Time and Place: MWF 104 Lov 10:10-11:00
Instructor: David A. Kopriva
Contact Info: 112 Lov; 645-0185 (office); 644-2202 (front desk, math)
email: kopriva@math.fsu.edu; webpage: www.math.fsu.edu/~kopriva
Office Hours: MWF 11:00-12:00, also by appointment.Email, call or just come by otherwise.
Eligibility: Numerical methods for PDEs or equivalent + Programming ability with a compiled language suitable for scientific computation.
Textbook: Finite Difference Schemes and Partial Differential Equations by J.C. Strikwerda, SIAM. Publisher Info. Additional sources will be supplied in lecture.
Objectives: The material covered in the class covers tools that have been developed to solve problems numerically, generally on a computer. Thus, you will be expected to be able to implement the techniques and to solve problems with them. In addition, you will be expected to know how the methods were derived, when they are and are not appropriate to use and how they should behave. Lecture will cover the first, computer homework will give the hands-on experience with the second two.
Course Content:
This course covers the solution of elliptic, parabolic and hyperbolic partial differential equations by finite difference methods. This is second semester of a two semester course and will focus on advanced numerical techniques, particularly in multiple space dimensions.
I. Finite difference methods in multiple space dimensions
Finite difference methods on the square
Approximation of elliptic equations
Iterative solution
Basic Methods
Conjugate Gradient and Preconditioned Conjugate Gradient
Multigrid
Approximation of hyperbolic systems
Finite difference methods on general quadrilateral domains
Mappings and differential geometry
Algebraic grid generation
Elliptic grid generation
II. Finite Volume Methods
Conservation laws and conservation
Finite volume approximation of conservation laws
Monotonicity, TVD and limiters
Implementation of FVMs
Attendance: I strongly advise you to attend class regularly. A student absent from class bears the full responsibility for all subject matter and procedural information discussed in class.
Grading: There will be no exams. Graded homework will be given regularly. The final grade will be based on performance on the homework problems.
Homework: Graded homework will be given periodically and will often require computer programming. Do not skip an assignment. The format for computer homework can be found in the section How to Write Up Computer Problem Homework.
ALL SYLLABI ARE REQUIRED TO INCLUDE THE FOLLOWING STATEMENTS:
University Attendance Policy:
Excused absences include documented illness, deaths in the family and other documented crises, call to active military duty or jury duty, religious holy days, and official University activities. These absences will be accommodated in a way that does not arbitrarily penalize students who have a valid excuse. Consideration will also be given to students whose dependent children experience serious illness.
Academic Honor Policy:
The Florida State University Academic Honor Policy outlines the University’s expectations for the integrity of students’ academic work, the procedures for resolving alleged violations of those expectations, and the rights and responsibilities of students and faculty members throughout the process. Students are responsible for reading the Academic Honor Policy and for living up to their pledge to “. . . be honest and truthful and . . . [to] strive for personal and institutional integrity at Florida State University.” (Florida State University Academic Honor Policy, found at http://fda.fsu.edu/Academics/Academic-Honor-Policy.)
Americans With Disabilities Act:
Students with disabilities needing academic accommodation should:
(1) register with and provide documentation to the Student Disability Resource Center; and
(2) bring a letter to the instructor indicating the need for accommodation and what type. This should be done during the first week of class.
This syllabus and other class materials are available in alternative format upon request.
For more information about services available to FSU students with disabilities, contact the:
Student Disability Resource Center
874 Traditions Way
108 Student Services Building
Florida State University
Tallahassee, FL 32306-4167
(850) 644-9566 (voice)
(850) 644-8504 (TDD)
sdrc@admin.fsu.edu
http://www.disabilitycenter.fsu.edu/
RECOMMENDED LANGUAGE FOR SYLLABI:
Free Tutoring from FSU
On-campus tutoring and writing assistance is available for many courses at Florida State University. For more information, visit the Academic Center for Excellence (ACE) Tutoring Services’ comprehensive list of on-campus tutoring options - see http://ace.fsu.edu/tutoring or contact tutor@fsu.edu. High-quality tutoring is available by appointment and on a walk-in basis. These services are offered by tutors trained to encourage the highest level of individual academic success while upholding personal academic integrity.
Syllabus Change Policy
"Except for changes that substantially affect implementation of the evaluation (grading) statement, this syllabus is a guide for the course and is subject to change with advance notice.”