Student Projects and Theses

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Student projects

If interested please contact the lecturer offering the project.

Note: Most projects are suitable for both students of mathematics and computational science and engineering.

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Lecturer: Prof. Habib Ammari

Our goal is to develop new mathematical models and methods of broad utility to science and engineering and to make fundamental advances in the mathematical and physical sciences themselves. We have been developing mathematical and computational frameworks to achieve super-resolution in biomedical imaging. Our work on biomimetics focuses on elucidating mechanisms exploited by bats and weakly electric fish for imaging. Nanophotonics is the study of electromagnetic wave phenomena in media structured on the same lengthscale as the wavelength, and is also a very active area of study in our group. Thesis projects on these current topics of research are available on request.

Lecturer: Prof. Ralf Hiptmair

Lecturer: Prof. Christoph Schwab

Student projects are available in Mathematical Analysis (error estimates) and Computer Implementation of efficient direct and inverse problem solution for deterministic and stochastic Partial Differential Equations with either many (several hundred) parameters, or with solutions on very high dimensional state- and phase spaces.

Close connections exist to Statistical Modelling, Computational Uncertainty Quantification, Computational Risk Analysis, Computational Biology and particular background and interest of students in these directions is welcome, but not a requirement.

Examples and Applications include (but are not restricted to)

  • computational finance: pricing and hedging options on large baskets,
  • computational biology: reaction rate models in complex biochemical reaction networks,
  • computational engineering: problems with multiple scales as arise in eg., in high frequency electromagnetic scattering, homogenization, turbulent flow simulations,...
  • exascale computing: mathematical modelling and computational analysis of fault tolerant computational methods.

Methods include (but are not restricted to)

  • Finite Element Methods (Multiscale-, High-Order, WaveletFEM,...),
  • Discontinuous Galerkin Methods,
  • Finite Volume Methods,
  • Wavelets,
  • high-order, dimension adaptive integration and interpolation algorithms (in particular adaptive Smolyak, Quasi-Monte Carlo, adaptive stochastic Galerkin Methods, reduced basis approximations, tensor structured linear algebra approaches),
  • MCMC and MLMCMC,
  • Quasi Monte-Carlo Methods.


Projects can be mainly computational (eg. for BSc / MSc Applied Mathematics and RW/CSE), or mainly analytical (eg. for BSc/ MSc in Mathematics).

  • Projects in BSc/ MSc Applied Math will use mainly MATLAB / PYTHON programming.
  • Projects in RW/CSE will usually require C, C++ programming and, in some projects, knowledge in MPI or other parallel programming (Introduction to Parallel Computing).

