phy611 - Theoretical Methods

180 h

basic programming skills (matlab, python, C/C++)

The goal of this module is to extend the training in theoretical methods for engineering physics through the acquisition of solid and in-depth knowledge of advanced concepts and through their practice with computer simulations. Depending on the chosen course, the students will have the opportunity to strengthen their knowledge in quantum material modelling (Density-functional theory), signal processing, fluid dynamics (Modelling and Simulation), computational physics, and machine learning. In this way, they will develop skills to relate the conceptual design of models, their numerical implementation, and the physical analysis of the produced data, with the results of field and/or laboratory measurements.

• Computer Physics
  • Debugging; data structures; algorithms; random numbers; data analysis; percolation; Monte Carlo simulations; finite-size scaling; quantum Monte Carlo; molecular dynamics simulations; event-driven simulations; graphs and algorithms; genetic algorithms; optimization problems.
• Machine learning
  • Unsupervised learning methods; algorithms for clustering, classification, component extraction, feature learning, blind source separation and dimensionality reduction; Relations to neural network models; learning in biological systems.
• Modelling and Simulation
  • Advanced fluid dynamics including 3D, transient and compressible processes; Theory of similarity, range of dimensionless numbers; Potential Theory; Numerical Algorithms and possibilities of independent coding of simplest mathematical models; Introduction of a complete chain of Open-Source-CFD-Tools; Contactless high-resolving measuring techniques in the fluid dynamics.
• Digital Signal processing
  • System properties; Discrete-time signal processing; Statistical signal processing; Adaptive filters.
• Introduction to numerical methods for partial differential equations
  • Learning basic numerical methods for solving partial differential equations
  • Understanding basic numerical methods and their mathematical convergence properties
  • Development and practical implementation of algorithms for solving PDEs
  • Acquiring deeper understanding and interplay between different fields of theoretical analysis, scientific computing and natural sciences.

• Computer Physics
  • T. H. Cormen, S. Clifford, C.E. Leiserson, und R.L. Rivest: Introduction to Algorithms. MIT Press, 2001;
  • K. Hartmann: Practical guide to computer simulation. World- Scientific, 2009;
  • J. M. Thijssen: Computational Physics. Cambridge University Press, 2007;
  • M. Newman, G. T. Barkema: Monte Carlo Methods in Statistical Physics. Oxford University Press, 1999.
• Machine learning
  • C. M. Bishop, Pattern Recognition and Machine Learning, Springer 2006;
  • D. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge.
• Modelling and Simulation
  • Versteeg, K.H. , Malalasekera, W.: An Introduction to Computational Fluid Dynamics. Prentice Hall, 2nd rev. Ed., 2007.
• Digital Signal processing
  • A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing", Prentice Hall, 2013;
  • J. G. Proakis, D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, Prentice Hall, 2013;
  • S. Haykin, Adaptive Filter Theory, Pearson, 2013;
  • P. P. Vaidyanathan, Multirate systems and lter banks, Prentice Hall, 1993;
  • K.-D. Kammeyer, K. Kroschel, Digitale Signalverarbeitung: Filterung und Spektralanalyse mit MATLAB-Übungen, Broschiert, 2018;
• Introduction to numerical methods for partial differential equations
  • S. Brenner and L. Scott, The Mathematical Theory of Finite Element Methods, 2008 
  • P. Knabner and L. Angermann, Numerical Methods for Elliptic and Parabolic Partial Differential Equations, 2021
  • P. G. Ciarlet, The finite element method for elliptic problems, 1980
  • D. Braess, Finite elements: theory, fast solvers, and applications in elasticity theory, 2010
  • A. Chernov, Numerical Methods for Diffusion Problems, Energy of the future Oldenburg: BIS-Verlag der Carl von Ossietzky Universität (2018), pp 185-218

Lectures (2 or 4 hours per week) / Exercises (1 or 2 hours per week)