Source: Center for Applied Scientific Computing (CASC) at LLNL.
Course Details:
Time: TR 2:30-3:45pm
Room: Van Vleck B135
Instructor: Saverio Spagnolie
Piazza page (all other discourse)
Course Content:
The goal of this course is to provide a graduate-level introduction to the numerical solution of partial differential equations, primarily of elliptic type. Topics include the finite element method, continuous and discontinuous Galerkin methods, multigrid methods, and error estimates. The course also covers boundary element and boundary integral techniques for the numerical solution of PDEs recast into integral form. Fast algorithms in numerical linear algebra will be reviewed and incorporated. The course will involve both mathematical analysis and direct implementation, with an aim of a fully integrated understanding of the techniques.
By the end of this course students will be able to compute solutions to elliptic partial differential equations in complex domains using a variety of numerical methods, including the finite element method, boundary integral methods, and the fast multipole method. Moreover, students will be able to show analytically the expected convergence rate of these different methods, whether in the number of iterations or the spatial discretization size, and they will have substantial practice testing the output of numerical simulations to ensure that the expected rate is recovered. They will also be able to solve the large linear systems of equations which arise in these settings efficiently and accurately, and will have an appreciation for which methods are most appropriate depending on the situation.
Textbooks:
For the calculus of variations:
For numerical linear algebra:
For the finite element method:
Homework/Grading:
The final grade will be determined by scores on homework assignments, which will be both analytical and computational in nature, on in-class quizzes, 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:
