Advanced Topics for Numerical Methods
MATH 612
Fall 2013



Instructor: Horng, Tzyy-Leng
Class Location: Science Hall 411
Class Time: Mon. 1-4 PM
Office Hours: Tue. 9-11 AM


Grade Distribution

40% homeworks
30% midterm
30% final

Text Book

Recipes for Continuation, Harry Dankowica and Frank Schilder, SIAM, 2013.


Syllabus

1.A Continuation Paradigm
2.Encapsulation
3.Construction
4.Toolbox Development
5.Task Embedding
6.Task Embedding
7.The Collocation Continuation Problem
8.Single-Segment Continuation Problems
9.Multisegment Continuation Problems
10.The Variational Collocation Problem
11.Covering Manifolds
12.Single-Dimensional Atlas Algorithms

13.Multidimensional Manifolds

14.Computational Domains

15.Special Points and Events

16.Atlas Events and Toolbox Integration

17.Event Handlers and Branch Switching

18.Pointwise Adaptation and Comoving Meshes

19.A Spectral Toolbox

20.Integrating Adaptation in Atlas Algorithms

21.Toolbox Projects