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The IMA Hot Topics workshop on compatible spatialdiscretizations was held May 11-15, 2004 at the University of Minnesota. The purpose of the workshop was to bring together scientists at the forefront of the research in the numerical solution of PDEs to discuss recent advances and novel applications of geometrical and homological approaches to discretization. This volume contains original contributions based on the material presented at the workshop. A unique feature of the collection is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Compatible spatial discretizations are those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. The papers in the volume offer a snapshot of the current trends and developments in compatible spatial discretizations. The reader will find valuable insights on spatial compatibility from several different perspectives and important examples of applications compatible discretizations in computational electromagnetics, geosciences, linear elasticity, eigenvalue approximations and MHD. The contributions collected in this volume will help to elucidate relations between different methods and concepts and to generally advance our understanding of compatible spatial discretizations for PDEs. Abstracts and presentation slides from the workshop can be accessed at http://www.ima.umn.edu/talks/workshops/5-11-15.2004/.

Differential equations, Partial --- Finite element method --- Numerical solutions. --- Mathematics. --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Differential equations, partial. --- Numerical analysis. --- Applications of Mathematics. --- Partial Differential Equations. --- Numerical Analysis. --- Partial differential equations --- Mathematical analysis --- Math --- Science --- Applied mathematics. --- Engineering mathematics. --- Partial differential equations. --- Engineering --- Engineering analysis --- Mathematics

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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.

Electromagnetism --- Finite element method. --- Antennas (Electronics) --- Mathematics. --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Finite elements. --- Integral equations. --- Volume integral methods. --- Hybrid techniques. --- Numerical methods. --- Antennas. --- Radiation. --- Radar scattering. --- Electromagnetics. --- Periodic media. --- Metamaterials. --- Design. --- Optimization. --- Electronic apparatus and appliances --- Numerical analysis --- Isogeometric analysis --- Antenna arrays. --- Electromagnetism. --- Electromagnetics --- Magnetic induction --- Magnetism --- Metamaterials --- Arrays, Antenna --- Large space structures (Astronautics)

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FEM, and the associated computer software are widely recognized as some of the most effective tools for solutions of large-scale engineering applications. Efficient equation and eigen-solvers play critical roles in solving these problems. Sparse matrix technologies have evolved and are now mature enough that all popular and commercialized FEM codes have inserted sparse solvers into their software. So far, however, few books include detailed discussion and explanation of sparse equation-solvers and Lanczos domain decomposition (DD) or finite element formulation for parallel computing purposes. The material in Finite Element Methods: Parallel-Sparse Statics and Eigen-Solutions has evolved over the past several years from the author's research work and his graduate courses. This book is ideal for graduate students, practicing engineers and researchers, as well as mathematicians and computer scientists. Dr. Duc T. Nguyen is the founding Director of the Institute for Multidisciplinary Parallel-Vector Computation and Professor of Civil and Environmental Engineering at Old Dominion University. Dr. Nguyen has been listed as an ISI Highly Cited Researcher™ in the field of engineering.

Engineering. --- Microprocessors. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Physics. --- Computational intelligence. --- Appl.Mathematics/Computational Methods of Engineering. --- Applications of Mathematics. --- Computational Intelligence. --- Numerical and Computational Physics. --- Processor Architectures. --- Computational Mathematics and Numerical Analysis. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Engineering --- Engineering analysis --- Mathematical analysis --- Minicomputers --- Construction --- Industrial arts --- Technology --- Mathematics --- Finite element method. --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Mathematics. --- Computer science. --- Computer science --- Mathematical and Computational Engineering. --- Numerical and Computational Physics, Simulation. --- Informatics --- Science --- Math --- Numerical analysis.

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The Finite Element Method and Applications with ANSYS® provides the reader with theoretical and practical knowledge of the finite element method and with the skills required to analyze engineering problems with ANSYS®, a commercially available FEA program. This self-contained, introductory text minimizes the need for additional reference material, covering the fundamental topics in finite element methods, as well as advanced topics concerning modeling and analysis with ANSYS®. These subjects are introduced through extensive examples from various engineering disciplines and are presented in a clear, step-by-step fashion. The book focuses on the use of ANSYS® through both the Graphics User Interface (GUI) and the ANSYS® Parametric Design Language (APDL). This volume addresses these specific areas: An introduction to FEM Fundamentals and analysis capabilities of ANSYS®, with practical modeling considerations Fundamentals of discretization and approximation functions Modeling techniques and details of mesh generation in ANSYS® Creating solutions and reviewing results Finite element equations based on the method of weighted residuals and on the principle of minimum potential energy The use of commands and APDL and the development of macro files Example problems and solutions corresponding to linear structural analysis Example problems and solutions related to heat transfer and moisture diffusion Nonlinear structural problems Advanced subjects such as submodeling, substructuring, interaction with external files, and modification of ANSYS®-GUI Additional materials for this book, including the "input" files for the example problems, as well as the colored figures and screen shots, allowing them to be regenerated on the reader’s own computer, may be downloaded from http://extras.springer.com. Students, researchers, and practicing engineers will find this an essential reference for use in predicting and simulating the physical behavior of complex engineering systems using ANSYS®.  .

Finite element method. --- ANSYS (Computer system) --- ANSYS Engineering Analysis System (Computer system) --- Computer systems --- Engineering --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Data processing --- ANSYS (Computer system). --- Mechanical engineering. --- Engineering mathematics. --- Computer aided design. --- Computer simulation. --- Computer science. --- Mechanical Engineering. --- Mathematical and Computational Engineering. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Simulation and Modeling. --- Computational Science and Engineering. --- Engineering, Mechanical --- Machinery --- Steam engineering --- Informatics --- Science --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Engineering analysis --- Mathematical analysis --- Mathematics --- Applied mathematics. --- Computer-aided engineering. --- Computer mathematics. --- Computer mathematics --- Electronic data processing --- CAE

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- A proven keystone reference in the library of any engineer needing to apply the finite element method to solid mechanics and structural design.
- Founded by an influential pioneer in the field and updated in this seventh edition by an author team incorporating academic authority and industrial simulation experience.
- Features new chapters on topics including material constitution using representative volume elements, as well as consolidated and expanded sections on rod and shell models.

The Finite Element Method *for Solid and Structural Mechanics* is the key text and reference for engineers, researchers and senior students dealing with the analysis and modeling of structures, from large civil engineering projects such as dams to aircraft structures and small engineered components.

This edition brings a thorough update and rearrangement of the books content, including new chapters on:

- Material constitution using representative volume elements
- Differential geometry and calculus on manifolds
- Background mathematics and linear shell theory

Focusing on the core knowledge, mathematical and analytical tools needed for successful structural analysis and modeling, ***The Finite Element Method for Solid and Structural Mechanics*** is the authoritative resource of choice for graduate level students, researchers and professional engineers.


Mechanical properties of solids --- CAE (computer aided engineering) --- eindige elementen --- computer-aided engineering --- finite element method --- 539.4.01 --- prijs voor de 3 delen --- Continuum mechanics --- Finite element method --- Structural analysis (Engineering) --- algebra --- materialen --- mechanica --- niet-lineaire systemen --- sterkteleer --- toegepaste mechanica --- vaste stoffen --- wiskunde --- 519.63 --- 519.6 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Architectural engineering --- Engineering, Architectural --- Structural mechanics --- Structures, Theory of --- Structural engineering --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Finite differences. Functional and integral equations --- Continuum mechanics. --- Finite element method. --- Structural analysis (Engineering). --- Element fini