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 in C++. The course does not provide an introduction to C++, which INF205 covers. The programming part covers essential and valuable tools in C++ required for efficient scientific computing.

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 in C++.
• 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.
• Verification and validation.
• How to parallelize your code using MPI.

After completing the course, you will be able to

• implement physical balance laws in C++ using standard libraries for scientific computing.
• write parallel code using Message Passing Interface (MPI)
• verify and validate your program.
• understand different solution concepts such as classical, weak, and entropy solutions.
• understand the concepts of consistency, stability, and convergence.