1 Outline for this module Overview of Integral Equation Methods Important for many exterior problems (Fluids, Electromagnetics, Acoustics Quadrature and Cubature for computing integrals One and Two dimensional basics Dealing with Singularities 1st and 2nd Kind Integral Equations Collocation, Galerkin and Nystrom theory Alternative Integral Formulations Ansatz approach and Green's theorem Fast Solvers Fast Multipole and FFT-based methods 2 Outline SLIDE 2 Integral Equation Methods Exterior versus interior problems Start with Standard solution methods Collocation Method Galerkin Method Some issues in 3D 3 Interior vs Exterior Problems SLIde 3 Interior Exterior yn on surtace known on surfac Temperature in a tank""Ice cube in a bath What is the heat Heat flow =Thermal conductivity sur face an Note 1 Why use integral equation methods? For both of the heat conduction examples in the above figure, the temperature, T, is a function of the spatial coordinate, z, and satisfies V2T(a)=0. In both1 Outline for this Module Slide 1 Overview of Integral Equation Methods Important for many exterior problems (Fluids, Electromagnetics, Acoustics) Quadrature and Cubature for computing integrals One and Two dimensional basics Dealing with Singularities 1st and 2nd Kind Integral Equations Collocation, Galerkin and Nystrom theory Alternative Integral Formulations Ansatz approach and Green’s theorem Fast Solvers Fast Multipole and FFT-based methods. 2 Outline Slide 2 Integral Equation Methods Exterior versus interior problems Start with using point sources Standard Solution Methods Collocation Method Galerkin Method Some issues in 3D Singular integrals 3 Interior Vs Exterior Problems Slide 3 Interior Exterior Temperature known on surface 2 ∇ = T 0 inside 2 ∇ = T 0 outside Temperature known on surfac "Temperature in a tank" "Ice cube in a bath" What is the heat flow? Heat flow = Thermal conductivity
surface ∂T ∂n Note 1 Why use integral equation methods? For both of the heat conduction examples in the above figure, the temperature, T , is a function of the spatial coordinate, x, and satisfies ∇2T (x)=0. In both 1