An Integral Equation Method for Low Frequency Electromagnetic Fields in Three-dimensional Marine Environments PDF Download
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Author: Johan Mattsson
Publisher:
ISBN:
Category :
Languages : en
Pages : 13
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Author: Johan Mattsson
Publisher:
ISBN:
Category :
Languages : en
Pages : 13
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Author: Weng Cho Chew
Publisher: Morgan & Claypool Publishers
ISBN: 1598291483
Category : Elastic waves
Languages : en
Pages : 259
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Book Description
Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms
Author: Evan Schankee Um
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 207
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Book Description
The survey design and data interpretation of the marine controlled-source electromagnetic (CSEM) method require modeling of complex and often subtle offshore geology with accuracy and efficiency. In this dissertation, I develop two efficient finite-element time-domain (FETD) algorithms for the simulation of three-dimensional (3D) electromagnetic (EM) diffusion phenomena. The two FETD algorithms are used to investigate the time-domain CSEM (TDCSEM) method in realistic shallow offshore environments and the effects of seafloor topography and seabed anisotropy on the TDCSEM method. The first FETD algorithm directly solves electric fields by applying the Galerkin method to the electric-field diffusion equation. The time derivatives of the magnetic fields are interpolated at receiver positions via Faraday's law only when the EM fields are output. Therefore, this approach minimizes the total number of unknowns to solve. To ensure both numerical stability and an efficient time-step, the system of FETD equations is discretized using an implicit backward Euler scheme. A sparse direct solver is employed to solve the system of equations. In the implementation of the FETD algorithm, I effectively mitigate the computational cost of solving the system of equations at every time step by reusing previous factorization results. Since the high frequency contents of the transient electric fields attenuate more rapidly in time, the transient electric fields diffuse increasingly slowly over time. Therefore, the FETD algorithm adaptively doubles a time-step size, speeding up simulations. Although the first FETD algorithm has the minimum number of unknowns, it still requires a large amount of memory because of its use of a direct solver. To mitigate this problem, the second FETD algorithm is derived from a vector-and-scalar potential equation that can be solved with an iterative method. The time derivative of the Lorenz gauge condition is used to split the ungauged vector-and-scalar potential equation into a diffusion equation for the vector potential and Poisson's equation for the scalar potential. The diffusion equation for the time derivative of the magnetic vector potentials is the primary equation that is solved at every time step. Poisson's equation is considered a secondary equation and is evaluated only at the time steps where the electric fields are output. A major advantage of this formulation is that the system of equations resulting from the diffusion equation not only has the minimum number of unknowns but also can be solved stably with an iterative solver in the static limit. The developed FETD algorithms are used to simulate the TDCSEM method in shallow offshore models that are derived from SEG salt model. In the offshore models, horizontal and vertical electric-dipole-source configurations are investigated and compared with each other. FETD simulation and visualization play important roles in analyzing the EM diffusion of the TDCSEM configurations. The partially-'guided' diffusion of transient electric fields through a thin reservoir is identified on the cross-section of the seabed models. The modeling studies show that the TDCSEM method effectively senses the localized reservoir close to the large-scale salt structure in the shallow offshore environment. Since the reservoir is close to the salt, the non-linear interaction of the electric fields between the reservoir and the salt is observed. Regardless of whether a horizontal or vertical electric-dipole source is used in the shallow offshore models, inline vertical electric fields at intermediate-to-long offsets are approximately an order of magnitude smaller than horizontal counterparts due to the effect of the air-seawater interface. Consequently, the vertical electric-field measurements become vulnerable to the receiver tilt that results from the irregular seafloor topography. The 3D modeling studies also illustrate that the short-offset VED-Ex configuration is very sensitive to a subtle change of the seafloor topography around the VED source. Therefore, the VED-Ex configuration is vulnerable to measurements and modeling errors at short offsets. In contrast, the VED-Ez configuration is relatively robust to these problems and is considered a practical short-offset configuration. It is demonstrated that the short-offset configuration can be used to estimate the lateral extent and depth of the reservoir. Vertical anisotropy in background also significantly affects the pattern in electric field diffusion by elongating and strengthening the electric field in the horizontal direction. As the degree of vertical anisotropy increases, the vertical resistivity contrast across the reservoir interface decreases. As a result, the week reservoir response is increasingly masked by the elongated and strengthened background response. Consequently, the TDCSEM method loses its sensitivity to the reservoir.
Author: A. B. Samokhin
Publisher: VSP
ISBN: 9789067643368
Category : Science
Languages : en
Pages : 122
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Book Description
The analysis of scattering of electromagnetic waves in inhomogeneous three-dimensional bounded media is extremely important from both theoretical and practical viewpoints, and constitutes the core family of problems in electromagnetics. In this monograph the following fundamental topics relating to these problems are considered: mathematical problems and methods related to the scattering of electromagnetic waves by inhomogeneous three-dimensional anisotropic bodies and their reduction to volume singular integral equations; iteration techniques for solving linear operator equations; and efficient methods for solving volume integral equations that employ iteration procedures. Nowadays, volume singular integral equations are widely used as an efficient tool of numerical solution to the problems of complicated three-dimensional structures. Analysis of integral equations and corresponding scattering problems, including nonclassical ones, is performed in the general formulation. The necessary and sufficient conditions that provide fulfilment of the Noether property of operators and sufficient conditions for the Fredholm property are obtained. Existence and uniqueness theorems for scattering problems considered in both classical and nonclassical settings are proved. Much attention is given to iteration techniques and development of corresponding computational algorithms. This monograph will be of interest to researchers in electromagnetics, integral equations, iteration methods and numerical analysis both in academia and industry.
