lec24_notes

# lec24_notes - Numerical Methods for PDEs Integral Equation...

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Numerical Methods for PDEs Integral Equation Methods, Lecture 4 Formulating Boundary Integral Equations Notes by Suvranu De and J. White April 30, 2003

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1 Outline Slide 1 Laplace Problems Exterior Radiation Condition Green’s function Ansatz or Indirect Approach Single and Double Layer Potentials First and Second Kind Equations Greens Theorem Approach First and Second Kind Equations 23 - D L a p l a c e P r o b l e m s 2.1 Diferential Equation Slide 2 Laplace’s equation in 3-D 2 u ( ~x )= 2 u ( ~x ) ∂x 2 + 2 u ( ~x ) ∂y 2 + 2 u ( ~x ) ∂z 2 =0 where ~x = x, y, z and is bounded by Γ . 2.2 Boundary Conditions Slide 3 Dirichlet Condition u ( ~x u Γ ( ~x ) ~x Γ OR Neumann Condition ∂u ( ~x ) ∂n ~x = Γ ( ~x ) ~x ~x Γ PLUS A Radiation Condition 2.2.1 Radiation Condition Slide 4 The Radiation Condition lim k ~x k→∞ u ( ~x ) 0 not speci±c enough! Need lim k ~x k→∞ u ( ~x ) O ( k ~x k 1 ) 1
OR lim k ~x k→∞ u ( ~x ) O ( k ~x k 2 ) 2.3 Greens Function Slide 5 Laplace’s Equation Greens Function 2 G ( ~x )=4 πδ ( ~x )

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## This note was uploaded on 11/08/2011 for the course AERO 16.872 taught by Professor Danielhastings during the Fall '03 term at MIT.

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lec24_notes - Numerical Methods for PDEs Integral Equation...

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