Syllabus for Scientific Computing for Partial Differential Equations

Learning outcomes

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.

   

Content

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.

Instruction

Lectures, problem solving sessions, laboratory exercises, mandatory projects. Guest lecture.

Assessment

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.

Other directives

Cannot be included in the same degree as Computational Science III (1TD397).