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

**Course Details:**

Time: TuTh: 1:00pm-2:15pm

Room: Van Vleck B131

Office hours: TuTh 2:30pm-3:45pm or by appointment

Instructor: Saverio Spagnolie

Office: Van Vleck 505

Course website: http://www.math.wisc.edu/~spagnolie/Courses/MATH715/index.html

**Textbooks:**

There is no official course textbook. You may be interested in visiting the following supplementary texts, which will be placed on reserve in the Math Library (Van Vleck B224):

- Trefethen & Bau, Numerical Linear Algebra (SIAM)
- Golub & Van Loan, Matrix Computations (JHU Press)
- Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method (Dover)
- Brenner & Scott, The Mathematical Theory of Finite Element Methods (Springer)
- Briggs, Henson & McCormick, A Multigrid Tutorial (SIAM)

**Course Content:**

Topics: numerical linear algebra, finite element methods, boundary integral method.

We will begin by covering a number of issues in numerical linear algebra, such as 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.

Incoming students should be comfortable with programming (in C++, Fortran, Python, or Matlab, or...), should have completed coursework in linear algebra, and should have familiarity with solving partial differential equations.

**Homework/Grading:**

The final grade will be determined by scores on homework assignments, which will be both analytical and computational in nature. Feel free to discuss the homework with each other, but you are required to code/write up your own solutions. Your work and results should be communicated clearly: *points will be deducted for lack of clarity!*

**Homework sets:**

Homework set #1 (Due 2/21/2013): HW #1

Homework set #2 (Due 3/12/2013): HW #2

Homework set #3 (Due 4/4/2013): HW #3 (soln to 1a, courtesy of Leland Jefferis)

Homework set #4 (Due 4/25/2013): HW #4

Homework set #5 (Due 5/16/2013): HW #5

**Miscellaneous:**

- Journal of Computational Physics
- SIAM Journal on Scientific Computing
- List of finite element software packages