七个小矮人

pthiiu 2010-10-15 05:32:09

有人能大概介绍一下七个小矮人吗？这是我找到的英文资料

We were inspired by the work of Phil Colella, who identified seven numerical methods that he believed will be important for science and engineering for at least the next decade [Colella 2004]. Figure 3 introduces the Seven Dwarfs, which constitute classes where membership in a class is defined by similarity in computation and data movement. The dwarfs are specified at a high level of abstraction to allow reasoning about their behavior across a broad range of applications.

The Landscape of Parallel Computing Research: A View from Berkeley

Seven Dwarfs

1. Dense Linear Algebra
Data are dense matrices or vectors. (BLAS Level 1 = vector-vector; Level 2 = matrix-vector; and Level 3 = matrix-matrix.) Generally, such applications use unit-stride memory accesses to read data from rows, and strided accesses to read data from columns.
(e.g., BLAS [Blackford et al 2002], ScaLAPACK [Blackford et al 1996], or MATLAB [MathWorks 2006])

2. Sparse Linear Algebra
Data sets include many zero values. Data is usually stored in compressed matrices to reduce the storage and
bandwidth requirements to access all of the nonzero values. One example is block compressed sparse row (BCSR). Because of the compressed formats, data is generally accessed with indexed loads and stores.
(e.g., SpMV, OSKI [OSKI 2006], or SuperLU [Demmel et al 1999])

3. Spectral Methods
Data are in the frequency domain, as opposed to time or spatial domains. Typically, spectral methods use multiple butterfly stages, which combine multiply-add operations and a specific pattern of data permutation, with all-to-all communication for some stages and strictly local for others.
(e.g., FFT [Cooley and Tukey 1965])

4. N-Body Methods
Depends on interactions between many discrete points. Variations include particle-particle methods, where every point depends on all others, leading to an O(N2) calculation, and hierarchical particle methods, which combine forces or potentials from multiple points to reduce the computational complexity to O(N log N) or O(N).
(e.g., Barnes-Hut [Barnes and Hut 1986], Fast Multipole Method [Greengard and Rokhlin 1987])

5. Structured Grids
Represented by a regular grid; points on grid are conceptually updated together. It has high spatial locality. Updates may be in place or between 2 versions of the grid. The grid may be subdivided into finer grids in areas of interest (“Adaptive Mesh Refinement”); and the transition between granularities may happen dynamically.
(e.g., Cactus [Goodale et al 2003] or Lattice-Boltzmann Magnetohydrodynamics [LBMHD 2005])

6. Unstructured Grids
An irregular grid where data locations are selected, usually by underlying characteristics of the application. Data point location and connectivity of neighboring points must be explicit. The points on the grid are conceptually updated together. Updates typically involve multiple levels of memory reference indirection, as an update to any point requires first determining a list of neighboring points, and then loading values from those neighboring points.
(e.g., ABAQUS [ABAQUS 2006] or FIDAP [FLUENT 2006])

7. Monte Carlo
Calculations depend on statistical results of repeated random trials. Considered embarrassingly parallel.
(e.g., Quantum Monte Carlo [Aspuru-Guzik et al 2005])

References:

[ABAQUS 2006] ABAQUS finite element analysis home page. http://www.hks.com
[Aspuru-Guzik et al 2005] A. Aspuru-Guzik, R. Salomon-Ferrer, B. Austin, R. Perusquia-Flores, M.A. Griffin, R.A. Oliva, D. Skinner, D. Domin, and W.A. Lester, Jr., “Zori 1.0: A Parallel Quantum Monte Carlo Electronic Package,” Journal of Computational Chemistry, vol. 26, no. 8, Jun. 2005, pp. 856–862.
[Barnes and Hut 1986] J. Barnes and P. Hut, “A Hierarchical O(n log n) force calculation algorithm,” Nature, vol. 324, 1986.
[Blackford et al 1996] L.S. Blackford, J. Choi, A. Cleary, A. Petitet, R.C. Whaley, J. Demmel, I. Dhillon, K. Stanley, J. Dongarra, S. Hammarling, G. Henry, and D. Walker, “ScaLAPACK: a portable linear algebra library for distributed memory computers - design issues and performance,” in Proceedings of the 1996 ACM/IEEE conference on Supercomputing, Nov. 1996.
[Blackford et al 2002] L.S. Blackford, J. Demmel, J. Dongarra, I. Du, S. Hammarling, G. Henry, M. Heroux, L. Kaufman, A. Lumsdaine, A. Petitet, R. Pozo, K. Remington, R.C. Whaley, “An updated set of basic linear algebra subprograms (BLAS),” ACM Transactions on Mathematical Software (TOMS), vol. 28, no. 2 , Jun. 2002, pp. 135–151.
[Cooley and Tukey 1965] J. Cooley and J. Tukey, “An algorithm for the machine computation of the complex Fourier series,” Mathematics of Computation, vol. 19, 1965, pp. 297–301.
[Demmel et al 1999] J. Demmel, S. Eisenstat, J. Gilbert, X. Li, and J. Liu, “A supernodal approach to sparse partial pivoting,” SIAM Journal on Matrix Analysis and Applications, vol. 20, no. 3, pp. 720–755.
[FLUENT 2006] FIDAP finite element for computational fluid dynamics analysis home page. http://www.fluent.com/software/fidap/index.htm
[Goodale et al 2003] T. Goodale, G. Allen, G. Lanfermann, J. Masso, T. Radke, E. Seidel, and J. Shalf, “The cactus framework and toolkit: Design and applications,” in Vector and Parallel Processing (VECPAR’2002), 5th International Conference, Springer, 2003.
[MathWorks 2006] The MathWorks, MATLAB Function Reference, 2006.
[OSKI 2006] OSKI home page. http://bebop.cs.berkeley.edu/oski/about.html

Krste Asanovíc, Rastislav Bodik, Bryan Catanzaro, Joseph Gebis, Parry Husbands, Kurt Keutzer, David Patterson, William Plishker, John Shalf, Samuel Williams, and Katherine Yelick (December 18, 2006) The Landscape of Parallel Computing Research: A View from Berkeley, page 9-10 http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-183.pdf

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