Selection of completed theses

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Master theses

  1. Oded Stein, A Boundary Element Method for Eddy Currents (PDF, 2.6 MB), 2015, supervisor Prof. Ralf Hiptmair
  2. Simon Etter, Parallel Tensor-Formatted Numerics for the Chemical Master Equation (PDF, 2 MB), 2015, supervisor Robert Gantner and Prof. Dr. Christoph Schwab
  3. Jakob Zech, A Posteriori Error Estimation of hp-DG Finite Element Methods for Highly Indefinite Helmholtz Problems (PDF, 4.4 MB), 2014, supervisor Prof. Dr Stefan Sauter
  4. Lukas Herrmann, Isotropic Ramdom Fields on the Sphere - Stochastic Heat Equation and Regularity of Random Elliptic PDEs (PDF, 1.4 MB), 2013, supervisors Dr. Annika Lang, Prof. Dr. Christoph Schwab 
  5. Yann Poltera, MLMC-FD method for 2D statistical solutions of the Navier-Stokes equations (PDF, 1.4 MB), 2013, supervisor Prof. Dr. Christoph Schwab
  6. Helga Thum, Numerical Simulations of the Weak Approximation Error for Parabolic Stochastic Partial Differential Equations (PDF, 706 KB), 2013, supervisor Prof. Dr. Arnulf Jentzen
  7. Yulia Smirnova, Calderon Preconditioning for Higher Order Boundary Element Method (PDF, 1.9 MB), 2013, supervisor Prof. Ralf Hiptmair
  8. Raffael Casagrande, Sliding Interfaces for Eddy Current Simulations (PDF, 7.1 MB), 2013, supervisor Prof. Ralf Hiptmair
  9. Simon Pintarelli, Local Multi-trace Boundary Element Formulation for Diffusion Problems (PDF, 2.9 MB), 2013, supervisor Prof. Ralf Hiptmair
  10. Michel Verlinden, Adaptive Galerkin Methods for Infinite Dimensional Parabolic Equations (PDF, 580 KB), 2012, supervisor Prof. Christoph Schwab
  11. Severin Thaler, The Criticality Spectral Problem in Neutron Transport (PDF, 1.4 MB), 2012, supervisor Prof. Christoph Schwab
  12. Robbin Tops, Numerical Pricing of American Options for gerneral Bivariate Lévy Models (PDF, 3.8 MB), 2012, supervisor Prof. Christoph Schwab
  13. Elke Spindler, Second Kind Single Trace Boundary Element Methods (PDF, 5.4 MB), 2012, Prof. Ralf Hiptmair
  14. D. Bernhardsgrütter, Multi-Level Monte Carlo Methods for Stochastic Parabolic and 2nd Order Hyperbolic PDEs (PDF, 3.7 MB), 2011, supervisor Prof. Dr. Christoph Schwab
  15. Daniel Kövi, hp Finite Element Method pricing algorithms for lookback options in Lévy Markets (PDF, 1.3 MB), 2011, supervisor Prof. Christoph Schwab
  16. Barry Thornton, Electricity Spot Price Modelling and Derivatives Pricing (PDF, 5.3 MB), 2010, supervisor Prof. Christoph Schwab
  17. Nathaniel Zollinger, Multi-Level Monte Carlo Finite Element Method for Elliptic Partial Differential Equations with Stochastic Data (PDF, 720 KB), 2010, supervisor Prof. Christoph Schwab
  18. Alberto Paganini, Efficient Convolution Based Impedance Boundary Conditions (PDF, 731 KB), 2011, supervisor Prof. Ralf Hiptmair
  19. Michael Spreng, Resolution of Skin Layer in EM Simulation (PDF, 865 KB), 2010, supervisor Prof. Ralf Hiptmair
  20. Stefan Siebenmann, A Scalable Eddy-Current Solver for ANSYS (PDF, 1.3 MB), 2010, supervisor Prof. Ralf Hiptmair
  21. Lisa Powers, Numerical Study of Small-Jump Regularization on Exotic Contracts in Lévy Markets (PDF, 1.4 MB), 2008, supervisor Prof. Christoph Schwab 
  22. Franz Piehler, Boundary element discretisation of asymptotic layer models (PDF, 879 KB), 2008, supervisor Prof. Ralf Hiptmair
  23. Claude Gittelson, Plane wave discontinuous Galerkin methods (PDF, 1.6 MB), 2008, supervisor Prof. Ralf Hiptmair
  24. Chris Bardgett, Pricing Convertible Bonds using Finite Elements (PDF, 400 KB), 2007, supervisor Prof. Christoph Schwab
  25. Simone Riva, Computation of electrostatic forces by the virtual work method (PDF, 1.4 MB), 2007, supervisor Prof. Ralf Hiptmair
  26. Jan Kayatz, Cone Strategies for Formal Deformations of Non-Collapsible Simplicial Complexes (PDF, 412 KB), 2006,supervisor Prof. Ralf Hiptmair
  27. Oliver Pfeifer, Asymptotische Methode zur Berechnung elektrostatischer Kräfte (PDF, 489 KB), 2006, supervisor Prof. Ralf Hiptmair
  28. Julien Renggli, Quadtree techniques for the construction of structured auxiliary meshes (PDF, 429 KB), 2006, supervisor Prof. Ralf Hiptmair
  29. Gisela Widmer, Auxiliary Space Method for Edge Elements (PDF, 706 KB), 2003/04, supervisor Prof. Ralf Hiptmair
  30. Benjamin Guélat, Régularité des solutions des problèmes d'élasticité et d'écoulement de Stokes dans un polygone (PDF, 2.3 MB), 2001, supervisor Prof. Christoph Schwab

