Modeling and Computations in Electromagnetics

Download Modeling and Computations in Electromagnetics PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3540737782
Total Pages : 239 pages
Book Rating : 4.5/5 (47 download)

DOWNLOAD NOW!


Book Synopsis Modeling and Computations in Electromagnetics by : Habib Ammari

Download or read book Modeling and Computations in Electromagnetics written by Habib Ammari and published by Springer Science & Business Media. This book was released on 2008-01-12 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is nothing less than an essential text in what is a new and growing discipline. Electromagnetic modeling and computations is expanding as a result of the steadily increasing demand for designing electrical devices, modeling electromagnetic materials, and simulating electromagnetic fields in nanoscale structures. The aim of this volume is to bring together prominent worldwide experts to review state-of-the-art developments and future trends of modeling and computations in electromagnetics.

Advanced Modeling in Computational Electromagnetic Compatibility

Download Advanced Modeling in Computational Electromagnetic Compatibility PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 0470116870
Total Pages : 541 pages
Book Rating : 4.4/5 (71 download)

DOWNLOAD NOW!


Book Synopsis Advanced Modeling in Computational Electromagnetic Compatibility by : Dragan Poljak

Download or read book Advanced Modeling in Computational Electromagnetic Compatibility written by Dragan Poljak and published by John Wiley & Sons. This book was released on 2007-02-26 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text combines the fundamentals of electromagnetics with numerical modeling to tackle a broad range of current electromagnetic compatibility (EMC) problems, including problems with lightning, transmission lines, and grounding systems. It sets forth a solid foundation in the basics before advancing to specialized topics, and allows readers to develop their own EMC computational models for applications in both research and industry.

Electromagnetic Field Computation by Network Methods

Download Electromagnetic Field Computation by Network Methods PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3540939466
Total Pages : 219 pages
Book Rating : 4.5/5 (49 download)

DOWNLOAD NOW!


Book Synopsis Electromagnetic Field Computation by Network Methods by : Leopold B. Felsen

Download or read book Electromagnetic Field Computation by Network Methods written by Leopold B. Felsen and published by Springer Science & Business Media. This book was released on 2009-03-05 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors propose a systematic and rigorous treatment of electromagnetic field representations in complex structures. The architecture suggested in this book accommodates use of different numerical methods as well as alternative Green's function representations in each of the subdomains resulting from a partitioning of the overall problem. The subdomains are regions of space where electromagnetic energy is stored and are described in terms of equivalent circuit representations based either on lumped element circuits or on transmission lines. Connection networks connect the subcircuits representing the subdomains. The connection networks are lossless, don't store energy and represent the overall problem topology. This is similar to what is done in circuit theory and permits a phrasing of the solution of EM field problems in complex structures by Network-oriented methods.

Human Interaction with Electromagnetic Fields

Download Human Interaction with Electromagnetic Fields PDF Online Free

Author :
Publisher : Academic Press
ISBN 13 : 012816624X
Total Pages : 282 pages
Book Rating : 4.1/5 (281 download)

DOWNLOAD NOW!


Book Synopsis Human Interaction with Electromagnetic Fields by : Dragan Poljak

Download or read book Human Interaction with Electromagnetic Fields written by Dragan Poljak and published by Academic Press. This book was released on 2019-06-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Human Interaction with Electromagnetic Fields: Computational Models in Dosimetry presents some highly rigorous and sophisticated integral equation techniques from computational electromagnetics (CEM), along with practical techniques for the calculation and measurement of internal dosimetry. Theory is accompanied by numerical modeling algorithms and illustrative computational examples that range from academic to full real-world scenarios. - Covers both deterministic and stochastic modeling - Presents implementations of integral equation approaches, overcoming the limitations of the FDTD approach - Presents various biomedical applications

Low-Frequency Electromagnetic Modeling for Electrical and Biological Systems Using MATLAB

Download Low-Frequency Electromagnetic Modeling for Electrical and Biological Systems Using MATLAB PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119052467
Total Pages : 616 pages
Book Rating : 4.1/5 (19 download)

DOWNLOAD NOW!


