Finite differences software for the numeric analysis of a non-destructive electromagnetic testing system
In this paper, theoretical bases for the development of a software for electromagnetic effects simulation based on the approximation method of finite differences using Scilab are presented. A methodology for programming the algorithm is discussed and a simulation test is conducted in order to validate it, which consists of a coil with a ferromagnetic core. Finally, this software is used in studies related to magnetic flux leakage by a simulation of a system for the measurement of magnetic flux density in plates with different defects, which include both 2D and 3D and defects with orientation of 45 degrees.
Solving the Generalized Poisson Equation Using the Finite-Difference Method (FDM)
The Poisson equation is a very powerful tool for modeling the behavior of electrostatic systems, but unfortunately may only be solved analytically for very simplified models. Consequently, numerical simulation must be utilized in order to model the behavior of complex geometries with practical value. Although there are several competing algorithms for achieving this goal, one of the simplest and more straightforward of these is called the finite-difference method (FDM). At its core, FDM is nothing more than a direct conversion of the Poisson equation from continuous functions and operators into their discretely-sampled counterparts. This converts the entire problem into a system of linear equations that may be readily solved via matrix inversion. The accuracy of such a method is therefore directly tied to the ability of a finite grid to approximate a continuous system, and errors may be arbitrarily reduced by simply increasing the number of samples. Despite the relative simplicity of FDM as a numerical tool, information on the subject is surprisingly scarce. This is especially true for the case of quasi-static systems experiencing current flow in conducting materials. Part of the reason for this likely has to do with the fact that FDM is, at its core, nothing more than a simplified form of the finite element method (FEM). The only difference is that FDM is solved through a fixed, rectangular geometry, while FEM utilizes a flexible, triangular mesh. Nevertheless, the uniform grids inherent to FDM make it very intuitive to learn and to program, especially for students unfamiliar with techniques in numerical methods. Consequently, the learning curve for FEM is far steeper than it is for FDM, and often requires a whole semester of study to fully understand. On the other hand, expertise with FDM may be readily achieved in only a few weeks, and even serves as an intuitive springboard from which to study the more complex nature of FEM. The goal of this paper is to serve as a comprehensive introduction to the principles of FDM. Much of the basic information is readily found in standard textbooks [1, 2], though many of the practical details and advanced topics are difficult to find anywhere at all. This paper is therefore a compilation of knowledge based on my experience with FDM, as well as a primer on some of the more advanced topics that are almost nonexistent in the literature. The audience is specifically intended to include first-year students in computational electromagnetics, but more advanced professionals should still find useful reference material as well. The basic governing
Measuring Sheet Resistances of Dielectrics Using Co‐Planar Hydrogel Electrochemical Cells with Practical Applications to Characterize the Protective Quality of Paints on Sculptures
Electrical properties of thin dielectric films at the solid-liquid phase boundary are an important performance characteristic of many devices, coatings and sensors. In this paper, co-polymeric hydrogels of polyacrylic acid co-sulfonic acid, swollen with a salt solution to act as the solid electrolyte, were used to assess interfaces using electrochemical impedance spectroscopy (EIS) in a co-planar geometry. Silane-modified glasses were characterized by the co-planar hydrogel EIS cell and found to be distinguishable based on their surface monolayer chemistry. EIS measurements were also made on primed and painted metal substrates, using both test panels and an outdoor sculpture, Tony Smith's Stinger. The panels were then exposed to accelerated and outdoor weathering and showed degradation on the surface paint layers, which was observable electrochemically using EIS and confirmed visually by SEM. Electrochemical spectral features were compared between data from a standard paint-test cell versus this co-planar hydrogel cell; both cell types were able to measure coating capacitance, providing useful information about the condition of the bulk coating. Yet, sheet resistance (Rs) was a spectral feature seen only by the co-planar hydrogel cell. Thus, it can be concluded that the use of such co-planar hydrogel cells can provide an earlier warning sign to coating degradation and such cells provide a new type of spectral information that is not assessable by the standard geometry.