Source: Center for Applied Scientific Computing (CASC) at LLNL.

**Course Details:**

Time: TR 9:30-10:45am

Room: Van Vleck Hall B309

Instructor: Saverio Spagnolie

Piazza page (all other discourse)

**Course Content:**

The goal of this course is to provide a graduate-level introduction to numerical linear algebra and the numerical solution of elliptic partial differential equations. Topics in numerical linear algebra to be covered include matrix decomposition theorems, conditioning and stability in the numerical solution of linear systems, and iterative methods. With these tools in hand, we will proceed to discuss the finite element method, continuous and discontinuous Galerkin methods, multigrid methods, and error estimates. We will also cover boundary element and boundary integral techniques for the numerical solution of PDEs recast into integral form. Coding up and exploring different numerical methods will play a substantial role in the course.

**Textbooks:**

For numerical linear algebra we will work through most of the following book, I suggest that you acquire it:

For the finite element method a short, accessible, and affordable option which I suggest you acquire is:

As supplementary texts consider the following (they will be on reserve in the AMP Library in Chamberlain Hall):- Braess, Finite Elements (Cambridge Univ Press)
- Brenner & Scott, The Mathematical Theory of Finite Element Methods (Springer)

**Homework/Grading:**

The final grade will be determined by scores on homework assignments, which will be both analytical and computational in nature, and on a course project. Students are welcome to work together on homework sets but are required to code/write up their own solutions.

**Miscellaneous:**

- Journal of Computational Physics
- SIAM Journal on Scientific Computing
- List of finite element software packages
- Top Ten Algorithms of the 20th Century