Book Synopsis Low-Frequency Electromagnetic Modeling for Electrical and Biological Systems Using MATLAB by : Sergey N. Makarov

Download or read book Low-Frequency Electromagnetic Modeling for Electrical and Biological Systems Using MATLAB written by Sergey N. Makarov and published by John Wiley & Sons. This book was released on 2015-05-13 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a detailed and systematic description of the Method of Moments (Boundary Element Method) for electromagnetic modeling at low frequencies and includes hands-on, application-based MATLAB® modules with user-friendly and intuitive GUI and a highly visualized interactive output. Includes a full-body computational human phantom with over 120 triangular surface meshes extracted from the Visible Human Project® Female dataset of the National library of Medicine and fully compatible with MATLAB® and major commercial FEM/BEM electromagnetic software simulators. This book covers the basic concepts of computational low-frequency electromagnetics in an application-based format and hones the knowledge of these concepts with hands-on MATLAB® modules. The book is divided into five parts. Part 1 discusses low-frequency electromagnetics, basic theory of triangular surface mesh generation, and computational human phantoms. Part 2 covers electrostatics of conductors and dielectrics, and direct current flow. Linear magnetostatics is analyzed in Part 3. Part 4 examines theory and applications of eddy currents. Finally, Part 5 evaluates nonlinear electrostatics. Application examples included in this book cover all major subjects of low-frequency electromagnetic theory. In addition, this book includes complete or summarized analytical solutions to a large number of quasi-static electromagnetic problems. Each Chapter concludes with a summary of the corresponding MATLAB® modules. Combines fundamental electromagnetic theory and application-oriented computation algorithms in the form of stand alone MATLAB® modules Makes use of the three-dimensional Method of Moments (MoM) for static and quasistatic electromagnetic problems Contains a detailed full-body computational human phantom from the Visible Human Project® Female, embedded implant models, and a collection of homogeneous human shells Low-Frequency Electromagnetic Modeling for Electrical and Biological Systems Using MATLAB® is a resource for electrical and biomedical engineering students and practicing researchers, engineers, and medical doctors working on low-frequency modeling and bioelectromagnetic applications.

Computational Methods in Geophysical Electromagnetics

Download Computational Methods in Geophysical Electromagnetics PDF Online Free

Author :
Publisher : SIAM
ISBN 13 : 1611973805
Total Pages : 148 pages
Book Rating : 4.6/5 (119 download)

DOWNLOAD NOW!


Book Synopsis Computational Methods in Geophysical Electromagnetics by : Eldad Haber

Download or read book Computational Methods in Geophysical Electromagnetics written by Eldad Haber and published by SIAM. This book was released on 2014-12-11 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a framework for students and practitioners who are working on the solution of electromagnetic imaging in geophysics. Bridging the gap between theory and practical applied material (for example, inverse and forward problems), it provides a simple explanation of finite volume discretization, basic concepts in solving inverse problems through optimization, a summary of applied electromagnetics methods, and MATLAB??code for efficient computation.

Mathematical Foundations of Computational Electromagnetism

Download Mathematical Foundations of Computational Electromagnetism PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3319708422
Total Pages : 460 pages
Book Rating : 4.3/5 (197 download)

DOWNLOAD NOW!


Book Synopsis Mathematical Foundations of Computational Electromagnetism by : Franck Assous

Download or read book Mathematical Foundations of Computational Electromagnetism written by Franck Assous and published by Springer. This book was released on 2018-06-09 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.

Essentials of Computational Electromagnetics

Download Essentials of Computational Electromagnetics PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 0470829656
Total Pages : 291 pages
Book Rating : 4.4/5 (78 download)

DOWNLOAD NOW!


Book Synopsis Essentials of Computational Electromagnetics by : Xin-Qing Sheng

Download or read book Essentials of Computational Electromagnetics written by Xin-Qing Sheng and published by John Wiley & Sons. This book was released on 2012-03-22 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essentials of Computational Electromagnetics provides an in-depth introduction of the three main full-wave numerical methods in computational electromagnetics (CEM); namely, the method of moment (MoM), the finite element method (FEM), and the finite-difference time-domain (FDTD) method. Numerous monographs can be found addressing one of the above three methods. However, few give a broad general overview of essentials embodied in these methods, or were published too early to include recent advances. Furthermore, many existing monographs only present the final numerical results without specifying practical issues, such as how to convert discretized formulations into computer programs, and the numerical characteristics of the computer programs. In this book, the authors elaborate the above three methods in CEM using practical case studies, explaining their own research experiences along with a review of current literature. A full analysis is provided for typical cases, including characteristics of numerical methods, helping beginners to develop a quick and deep understanding of the essentials of CEM. Outlines practical issues, such as how to convert discretized formulations into computer programs Gives typical computer programs and their numerical characteristics along with line by line explanations of programs Uses practical examples from the authors' own work as well as in the current literature Includes exercise problems to give readers a better understanding of the material Introduces the available commercial software and their limitations This book is intended for graduate-level students in antennas and propagation, microwaves, microelectronics, and electromagnetics. This text can also be used by researchers in electrical and electronic engineering, and software developers interested in writing their own code or understanding the detailed workings of code. Companion website for the book: www.wiley.com/go/sheng/cem

