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This paper aims to solve inhomogeneous dielectric problems by matching boundary conditions at the interfaces among homogeneous subdomains. The capabilities of Hilbert transform computations are deeply investigated in the case of limited numbers of samples, and a refined model is presented by means of investigating accuracies in a case study with three subdomains.

The accuracies, refined by Richardson extrapolation to zero error, are compared to finite element (FEM) and finite difference methods. The boundary matching procedures can be easily applied to the results of a previous Schwarz–Christoffel (SC) conformal mapping stage in SC + BC procedures, to cope with field singularities or with open boundary problems.

The proposed field computations are of general interest both for electrostatic and magnetostatic field analysis and optimization. They can be useful as comparison tools for FEM results or when severe field singularities can impair the accuracies of other methods.

This static field methodology, of course, can be used to analyse transverse electro magnetic (TEM) or quasi-TEM propagation modes. It is possible that, in some case, these may make a contribution to the analysis of axis symmetrical problems.

The most relevant result is the possible introduction of SC + BC computations as a standard tool for solving inhomogeneous dielectric field problems.

At present numerical simulation of seismicity, used in mining and hydraulic fracturing practice, is quite time expensive what hampers its combined employing with observed seismicity in real time. The purpose of this paper is to suggest a mean for drastic speeding up numerical modeling seismic and aseismic events.

The authors propose the means to radically decrease the time expense for the bottleneck stage of simulation: calculations of stresses, induced by a large group of already activated flaws (sources of events), at locations of flaws of another large group, which may be activated by the stresses. This is achieved by building a hierarchical tree and properly accounting for the sizes of activated flaws, excluding check of their influence on flaws, which are beyond strictly defined near-regions of strong interaction.

Comparative simulations of seismicity by conventional and improved methods demonstrate high efficiency of the means developed. When applied to practical mining and hydrofracturing problems, it requires some two orders less time to obtain practically the same output results as those of conventional methods.

The proposed improvement provides a means for simulation of seismicity in real time of mining steps and hydrofracture propagation. It can be also used in other applications involving seismic and aseismic events and acoustic emission.

Crystallization is the process widely used for components separation and solids purification. The systems for crystallization process evaluation applied so far, involve numerous non-invasive tomographic measurement techniques which suffers from some reported problems. The purpose of this paper is to show the abilities of three-dimensional Electrical Capacitance Tomography (3D ECT) in the context of non-invasive and non-intrusive visualization of crystallization processes. Multiple aspects and problems of ECT imaging, as well as the computer model design to work with the high relative permittivity liquids, have been pointed out.

To design the most efficient (from a mechanical and electrical point of view) 3D ECT sensor structure, the high-precise impedance meter was applied. The three types of sensor were designed, built, and tested. To meet the new concept requirements, the dedicated ECT device has been constructed.

It has been shown that the ECT technique can be applied to the diagnosis of crystallization. The crystals distribution can be identified using this technique. The achieved measurement resolution allows detecting the localization of crystals. The usage of stabilized electrodes improves the sensitivity of the sensor and provides the images better suitable for further analysis.

The dedicated 3D ECT sensor construction has been proposed to increase its sensitivity in the border area, where the crystals grow. Regarding this feature, some new algorithms for the potential field distribution and the sensitivity matrix calculation have been developed. The adaptation of the iterative 3D image reconstruction process has also been described.