Welcome to MATH 9830 The Finite Element Method in Scientific Computing (Spring 2014)

1. This site: http://www.math.clemson.edu/~heister/math983-spring2014/
2. Blackboard: http://bb.clemson.edu
3. Syllabus
4. deal.II homepage: http://www.dealii.org
5. deal.II manual, tutorials
6. Video lectures
7. Some slides: file:slides.pdf
8. Labs:
   1. lab01.pdf
   2. lab02.pdf
   3. lab03.pdf
   4. lab04.pdf
   5. lab05.pdf

This course teaches practical aspects of the finite element method. We will be using the Open Source library deal.II, which is written in C++. This is a project based course, so large parts of the semester are spent on individual student projects.

Contents:

• basics of FEM, structure of FEM codes, algorithmic aspects
• modern tools for software development (IDEs, debuggers, …)
• some C++ topics (templates, …) used in large software projects
• iterative solvers and preconditioners
• coupled PDEs, block systems
• nonlinear problems
• time discretization
• parallel computations
• software engineering practices

Prerequisites:

• MATH 866 (Finite Element Method) or Numerical Analysis with approval of instructor
• Knowledge of the C++ programming language

Optional reading material:

• The Unix Shell: http://software-carpentry.org/v4/shell/index.html
• A Tour of C++, Stroustrup
• C++ Programming Language (4th Edition), Stroustrup
• The Mathematical Theory of Finite Element Methods, Brenner/Scott
• Theory and Practice of Finite Elements, Ern/Guermond
• Iterative Methods for Sparse Linear Systems, Saad
• Version Control with Subversion: http://software-carpentry.org/v4/vc/commandline.html and http://svnbook.red-bean.com/

See http://www.registrar.clemson.edu/pdf/academicCalendar.pdf for important dates.

Schedule:

• January 8:
  • Introduction
  • Syllabus
  • Course outline, what is deal.II
• January 10:
  • Intro to FEM (Laplace Problem, weak formulation, …)
• January 13:
  • deal.II installation
• January 15:
  • lab1, step-1&2
• January 22:
  • presentations
  • work on step-2&3
• January 27:
  • c++ templates, step-4
• January 29 (snow)
• February 3:
  • constraints for hanging nodes
• February 5:
  • lab3
• February 10:
  • Neumann boundaries, computing errors
• February 14:
  • lab4
• February 17:
  • time dependent problems
• February 19:
  • lab5
• February 24:
  • introduction to linear solvers
• February 26:
  • project work