Master thesis project for students at KTH
http://www.nada.kth.se/~jaun/Projects.html
NADA, Royal Institute of Technology, Stockholm, Sweden

Parallel solver for electromagnetic wavefields in tokamaks

Electromagnetic waves and the interactions with charged particles play a fundamental role in fusion energy research. Theoretical models are used to interpret experiments in the world's largest tokamak (the Joint European Torus - JET, Oxford, UK) and predict future facilities (e.g. the International Thermonuclear Tokamak Reactor - ITER). Numerical calculations using the PENN code in particular are unique in accounting for the toroidal mode conversion mechanisms that couple waves from different spatial scales: they affect the power deposition in the ion cyclotron frequency heating and control the stability of Alfvén eigenmodes.

Without entering into details that are not useful for the realization of this project, the toroidal wavefield is modeled in 2D with a set of coupled integro- / differential equations for the electromagnetic potentials that are discretized with bi-cubic finite elements. The work carried out previously performed in MSc projects by K. Blomqvist and Li Fei Windy [1] showed that iterative Krylov space methods readily available in the PetSc library could dramatically reduce the memory and the time required to solve the large linear system -- paving the way for an efficient parallelisation of the code.

To succeed in this last major undertaking, we will terminate replacing the intrinsically sequential ILU(0) preconditionner with a parallel SPAI algorithm [2] and study the convergence of different operators for an increasing numerical resolution. Further optimizations are required to exploit the full potential of the PENN code on one of the most powerful computers in Scandinavia.

A certain knowledge of UNIX, FORTRAN or C programming, and a strong taste for numerical analysis is desirable to handle large codes that represent now the state of the art in this field of research.

  1. Iterative Solution of Global Electromagnetic Wavefields with Finite Elements, A. Jaun et al., Comput. Phys. Commun. 135 (2001) 74
  3. A Sparse Parallel Approximative Inverse Preconditionner, M. J. Grote, T. Huckle, SIAM J. Sci. Comput. 18 (1997) 838
For further information, contact André JAUN and consult http://www.nada.kth.se/~jaun.