Presented in this lecture are both forward and inverse analyses for initial and boundary value problems in civil engineering field. In the forward analysis, fundamental formulations of finite element method and boundary element method are explained, and in the inverse analysis, mathematical treatment for linearized inverse problems is presented.
To understand fundamentals of forward and inverse analyses of initial and boundary value problems in civil engineering.
1. Introduction ; forward and inverse problems
2. Variational method - stationary problem & basic formula
3. Variational method - 2D,3D problems, Lagrange窶冱 multiplier
4. Variational method - boundary conditions, Ritz窶冱 method
5. Weighted residual methods
6. Finite element method - fundamentals on FEM and examples
7. Finite element method - numerical schemes
8. Midterm Examination
9. Boundary element method - fundamentals on BEM
10.Boundary element method - formulation of BEM
11.Boundary element method - numerical implementation
12.Linearized inverse problems
13.Generalized inverse matrix
14.Instability and regularization of inverse problems
Lecture materials will be distributed by the lecturer.
Advanced numerical analyais II (related subject)
Homework(20%) and examination(80%)