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

Course Outline Overview of pdes(1) o Finite differences methods(6) Finite volume methods(3) Finite element methods(7) Boundary integral methods(6)

Motivation Consider a standard second order finite difference discretization

1 Background Brandt(1973)published first paper SLIDE 1 Offers the possibility of solving a problem with work and storage propor tional to the number of unknowns Well developed for elliptic proble

1 Motivation SLIDE 1 Consider a standard second order finite difference discretization of V-u= on a regular g 1.2. and 3 dimensions 1.1 1D Finite differences

最小二乘法 一、线性最小二乘法 二、非线性最小二乘法 1.改进的 Gauss-Newton-法 2. Levenberger-Marquart-方法

1.1 线性代数基础 1.2 向量序列与矩阵序列 1.3 几类特殊矩阵 1.4 数值域 1.5 Chebyshev 多项式