Scientific Computing

Abstract

Numerical simulation is an essential tool in modern engineering. The course "Scientific Computing" provides Civil Engineering students with both theoretical knowledge of the most important numerical methods and practical experience in implementing them using MATLAB. A mix of lectures, exercises, and project work ensures students can apply these methods to solve real-world engineering problems.

Objective

After this course, the students are able to write MATLAB code to solve a relevant engineering problem based on provided equations, pseudocode, or a written description of the algorithm. In particular, they are able to: • Choose and apply suitable numerical techniques to solve ◦ systems of linear equations, ◦ systems of ordinary differential equations (ODEs), ◦ partial differential equations (PDEs), in 1D or in rectangular domains, and ◦ optimization problems • Calibrate a computer model with given data • Debug and extend existing code • Create and interpret convergence plots • Recognize, explain, and address common issues in numerics such as stability, discretization, cost-accuracy trade-off, curse of dimensionality • Version code using git, and submit jobs on high performance computing facilities

Content

The course is structured into four modules, each consisting of lectures, exercises, and a mini-project. 1. All about matrices: Properties, solving linear systems of equations, matrix decompositions, eigenvalue decomposition, singular value decomposition 2. Ordinary differential equations: Finite difference method, order of accuracy, discretization error, explicit vs. implicit schemes 3. Partial differential equations: Shooting method, finite difference method, introduction to finite elements in 1D 4. Optimization: Root finding, optimization in 1D, types of optimization problems, calibration, using a supercomputer The course uses the programming language MATLAB.

Resources