2007 , Volume 12, № 6, p.18-33

The results of the joint project of the Institute of Computational Technologies of Siberian Branch of Russian Academy of Sciences (ICT SB RAS, Novosibirsk, Russia) and the High Performance Computing Center Stuttgart (HLRS, Stuttgart, Germany) are presented. The project is realized within the framework of the activities of the German-Russian Center for Computational Technologies and High Performance Computing (http://www.grc-hpc.de). The parallel realization of the problem on mathematical modelling of three-dimensional electromagnetic fields in inhomogeneous domains in frequency domain is presented. The computational schemes are investigated in domains, which are inhomogeneous with respect to physical (electroconductivity) and geometrical (different scales of individual fragments of a modelling domain) characteristics, in the presence of field sources changing geometrical position with respect to interfragmentary boundaries, which separate individual subdomains. The three-dimensional vector Helmholtz equation is approximated on inhomogeneous tetrahedral grid with local grid refinements using the vector finite element method on the vector basis functions of high order. The basis functions (edge-elements) for calculating the electric field guarantee continuity of tangential components of the field on interelement and interfragmentary boundaries. For exact calculation of a jump of electric field normal component the special procedure for taking into account a weak divergence on basis functions of high order is realized. The problem on high-frequency induction logging isoparametric soundings (the VIKIZ-method in Russia) in a domain with complicated geometry is solved. The parallelization is done by formulating of $n$ independent problems, where $n$ is a number of probe positions, and associating each of these problems with a separate processor of computing system. The calculation results are presented, obtained on NEC SX-8 cluster.