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AMS 290B Advanced Topics in the Numerical Solution of PDEs Topic 2008: An Introduction to Parallel Computation and Large CFD Codes Nic Brummell (831) Applied Math & Statistics (AMS) University of California, Santa Cruz

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Maybe we want to model something complicated …

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Global simulations: Differential rotation/Dynamo Brun, Brown, Browning, Clune, Elliot, Miesch, Toomre (University of Colorado) Largest global simulations in the world – spherical harmonic degree l ~ O(1000) Problem: resolves from largest scale down => diffuses smallest scale ~ supergranules

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Local simulations: Convection zone and tachocline

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Local simulations: Penetrative convection movie Brummell, Clune, Toomre

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Local simulations: Magnetic transport? Tobias, Brummell, Clune, Toomre

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Magnetic buoyancy?: 1D shear (Grad student: Geoff Vasil ) Success? But this was all very laminar. How about a much more turbulent case? Success? Much harder to produce clean rising tubes. Magnetic field feeds back strongly on shear that manufactures field.

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Side viewTop view 3D simulation (Cattaneo, 1999)

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3D simulation - Cattaneo, 1999 Temp flucs near surface top B middle ->

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Cost! One simulation costs 60,000 supercomputing hours. = 2500 days = 83 months = 7 years! How come we’ve done so many? Are we that old? NO! NO! (don’t be cheeky) PARALLEL COMPUTERS PARALLEL COMPUTERS => 60,000 supercomputing hours can be done in 1 wall clock hour on 60,000 processors (or 120 wall clock hours = 5 days on 500 processors)

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Computing power steadily increases! Moore’s Law: (Gordon E. Moore, Intel co-founder, “Electronics Magazine”, 1965) “Number of transistors that can be placed cheaply on an integrated circuit board will double every two years” ~ computing power doubles every two years = exponential rate of increase! Can link almost any computational capability to Moore’s Law: Processing speed Memory capacity Resolution of digital cameras!

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Computing power steadily increases! Pentium Pentium II Pentium III Itanium 2 Itanium 2+cache Year 286 Intel processors Double every 2 years Double every 18 months No of transistos ,000,000

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Computing power steadily increases! However … 1. Exponentially improving hardware does not mean exponentially improving software to go with it! Wirth’s Law: “Software gets slower faster than hardware gets faster” Software must get larger and more complex = slower! 2.Moore’s Law can’t go on forever (even Moore acknowledged this). Technological singularity?? Eventually transistors will become size of an atom. Krauss & Starkman: 600 years. 3.BUT new technology come along and replace integrated circuits? (R. Kurzweil: “The Law of Accelerating Returns”)

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Computing power steadily increases!

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SpecificationCray-1AIBM POWER5+Approx Ratio Year installed ArchitectureVector processorDual Cluster of scalar CPUs Number of CPUs 1~5,0005,000:1 Clock Speed12.5 nsec (80 MHz)0.53 nsec (1.9 GHz)24:1 Peak perf per CPU160 MFLOPS7.6 GFLOPS48:1 Peak perf per system 160 MFLOPS~38 TFLOPS250,000:1 Sustained performance ~50 MFLOPS~4 TFLOPS80,000:1 Memory8 Mbytes~10 Tbytes1,000,000:1 Disk Space2.5 Gbytes~100 Tbytes40,000:1

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Computing power steadily increases!

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Technology over the years: 1942 ENIAC kops

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Technology over the years: 1947 Whirlwind 3

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Technology over the years: 1951 Univac 250 kops

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Technology over the years: IBM 1950s IBM 650 IBM 701 IBM 704

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Technology over the years: 1964 IBM 360

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Technology over the years: 1965 CDC Mflops

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Technology over the years: 1976 Cray Mflops

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Technology over the years: 1978 VAX

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Technology over the years: 1982 Cray X-MP 941 Mflops

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Technology over the years: 1985 TM CM-1 1 Gflops

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Technology over the years: 1990 NEC SX2/3 23 Gflops

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Technology over the years: 1993 Cray T3D 1993 also: TM CM-5 ~ 65 Gflops, Intel Paragon ~ 143 Gflops

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Technology over the years: 2002 NEC ESS Fastestin world until 2004 Holistic simulations of global earth climate and oceans down to 10km resolution 5120 processors 35 Tflops

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Technology over the years: 2007 IBM Blue Gene/L Fastest machine in the world! ~ 213,000 cpus 596 Tflops peak, 478 sustained

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Technology over the years: 2007 Cray XT5

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What is the point of this course? Learn how to harness all this computing power! In particular, learn how to program MASSIVELY PARALLEL MACHINES Elusive mixture of theory and practice … Highly interdisciplinary! These days need: Engineering skills: architecture, hardware, network knowledge Mathematical skills: applied math methods, numerical analysis Computer science skills: algorithm design, software engineering, compilers, operating systems, ftp, … Scientific skills: design of problem, setup of models/equations, analysis of results Artistic skills: visualisation, movies, …

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The syllabus PART A: CONCEPTS oIntro to Parallel Computing Parallel machine models Parallel programming models oDesigning Parallel algorithms Partitioning, communication, agglomeration, mapping Performance analysis PART B: TOOLS MPI OpenMP Debugging, Performance, Analysis (IDL, VAPOR) PART C: CASE STUDIES Spectral Methods (HPS) Finite-Volume PART D: SPECIAL TOPICS IN TURBULENCE DNS vs LES/SGS AMR

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Expectations Course is BRAND NEW = an EXPERIMENT! Materials are “in preparation” (sorry, guinea pigs!) Expectations of the student: oLearn something useful! oThere will be exercises and tasks oBut very seldom “right” and “wrong” answers oOften I won’t know the answer! oThe expectation is only that the student try and make use of what they’ve learned.

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Baseline TEST!

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