Math  690N:  Advanced Numerical Methods

Fall  2005 @ ISU

  • Instructors

Name

Office

Tel

Email

Office hours

Teaching Schedule

Steven Hou

Carver426

 

48138

 

hou@iastate.edu

 

By appointment

 8/22-10/06 (Week 1-Week 7)
Domain  Decomposition

Hailaing Liu

Carver 434

40392

hliu@iastate.edu

By appointment

 10/11—12/09 (Week 8--Week15)

Level Set Method   

(a tentative syllabus)   (Homework Assigments)

 

 

 

 

  • Lectures:  Section HL, TR 11:00A-12:15P, Black 1026,  08/22/05-12/16/05 
  • Course description: 3 credits course.  This course is designed for graduate students in applied mathematics whose primary interest is in computing and modeling
    of scientific problems.  Provides an overview of some advanced numerical methods that are often used in applied mathematics. Emphasis is put on two classes
    of methods that involve frontiers or interfaces: domain decomposition and level set method. Lectures will be particularly geared to students using or interested in using these approaches in their ongoing/future research.
  • Content:

A. Domain Decomposition Methods
1. Classification of Domain Decomposition Methods (DDM) and Principles for Deriving DDM Iterations
2. Non-overlapping DDM and Examples
3. Applications and Research Topics


B. Level Set Methods
1. Basic concepts of level set method, e.g. motion law, distance function, initialization;
2. Basic techniques: e.g., discretization, projection, re-initialization, data extension;
3. Examples of application: e.g. geometric motion, geometric optics, complex fluids, image segmentation

  • Sample References

    A. D. Keyes and J. Xu, Domain Decomposition Methods in Scientific and Engineering Computing. AMS, Providence, 1994

    B. S. Osher and R. Fedkiw, Level set methods and dynamic implicit surfaces. Applied Mathematical Sciences, 153. Springer-Verlag, New York, 2003
     
  • Prerequisites: Differential equations, Finite difference methods and a programming  language  is preferred.
  • Project Assignments: 
There will be 2X4 project assignments for this course.
Project assignments consist of both theoretical and computational work.
For the computational assignments, we will be using Matlab.
No late project will be accepted.
  • Computing: Enrolled students will have accounts in the computer labs in Carver Hall  449.
    The mathematical software Matlab will be used for all computational project problems.
  • Examinations:   One midterm oral exam and one final take-home project. 
  • Grading Policy:  Project assignments: 60%. Midterm: 20%. Final: 20%.