3 edition of **Scalable parallel sparse LU factorization methods on shared memory multiprocessors** found in the catalog.

Scalable parallel sparse LU factorization methods on shared memory multiprocessors

Olaf Schenk

- 292 Want to read
- 15 Currently reading

Published
**2000**
by Hartung-Gorre in Konstanz
.

Written in English

- Parallel processing (Electronic computers),
- Parallel computers -- Programming.,
- Parallel algorithms.

**Edition Notes**

Statement | Olaf Schenk. |

Series | Series in microelectronics,, v. 89 |

Classifications | |
---|---|

LC Classifications | QA76.58 .S3455 2000 |

The Physical Object | |

Pagination | x, 131 p. : |

Number of Pages | 131 |

ID Numbers | |

Open Library | OL6867539M |

ISBN 10 | 3896495321 |

LC Control Number | 00392595 |

In parallel implementation of sparse LU factorization, the CPU is responsible for initializing the matrix and doing the symbolic analysis. The GPU only concentrates on numerical factorization. CPU is also responsible for allocating device memory, copy host inputs to device memory, and copy the computed device results back to the host. An algorithm for computing in parallel the general LU-factorization of a matrix is presented. As special cases, one obtains the Doolittle, Crout, and Cholesky methods. The algorithm was implemented and tested on the Cray X-MP/ 10 refs., 1 fig., 1 tab.

2. Parallel Bordered-Diagonal-Block Sparse LU Factorization Introduction to LU Factorization This section presents an overview of the LU factorization problem [4, 28, 29, 30]. Solving the following system of N linear equations is the core computation of many engineering and . PARDISO PARDISO Solver Project (April ) The package PARDISO is a thread-safe, high-performance, robust, memory efficient and easy to use software for solving large sparse symmetric and unsymmetric linear systems of equations on shared-memory and distributed-memory multiprocessors.

Usually, sparse direct solvers solve the task by th e following stages: Phase 1: Fill-reduction analysis and symbolic fact orization A =P^tA P Phase 2: Numerical factorization A = LU (LL^t, LDL^t) Phase 3: Forward and Backward solve including ite rative refinements Ax=f LUx=f Ly=f, Ux=y Termination and Memory Release Phase (phase. A thread-safe, memory efficient software for solving large sparse symmetric and unsymmetric linear systems of equations on shared memory multiprocessors. ParaSails. A parallel sparse approximate inverse preconditioner for the iterative solution of large, sparse systems of linear equations. pARMS.

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Abstract. An efficient sparse LU factorization algorithm on popular shared memory multiprocessors is presented. Interprocess communication is critically important on these architectures—the algorithm introduces O(n) synchronization events only.

No global barrier is used and a completely asynchronous scheduling scheme is one central point of the by: CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An efficient sparse LU factorization algorithm on popular shared memory multiprocessors is presented.

Interprocess communication is critically important on these architectures - the algorithm introduces O(n) synchronization events only. No global barrier is used and a completely asynchronous scheduling.

verteilte algorithmen + parallele algorithmen (programmiermethoden); parallelprozessoren + parallelcomputer + parallelarchitekturen (computersysteme); verteilte speicher (betriebssysteme); distributed algorithms + parallel algorithms (programming methods); parallel processors + parallel computers + parallel architectures (computer systems); shared memories + distributed memories Cited by: An efficient sparse LU factorization algorithm on popular shared memory multiprocessors is presented.

Interprocess communication is critically important on these architectures - the algorithm introduces O(n) synchronization events only. Abstract. We present PARDISO, a new scalable parallel sparse direct linear solver on shared memory multiprocessors. In this paper, we describe the parallel factorization algorithm which utilizes the supernode structure of the matrix to reduce the number of memory Cited by: 1.

