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Disclaimer The following slides reuse materials from SIGGRAPH 2001 Course Notes on Physically-based Modeling (copyright 2001 by David Baraff at Pixar). UNC Chapel Hill M. C. Lin
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Determining Step Size Explicit Integration Implicit Methods
Too big, unstable! Too small, too slow Adaptive, maybe Ultimately the constants decide! Implicit Methods Taking large steps when possible UNC Chapel Hill M. C. Lin
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An Example UNC Chapel Hill M. C. Lin
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Speed Limitation of Euler’s Method
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Stiff Equations UNC Chapel Hill M. C. Lin
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A Stiff Energy Landscape
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Example: Particle-on-line
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Example: Particle-on-line
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Example: Particle-on-line
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Example: Particle-on-line
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Explicit Integration UNC Chapel Hill M. C. Lin
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Problems UNC Chapel Hill M. C. Lin
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Explicit vs. Implicit Euler Method
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One Step: Implicit vs. Explicit
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Large Systems UNC Chapel Hill M. C. Lin
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Implicit Integration UNC Chapel Hill M. C. Lin
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Implicit Integration UNC Chapel Hill M. C. Lin
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Implicit Integration UNC Chapel Hill M. C. Lin
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Linearized Implicit Integration
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Single-Step Implicit Euler Method
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Solving Large Systems Matrix structure reflects force-coupling:
(i , j)th entry exists iff fi depends on Xj Conjugate gradient a good first choice UNC Chapel Hill M. C. Lin
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