1. Degree of Engineering in Mechanical Engineering or a degree in a related field. All degrees must be equivalent to at least 180 higher education credits.

2. At least 22.5 credits of Mathematics.

3. The equivalent of English B in Swedish secondary school or equivalent

4. Passed courses:

• MA620A Scientific Programming, 7,5 hp

• MA623A Numerical Methods, 7.5 hp

The course objective is for the student to learn fundamental theory within mathematical modelling with partial differential equations (PDEs) and how to solve these using fundamental principles in the finite difference and finite element method.

The course covers the following:

• Classical formulation of partial differential equations

• Boundary conditions

• Finite difference method (FDM)

• Convergence and stability analysis for FDM

• Weak formulation of thermo-mechanical problems

• Finite element discretisation of PDE

• Convergence and stability analysis for FEM

• Numerical simulation of heat transfer

• Numerical calculations of mechanics for linear elastic material

• Isoparametric element and Gaussian quadrature

• Project work within materials science

Once the course is completed, the student shall:

• understand the principles within mathematic modelling of materials science;

• demonstrate the ability describe the mathematical components in mechanical and thermal analyses;

• be able to describe the link between thermo and mechanical fields and identify the physical phenomena that cause non-linear thermo and mechanical behaviour;

• be able to describe further steps in FDM and FEM for non-linear problems compared with linear problems;

• be able to describe the conditions in numerical code for solving stress loading problems

• demonstrate the ability to perform numerical analyses for linear problems with simple geometry; and

• demonstrate specialised understanding of how to plan and execute a scientific project.

Once the course is completed, the student shall:

• demonstrate specialised ability to formulate simplified mathematical models for real phenomena and processes within materials science;

• demonstrate the ability to execute different types of discretisation for PDE;

• demonstrate the ability to set up correct formulation for linear thermo-mechanical analysis;

• demonstrate the ability to choose the appropriate method to identify a numerical solution for each type of PDE;

• demonstrate specialised ability to plan and execute a scientific project; and

• demonstrate the ability to write a scientific report and present the results orally in both a national and international setting.

Once the course is completed, the student shall:

• demonstrate specialised ability to critically investigate and analyse a scientific report and understand the strengths and weaknesses of the applied methods;

• demonstrate the ability to argument for the applicability and limitations of a specific mathematical model; and

• the ability to evaluate their own knowledge and competencies, and independently identify new knowledge required to follow and take part in developments within the field of modelling and simulation.

The course is comprised of lectures, computer laboratory sessions, project supervision, project presentation and independent study.

Requirements for pass (A-E): passed written exam (7 credits), passed written assignments (4 credits) and passed project report with related oral account (4 credits).

The final grade is based on the written exam and the project report with related oral account which are weighted.

Recommended reading:

The University provides students who are taking or have completed a course with the opportunity to share their experiences of and opinions about the course in the form of a course evaluation that is arranged by the University. The University compiles the course evaluations and notifies the results and any decisions regarding actions brought about by the course evaluations. The results shall be kept available for the students. (HF 1:14).

When a course is no longer given, or the contents have been radically changed, the student has the right to re-take the examination, which will be given twice during a one year period, according to the syllabus which was valid at the time of registration.

The syllabus is a translation of a Swedish source text.