Electromagnetic Nondestructive Testing by Perturbation Homotopy Method

Now electromagnetic nondestructive testing methods have been applied to many fields of engineering. But traditional electromagnetic methods (usually based on least square and local iteration) just roughly give the information of location, scale, and quality. In this paper we consider inverse electromagnetic problem which is concerned with the estimation of electric conductivity of Maxwell's equations (2D and 3D). A perturbation homotopy method combined with damping Gauss-Newton methods is applied to the inverse electromagnetic problem. This method differs from traditional homotopy method. The structure of homotopy function is similar to Tikhonov functional. Sets of solutions are produced by perturbation for every homotopy parameter λ=λi, i=0,…,L. At each iterative step of the algorithm, we add stochastic perturbation to numerical solutions. The previous solution and perturbation solution are regarded as the initial value in the next iteration. Although the number of solution in set increased, it increased the likelihood of obtaining correct solution. Results exhibits clear advantages over damping Gauss-Newton method and testify that it is an available method, especially on aspects of wide convergence and precision

Elastic Full-Waveform Inversion in the Presence of Fracture-Induced Anisotropy

Seismic imaging of the subsurface is essential in both the exploration and production of hydrocarbon reservoirs. Seismic full-waveform modelling and inversion methods can be used to obtain high-resolution images of the elastic properties. This work aims to develop further methods for non-linear elastic waveform inversion in anisotropic media associated with fractures. Based on previous research, the goal is to investigate which approach is the most reliable at estimating stiffness parameters. In this context, the rock physics t-matrix method was used to represent the stiffness perturbation due to fractures in a complex porous medium. The elastodynamic wave equation was solved using the full integral-equation solution of the Lippmann-Schwinger type. The frequency-domain scattered wavefield was used as synthetic data, to simulate the particle displacement from a fracture-induced anisotropic medium. Elastic Full-Waveform Inversion (FWI) makes use of all the information in the wavefield and is implemented by using the distorted Born iterative method (DBI). The DBI method is consistent with the Gauss-Newton iterative method and was performed using the self-adaptive regularisation scheme. For each iteration, both the Green's function and the sensitivity matrix were updated for the actual medium. Two models with different geological features, i.e. the syncline and anticline model, were used in the synthetic numerical experiments to simulate a fractured reservoir with transversely isotropic symmetry. Different levels of noise, as well as source-configurations, were investigated. For the models considered in this work, fracture-based inversion results were shown to match the actual model better than the stiffness-based inversion. When evaluating the results for noisy data of 40 dB SNR, it is evident that the stiffness-inversion is insufficient, particularly for the C13 parameter, when compared to fracture-inversion. On this basis, inverting for fracture parameters is recommended when characterising a reservoir associated with fractures. Future research is needed to identify more desirable fracture models and more efficient calculation of the full integral-equation solution.Masteroppgave i geovitenskapGEOV399MAMN-GEO

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

New Challenges Arising in Engineering Problems with Fractional and Integer Order

Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem

Mathematical Methods, Modelling and Applications

This volume deals with novel high-quality research results of a wide class of mathematical models with applications in engineering, nature, and social sciences. Analytical and numeric, deterministic and uncertain dimensions are treated. Complex and multidisciplinary models are treated, including novel techniques of obtaining observation data and pattern recognition. Among the examples of treated problems, we encounter problems in engineering, social sciences, physics, biology, and health sciences. The novelty arises with respect to the mathematical treatment of the problem. Mathematical models are built, some of them under a deterministic approach, and other ones taking into account the uncertainty of the data, deriving random models. Several resulting mathematical representations of the models are shown as equations and systems of equations of different types: difference equations, ordinary differential equations, partial differential equations, integral equations, and algebraic equations. Across the chapters of the book, a wide class of approaches can be found to solve the displayed mathematical models, from analytical to numeric techniques, such as finite difference schemes, finite volume methods, iteration schemes, and numerical integration methods

Numerical Simulation

Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students

Numerical study of convective fluid flow in porous and non-porous media.

Ph. D. University of KwaZulu-Natal, Pietermaritzburg 2015.Abstract available in PDF file

Heat transfer in cavities: configurative systematic review

No abstract available