Research subjects

NUMERICAL LINEAR ALGEBRA

• Iterative methods for sparse systems of linear equations
  • Theory & Algorithms
  • Convergence, Stability, Accuracy
  • Krylov subspace methods:
    • Conjugate Gradient, Conjugate Gradient Squared, BiCGSTAB, BiCGstab(ell)
  • Applications in Computational Fluid Dynamics, in Semiconductor Device Simulation.
  • Multigrid methods
• Iterative methods for eigenproblems
  • Krylov subspace methods:
    • Lanczos, Arnoldi
  • Other methods:
    • Davidson method, Jacobi-Davidson method
  • Applications in Quantum Chemistry, in Magneto hydrodynamics, in Acoustics.
• Iterative methods for non-linear problems:
  • Combination of Newton and Krylov subspace type of methods
  • Optimisation.
• Precondition techniques:
  • Linear systems (ILU)
  • Eigenvalue problems (MRILU)
  • Eigenvalue problems (domain decomposition).

PARTIAL DIFFERENTIAL EQUATIONS

• Initial value problems
• Finite & mixed finite element methods (convergence)

APPROXIMATION THEORY

• Wavelets, splines

• Environmental chemistry, Electric Power Systems