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Math 767, Topics in Numerical Analysis

Multilevel Adaptive Methods and Fast Solvers

Spring 2011

(01/18/2011-05/05/2011)

COURSE DESCRIPTION:

This course is aimed to both practical users and researchers who are interest in multilevel adaptive methods and fast solvers for scientific and engineering computing. We shall focus on numerical solutions for the elliptic equations, and study multigrid method, domain decomposition methods, adaptive mesh method, and etc. Time-dependent problems will be discussed in the future course. In addition, we may also pay attention to finite element/finite volume algorithm abstraction and software development by virtue of an automated finite element/finite volume program generation. Some classical and modern engineering problems such as solid mechanics and fuel cell dynamics are demonstrated as well. More precisely, I plan to cover the following topics:

• Basic iterative methods

• Fast solvers: Conjugate Gradient method and multigrid method

• Domain decomposition methods

• Adaptive multiscale finite element methods

• Iterative methods on nonlinear elliptic equations

• Convection-diffusion problems

• Automated finite element/finite volume program generation

• Solid mechanics, fuel cell dynamics problems

Lecture notes will be distributed in the class.

PREREQUISITE: MATH 466/MAT 665 or the equivalence are the minimum, MATH 765/766 are the optimal.
 

TEST AND GRADING POLICY: There will be four (75-120 minutes) tests given in this semester, the lowest one will be dropped. Each test is worth 25%, covering the recently learned 1-2 chapters. The rest 25% points go to homework.

Grades will be assigned on the basis of total 100 points, distributed as follows:

Final course letter grades will be assigned as follows:

NOTE: Your grade will be based EXCLUSIVELY on the tests, homework and class attendance record.

CLASS POLICIES:

HOMEWORK:

The homework problems that you should work after each lecture are on the assignment list. You are required to do the homework outside of class for each section after we have completed the lesson.  Homework are collected on a weekly basis. The tests will be based on the assigned homework questions.

 

ATTENDANCE:

You are required to attend class regularly. If you miss a class for any reason, you are responsible for all missed lectures, materials and announcements made in class.

 

MISSED EXAMS:

You will have one opportunity to make up a test given on a day you were absent if you can provide sufficient reason for this missed exam.

ACADEMIC INTEGRITY:

Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. Academic integrity is a basic guiding principle for all academic activity at University of Nevada, Las Vegas, and all members of the University community are expected to act in accordance with this principle. Consistent with this expectation, the University's Code of Conduct states that all students should act with personal integrity, respect other students' dignity, rights and property, and help create and maintain an environment in which all can succeed through the fruits of their efforts.

Academic integrity includes a commitment not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others. Based on the University's Student Academic Misconduct Policy, a range of academic sanctions may be taken against a student who engages in academic dishonesty.

LECTURE SCHEDULE (Tentatively):