Numerical Methods for PDEs Integral Equation Methods, Lecture 1 Discretization of Boundary Integral equations Notes by Suvranu De and J. White Apri23,2003
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 18 and 2a Kind Integral Equations Collocation, Galerkin and Nystrom theory Alternative Integral Formulations Ansatz approach and Green's theorem SMA+HPC⊙2003M Discretization of Boundary Integral Equations 1
Outline for this Module Fast solvers Fast Multipole and FFT-based methods SMA+HPC⊙2003M Discretization of Boundary Integral Equations 1
Outline 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 SMA+HPC⊙2003M Discretization of Boundary Integral Equations 2
Interior vs Exterior Problems Interior Exterior V2T=0 outside V2T=0 Inside Temperature Temperature known on surface known on surface Temperature in a tank""lce cube in a bath What is the heat flow? Heat flow =Thermal conductivity / sur face an SMA+HPC⊙2003M Discretization of Boundary Integral Equations 3