INF305 Scientific Computing

This course introduces students to scientific computing, the collection of tools, techniques, and theories required to solve mathematical models of problems in Science and Engineering on the computer. A particular focus lies in theoretically understanding and efficiently implementing discussed algorithms to solve physical balance laws. Implementations can be done in Python, Julia, or C++.

Specific topics and questions that will be answered are:

• What is Scientific Computing? What is a numerical simulation?
• Physical balance laws and their connection to physics, engineering, and data science.
• How do you verify an algorithm? Determining a test problem with an analytic solution.
• Implementation of difference schemes.
• What are the solutions an algorithm should provide?
• Consistency, stability, and convergence of an algorithm.
• Libraries for Scientific Computing.
• Implementation of a 2D finite volume method.

After completing the course, you will be able to

• implement physical balance laws to run numerical simulations
• translate a physical problem to the computer
• validate your program.
• understand different solution concepts such as classical, weak, and entropy solutions.
• understand the concepts of consistency, stability, and convergence.