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Anshul Gupta. Analysis and Design of Scalable Parallel Algorithms for Scientific Computing. PhD thesis, University of Minnesota, Minneapolis, MN, 1995.

....l ) 2=3 ) for 2 D and 3 D problems, respectively. The number of non zeros in L is N log N for 2 D problems, and N 4=3 for 3 D problems. Using this information, the parallel algorithms presented earlier in this section have been analyzed for their parallel runtime. For details, refer to [2, 3]. Table 1 shows the serial runtime complexity, parallel overhead, and isoefficiency functions [7] for all four phases. It can be seen that all the phases are scalable to varying degrees. Since the overall time complexity is dominated by the numerical factorization phase, the isoefficiency function ....

Anshul Gupta, Analysis and Design of Scalable Parallel Algorithms for Scientific Computing, Ph.D. Thesis, Department of Computer Science, University of Minnesota, Minneapolis, 1995.

....matrices. This algorithm, while performing the ordering in parallel, also distributes the data among the processors in way that the remaining steps can be carried out with minimum data movement. At the end of the parallel ordering step, the parallel symbolic factorization algorithm described in [19] can proceed without any redistribution. In [19, 26] we present efficient parallel algorithms for solving the upper and lower triangular systems. The experimental results in [19, 26] show that the data mapping scheme described in Section 3 works well for triangular solutions. We hope that the ....

....ordering in parallel, also distributes the data among the processors in way that the remaining steps can be carried out with minimum data movement. At the end of the parallel ordering step, the parallel symbolic factorization algorithm described in [19] can proceed without any redistribution. In [19, 26], we present efficient parallel algorithms for solving the upper and lower triangular systems. The experimental results in [19, 26] show that the data mapping scheme described in Section 3 works well for triangular solutions. We hope that the work presented in this paper, along with [19, 26, 33] ....

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Anshul Gupta. Analysis and Design of Scalable Parallel Algorithms for Scientific Computing. PhD thesis, University of Minnesota, Minneapolis, MN, 1995. 28

....parallel solver in a message passing environment, where each node can either be a uniprocessor or a shared memory multiprocessor. WSSMP uses a modified version of the multifrontal algorithm [9] for sparse Cholesky factorization and a highly scalable parallel sparse Cholesky factorization algorithm [6, 3]. The package also uses scalable parallel sparse triangular solvers [7] and an improved and parallelized version of the previously released package WGPP [4, 5] for computing fill reducing orderings. Sparse symmetric factorization in WSSMP has been clocked at up to 210 MFLOPS on an RS6000 590, 500 ....

Anshul Gupta. Analysis and Design of Scalable Parallel Algorithms for Scientific Computing. PhD thesis, University of Minnesota, Minneapolis, MN, 1995.

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