Overview: This class is about numerical methods for discrete differential forms. After an overview the subject, the course will be divided into 3 parts : Calculus on Manifolds , Discretization of Exterior Calculus, and Finite Element Methods. Suitable for graduate students in Numerical Analysis, Computational Science and Engineering, Mathematics, and Computer Graphics. There are no prerequisites since the class will be self-contained.
Lecture Notes: (Class members access only) Download this file.
Homework Assignments: Available here
Collaboration: Collaboration in homeworks is highly encouraged. Please do discuss and collaborate, but write up your solutions yourself. For the programming part also, discussion is encouraged, but write your own code.
Course Goals: On completing the course students should understand (i) basic exterior calculus; (ii) theory and applications of discrete differential forms; and (iii) basic numerical methods for PDEs and topology using discrete differential forms.
Class Format: Lectures by instructor, 5 homeworks including some simple MATLAB programming, midterm exam, final exam. Lecture notes will be provided through the semester.
Contacts:
Instructor : Prof. Anil N. Hirani, hirani at cs dot uiuc dot edu ; 217-333-2727;
Room 4320 Siebel Center; Office hours Thursdays by appointment.
Teaching Assistant : Evan VanderZee, vanderze at illinois dot edu
Required Textbooks:
Other Resources: Some other useful books, papers, etc.