Element Master is a story that revolves around a young lad named Charles Magruth. He lives in a thorp called Dauni Village. A thorp isolated a long way from the outdoor world. Charles was gifted to master a certain element. As weak and slow as he was, he had vast dreams. Charles lead a simple life until a certain festive occasion took a turn in his life when he was spot witnessing a homicide which pressured him to depart from his village and cherished ones. He had a gratifying journey to the new city as he saw lifestyles in the town was full of excitement. Though, there came a time where he had to decide if he wants to run abroad his entire existence for fear concerning of The Order or remain and emerge as a fighter to stand against them. The whole plot takes a turn when Charles discovers that he possesses the ability to control several elements. Come and join Charles in his interesting journey as he strives to discover his true potential and finds the love of his life.

This series lecture is an introduction to the finite element method with applications in electromagnetics. The finite element method is a numerical method that is used to solve boundary-value problems characterized by a partial differential equation and a set of boundary conditions. The geometrical domain of a boundary-value problem is discretized using sub-domain elements, called the finite elements, and the differential equation is applied to a single element after it is brought to a “weak” integro-differential form. A set of shape functions is used to represent the primary unknown variable in the element domain. A set of linear equations is obtained for each element in the discretized domain. A global matrix system is formed after the assembly of all elements. This lecture is divided into two chapters. Chapter 1 describes one-dimensional boundary-value problems with applications to electrostatic problems described by the Poisson's equation. The accuracy of the finite element method is evaluated for linear and higher order elements by computing the numerical error based on two different definitions. Chapter 2 describes two-dimensional boundary-value problems in the areas of electrostatics and electrodynamics (time-harmonic problems). For the second category, an absorbing boundary condition was imposed at the exterior boundary to simulate undisturbed wave propagation toward infinity. Computations of the numerical error were performed in order to evaluate the accuracy and effectiveness of the method in solving electromagnetic problems. Both chapters are accompanied by a number of Matlab codes which can be used by the reader to solve one- and two-dimensional boundary-value problems. These codes can be downloaded from the publisher's URL: www.morganclaypool.com/page/polycarpou This lecture is written primarily for the nonexpert engineer or the undergraduate or graduate student who wants to learn, for the first time, the finite element method with applications to electromagnetics. It is also targeted for research engineers who have knowledge of other numerical techniques and want to familiarize themselves with the finite element method. The lecture begins with the basics of the method, including formulating a boundary-value problem using a weighted-residual method and the Galerkin approach, and continues with imposing all three types of boundary conditions including absorbing boundary conditions. Another important topic of emphasis is the development of shape functions including those of higher order. In simple words, this series lecture provides the reader with all information necessary for someone to apply successfully the finite element method to one- and two-dimensional boundary-value problems in electromagnetics. It is suitable for newcomers in the field of finite elements in electromagnetics.

An introductory textbook for engineering students, connecting finite element theory with practical application and implementation.

This book is a self-contained, programming-oriented and learner-centered book on finite element method (FEM), with special emphasis given to developing MATLAB® programs for numerical modeling of electromagnetic boundary value problems. It provides a deep understanding and intuition of FEM programming by means of step-by-step MATLAB® programs with detailed descriptions, and eventually enabling the readers to modify, adapt and apply the provided programs and formulations to develop FEM codes for similar problems through various exercises. It starts with simple one-dimensional static and time-harmonic problems and extends the developed theory to more complex two- or three-dimensional problems. It supplies sufficient theoretical background on the topic, and it thoroughly covers all phases (pre-processing, main body and post-processing) in FEM. FEM formulations are obtained for boundary value problems governed by a partial differential equation that is expressed in terms of a generic unknown function, and then, these formulations are specialized to various electromagnetic applications together with a post-processing phase. Since the method is mostly described in a general context, readers from other disciplines can also use this book and easily adapt the provided codes to their engineering problems. After forming a solid background on the fundamentals of FEM by means of canonical problems, readers are guided to more advanced applications of FEM in electromagnetics through a survey chapter at the end of the book. Offers a self-contained and easy-to-understand introduction to the theory and programming of finite element method. Covers various applications in the field of static and time-harmonic electromagnetics. Includes one-, two- and three-dimensional finite element codes in MATLAB®. Enables readers to develop finite element programming skills through various MATLAB® codes and exercises. Promotes self-directed learning skills and provides an effective instruction tool.

