1 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
1 Motivation The Poisson problem has a strong formulation a minimization formulation and a weak formulation T weak formulations are more general than the strong formulation in terms of regularity and admissible data SLIDE 2 The minimization/weak formulations are defined by: a space X; a bilinear The minimization/weak formulations identify ESSENTIAL boundary conditions NATURAL boundary conditions ed in a The points of departure for the finite element method are the weak formulation(more generally) the minimization statement (if a is SPD) 2 The dirichlet problem 2.1 Strong Formulation Find u such that