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fractals & statistical growth 35113.11 Quiz1. Recall how box counting is used to determine the fractal dimension ofan object. Imagine that the result of some experiment or simulation is aninteresting geometric figure.a. What might be the physical/theoretical importance of determining thatthis object is a fractal?b. What might be the importance of determining its fractal dimension?c. Why is it important to use more than two sizes of boxes?d. Below is a figure composed of boxes of side 1.1 1 11 1 11 1 1Use box counting to determine the fractal dimension of this figure.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 351
14High-Performance Computing Hardware,Tuning, and Parallel ComputingC DIn this chapter and in Appendix D we discuss a number of topics associated with highperformancecomputing (HPC). If history can be our guide, today’s HPC hardwareand software will be on desktop machines a decade from now. In Unit I we discussthe theory of a high-performance computer’s memory and central processor design.In Unit II we examine parallel computers. In Appendix D we extend Unit II bygiving a detailed tutorial on use of the message-passing interface (MPI) package,while a tutorial on an earlier package, Parallel virtual machine (PVM), is providedon the CD. In Unit III we discuss some techniques for writing programs that areoptimized for HPC hardware, such as virtual memory and cache. By running theshort implementations given in Unit III, you will experiment with your computer’smemory and experience some of the concerns, techniques, rewards, and shortcomingsof HPC.HPC is a broad subject, and our presentation is brief and given from a practitioner’spoint of view. The text [Quinn 04] surveys parallel computing and MPI from acomputer science point of view. References on parallel computing include [Sterl 99,Quinn 04, Pan 96, VdeV 94, Fox 94]. References on MPI include Web resources[MPI, MPI2, MPImis] and the texts [Quinn 04, Pach 97, Lusk 99]. More recentdevelopments, such as programming for multicore computers, cell computers, andfield-programmable gate accelerators, will be discussed in future books.14.1 Unit I. High-Performance Computers (CS)By definition, supercomputers are the fastest and most powerful computers available,and at this instant, the term “supercomputers” almost always refers to parallelmachines. They are the superstars of the high-performance class of computers. Unixworkstations and modern personal computers (PCs), which are small enough insize and cost to be used by a small group or an individual, yet powerful enough forlarge-scale scientific and engineering applications, can also be high-performancecomputers. We define high-performance computers as machines with a good balanceamong the following major elements:• Multistaged (pipelined) functional units.• Multiple central processing units (CPUs) (parallel machines).−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 352
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Copyright © 2008 by Princeton Univ
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viiicontents2.3 Experimental Error
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7Differentiation & SearchingIn this
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Appendix A: Glossaryabsolute value
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glossary 557control character — A
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glossary 559log in (on) — To sign
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glossary 561supercomputer — The c
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installing ptplot & java developer
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industrial-strength data visualizat
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Appendix D: An MPI TutorialIn this
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an mpi tutorial 595• Open a shell
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an mpi tutorial 597of all the compu
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an mpi tutorial 599TABLE D.1Some Co
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an mpi tutorial 601jobs to MPI. 2 A
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an mpi tutorial 603✞> cd $HOME Do
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an mpi tutorial 605✞/ / MPIhello
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an mpi tutorial 607Argument Namemsg
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an mpi tutorial 609D.3.4 Broadcast
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an mpi tutorial 611D.4 Parallel Tun
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an mpi tutorial 613✝}MPI_Recv ( &
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an mpi tutorial 615✞/ / Code list
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an mpi tutorial 617-1) does not sen
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an mpi tutorial 619D.6.1 Nonblockin
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an mpi tutorial 621D.9 List of MPI
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Appendix E: Calling LAPACK from CCa
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calling LAPACK from C 625E.2 Compil
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software on the CD 627JavaCodes Con
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software on the CD 629JavaCodes Con
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software on the CD 631Applets Direc
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software on the CD 633Fortran77code
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Appendix G: Compression via DWTwith
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compression via DWT with thresholdi
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compression via DWT with thresholdi
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BIBLIOGRAPHY[Abar 93] Abarbanel, H.
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ibliography 643[Erco] Ercolessi, F.
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ibliography 645[L&F 93] Landau, R.
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ibliography 647[P&W 91] Pinson, L.
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ibliography 649[VdeV 94] van de Vel
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IndexAbstract data structures,70Abs
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index 653drand, 114Driving force, 2
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index 655Libraries, see Subroutines
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index 657structured, 10for virtual
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