CS 3220: Introduction to Scientific Computing. Steve Marschner Spring 2010
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1 CS 3220: Introduction to Scientific Computing Steve Marschner Spring 2010
2 scientific computing: The use of computers to solve problems that arise in science (and engineering, medicine, ). numerical methods: Algorithms (methods) for solving problems with real numbers by numerical (as opposed to symbolic) means. If your variables represent real-valued quantities, you re doing numerical computing. Perhaps surprising are: audio (stream of sound pressure samples) video (grids of intensity or color samples) computational geometry (positions in space) computer graphics and vision (geometry, color, light ) information retrieval (more on this in a moment) with abundant computing power, more applications are using numerical methods all the time.
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4 Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of proteins Climatology: predicting global warming
5 Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of proteins Climatology: predicting global warming U.S. FDA Steven W. Smith dspguide.com
6 Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of proteins Climatology: predicting global warming
7 Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of proteins Climatology: predicting global warming
8 Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of proteins Climatology: predicting global warming Thomas Splettstoesser Wikimedia Commons
9 Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of proteins Climatology: predicting global warming Simulated deformation of citrate synthase during substrate binding Kalju Kahn, UCSB
10 Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of proteins Climatology: predicting global warming NOAA
11 Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of proteins Climatology: predicting global warming Robert A. Rohde
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13 Numerical computing in automotive engineering Safe cars: electronic stability control Autonomous vehicles: path planning
14 Numerical computing in automotive engineering Safe cars: electronic stability control Autonomous vehicles: path planning images from: Liebemann et al. Safety and Performance Enhancement: The Bosch Electronic Stability Control (ESP) in The 19th International Technical Conference on the Enhanced Safety of Vehicles (ESV)
15 Yaw rate control at work Fifth Gear demo of Bosch ESP system
16 Numerical computing in automotive engineering Safe cars: electronic stability control Autonomous vehicles: path planning Liebemann et al. Liebemann et al.
17 Yaw rate control by braking Fifth Gear demo of Bosch ESP system
18 Numerical computing in automotive engineering Safe cars: electronic stability control Mark Campbell Cornell DARPA Urban Challenge team Autonomous vehicles: path planning
19 Numerical computing in automotive engineering Safe cars: electronic stability control Autonomous vehicles: path planning Mark Campbell Cornell DARPA Urban Challenge team
20 Mark Campbell Cornell DARPA Urban Challenge team
21 Mark Campbell Cornell DARPA Urban Challenge team
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23 Numerical computing in entertainment Game physics: new kinds of gameplay Movie graphics: realistic lighting Movie vision: camera tracking, or matchmove
24 Numerical computing in entertainment Game physics: new kinds of gameplay Movie graphics: realistic lighting Movie vision: camera tracking, or matchmove Crytek GmBH advertisement for CryEngine 2 game engine
25 Numerical computing in entertainment Game physics: new kinds of gameplay Movie graphics: realistic lighting Movie vision: camera tracking, or matchmove Hand with Reflecting Sphere. M. C. Escher, lithograph Gene Miller & Ken Perlin, 1982
26 Numerical computing in entertainment Game physics: new kinds of gameplay Movie graphics: realistic lighting Movie vision: camera tracking, or matchmove Real environment, computed objects Jonas Unger
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28 Numerical computing in entertainment Game physics: new kinds of gameplay Movie graphics: realistic lighting Movie vision: camera tracking, or matchmove Torr & Zisserman, in Vision Algorithms: Theory and Practice, 2000
29 Rendered model added Scenespector Systems VooCAT product demo Zaha Hadid Architects proposed Guggenheim Vilnius museum Camera footage
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31 Numerical computing in non-numerical applications Information retrieval: Google s PageRank
32 Numerical computing in non-numerical applications Information retrieval: Google s PageRank Idea 1: importance = citation count simple integer exact answer Idea 2: importance = citation count weighted by importance now it is a self-referencing definition for a real-valued quantity (and it must be approximated numerically) Computing PageRank works out to be a linear algebra problem: finding the largest eigenvalue of a matrix.
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34 Problem taxonomy linear or nonlinear? how many unknowns? what kind of equations? LINEAR 1-D n-d solve minimize diff. eq. (arithmetic) (projection) linear ODEs linear systems linear least squares linear PDEs It s all about converting hard problems to easier ones. NONLINEAR 1-D n-d solve minimize diff. eq. root finding nonlinear equations minimum searching optimization ODEs PDEs go that way!
35 Method characteristics accuracy stability robustness Never in the history of mankind has it been possible to produce so many wrong answers so quickly! Carl-Erik Fröberg
36 prerequisites calculus, linear algebra some programming experience Matlab CS1132: Transition to Matlab A one-credit course for students who know another language (e.g. Java) and need to map the ideas over to Matlab. Informational meetings: Tuesday (1/26) 3:35 Phillips 219 Thursday (1/28) 4:40 Thurston 205
37 course mechanics
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