Numerical solution of differential and integral equations
Vector finite element method (VFEM) is one of the up-to-date methods of approximation of vector three-dimensional fields in inhomogeneous media. In the work the analysis of VFEM for approximation of time-harmonic electromagnetic fields is implemented.
Depending on presence the materials with contrasting electric or magnetic properties different variational formulations are proposed. The necessity of the application mixed variational formulations is analyzed for model problems for a number of frequencies.
The theoretical as well as experimental analysis of interpolation properties for different types of vector finite elements is impemented. The computational expenses required for solving discrete problems by means of VFEM in comparison with classical scalar FEM are evaluated. The investigation of different types of iterative methods for solving system of linear algebraic equations is carried out. The results of a number of computational experiments are presented.
The proposed VFEM-approximations is applied for modeling time-harmonic electromagnetic fields originated from logging of inclined oil-and-gas wells. The results of the modeling are presented.
Note. Abstracts are published in author's edition
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