Numerical Methods for PDEs Integral Equation Methods, Lecture 4 Formulating Boundary Integral Equations Notes by Suvranu De and J. White Apri30,2003
Outline 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 SMA+HPC⊙2003M Formulating Equations 1
3-D Laplace Differential Equation Problems Laplace's equation in 3-D 02(x)82u(x),82u() VAu(i) 0 where =,y,z∈ and n is bounded by r SMA+HPC⊙2003M Formulating Equations 2
3-D Laplace Boundary Conditions Problems Dirichlet condition ()=ur()∈ OR Neumann Condition 0u(d)8ur() c∈T an PLUS A Radiation Condition SMA+HPC⊙2003M Formulating Equations 3
3-D Laplace Boundary Conditions Problems Radiation Condition The Radiation Condition 10m|d→0()→>0 not specific enough! Need →。 ()→O(列-) OR 12mix(6)→O(|l-2 SMA+HPC⊙2003M Formulating Equations 4