4301IntroToCSE08

4301IntroToCSE08 - Lecture #1 (Part B) 3 September 2008...

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Applied Mathematics 4301: Numerical Methods for PDEs Introduction to Computational Science & Engineering Lecture #1 (Part B) 3 September 2008 Wed aft. 4:10-6:40 S. W. Mudd Bldg. 1024 Prof. David Keyes, instructor S. W. Mudd Bldg. 215 apma4301@gmail.com Yan Yan, teaching assistant S. W. Mudd Bldg. 292 yy2250.columbia.edu
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Outline • Context of CS&E – Perspective, historical to present – Definitions and examples • Content of CS&E – Some great themes – An important equation and its discretization
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Three “pillars” of scientific investigation • Experiment • Theory • Simulation (“theoretical experiments”) Computational simulation := “a means of scientific discovery that employs a computer system to simulate a physical system according to laws derived from theory and experiment”
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Can simulation produce more than “insight”? “The purpose of computing is insight , not numbers… the purpose of computing numbers is not yet in sight.” R. W. Hamming (1961) “What changed were simulations that showed that the new ITER design will, in fact, be capable of achieving and sustaining burning plasma.” R. L. Orbach (2003, in Congressional testimony about why the U.S. is rejoining the International Thermonuclear Energy Reactor (ITER) consortium) “The computer literally is providing a new window through which we can observe the natural world in exquisite detail.” J. S. Langer (1998)
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Can simulation lead to scientific discovery? Images c/o R. Cheng (left), J. Bell (right), LBNL, and NERSC 2003 SIAM/ACM Prize in CS&E (J. Bell & P. Colella) Instantaneous flame front imaged by density of inert marker Instantaneous flame front imaged by fuel concentration
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Turbulent combustion example… • Simulation models and methods: Detailed chemical kinetics with 84 reactions and 21 species Acoustically filtered compressible fluid model Adaptive mesh refinement, 10 4 × speedup Message-passing parallelism, 2048 procs • Reaction zone location a delicate balance of fluxes of: species, momentum, internal energy • Directly relevant to: engines, turbines, furnaces, incinerators (energy efficiency, pollution mitigation) • Component model of other computational apps: firespread, stellar dynamics, chemical processing • Theory, experiment, and simulation feed on and enrich each other This simulation sits at the pinnacle of numerous prior achievements in experiment, theory , and computer science
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Computation vs. Theory • Computation is usually better for: – Generality (dimension, geometry, properties, boundary conditions) – Transferability of technique (to less expert users) • Theory is usually better for: – Compactness – Generalizability – Insight
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Computation vs. Experiment • Computation is usually better for: – Economy – Feasibility – Latency (from posing question to first results) – Idealizations (can create any desired “world”) – Safety and/or political repercussions • Experiment is usually better for: – Reliability – Reality
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Example: Recent Gordon Bell “special” prize Cortical bone Trabecular bone
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This note was uploaded on 08/30/2011 for the course APMA 4301 taught by Professor Keyes during the Fall '08 term at Columbia.

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4301IntroToCSE08 - Lecture #1 (Part B) 3 September 2008...

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