TUDMATH / CMS SoSe26: Modul Math Ma 32: Scientific computing – Advanced concepts

Content of the course

The course focuses on crucial aspects of Scientific Computing, providing an overview of the steps required to perform numerical simulations of mathematical and physical problems, from selecting optimal strategies to applying them. Moreover, it covers specific advanced tools involving both numerical and modeling aspects (such as, e.g., the so-called phase-field model), which proved helpful in addressing state-of-the-art problems in applied scientific computing. 

The major aspects covered by lectures are:
i) Numerical methods for solving ODEs and PDEs (focus on Finite Difference and Spectral Methods);
ii) Diffuse Interface Approaches (e.g., phase-field methods) and other convenient approaches for solving specific classes of equations/problems (e.g., Monte Carlo methods)
iii) Implementing methods and numerical schemes, testing algorithms and models, comparing performances
iv) Basics of programming in Python to perform computations/simulations

Exercises will be assigned periodically to apply the concepts discussed in the lectures and to develop practical skills, allowing students to further exploit scientific computing in their careers. Their solution will also be provided and discussed during classes. Lecture notes will be provided.

General Information

- Enroll as a "Student" to access the content of the page (lecture notes, scripts, links to recordings, uploaded after lectures).

- Register in K0108-M0x32xV Scientific computing – Advanced concepts (V+Ü)- necessary to take the exam.

- Scheduling: Monday (5): 14:50--16.20  + Wednesday (5): 14:50-16.20

- Lecture Room: TBA

- Course MATRIX room for sharing information/questions: Matrix SCCOMP '26 Room

- Online attendance (suggested occasionally only) via Zoom at TBA or BBB, TBA

For additional information, please contact Prof. Dr. Marco Salvalaglio (marco.salvalaglio@tu-dresden.de)

Exam:

Given the expected number of students, the exam is planned to be ORAL (~ 25-30 min). One of the optional exercises assigned at the end of the course may be used as a topic to begin the exam (~10min). Changes with respect to this plan will be communicated during the semester if necessary.