MATH/CS 715: Methods of Computational Mathematics II, Spring 2015

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


Course Details:

Time: TuTh: 9:30pm-10:45pm

Room: Van Vleck B123

Office hours: TuTh 1:00pm-2:00pm, or by appointment

Instructor: Saverio Spagnolie

Office: Van Vleck 505

Syllabus


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), or may be available online through the math library:

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, 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 2/17/2015): HW #1 (UWlogo.jpg)

Homework set #2 (Due 3/17/2015): HW #2

Reading: Conjugate Gradient Method

Homework set #3 (Due 4/9/2015): HW #3

Mesh generation: DistMesh

Reading: Per-Olof Persson and Gilbert Strang, A Simple Mesh Generator in Matlab, SIAM Rev. (2006).

Enjoy: DistMesh Gallery

Homework set #4 (Due 4/28/2015): HW #4

Homework set #5 (Due 5/12/2015): HW #5


Miscellaneous: