Lecture Room: | B123 Van Vleck Hall |

Lecture Time: | 14:30–15:45 TuTh |

Lecturer: | Jean-Luc Thiffeault |

Office: | 503 Van Vleck |

Phone: | (608)263-4089 |

Email: | |

Office Hours: | Tue 10:00–11:00, Thu 12:30–13:15 |

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.

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)
- Higham, Accuracy and Stability of Numerical Algorithms (SIAM)

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 set #1 (Due 02/08): HW #1 [UWlogo.jpg]

Homework set #2 (Due 03/01): HW #2

lecture |
date |
pages |
topic |

1 | 01/23 | T&B 3–24 | Norms |

2 | 01/25 | T&B 25–36 | The Singular Value Decomposition |

3 | 01/30 | T&B 41–61 | Projectors; QR Factorization & Gram–Schmidt |

4 | 02/01 | T&B 69–85 | Householder Triangularization; Least Squares |

5 | 02/06 | T&B 89–100 | Condition Number; Floating Point Arithmetic |

6 | 02/08 | T&B 102–116 | Accuracy and Stability |

7 | 02/13 | T&B 116–127; 147–150 | Stability of Backsubstitution; LU Factorization |

8 | 02/15 | T&B 147–170 | LU Factorization; Stability of LU |

9 | 02/20 | T&B 172–187 | Cholesky Factorization; Eigenvalue Problems |

10 | 02/22 | T&B 187– | Schur Factorization; |