Computational Electromagnetic-Aerodynamics

Download Computational Electromagnetic-Aerodynamics PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119155940
Total Pages : 456 pages
Book Rating : 4.1/5 (191 download)

DOWNLOAD NOW!


Book Synopsis Computational Electromagnetic-Aerodynamics by : Joseph J. S. Shang

Download or read book Computational Electromagnetic-Aerodynamics written by Joseph J. S. Shang and published by John Wiley & Sons. This book was released on 2016-03-22 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents numerical algorithms, procedures, and techniques required to solve engineering problems relating to the interactions between electromagnetic fields and fluid flow and interdisciplinary technology for aerodynamics, electromagnetics, chemical-physic kinetics, and plasmadynamics Integrates interlinking computational model and simulation techniques of aerodynamics and electromagnetics Combines classic plasma drift-diffusion theory and electron impact ionization modeling for electromagnetic-aerodynamic interactions Describes models of internal degrees of freedom for vibration relaxation and electron excitations

Applied Computational Electromagnetics

Download Applied Computational Electromagnetics PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642596290
Total Pages : 533 pages
Book Rating : 4.6/5 (425 download)

DOWNLOAD NOW!


Book Synopsis Applied Computational Electromagnetics by : Nikolaos K. Uzunoglu

Download or read book Applied Computational Electromagnetics written by Nikolaos K. Uzunoglu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: @EOI: AEI rEOMETPEI Epigram of the Academy of Plato in Athens Electromagnetism, the science of forces arising from Amber (HAEKTPON) and the stone of Magnesia (MArNHLIA), has been the fOWldation of major scientific breakthroughs, such as Quantum Mechanics and Theory of Relativity, as well as most leading edge technologies of the twentieth century. The accuracy of electromagnetic fields computations for engineering purposes has been significantly improved during the last decades, due to the deVelopment of efficient computational techniques and the availability of high performance computing. The present book is based on the contributions and discussions developed during the NATO Advanced Study Institute on Applied Computational Electromagnetics: State of the Art and Future Trends, which has taken place in Hellas, on the island of Samos, very close to the birthplace of Electromagnetism. The book covers the fundamental concepts, recent developments and advanced applications of Integral Equation and Metliod of Moments Techniques, Finite Element and BOWldary Element Methods, Finite Difference Time Domain and Transmission Line Methods. Furthermore, topics related to Computational Electromagnetics, such as Inverse Scattering, Semi-Analytical Methods and Parallel Processing Techniques are included. The collective presentation of the principal computational electromagnetics techniques, developed to handle diverse challenging leading edge technology problems, is expected to be useful to researchers and postgraduate students working in various topics of electromagnetic technologies.

Computational Geo-Electromagnetics

Download Computational Geo-Electromagnetics PDF Online Free

Author :
Publisher :
ISBN 13 : 0128196319
Total Pages : 462 pages
Book Rating : 4.1/5 (281 download)

DOWNLOAD NOW!


Book Synopsis Computational Geo-Electromagnetics by : Viacheslav V. Spichak

Download or read book Computational Geo-Electromagnetics written by Viacheslav V. Spichak and published by . This book was released on 2020-02 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Geo-Electromagnetics: Methods, Models, and Forecasts, Volume Five in the Computational Geophysics series, is devoted to techniques for building of geoelectrical models from electromagnetic data, featuring Bayesian statistical analysis and neural network algorithms. These models are applied to studying the geoelectrical structure of famous volcanoes (i.e., Vesuvio, Kilauea, Elbrus, Komagatake, Hengill) and geothermal zones (i.e., Travale, Italy; Soultz-sous-Forets, Elsace). Methodological recommendations are given on electromagnetic sounding of faults as well as geothermal and hydrocarbon reservoirs. Techniques for forecasting of petrophysical properties from the electrical resistivity as proxy parameter are also considered. Computational Geo-Electromagnetics: Methods, Models, and Forecasts offers techniques and algorithms for building geoelectrical models under conditions of rare or irregularly distributed EM data and/or lack of prior geological and geophysical information. This volume also includes methodological guidelines on interpretation of electromagnetic sounding data depending on goals of the study. Finally, it details computational algorithms for using electrical resistivity for properties beyond boreholes. Provides algorithms for inversion of incomplete, rare or irregularly distributed EM data Features methodological issues of building geoelectrical models Offers techniques for retrieving petrophysical properties from EM sounding data and well logs