Author: Zhiguo Qian
Publisher:
ISBN: 9781109219807
Category :
Languages : en
Pages : 222
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Book Description
Several fundamental aspects of the surface integral equation (SIE) method including the low-frequency breakdown, the skin effect, and the substrate effect, have been addressed for full-wave electromagnetic analysis in the low-frequency regime, especially the modeling of electrical interconnects on chip and package levels. The augmentation technique is a simple and efficient remedy for the low-frequency breakdown, which is the bottleneck of the broadband simulation. Based on the augmented formulations, very complicated problems in the real world can be efficiently solved with appropriate preconditioning and fast algorithm acceleration. As required in many applications, a generalized impedance boundary condition (GIBC) formulation is developed to handle the skin effect rigorously and efficiently. It degenerates into traditional methods with two steps of approximations. These new techniques are also combined together into a comprehensive formulation to cover both the skin effect and the substrate effect without any low-frequency instability.
Author: P.E. Wannamaker
Publisher: Elsevier
ISBN: 0080542999
Category : Science
Languages : en
Pages : 305
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Book Description
"3-D modeling and inversion is a reality, and not an illusion." This is the clear conclusion of the Second International Symposium on Three-Dimensional Electromagnetics held at the University of Utah in 1999. Containing papers submitted by 36 authors, this volume, by the sheer number of works, their diversity, and the truly international character of the efforts attests to the vigor with which the problems of the field are pursued today. The papers in this book are grouped in three parts: 3-D EM modeling; 3-D EM inversion; and 3-D EM in practice. They cover a wide range of topics in forward modeling and inversion based on new fast approximate approaches and new efficient solutions by integral equation, finite difference and finite elements techniques. If the 1980s were the decade of rapid development in 3D seismics, the 1990s became the decade of growing interest of practical geophysicists in 3D EM modeling and inversion methods. The contributions contained in this volume represent a snapshot of today's state-of-the-art in three-dimensional electromagnetics.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 700
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Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author: Utkarsh Patel
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Despite vast advancements in computational hardware capabilities, full-wave electromagnetic simulations of many multiscale problems continue to be a daunting task. Multiscale problems are encountered, for example, when modeling interconnects in an integrated circuit or when simulating complex electromagnetic structures. In interconnect problems, the main challenge is to model the multiscale skin effect that develops inside the conductors at high frequency. Similarly, complex electromagnetic structures are multiscale because these surfaces are tens of wavelengths large, while each unit cell often contains subwavelength geometrical features. This thesis presents reduced-order integral equation methods to solve complex multiscale problems. For interconnect problems, it proposes a single-source surface integral equation method to model 2-D and 3-D conductors or dielectrics of arbitrary shape. In this approach, electromagnetic fields inside a conductor or a dielectric object are accurately modeled by a differential surface admittance operator and an equivalent electric current density on the object's surface. Since the proposed method does not use any volumetric unknowns, it is more efficient than volumetric methods encountered in the literature and commercial solvers, which require a fine mesh to model the skin effect. Furthermore, since the proposed approach is single-source, it is more efficient than other surface methods in the literature that require both equivalent electric and magnetic current densities. Numerical results show that the proposed method can be over 100x and 20x faster than commercial FEM solvers for 2-D and 3-D problems, respectively, while consuming significantly lower memory. The proposed surface method for conductors and dielectrics is further generalized to develop the so-called macromodeling technique to simulate complex scatterers. In this technique, a heterogeneous scatterer composed of dielectric and PEC objects is accurately modeled by equivalent electric and magnetic current densities that are introduced on a fictitious surface enclosing the element. The crux of the technique is to solve for unknowns only on the fictitious surface, instead of the scatterers, which results in fewer unknowns. Numerical results show that the proposed macromodeling technique can efficiently simulate electrically large reflectarrays composed of square patches and Jerusalem crosses, that are difficult to simulate even with commercial solvers.
Author: Safwat Zaky George Zaky
Publisher:
ISBN:
Category : Electromagnetic fields
Languages : en
Pages :
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Author: Michael S Zhdanov
Publisher: Elsevier
ISBN: 044462712X
Category : Science
Languages : en
Pages : 731
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Book Description
Geophysical Inverse Theory and Applications, Second Edition, brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion. It’s the first book of its kind to treat many kinds of inversion and imaging techniques in a unified mathematical manner.The book is divided in five parts covering the foundations of the inversion theory and its applications to the solution of different geophysical inverse problems, including potential field, electromagnetic, and seismic methods. Unique in its focus on providing a link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, it represents an exhaustive treatise on inversion theory.Written by one of the world’s foremost experts, this work is widely recognized as the ultimate researcher’s reference on geophysical inverse theory and its practical scientific applications. Presents state-of-the-art geophysical inverse theory developed in modern mathematical terminology—the first to treat many kinds of inversion and imaging techniques in a unified mathematical way Provides a critical link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, and represents an exhaustive treatise on geophysical inversion theory Features more than 300 illustrations, figures, charts and graphs to underscore key concepts Reflects the latest developments in inversion theory and applications and captures the most significant changes in the field over the past decade
