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

1 Model problem 1.1 Formulations 1.1.1 Strong formulation LIDE Find a such that for Q a polygonal domain Generalizat ion We look here at a particularly simple but nevertheless illustrative problem

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

Goals Theory A priori A priori error estimates N1 bound various“ measures” of u exact]-un [approximate] in terms of C(n, problem parameters h [mesh diameter, and u

Formulations Model problem Strong Formulation Find u such that Vu=f in n2 a =0 on I for a polygonal domain

Outline Reminder about 1-D 1st and 2nd Kind egns Three-D Laplace Problems Interior Neumann Problem Null space issue First Kind Theory for 3-D Laplace Informal Convergence Theory

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

麻省理工学院：偏微分方程式数字方法（英文版）_lec26

7.1港口规划阶段与可行性研究 7.2港址选择 7.3港口专业区划分 7.4方案比选的综合评价方法 7.5港口经济效益分析

8.7 QTQ02型电缆探测器测试方法综述 8.7.1 电缆探测器用途及基本原理 8.7.2 QTQ02型电缆探测器介绍 8.7.3 QTQ02型电缆探测器使用方法