lec23 - Introduction to Simulation - Lecture 23 Thanks to...

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Unformatted text preview: Introduction to Simulation - Lecture 23 Thanks to Deepak Ramaswamy, Michal Rewienski, and Karen Veroy Fast Methods for Integral Equations Jacob White Outline olving Discretized Integral Equations Using Krylov Subspace Methods Fast Matrix-Vector Products ultipole Algorithms Multipole Representation. Basic Hierarchy lgorithmic Improvements Local Expansions Adaptive Algorithms omputational Results MA-HPC 2003 MIT v +- 2 0 Outside = is given on Surface potential Exterior Problem in Electrostatics First Kind Integral Equation For Charge: Dirichelet Problem potential ( ) ( ) { arg 1 ' surface x x x Green x Ch s Function e D d y S ensit = 14243 MA-HPC 2003 MIT Resonator Discretized Structure Computed Forces Bottom View Computed Forces Top View Drag Force in a Microresonator Courtesy of Werner Hemmert, Ph.D. Used with permission. MA-HPC 2003 MIT Basis Function Approach Piecewise Constant Basis 3-D Laplaces Equation Integral Equation: ( ) 1 if is on panel j j x x = ( ) 0 otherwise j x = Discretize Surface into Panels Panel j ( ) ( ) 1 surface x d x x x S = ( ) ( ) { 1 Basis Functions Represent n i i i x x = MA-HPC 2003 MIT 3-D Laplaces Equation Basis Function Approach Centroid Collocation ( ) ( ) 1 , , i i n c j c j i j panel j x G x x d S A = = 144424443 ( ) ( ) 1 1,1 1, 1 ,1 , n c n n n n n c x A A A A x...
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lec23 - Introduction to Simulation - Lecture 23 Thanks to...

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