A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods

summary:The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical experiments performed are studied from the point of view of the time and storage requirements and the achieved accuracy of the solution

Refined models of the conductivity distribution at the transition from the Bohemian Massif to the West Carpathians using stochastic MCMC thin sheet inversion of the geomagnetic induction data

International audienceAlthough volume 3D modeling solutions has become widespread in recent time, thin sheet approximation of Earth's conductivity distribution can still serve as a useful tool when quasi-3D conductivity structures in the heterogeneous subsurface are investigated and the available database of observations is limited to long-period electromagnetic induction data from large-scale deep sounding arrays. We present results of stochastic Monte Carlo-Markov Chains MCMC inversion of long-period induction arrows based on the Bayesian statistics strategy.We concentrated on the different methodological aspects of MCMC for Gibbs sampling and for adaptive Metropolis algorithm together with convergence of these methods. The results are presented on a case study from the transition zone between the Bohemian Massif and the West Carpathians where a phantom effect caused by superposition of the prominent SW-NE trending Carpathian Conductivity Anomaly and NW-SE trending anomalous structure related to the fault system at the eastern boundary of the Bohemian Massif appears