phy611 Theoretical Methods (Vollständige Modulbeschreibung)

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

This module aims to broaden the training of the students in theoretical methods for engineering physics by providing a solid and in-depth understanding of advanced concepts and their application through computer simulations. Depending on the course chosen, the students may strengthen their knowledge of computer physics, machine learning, signal processing, modelling and simulation, or numerical methods for differential equations. The module enables the students to develop the skills needed to link model design, numerical implementation, and physical data analysis with the interpretation 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 (stability, linearity, time-invariance, causality)
  • Discrete-time signal processing: sampling theorem, time-domain analysis (impulse response, convolution), z-transform, frequency-domain analysis (transfer function, discrete-time Fourier transform, discrete Fourier transform, FFT, STFT), digital filter design (FIR, IIR, linear phase filter, signal flow graph), multi-rate signal processing (down/up-sampling, filter banks)
  • Statistical signal processing: stationarity, ergodicity, correlation, Wiener-Khinchin theorem, spectral estimation
  • Adaptive filters: optimal filters, Wiener filter, time-domain algorithms (RLS, NLMS), frequency-domain algorithms (FDAF)
  • Matlab exercises about discrete-time signal processing and 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

Aufnahmekapazität:
unbegrenzt

Lehr-/Lernform:
1 Prüfung: – Klausuren zwischen 90 Min. und 180 Min., – Mündliche Prüfung zwischen 20 Min. und 45 Min., – Referat zwischen 10 Seiten und 20 Seiten schriftlicher Auseinandersetzung und zwischen 15 Min. und 30 Min. Vortrag, – Hausarbeit zwischen 15 und 30 Seiten