MATH 5373 (Spring 2022)

Syllabus

Spring 2022 MATH 5373: Finite Element Methods and Solution of Sparse Linear Systems

Instructor: Dr. Tulin Kaman
Email: tkaman@uark.edu
Office: SCEN 218
Office Hours: By appointment

Lecture: MWF 9:40 AM – 10:30 AM in SCEN0205

References:

  • M. G. Larson, F. Bengzon: The Finite Element Method: Theory, Implementation, and Applications.
    Springer, Heidelberg, 2013.
  • T. Davis. Direct Methods for Sparse Linear Systems. SIAM, 2006.Matrix Computations, 4th edition, G.
    H. Golub and C.Van Loan. Johns Hopkins, 2012.
  • Y. Saad. Iterative methods for sparse linear systems (2nd ed.). SIAM, 2003.
    (www-users.cs.umn.edu/~saad/books.html)

Course Description: The course provides an in-depth understanding of numerical methods for the solution of partial di differential equations using Finite Element Methods, Direct and Iterative Methods for the Sparse Linear Systems.

Prerequisites: MATH 4353/5393 Numerical Linear Algebra or department consent

Course Outline: The detailed weekly schedule will be posted on Blackboard.
The Finite Element Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Direct and Iterative Methods for Solving Sparse Linear System . . . . . . . . . . .

Grading: The performance assessments will be based on
Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  60 %
Final Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 %
Grades are assigned according to the percentage scale A  90, B  80, C  70, D  60, F < 60.

Projects: The term projects will be on the use of the finite element element methods in application areas. Depending on your research interest, you will be assigned to a specific project. You will need to work on the projects outside class and I will provide guidance throughout the semester.

  • At the beginning of the semester, each student will give a short presentation to outline his/her research interest. 
  • At the middle of the semester, you will submit a 2-pg written report and give a short presentation to show your progress.
  • At the end of the semester, you will submit your final report outlining the results you have achieved and give a final presentation.

Important Dates:
Final Exam . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wednesday, May 5, 2022. 10:15 AM to 12:15 PM (as listed in UAConnect)

Academic Integrity Policy: Cases of suspected academic dishonesty are referred to the All University Academic Integrity Board for adjudication and will also incur a grade sanction at the discretion of the instructor. The following passage is quoted from the referenced website and is the policy in this course: As a core part of its mission, the University of Arkansas provides students with the opportunity to further their educational goals through programs of study and research in an environment that promotes freedom of inquiry and academic responsibility. Accomplishing this mission is only possible when intellectual honesty and individual integrity prevail. Each University of Arkansas student is required to be familiar with and abide by the University’s Academic Integrity Policy which may be found at http://honesty.uark.edu/policy/index.php There are harsh penalties for violations as prescribed by the Sanction Rubric http://honesty.uark.edu/ sanction-rubric Students with questions about how these policies apply to a particular course or assignment should immediately contact their instructor.

Classroom Etiquette: Students and instructors each have an important role in maintaining a classroom environment optimal for learning, and are expected to treat each other with respect during class, using thoughtful dialogue, and keeping disruptive behaviors to a minimum. Both students and faculty perceive abusive language directed towards others as the most disruptive behavior. Other behaviors that can be disruptive are chatting
and whispering during class, the use of smartphones or laptops for texting or in other ways unrelated to the course, preparing to leave before class is over, and consistently arriving late to class. Inappropriate behavior in the classroom may result in a request to leave the class and/or a referral to the Office of Academic Integrity and Student Conduct.

Disability Act: If you have a physical, psychological, medical or learning disability that may impact your ability to carry out assigned course work, I would urge you to contact the staff in the Division of Student A affairs, Center for Educational Access cea.uark.edu, 209 ARKU, who will review your concerns and determine with you what accommodations are necessary and appropriate. All information and documentation of disability are
confidential.

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