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

本文首先介绍了重复数据删除技术的定义分类,以及一般过程。然后对重复数据删除领域一些热门问题的研究现状进行了总结。热门的研究问题包括主存储和二级存储数据集特性、数据划分方法、减轻磁盘索引瓶颈、提高恢复性能、可靠性、可扩展性等。最后通过对研究现状进行总结,结合存储和高性能计算的新兴技术,指出重复数据删除技术未来可能的研究方向

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