575. Numerical Solution of Partial Differential Equations. The course goals consist of design, analysis and implementation of the most commonly used numerical methods for solutions to partial differential equations. We will discuss various discretization schemes such as finite difference, finite element and finite volume methods as well as iterative solvers such as multigrid methods. The course will maintain a balance between in-depth mathematical theories for algorithmic techniques and computer implementations and students will have the opportunity to study not only theoretical backgrounds in developing and understanding the numerical algorithms, but also a hands-on experience to implement the methods. Matlab (or scilab) will be used for the computational component of the course and a number of source codes will be provided to minimize the coding efforts from students.

Dietrich Braess. Theory, fast solvers, and applications in solid mechanics, 3rd Ed., Cambridge University, 2007


Note* : Most of lectures will be based on hand outs prepared by the instructor.

Homework assignments in the course consist of both theoretical and computational work. For the computational component, the students should use a language/environment that possesses high level data types so that the students spend more time working with algorithms and not worrying about the details of writing computer code. Matlab is a good choice. Fortran 77/90/95 and C++ with appropriate class libraries can also be used.

Advanced Calculus, Linear Algebra, and familiarity with differential equations.

Topics listed above is temporary and may be modified.