High Performance Computing for Computational Science -- - download pdf or read online

By Michel Daydé, Osni Marques, Kengo Nakajima

ISBN-10: 3319173529

ISBN-13: 9783319173528

ISBN-10: 3319173537

ISBN-13: 9783319173535

This e-book constitutes the completely refereed post-conference complaints of the eleventh overseas convention on excessive functionality Computing for Computational technology, VECPAR 2014, held in Eugene, OR, united states, in June/July 2014.

The 25 papers offered have been rigorously reviewed and chosen of various submissions. The papers are geared up in topical sections on algorithms for GPU and manycores, large-scale purposes, numerical algorithms, direct/hybrid equipment for fixing sparse matrices, functionality tuning. the quantity additionally comprises the papers offered on the ninth overseas Workshop on automated functionality Tuning.

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Additional info for High Performance Computing for Computational Science -- VECPAR 2014: 11th International Conference, Eugene, OR, USA, June 30 -- July 3, 2014, Revised Selected Papers

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D-CholQR time breakdown. d−SYRK dd−SYRK (Cray) d−GEMM dd−GEMM (Cray) 10 0 0 50K 100K 150K 200K 250K 300K 350K 400K 450K 500K Number of rows Fig. 9. d/dd-CholQR performance. of B and reads V (k,j) once for computing a diagonal block. Our performance studies in the next subsection are based on this batched kernel. 2 Performance Figure 7 compares the standard and mixed-precision InnerProds performance on different GPUs, where the mixed-precision InnerProds reads the input matrix in the standard 64-bits double precision, but accumulates its intermediate results into the output matrix in the double-double precision.

The first observation is the large matrix sizes (beyond 5000) required to take advantage of the benefits that the devices offer and, consequently, outperform the peak performance of the CPU. Similarly, adding the second Xeon Phi is beneficial for matrix sizes larger than 10, 000 for Cholesky, 12, 000 for LU, and QR factorizations. Finally, the addition of the third Xeon Phi benefits all three factorizations only beyond matrices of size 16, 000. This behavior is to be expected from a compute-oriented device that is connected to the CPU through a high-latency, low-bandwidth bus such as the PCI Express.

5. 2 Communication-Avoiding GMRES The Generalized Minimum Residual (GMRES) method [6] is a popular Krylov subspace projection method for solving a nonsymmetric linear system of equations, Ax = b. The GMRES’s j-th iteration generates the (j + 1)-th Krylov basis vector vj+1 . This is done through a sparse matrix-vector multiply (SpMV ) with the previously-generated basis vector vj , followed by the orthonormalization (Orth) of the resulting vector against all the previously-generated basis vectors v1 , v2 , .

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High Performance Computing for Computational Science -- VECPAR 2014: 11th International Conference, Eugene, OR, USA, June 30 -- July 3, 2014, Revised Selected Papers by Michel Daydé, Osni Marques, Kengo Nakajima


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