Syllabus for Scientific Computing for Partial Differential Equations
Beräkningsvetenskap för partiella differentialekvationer
- 5 credits
- Course code: 1TD354
- Education cycle: Second cycle
Main field(s) of study and in-depth level:
Computational Science A1N,
Computer Science A1N,
- Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Established: 2022-03-03
- Established by: The Faculty Board of Science and Technology
- Applies from: Autumn 2022
120 credits in science/engineering. Scientific Computing II or Introduction to Scientific Computing or Scientific Computing, Bridging Course. Several Variable Calculus. Linear Algebra II. Proficiency in English equivalent to the Swedish upper secondary course English 6.
- Responsible department: Department of Information Technology
On completion of the course, the student should be able to:
- account for and use basic theory for mathematical modeling with partial differential equations;
- analyze finite difference and finite element approximations for efficient numerical solution of partial differential equations;
- account for the fundamental difference between methods based on finite differences and finite elements and the advantages and disadvantages of the methods given different application problems;
- select, formulate and implement appropriate numerical method to solve partial differential equations describing technical and scientific problems;
- interpret, analyze and evaluate results from numerical computations;
- use common software to solve more complicated partial differential equations, for example in fluid dynamics and wave propagation;
- present, explain, summarize, evaluate and reason about mathematical modeling, solution methods and results and argue for conclusions in a short report.
The main focus of the course is on mathematical modeling with partial differential equations and numerical solution methods. Different types of well-posed boundary conditions. Analysis and implementation of numerical methods based on finite difference methods and finite element methods. The course contains the energy method, normalized vector spaces and iterative methods for solving linear systems of equations. The methods above are treated with regard to theory, practice, implementation and verification. Use of commercial and open source software. Examples of key concepts included in the course include well-poseness, verification, accuracy, efficiency, stability and convergence.
Lectures, problem solving sessions, laboratory exercises, mandatory projects. Guest lecture.
Written exam (3 hp). Problem solving, assignments and a project with a written report (2 hp).
If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.
Cannot be included in the same degree as Computational Science III (1TD397).
Applies from: Autumn 2022
Some titles may be available electronically through the University library.
LeVeque, Randall J.
Finite difference methods for ordinary and partial differential equations : steady-state and time-dependent problems
Philadelphia, PA: Society for Industrial and Applied Mathematics, 2007