lec24_notes

lec24_notes - Numerical Methods for PDEs Integral Equation...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Numerical Methods for PDEs Integral Equation Methods, Lecture 4 Formulating Boundary Integral Equations Notes by Suvranu De and J. White April 30, 2003
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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 )
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

lec24_notes - Numerical Methods for PDEs Integral Equation...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online