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Author: Kerry Key Publisher: ISBN: Category : Languages : en Pages :
Book Description
We present a parallel goal-oriented adaptive finite element algorithm that can be used to rapidly compute highly accurate solutions for 2.5D controlled-source electromagnetic (CSEM) and 2D magnetotelluric (MT) modeling problems. We employ unstructured triangular grids to permit efficient discretization of complex modeling domains such as those containing topography, dipping layers and multiple scale structures. Iterative mesh refinement is guided by a goal-oriented error estimator based on a form of dual residual weighting, which is carried out using hierarchical basis computations. Our formulation of the error estimator considers the relative error in the strike aligned fields and their spatial gradients, and therefore results in a more efficient use of mesh vertices than previous error estimators based on absolute field errors. This algorithm is parallelized over frequencies, transmitters, receivers and wave-numbers, where adaptive refinement can be performed in parallel on subsets of these parameters while nearby parameters are able to share the refined grid, thus enabling our algorithm to achieve accurate solutions in run-times of seconds to tens of seconds for realistic models and data parameters when run on cluster computers containing about a thousand processors. Application of this new algorithm to a complex model that includes strong seafloor topography variations and multiple thin stacked reservoirs demonstrates the performance and scalability on a large cluster computer.
Author: Kerry Key Publisher: ISBN: Category : Languages : en Pages :
Book Description
We present a parallel goal-oriented adaptive finite element algorithm that can be used to rapidly compute highly accurate solutions for 2.5D controlled-source electromagnetic (CSEM) and 2D magnetotelluric (MT) modeling problems. We employ unstructured triangular grids to permit efficient discretization of complex modeling domains such as those containing topography, dipping layers and multiple scale structures. Iterative mesh refinement is guided by a goal-oriented error estimator based on a form of dual residual weighting, which is carried out using hierarchical basis computations. Our formulation of the error estimator considers the relative error in the strike aligned fields and their spatial gradients, and therefore results in a more efficient use of mesh vertices than previous error estimators based on absolute field errors. This algorithm is parallelized over frequencies, transmitters, receivers and wave-numbers, where adaptive refinement can be performed in parallel on subsets of these parameters while nearby parameters are able to share the refined grid, thus enabling our algorithm to achieve accurate solutions in run-times of seconds to tens of seconds for realistic models and data parameters when run on cluster computers containing about a thousand processors. Application of this new algorithm to a complex model that includes strong seafloor topography variations and multiple thin stacked reservoirs demonstrates the performance and scalability on a large cluster computer.
Author: Publisher: ISBN: Category : Electronic books Languages : en Pages : 131
Book Description
Over the past 10 years, both academia and industry collected large amounts of EM data. Compared with the abundance of data, the processing capacity is the bottleneck to have deeper insight into the earth. To increase the 3D processing capacity, this dissertation focuses on developing a 3D EM data processing toolkit, which could connect from data to model, uncovering the conductivity distribution of the seafloor. The first part of the dissertation employs a parallel goal-oriented adaptive finite element method for 3D electromagnetic modeling. To efficiently discretize the model, we use the unstructured tetrahedral mesh to accommodate arbitrarily complex 3D conductivity variations. Accuracy of the finite element solution could be achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by the goal-oriented error estimation approach to generate the optimal mesh, such that accurate EM responses at the locations of the EM receivers could be calculated. To further improve the computational efficiency, our algorithm is parallelized over frequencies, transmitters and receivers. We benchmark the newly developed algorithm by validating the controlled-source EM solutions on a 1D layered model. Furthermore, we employ a 3D model with significant seafloor bathymetry variations and a heterogeneous subsurface to demonstrate the code's ability to model complex features. In the second part, we introduce the framework for 3D inversion of marine controlled-source electromagnetic (CSEM) data. Our code, named Modeling with Adaptively Refined Elements for 3D EM (MARE3DEM), uses a new variant of the regularized Occam method for the inversion. The forward solver introduced previously serves as the backbone to calculate the model response and jacobians. The forward and inverse meshes are decoupled, such that we could accommodate the size of the inverse problem without sacrificing the accuracy of the forward solution. The sensitivity kernels which describe the change of the responses with respect to the variation of model parameters are efficiently calculated using the adjoint method. We show the reliability and the potential of the inversion algorithm by applying it to the inversion of synthetic marine controlled-source EM data.
Author: Magdalena Salazar-Palma Publisher: Artech House Publishers ISBN: Category : Mathematics Languages : en Pages : 824
Book Description
Ensure the accuracy of your results when applying the Finite Element Method (FEM) to electromagnetic and antenna problems with this self-contained reference. It provides you with a solid understanding of the method, describes its key elements and numerical techniques, and identifies various approaches to using the FEM in solving real-world microwave field problems.
