Entry requirements

BSc degree where Scientific Computing II and Vector Calculus (Green's theorem and Stokes' theorem must be covered) is included.

Learning outcomes

To pass, the student should be able to

• explain the idea behind the algorithms that are considered in the course;
• account for the fundamental difference between methods based on finite differences and finite elements and their advantages and disadvantages given different application problem;
• interpret and relate computational results to the concepts consistency, stability and convergence;
• solve problems in science and engineering given a mathematical model, by structuring the problem, choose appropriate numerical method and use advanced software and self-written code to generate solution;
• use advanced computational software and interpret results from the computations;
• present, explain, summarise, evaluate and discuss solution methods and results and formulate conclusions in a written report

Content

The main focus is on solutions to partial differential equations and methods for solving the resulting equation system. Solution methods based on finite differences and finite element methods. Iterative methods for solutions to linear systems of equations. The Power method for eigenvalue problems. Theoretical, practical, implementational as well as validation aspects are discussed in relation to the methods presented in the course. Use of computational software (Comsol Multiphysics and MATLAB).

Key concepts covered in the course: accuracy and order of accuracy, efficiency, consistency, stability, convergence.

Instruction

Lectures, problem classes/workouts, laboratory work, compulsory assignments.

Assessment

Written examination at the end of the course and approved assignments.