O. Schenk, Scalable parallel sparse LU factorization methods on shared memory multiprocessors, Ph.D. Thesis, ETH Zürich, Google Scholar. Schenk, K. GärtnerPARDISO: A high performance serial and parallel sparse linear solver in semiconductor device simulation. This paper concerns parallel, local computations with a data structure such a graph or mesh, which may be structured or unstructured.

The target machine is a distributed-memory parallel processor with vector or pipeline hardware on the processors, but software based on voxel databases also runs efficiently on shared-memory and uniprocessor machines with and without vector hardware. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication patterns, which lets us exploit techniques used in parallel sparse Cholesky algorithms to better parallelize both LU decomposition and triangular solution on large-scale distributed machines.

Scalable parallel sparse LU factorization methods on shared memory multiprocessors. O Schenk. ETH Zurich, Weighted matchings for preconditioning symmetric indefinite linear systems. M Hagemann, O Schenk.

SIAM Journal on Scientific Computing 28 (2),[31] E. Rothberg. Exploiting the memory hierarchy in sequential and parallel sparse Cholesky factorization.

PhD thesis, Dept. of Computer Science, Stanford University, December [32] O. Schenk, K. G¨artner, and W. Fichtner. Eﬃcient sparse LU factorization with left–right looking strategy on shared memory multiprocessors.

() Highly scalable parallel algorithms for sparse matrix factorization. IEEE Transactions on Parallel and Distributed Systems() Efficient parallel algorithm for dense matrix LU decomposition with pivoting on hypercubes.

A parallel LU factorization algorithm for general sparse linear systems arising in semiconductor device simulation problems has been presented. In order to improve sequential and parallel sparse numerical factorization performance, the proposed methods are based on a Level-3 BLAS update and pipelining parallelism is exploited with a combination.

In this article the orthogonal decomposition of large sparse matrices on a hypercube multiprocessor is considered. The proposed algorithm offers a parallel implementation of the general row merging scheme for sparse Givens transformations recently developed by Joseph Liu.

The proposed parallel algorithm is novel in several aspects. Although highly parallel formulations of dense matrix factorization are well known, it has been a challenge to implement efficient sparse linear system solvers using direct methods, even on.

Cedar multiprocessors, based on Aliant shared memory clusters. This paper focuses on parallelization issues for a given column ordering, with row interchanges to maintain numerical stability.

Parallelization of sparse LU with partial pivoting is also studied in [21] on a shared memory ma-chine by using static symbolic LU factorization to overesti. The current trend is for processors to deliver dramatic improvements in parallel performance while only modestly improving serial performance.

Parallel performance is harvested through vector/SIMD. Scalable parallel sparse LU factorization methods on shared memory multiprocessors By Olaf Schenk Topics: Computing and Computers. In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze its performance and scalability, and present experimental results of its implementation on a In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their per-formance and scalability, and present experimental results for up to processors on a Cray T3D parallel computer.

Through our analysis and experimental results, we. Parallel Symbolic Factorization for Sparse LU Factorization with Static Pivoting have designed a parallel algorithm for shared memory machines, and they have observed a SuperLU DIST: A Scalable Distributed-memory Sparse Direct Solver for Unsymmetric linear systems.

ACM Transactions on Mathematical Software, 29(2). text book on sparse direct methods [1] and a recent survey article [2] cover a number of these methods. Sparse LU factor- izations are the direct method of choice for solving unsymmetric linear systems.

Scalable sparse direct linear solvers play a pivotal role in the eﬃciency of several such simulation codes on parallel systems.on distributed-memory parallel computers [8, 47, 10, 35].

We show that the parallel Cholesky factorization algorithms described here are as scalable as the best parallel formulation of dense matrix factorization on both mesh and hypercube architectures for a wide class of sparse matrices, including those arising in two- and.high-performance parallel systems within FPGAs in order to enable the solution of large sparse linear systems of equations.

We have implemented a scalable shared-memory multiprocessor within a single FPGA based on configurable processor IP cores; we investigated parallel LU factorizationof large sparse BDB matrices on our machine [14].