Complex multiscale systems such as combined free or porous flow regimes and transport processes governed by combined diffusion, convection and reaction mechanisms, which cannot be readily modeled using traditional methods, can be solved by multiscale or stabilized finite element schemes. Due to the importance of the described multiscale processes in applications such as separation processes, reaction engineering and environmental systems analysis, a sound knowledge of such methods is essential for many researchers and design engineers who wish to develop reliable solutions for industrially relevant problems. The main scope of this book is to provide an authoritative description of recent developments in the field of finite element analysis, with a particular emphasis on the multiscale finite element modeling of transport phenomena and flow problem.

Covers the latest developments in modeling elastohydrodynamic lubrication (EHL) problems using the finite element method (FEM) This comprehensive guide introduces readers to a powerful technology being used today in the modeling of elastohydrodynamic lubrication (EHL) problems. It provides a general framework based on the finite element method (FEM) for dealing with multi-physical problems of complex nature (such as the EHL problem) and is accompanied by a website hosting a user-friendly FEM software for the treatment of EHL problems, based on the methodology described in the book. Finite Element Modeling of Elastohydrodynamic Lubrication Problems begins with an introduction to both the EHL and FEM fields. It then covers Standard FEM modeling of EHL problems, before going over more advanced techniques that employ model order reduction to allow significant savings in computational overhead. Finally, the book looks at applications that show how the developed modeling framework could be used to accurately predict the performance of EHL contacts in terms of lubricant film thickness, pressure build-up and friction coefficients under different configurations. Finite Element Modeling of Elastohydrodynamic Lubrication Problems offers in-depth chapter coverage of Elastohydrodynamic Lubrication and its FEM Modeling, under Isothermal Newtonian and Generalized-Newtonian conditions with the inclusion of Thermal Effects; Standard FEM Modeling; Advanced FEM Modeling, including Model Order Reduction techniques; and Applications, including Pressure, Film Thickness and Friction Predictions, and Coated EHL. This book: Comprehensively covers the latest technology in modeling EHL problems Focuses on the FEM modeling of EHL problems Incorporates advanced techniques based on model order reduction Covers applications of the method to complex EHL problems Accompanied by a website hosting a user-friendly FEM-based EHL software Finite Element Modeling of Elastohydrodynamic Lubrication Problems is an ideal book for researchers and graduate students in the field of Tribology.

The second edition of An Introduction to Nonlinear Finite Element Analysis has the same objective as the first edition, namely, to facilitate an easy and thorough understanding of the details that are involved in the theoretical formulation, finite element model development, and solutions of nonlinear problems. The book offers an easy-to-understand treatment of the subject of nonlinear finite element analysis, which includes element development from mathematical models and numerical evaluation of the underlying physics. The new edition is extensively reorganized and contains substantial amounts of new material. Chapter 1 in the second edition contains a section on applied functional analysis. Chapter 2 on nonlinear continuum mechanics is entirely new. Chapters 3 through 8 in the new edition correspond to Chapter 2 through 8 of the first edition, but with additional explanations, examples, and exercise problems. Material on time dependent problems from Chapter 8 of the first edition is absorbed into Chapters 4 through 8 of the new edition. Chapter 9 is extensively revised and it contains up to date developments in the large deformation analysis of isotropic, composite and functionally graded shells. Chapter 10 of the first edition on material nonlinearity and coupled problems is reorganized in the second edition by moving the material on solid mechanics to Chapter 12 in the new edition and material on coupled problems to the new chapter, Chapter 10, on weak-form Galerkin finite element models of viscous incompressible fluids. Finally, Chapter 11 in the second edition is entirely new and devoted to least-squares finite element models of viscous incompressible fluids. Chapter 12 of the second edition is enlarged to contain finite element models of viscoelastic beams. In general, all of the chapters of the second edition contain additional explanations, detailed example problems, and additional exercise problems. Although all of the progr