Bachelor theses

  1. Thomas Haener, Numerical Solution of a Coefficient Identification Problem for the Poisson Equation (PDF, 3.9 MB), September 2014, supervisor Prof. Ralf Hiptmair
  2. Elke Spindler, A Posteriori Error Estimates for hp-FEM: Comparison and Implementation (PDF, 545 KB), 2010, supervisor Prof. Ralf Hiptmair
  3. Robert Gantner, Rayleigh Quotient Multigrid (PDF, 4.2 MB), 2011, supervisor Prof. Ralf Hiptmair
  4. Simon Pintarelli, Duality based error estimation for electrostatic force computation (PDF, 13.6 MB), 2010, supervisor Prof. Ralf Hiptmair
  5. Julia Slipantschuk, Numerical Validation of Emergent Behavior in Flocks (PDF, 4.5 MB), 2008, supervisors Prof. Christoph Schwab, Claude Jeffrey Gittelson
  6. Sabine Elmiger, Convergence of Binomial Tree Methods for European/American Path-Dependent Options (PDF, 5.8 MB), 2008, supervisors Prof. Christoph Schwab
  7. Claude Gittelson, Non-equidistant approximate DFT based on Z-Splines (PDF, 382 KB), 2006, supervisor Prof. Ralf Hiptmair

Semester theses

  1. Simon Etter, MPI-Based Tensor Network Library (PDF, 528 KB), 2014, supervisors Robert Gantner, Vladimir Kazeev, Prof. Christoph Schwab (RW/CSE)
  2. Jakob Zech, Nonlinear n-term approximation for the solution of the dirichlet problem (PDF, 288 KB), 2013, supervisors Dr. Markus Hansen, Prof. Christoph Schwab
  3. Simon Härdi, Parallelization of a radiative transfer solver (PDF, 444 KB), 2012, supervisor Prof. Christoph Schwab
  4. Yulia Smirnova, Dual Mesh Calderon Preconditioning for the Single Layer Boundary Integral Operator (PDF, 5 MB), 2012, supervisor Prof. Ralf Hiptmair
  5. Raffael Casagrande, Implementation of impedance boundary conditions in HADAPT (PDF, 1.3 MB), 2012, supervisor Prof. Ralf Hiptmair
  6. Anders Rosero, Spurious Solutions for transient Maxwell equations in 2D (PDF, 1.1 MB), 2011, supervisor Prof. Ralf Hiptmair
  7. Yavor Stoev, Variance-optimal hedging error in geometric Lévy models (PDF, 530 KB), 2010, supervisor Prof. Christoph Schwab
  8. Jonas Sukys, Discontinuous Galerkin discretization of magnetic convection (PDF, 2.5 MB), 2010, supervisor Prof. Ralf Hiptmair
  9. Andreas Hiltebrand, Fast solvers for Eulerian convection schemes, (PDF, 328 KB) 2010, supervisor Prof. Ralf Hiptmair
  10. Christoph Bossard, Hash Based Data Structures for Tetrahedral Meshes (PDF, 152 KB), 2005, supervisor Prof. Ralf Hiptmair
  11. Mathias Hack, Angle conditions for face and edge elements (PDF, 427 KB), 2005, supervisor Prof. Ralf Hiptmair
  12. Manuel Guidon, Transient Simulation of Eddy Currents in Ferromagnets (PDF, 3.7 MB), 2003/04, supervisor Prof. Ralf Hiptmair
  13. Philippe Corboz, Micromagnetism (PDF, 3.7 MB), 2003, supervisor Prof. Ralf Hiptmair
 
 
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Tue Apr 25 12:35:59 CEST 2017
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