MA788

MA788 - Numerical Nonlinear Partial Differential Equations

Spring 2022

Instructor

Dr. Alina Chertock Office Location: SAS 4152 Phone: (919) 515-3200 Fax: (919) 515-0657 Email: [email protected] Web Page: http://chertock.wordpress.ncsu.edu Office Hours: by appointment

Course Meetings

Days: Tuesday and Thursday Time: 11:45 a.m.-1 p.m. Campus: Main Location: SAS 1218

Course Resourses

To access your courses and project spaces, use WolfWare.

Course Description

The course is intended as a review of modern numerical techniques for a wide range of time-dependent nonlinear partial differential equations. Topics include Finite Difference, Finite Volume, Particle and Hybrid Eulerian-Lagrangian Methods; Splitting Methods and Implicit-Explicit Discretization; Spectral and Pseudo-Spectral Methods including Stochastic Galerkin and Stochastic Collocation Methods, and others. A significant part of the course will be devoted to a variety of applications including compressible and incompressible fluids, geophysical and atmospheric flows, various biological and traffic flow models, and others. The course is offered as a balanced blend of analysis and computation and should be very useful for students in applied and computational mathematics, engineering, and science. The course is designed for students who are familiar with basic concepts of numerical analysis and scientific programming. The course grade will be determined by a final project and presentation to the class.

Learning Outcomes

By the end of the course, the students will be able to:

• Outline key numerical methods for nonlinear time-dependent partial differential equations.
• Identify common and distinguished properties of these methods.
• Produce computer codes for benchmark model problems.
• Apply numerical methods to varies real word applications.

Requisites and Restrictions

Numerical analysis, ordinary and partial differential equations, scientific programming. Some programming experience (Matlab, Fortran, C, C++, ...). It is possible to participate in this class without part of the recommended background, but this will require you to do a lot of extra reading. Students from all scientific and engineering departments are welcome.

Textbook

No textbook is required. The instructor will use her own notes. Alternate reading will be posted in Moodle.

Homework and Projects

• Some homework will be assigned.

Final Projects

• A number of suggested projects will be posted on this webpage.
• You may either chose one of the suggested projects or a project of your own.
• Before start working on the project, you will need to discuss details of the project (including specific numerical experiments you will conduct) with the instructor.
• You will need to prepare your final project report in LaTeX.

LaTeX Resources:

• Essential LateX
• Essential Mathematical LateX
• LateX 2e introduction
• LATEX Software and Documentation
• Easy to install LateX for Windows
• Easy to install LateX for Macs

Tests and Exams

There will be a number of homework assignments and a final project.

Grading

Homework, final project and inclass presentation - 100%. This Course uses the Following (Non-Standard) Letter Grading Scale: 86≤A≤100, 71≤B≤85, 61≤C≤70, 55≤D≤60, F≤55 (+ and - will also be used). Requirements for Auditors (AU): Information about and requirements for auditing a course can be found at REG 02.20.04. Policies on Incomplete Grades: If an extended deadline is not authorized by the Graduate School, an unfinished incomplete grade will automatically change to an F after either (a) the end of the next regular semester in which the student is enrolled (not including summer sessions), or (b) by the end of 12 months if the student is not enrolled, whichever is shorter. Incompletes that change to F will count as an attempted course on transcripts. The burden of fulfilling an incomplete grade is the responsibility of the student. The university policy on incomplete grades is located at REG 02.50.03. Additional information relative to incomplete grades for graduate students can be found in the Graduate Administrative Handbook in Section 3.17.G. Attendance: Students are expected to arrive on time, to contribute to group work and class discussions, and to stay until the class ends. Attendance at all meetings of the class is expected. Absences: NCSU policy, including what constitutes an 'Excused Absence', is at REG 02.20.03.

Notifications

• Please check the course webpage regularly, as it will be continuously updated with announcements, any changes in the schedule, homework problems, solutions, review sheets, and other additional course materials.
• Students will also be notified in class or via email of announcements associated with this course. The email address registered with the NCSU online directory will be used for this purpose. It is the student's responsibility to maintain a valid email address and check the email sent to it.

End-of-semester class evaluation

• Schedule: Online class evaluations will be available for students to complete during the last week of class
• Students will receive an email message directing them to a website where they can login using their Unity ID and complete evaluations.
• All evaluations are confidential; instructors will never know how any one student responded to any question, and students will never know the ratings for any particular instructors.
• Evaluation website: https://oirp.ncsu.edu/classeval/for-students/
• Student help desk: [email protected]
• More information about ClassEval: https://oirp.ncsu.edu/classeval/about-classeval/

Academic Integrity

Academic Integrity: Students are required to comply with the university policy on academic integrity found in the Code of Student Conduct at Code of Student Conduct (POL 11.35.01). Academic Honesty: See POL 11.35.01 for a detailed explanation of academic honesty. Honor Pledge: Your signature on any test or assignment indicates "I have neither given nor received unauthorized aid on this test or assignment."

Accommodations for Disabilities

Reasonable accommodations will be made for students with verifiable disabilities. To take advantage of available accommodations, student must register with the Disability Services Office located at Holmes Hall, Suite 304, Campus Box 7509, 919-515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation at REG 02.20.01.

Non-Discrimination Policy

NC State provides equal opportunity and affirmative action efforts, and prohibits all forms of unlawful discrimination, harassment, and retaliation ("Prohibited Conduct") that are based upon a person's race, color, religion, sex (including pregnancy), national origin, age (40 or older), disability, gender identity, genetic information, sexual orientation, or veteran status (individually and collectively, "Protected Status"). Additional information as to each Protected Status is included in POL 04.25.02 (Discrimination, Harassment and Retaliation Complaint Procedure). NC State's policies and regulations covering discrimination, harassment, and retaliation may be accessed at POL 04.25.02 or the Office for Institutional Equity and Diversity. Any person who feels that he or she has been the subject of prohibited discrimination, harassment, or retaliation should contact the Office for Equal Opportunity (OEO) at 919-515-3148.