CS 3220: Introduction to Scientific Computing · Numerical computing in science and medicine...
Transcript of CS 3220: Introduction to Scientific Computing · Numerical computing in science and medicine...
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CS 3220: Introduction toScientific Computing
Steve MarschnerSpring 2010
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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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Numerical computing in science and medicine
Computed tomography: seeing into the body
X-ray crystallography: learning the shape of proteins
Climatology: predicting global warming
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Numerical computing in science and medicine
Computed tomography: seeing into the body
X-ray crystallography: learning the shape of proteins
Climatology: predicting global warming
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Numerical computing in science and medicine
Computed tomography: seeing into the body
X-ray crystallography: learning the shape of proteins
Climatology: predicting global warming
![Page 7: CS 3220: Introduction to Scientific Computing · Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of](https://reader036.fdocuments.us/reader036/viewer/2022071022/5fd72381a1014129a54aa767/html5/thumbnails/7.jpg)
Numerical computing in science and medicine
Computed tomography: seeing into the body
X-ray crystallography: learning the shape of proteins
Climatology: predicting global warming
![Page 8: CS 3220: Introduction to Scientific Computing · Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of](https://reader036.fdocuments.us/reader036/viewer/2022071022/5fd72381a1014129a54aa767/html5/thumbnails/8.jpg)
Numerical computing in science and medicine
Computed tomography: seeing into the body
X-ray crystallography: learning the shape of proteins
Climatology: predicting global warming
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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
, UCS
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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
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Numerical computing in science and medicine
Computed tomography: seeing into the body
X-ray crystallography: learning the shape of proteins
Climatology: predicting global warming
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Numerical computing in automotive engineering
Safe cars: electronic stability control
Autonomous vehicles: path planning
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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)
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Yaw rate control at work
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Numerical computing in automotive engineering
Safe cars: electronic stability control
Autonomous vehicles: path planning
Liebe
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Yaw rate control by braking
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Numerical computing in automotive engineering
Safe cars: electronic stability control
Autonomous vehicles: path planning
Mark
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Numerical computing in automotive engineering
Safe cars: electronic stability control
Autonomous vehicles: path planning
Mark
Camp
bell—
Corn
ell DA
RPA U
rban
Chall
enge
team
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Mark
Camp
bell—
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RPA U
rban
Chall
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team
![Page 21: CS 3220: Introduction to Scientific Computing · Numerical computing in science and medicine Computed tomography: seeing into the body X-ray crystallography: learning the shape of](https://reader036.fdocuments.us/reader036/viewer/2022071022/5fd72381a1014129a54aa767/html5/thumbnails/21.jpg)
Mark
Camp
bell—
Corn
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RPA U
rban
Chall
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team
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Numerical computing in entertainment
Game physics: new kinds of gameplay
Movie graphics: realistic lighting
Movie vision: camera tracking, or “matchmove”
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Numerical computing in entertainment
Game physics: new kinds of gameplay
Movie graphics: realistic lighting
Movie vision: camera tracking, or “matchmove”
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Numerical computing in entertainment
Game physics: new kinds of gameplay
Movie graphics: realistic lighting
Movie vision: camera tracking, or “matchmove”
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Numerical computing in entertainment
Game physics: new kinds of gameplay
Movie graphics: realistic lighting
Movie vision: camera tracking, or “matchmove”
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Real environment,computed objects
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Numerical computing in entertainment
Game physics: new kinds of gameplay
Movie graphics: realistic lighting
Movie vision: camera tracking, or “matchmove”
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Numerical computing in “non-numerical” applications
Information retrieval: Google’s PageRank
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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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Problem taxonomy
linear or nonlinear?
how many unknowns?
what kind of equations?
solve minimize diff. eq.
1-D
n-D
root finding minimum searching ODEs
nonlinear equations optimization PDEs
solve minimize diff. eq.
1-D
n-D
(arithmetic) (projection) linear ODEs
linear systems
linear least squares linear PDEsLI
NEA
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It’s all about converting hard problems to easier ones.
go that way!
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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
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prerequisites
calculus, linear algebra
some programming experience
Matlab
CS1132: Transition to MatlabA 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 219Thursday (1/28) 4:40 Thurston 205
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course mechanics
http://www.cs.cornell.edu/Courses/cs3220