A wavelet multilevel solution of the stationary geoelectrical field in the non-homogeneous environment

The contribution deals with a solution of the direct geophysical problem for the stationary electrical field in the non-homogeneous environment. The environment is represented by a planar domain composed from the several subdomains, i.e. homogeneous environments with different resistivity. The solution is based on a wavelet-Galerkin discretization of the problem via a fictitious domain formulation. Therefore two kinds of the Lagrange multipliers are considered: the first one enforces the boundary condition on the real domain while the second one is located on interfaces of the homogeneous environments and ensures the continuity of the potential of the electrical field. Multilevel structure of the wavelet spaces enables to solve efficiently the linear systems arising from the discretization. The presented solver uses the wavelet-based multigrid technique. The numerical experiments described in the paper confirm the efficiency of the method as well as the agreement with the physical reality.