# Syllabus for Scientific Computing III

Beräkningsvetenskap III

• 5 credits
• Course code: 1TD397
• Education cycle: Second cycle
• Main field(s) of study and in-depth level: Computer Science A1N, Technology A1N, Computational Science A1N
• Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
• Established: 2008-03-13
• Established by:
• Revised: 2020-02-12
• Revised by: The Faculty Board of Science and Technology
• Applies from: Autumn 2020
• Entry requirements:

120 credits including Scientific Computing II, 5 credits, or Scientific Computing, Bridging Course, 5 credits, or Simulation and Numerical Methods, 5 credits. Vector calculus and linear algebra. Proficiency in English equivalent to the Swedish upper secondary course English 6.

• Responsible department: Department of Information Technology

## Learning outcomes

On completion of the course, 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. Direct (based on LU-factorization) and iterative methods for solutions to linear systems of equations, and Newtons method for nonlinear systems. Theoretical, practical, implementational as well as validation aspects are discussed in relation to the methods presented in the course. Use of computational software (MATLAB PDE toolbox).

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

## Instruction

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

## Assessment

Written examination (3 credits) and approved assignments and tasks at problem solving classes (2 credits). The assignments are reported in English.

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.