Институт вычислительной математики
и математической геофизики

Abstracts

Numerical solution of differential and integral equations

This work is devoted to analysis of vector and scalar finite element methods (FEM) for solving non-stationary electromagnetic problems.

The main feature of vector FEM is automatic handling of discontinuity properties of the approximated fields across the material interfaces. In spite of the advantages of vector FEM this method is not well studied and investigation of this method is an actual problem of the numerical mathematics. In this work on base of vector FEM the effective procedure of modeling non-stationary vector fields in 3D inhomogeneous media is constructed.

We introduce special mixed variational formulations oriented to the vector and scalar FEM. The experimental investigation of different schemes of temporal approximation is carried out. The features of constructing the discrete analog of variational formulations for vector and scalar FEM are analyzed.

The proposed numerical schemes are applied to solving the problem of defectoscopy of oil-gas pipes. The comparison of numerial schemes based on vector and scalar FEM is implemented. The effectiveness of the vector FEM for solving electromagnetic problems in inhomogeneous media is shown.

Note. Abstracts are published in author's edition

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