Numerical Analysis and Mathematical Modelling NaM2

Research

Research topics (past and present)

The research performed within NaM2 mainly concerns the qualitative analysis and the numerical analysis of eigenvalue problems and of time-dependent boundary value problems for partial differential equations, arising from various physical and engineering disciplines. Among these disciplines the most important ones for NaM2 are at present:

  • problems from low frequency electromagnetism in ferromagnetic materials and from micro-magnetism;
  • convection-diffusion problems from chemical kinetics, metallurgy, heat transfer, flow and transport in porous media (e.g. soil).
The qualitative analysis includes existence, stability and regularity results of the exact solution. The numerical analysis concerns the development of numerical approximation schemes, and the study of their reliability and accuracy. The research deals with both direct problems (where all physical data entering the model are a priori known and where the relevant state quantity - response - must be determined) and inverse problems (where some missing data have to be recovered from partial a priori knowledge on the state quantity, which must be determined).

The major part of the research of NaM2 is performed in the frame of multi-disciplinary projects with engineering teams from inside and outside Ghent University. Most of the research topics have an ecological imperative, such as rational energy use, magnetic shielding, control / remediating of groundwater pollution. Whenever possible NaM2 works in close contact with industry.

Main actual research lines

  1. Numerical Analysis
    • Direct and inverse problems in low frequency electromagnetism and in micromagnetism;
    • Rothe finite element methods for time-dependent boundary value problems;
    • [in cooperation with the Department of Numerical Analysis and Optimalization, Comenius University Bratislava and with the Department of Modelling of Processes, Technical University Liberec]
  2. Mathematical and numerical Modelling
    • Direct and inverse problems in low frequency electromagnetism and in micromagnetism
    • [in cooperation with EELAB (UGent), ESAT (KULeuven), ELAP (ULg) and L2EP (Univ. Lille I)]
    • Contaminant transport and groundwater pollution;
    • [in cooperation with the Soil Mechanics Lab (UGent) and with the Research group Hydrogeology (UGent)]
    • Direct and inverse time-dependent problems from chemical kinetics;
    • [in cooperation with the Laboratory of Petrochemical Technology (UGent)]
    • Parabolic problems from chemical kinetics;
    • [in cooperation with the Department of Chemical Engineering and Technical Chemistry]
    • Direct and inverse diffusion problems in metallurgy;
    • [in cooperation with the Department of Metallurgy and Materials Science (UGent)]

NaM2 is co-founder and co-organiser of two international conferences

  1. ACOMEN: a triennial international conference on Advanced COmputational Methods in ENgineering, alternating at UGent and ULg
  2. MaCKiE: an biannual international workshop on Mathematics in Chemical Kinetics and Engineering, alternating at UGent, Houston Univ. and Heidelberg Univ.