Master’s studies

Syllabus for Scientific Computing III

Beräkningsvetenskap III

Syllabus

  • 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), 3, 4, 5
  • Established: 2008-03-13
  • Established by: The Faculty Board of Science and Technology
  • Revised: 2016-05-02
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 24, 2016
  • 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.
  • Responsible department: Department of Information Technology

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).
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.

Assessment

Written examination (3 credits) and approved assignments (2 credits). The assignments are reported in English.

Reading list

Reading list

Applies from: week 25, 2016

  • 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

    Find in the library

    Mandatory