Electromagnetics and Calculation of Fields

Download Electromagnetics and Calculation of Fields PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461206618
Total Pages : 583 pages
Book Rating : 4.4/5 (612 download)

DOWNLOAD NOW!


Book Synopsis Electromagnetics and Calculation of Fields by : Nathan Ida

Download or read book Electromagnetics and Calculation of Fields written by Nathan Ida and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to electromagnetic fields emphasizes the computation of fields and the development of theoretical relations. It presents the electromagnetic field and Maxwell's equations with a view toward connecting the disparate applications to the underlying relations, along with computational methods of solving the equations.

Mathematical Models and Numerical Simulation in Electromagnetism

Download Mathematical Models and Numerical Simulation in Electromagnetism PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3319029495
Total Pages : 440 pages
Book Rating : 4.3/5 (19 download)

DOWNLOAD NOW!


Book Synopsis Mathematical Models and Numerical Simulation in Electromagnetism by : Alfredo Bermúdez de Castro

Download or read book Mathematical Models and Numerical Simulation in Electromagnetism written by Alfredo Bermúdez de Castro and published by Springer. This book was released on 2014-07-22 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book represents a basic support for a master course in electromagnetism oriented to numerical simulation. The main goal of the book is that the reader knows the boundary-value problems of partial differential equations that should be solved in order to perform computer simulation of electromagnetic processes. Moreover it includes a part devoted to electric circuit theory based on ordinary differential equations. The book is mainly oriented to electric engineering applications, going from the general to the specific, namely, from the full Maxwell’s equations to the particular cases of electrostatics, direct current, magnetostatics and eddy currents models. Apart from standard exercises related to analytical calculus, the book includes some others oriented to real-life applications solved with MaxFEM free simulation software.

The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB® Simulations

Download The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB® Simulations PDF Online Free

Author :
Publisher : IET
ISBN 13 : 1613531753
Total Pages : 559 pages
Book Rating : 4.6/5 (135 download)

DOWNLOAD NOW!


Book Synopsis The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB® Simulations by : Atef Z. Elsherbeni

Download or read book The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB® Simulations written by Atef Z. Elsherbeni and published by IET. This book was released on 2015-11-25 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the best books on computational electromagnetics both for graduate students focusing on electromagnetics problems and for practicing engineering professionals in industry and government. It is designed as an advanced textbook and self-study guide to the FDTD method of solving EM problems and simulations. This latest edition has been expanded to include 5 entirely new chapters on advanced topics in the mainstream of FDTD practice. In addition to advanced techniques it also includes applications and examples, and some 'tricks and traps' of using MATLAB to achieve them. Compared to the previous version the second edition is more complete and is a good reference for someone who is performing FDTD research. This book is part of the ACES Series on Computational Electromagnetics and Engineering. Supplementary material can be found at the IET's ebook page Supplementary materials for professors are available upon request via email to [email protected].

Computational Electromagnetism

Download Computational Electromagnetism PDF Online Free

Author :
Publisher : Academic Press
ISBN 13 : 0080529666
Total Pages : 375 pages
Book Rating : 4.0/5 (85 download)

DOWNLOAD NOW!