Author: Sara Pollock Publisher: ISBN: 9781267366054 Category : Languages : en Pages : 123
Book Description
In this thesis we discuss convergence theory for goal-oriented adaptive finite element methods for second order elliptic problems. We develop results for both linear nonsymmetric and semilinear problems. We start with a brief description of the finite element method applied to these problems and some basic error estimates. We then provide a detailed error analysis of the method as described for each problem. In each case, we establish convergence in the sense of the quantity of interest with a goal-oriented variation of the standard adaptive finite element method using residual-based indicators. In the linear case we establish the adjoint as the appropriate differential operator for the dual problem. We establish contraction of the quasi-error for each of the primal and dual problems yielding convergence in the quantity of interest. We follow these results with a complexity analysis of the method. In the semilinear case we introduce three types of linearized dual problems used to establish our results. We give a brief summary of a priori estimates for this class of problems. After establishing contraction results for the primal problem, we then provide additional estimates to show contraction of the combined primal and dual system, yielding convergence of the goal function. We support these results with some numerical experiments. Finally, we include an appendix outlining some common methods used in a posteriori error estimation and briefly describe iterative methods for solving nonlinear problems.
Author: Jian-Ming Jin Publisher: John Wiley & Sons ISBN: 1118841980 Category : Science Languages : en Pages : 1212
Book Description
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The Finite Element Method in Electromagnetics, Third Edition explains the method’s processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applications—giving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems. Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes: A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonics The finite element analysis of wave propagation, scattering, and radiation in periodic structures The time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomena Novel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystals Along with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.
Author: John Leonidas Volakis Publisher: Morgan & Claypool Publishers ISBN: 1598290800 Category : Science Languages : en Pages : 157
Book Description
This book provides a brief overview of the popular Finite Element Method (FEM) and its hybrid versions for electromagnetics with applications to radar scattering, antennas and arrays, guided structures, microwave components, frequency selective surfaces, periodic media, and RF materials characterizations and related topics. It starts by presenting concepts based on Hilbert and Sobolev spaces as well as Curl and Divergence spaces for generating matrices, useful in all engineering simulation methods. It then proceeds to present applications of the finite element and finite element-boundary integral methods for scattering and radiation. Applications to periodic media, metamaterials and bandgap structures are also included. The hybrid volume integral equation method for high contrast dielectrics and is presented for the first time. Another unique feature of the book is the inclusion of design optimization techniques and their integration within commercial numerical analysis packages for shape and material design. To aid the reader with the method's utility, an entire chapter is devoted to two-dimensional problems. The book can be considered as an update on the latest developments since the publication of our earlier book (Finite Element Method for Electromagnetics, IEEE Press, 1998). The latter is certainly complementary companion to this one.
Author: Gérard Meunier Publisher: Wiley-ISTE ISBN: 9781848210301 Category : Science Languages : en Pages : 832
Book Description
Written by specialists of modeling in electromagnetism, this book provides a comprehensive review of the finite element method for low frequency applications. Fundamentals of the method as well as new advances in the field are described in detail. Chapters 1 to 4 present general 2D and 3D static and dynamic formulations by the use of scalar and vector unknowns and adapted interpolations for the fields (nodal, edge, face or volume). Chapter 5 is dedicated to the presentation of different macroscopic behavior laws of materials and their implementation in a finite element context: anisotropy and hysteretic properties for magnetic sheets, iron losses, non-linear permanent magnets and superconductors. More specific formulations are then proposed: the modeling of thin regions when finite elements become misfit (Chapter 6), infinite domains by using geometrical transformations (Chapter 7), the coupling of 2D and 3D formulations with circuit equations (Chapter 8), taking into account the movement, particularly in the presence of Eddy currents (Chapter 9) and an original approach for the treatment of geometrical symmetries when the sources are not symmetric (Chapter 10). Chapters 11 to 13 are devoted to coupled problems: magneto-thermal coupling for induction heating, magneto-mechanical coupling by introducing the notion of strong and weak coupling and magneto-hydrodynamical coupling focusing on electromagnetic instabilities in fluid conductors. Chapter 14 presents different meshing methods in the context of electromagnetism (presence of air) and introduces self-adaptive mesh refinement procedures. Optimization techniques are then covered in Chapter 15, with the adaptation of deterministic and probabilistic methods to the numerical finite element environment. Chapter 16 presents a variational approach of electromagnetism, showing how Maxwell equations are derived from thermodynamic principles.
Author: John Leonidas Volakis Publisher: Universities Press ISBN: 9788173713897 Category : Antennas (Electronics) Languages : en Pages : 370
Book Description
The finite element methods is one of the most popular and well-established numerical techniques in engineering. This book covers the theory, development, implementation and application of the finite element method and its hybrid versions to electromagnetics.
Author: Kerry Key
Author: Kerry Key
Author: 
Author: Magdalena Salazar-Palma
Author: Sara Pollock
Author: Jian-Ming Jin
Author: John Leonidas Volakis
Author: Gérard Meunier
Author: John Leonidas Volakis
Author: Leon Vardapetyan
Author: Xiaowei Zhan