Department of Mathematics, Chalmers University of Technology, Göteborg University

Master Thesis Topics

We are currently looking for new Masters Thesis Candidates. You will participate in the groups research activities and will be assigned problems with "front line" industerial/medical applications and interact with the PhD students. A few examples of current topics are:

  • Computational aspects of mathematical models in image compression: Continuation of a project investigated by 2 international master students (pdf)

  • Bipartition models for charged particles in radiation oncology: This project, in its final form, is about solving a convection-diffusion problem. The study includes modeling, analytical and numerical approaches for different aspects of charged particles used in radiation therapy. We are in particular interested in Galerkin type approximations for bi-partition models and comparing the results with those of the existing Mote-Carlo codes.
    Charged particles entering into a medium are subjected to elastic and inelastic collisions. The former alters the direction and energy of the particles, while the latter generally reduces the energy of particles but does not change the direction significantly. Due to collision, a portion of particles are scattered to the large-angle directions. Their transport behavior is similar to diffusion. The particles that still remain in the original beam obey a certain forward-peakedness scattering law and have a convective nature.
    The key factor in a bi-partition model is to determine the partition condition: a condition that separates the large-angle scattered particles from the collided straightforward particles. For light (low energy) particles this is due to an approximation made on the {\sl cross-section} in the collision term. In this setting the main application of bi-partition model is in radiation oncology.

  • Adaptive Burgers Solver: We consider the a posteriori study of the discontinuous Galerkin finite element method for a two dimensional model problem of the viscous Burgers equation. The code should be h adaptive. In particular we are interested in the qualitative behavior in vicinity of geometric singularities.

  • Adaptive Solver for Flow Interface Problems: In this project we are interesed in solving the interface problem in a, two component, muli-fluid with state equations satisfying a coupled system of nonlinear hyperbolic conservation laws. The project is to develop adaptive discontinuous Galerkin codes based on a posteriori error analysis. Some important applications are in e.g., oil reservoir, gas-liquid mixtures and the injected druggs in human blod.

  • Electron and Photon Beams: Here we consider the Fermi pencil beam equation. The goal is to develop an adaptive characteristis streamline diffusion finite element code based on the idea of exact transport + projection. The main application is in radiation therapy.

  • Spectral Sn Methods: This project concerns neutron transport equation with isotropic scattering. The spectral method will use orthogonal polynomial basis (e.g, Chebyshev). The idea is to compare the result with finite element basis and give conjecture of problem-dependent "best choices". The application is in nuclear engineeing and reactor physics.

  • Hypoelliptic estimates for the Fokker-Planck equation: In this project we deal with the discontinuous Galerkin method for the Fokker-Planck equation. The idea is similar to the first two projects: it is to develope adaptive codes; here we want to develop a code which is both h and p adaptive. Applications are in compuer chips, problems of gas dynamics, space shuttles, astrophysics.

  • p- parabolic equation: We consider here an initial-value problem of the so called p- parabolic equation with source term as a linear combination of characteristic functions. To begin with we are interested in investigating 1-space dimensional case for large p-values, e.g. p~50. p=2 corresponds to the heat equation, whereas p tending to infinity yields sand cones.
    This project is under common supervision with Professor Gunnar Aronsson, Department of Mathematics, University of Linköping.

    For more information contact

    Dr. M. Asadzadeh
    Department of Mathematics
    Chalmers University of Technology
    SE-412 96 Göteborg, Sweden
    Telefon: +46 31-772 3517
    E-mail: mohammad@chalmers.se

    Dr. M. L. Quiroga Teixeiro
    R&D Manager
    Gridcore AB
    Aschebergsgatan 46
    Göteborg (Sweden)
    Telephone +46(0)31 18 21 60
    Cell +46(0)707 268 100


    Mohammad Asadzadeh <mohammad@math.chalmers.se>
    Last modified: Jan 17 2010