Book Synopsis Computational Electromagnetism by : Alain Bossavit

Download or read book Computational Electromagnetism written by Alain Bossavit and published by Academic Press. This book was released on 1998-02-04 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Electromagnetism refers to the modern concept of computer-aided analysis, and design, of virtually all electric devices such as motors, machines, transformers, etc., as well as of the equipment inthe currently booming field of telecommunications, such as antennas, radars, etc. The present book is uniquely written to enable the reader-- be it a student, a scientist, or a practitioner-- to successfully perform important simulation techniques and to design efficient computer software for electromagnetic device analysis. Numerous illustrations, solved exercises, original ideas, and an extensive and up-to-date bibliography make it a valuable reference for both experts and beginners in the field. A researcher and practitioner will find in it information rarely available in other sources, such as on symmetry, bilateral error bounds by complimentarity, edge and face elements, treatment of infinite domains, etc. At the same time, the book is a useful teaching tool for courses in computational techniques in certain fields of physics and electrical engineering. As a self-contained text, it presents an extensive coverage of the most important concepts from Maxwells equations to computer-solvable algebraic systems-- for both static, quasi-static, and harmonic high-frequency problems.BenefitsTo the EngineerA sound background necessary not only to understand the principles behind variational methods and finite elements, but also to design pertinent and well-structured software.To the Specialist in Numerical ModelingThe book offers new perspectives of practical importance on classical issues: the underlying symmetry of Maxwell equations, their interaction with other fields of physics in real-life modeling, the benefits of edge and face elements, approaches to error analysis, and "complementarity."To the TeacherAn expository strategy that will allow you to guide the student along a safe and easy route through otherwise difficult concepts: weak formulations and their relation to fundamental conservation principles of physics, functional spaces, Hilbert spaces, approximation principles, finite elements, and algorithms for solving linear systems. At a higher level, the book provides a concise and self-contained introduction to edge elements and their application to mathematical modeling of the basic electromagnetic phenomena, and static problems, such as eddy-current problems and microwaves in cavities.To the StudentSolved exercises, with "hint" and "full solution" sections, will both test and enhance the understanding of the material. Numerous illustrations will help in grasping difficult mathematical concepts.

Deterministic and Stochastic Modeling in Computational Electromagnetics

Download Deterministic and Stochastic Modeling in Computational Electromagnetics PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119989264
Total Pages : 580 pages
Book Rating : 4.1/5 (199 download)

DOWNLOAD NOW!


Book Synopsis Deterministic and Stochastic Modeling in Computational Electromagnetics by : Dragan Poljak

Download or read book Deterministic and Stochastic Modeling in Computational Electromagnetics written by Dragan Poljak and published by John Wiley & Sons. This book was released on 2023-11-17 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deterministic and Stochastic Modeling in Computational Electromagnetics Help protect your network with this important reference work on cyber security Deterministic computational models are those for which all inputs are precisely known, whereas stochastic modeling reflects uncertainty or randomness in one or more of the data inputs. Many problems in computational engineering therefore require both deterministic and stochastic modeling to be used in parallel, allowing for different degrees of confidence and incorporating datasets of different kinds. In particular, non-intrusive stochastic methods can be easily combined with widely used deterministic approaches, enabling this more robust form of data analysis to be applied to a range of computational challenges. Deterministic and Stochastic Modeling in Computational Electromagnetics provides a rare treatment of parallel deterministic–stochastic computational modeling and its beneficial applications. Unlike other works of its kind, which generally treat deterministic and stochastic modeling in isolation from one another, it aims to demonstrate the usefulness of a combined approach and present particular use-cases in which such an approach is clearly required. It offers a non-intrusive stochastic approach which can be incorporated with minimal effort into virtually all existing computational models. Readers will also find: A range of specific examples demonstrating the efficiency of deterministic–stochastic modeling Computational examples of successful applications including ground penetrating radars (GPR), radiation from 5G systems, transcranial magnetic and electric stimulation (TMS and TES), and more Introduction to fundamental principles in field theory to ground the discussion of computational modeling Deterministic and Stochastic Modeling in Computational Electromagnetics is a valuable reference for researchers, including graduate and undergraduate students, in computational electromagnetics, as well as to multidisciplinary researchers, engineers, physicists, and mathematicians.

Computational Methods for Electromagnetics

Download Computational Methods for Electromagnetics PDF Online Free

Author :
Publisher : Universities Press
ISBN 13 : 9788173713774
Total Pages : 600 pages
Book Rating : 4.7/5 (137 download)

DOWNLOAD NOW!


Book Synopsis Computational Methods for Electromagnetics by : Andrew F. Peterson

Download or read book Computational Methods for Electromagnetics written by Andrew F. Peterson and published by Universities Press. This book was released on 2001 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an indispensable resource for making efficient and accurate formulations for electromagnetics applications and their numerical treatment, Employing a unified and coherent approach that is unmatched in the field, the authors deatil both integral and differential equations using the method-of-moments and finite-element procedures.