Multiscale Problems and Methods in Numerical Simulations PDF Download

Author: James H. Bramble
Publisher: Springer Science & Business Media
ISBN: 9783540200994
Category : Mathematics
Languages : en
Pages : 184

View

Book Description
This volume aims to disseminate a number of new ideas that have emerged in the last few years in the field of numerical simulation, all bearing the common denominator of the "multiscale" or "multilevel" paradigm. This covers the presence of multiple relevant "scales" in a physical phenomenon; the detection and representation of "structures", localized in space or in frequency, in the solution of a mathematical model; the decomposition of a function into "details" that can be organized and accessed in decreasing order of importance; and the iterative solution of systems of linear algebraic equations using "multilevel" decompositions of finite dimensional spaces.

Author: Alain Damlamian
Publisher: World Scientific
ISBN: 9814458120
Category : Mathematics
Languages : en
Pages : 314

View

Book Description
The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier-Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated.

Author: Weinan E
Publisher: Cambridge University Press
ISBN: 1107096545
Category : Mathematics
Languages : en
Pages : 485

View

Book Description
A systematic discussion of the fundamental principles, written by a leading contributor to the field.

Author: Sergio R. Idelsohn
Publisher: Springer
ISBN: 3319061364
Category : Technology & Engineering
Languages : en
Pages : 417

View

Book Description
This book presents and discusses mathematical models, numerical methods and computational techniques used for solving coupled problems in science and engineering. It takes a step forward in the formulation and solution of real-life problems with a multidisciplinary vision, accounting for all of the complex couplings involved in the physical description. Simulation of multifaceted physics problems is a common task in applied research and industry. Often a suitable solver is built by connecting together several single-aspect solvers into a network. In this book, research in various fields was selected for consideration: adaptive methodology for multi-physics solvers, multi-physics phenomena and coupled-field solutions, leading to computationally intensive structural analysis. The strategies which are used to keep these problems computationally affordable are of special interest, and make this an essential book.

Author: Björn Engquist
Publisher: Springer Science & Business Media
ISBN: 3540888578
Category : Computers
Languages : en
Pages : 332

View

Book Description
Most problems in science involve many scales in time and space. An example is turbulent ?ow where the important large scale quantities of lift and drag of a wing depend on the behavior of the small vortices in the boundarylayer. Another example is chemical reactions with concentrations of the species varying over seconds and hours while the time scale of the oscillations of the chemical bonds is of the order of femtoseconds. A third example from structural mechanics is the stress and strain in a solid beam which is well described by macroscopic equations but at the tip of a crack modeling details on a microscale are needed. A common dif?culty with the simulation of these problems and many others in physics, chemistry and biology is that an attempt to represent all scales will lead to an enormous computational problem with unacceptably long computation times and large memory requirements. On the other hand, if the discretization at a coarse level ignoresthe?nescale informationthenthesolutionwillnotbephysicallymeaningful. The in?uence of the ?ne scales must be incorporated into the model. This volume is the result of a Summer School on Multiscale Modeling and S- ulation in Science held at Boso ¤n, Lidingo ¤ outside Stockholm, Sweden, in June 2007. Sixty PhD students from applied mathematics, the sciences and engineering parti- pated in the summer school.

Author: Thomas Y. Hou
Publisher: World Scientific
ISBN: 9814273252
Category : Science
Languages : en
Pages : 379

View

Book Description
Multi-Scale Phenomena in Complex Fluids is a collection of lecture notes delivered during the ªrst two series of mini-courses from "Shanghai Summer School on Analysis and Numerics in Modern Sciences," which was held in 2004 and 2006 at Fudan University, Shanghai, China. This review volume of 5 chapters, covering various fields in complex fluids, places emphasis on multi-scale modeling, analyses and simulations. It will be of special interest to researchers and graduate students who want to work in the field of complex fluids.

Author: Alejandro A. Franco
Publisher: Springer
ISBN: 1447156773
Category : Technology & Engineering
Languages : en
Pages : 253

View

Book Description
The aim of this book is to review innovative physical multiscale modeling methods which numerically simulate the structure and properties of electrochemical devices for energy storage and conversion. Written by world-class experts in the field, it revisits concepts, methodologies and approaches connecting ab initio with micro-, meso- and macro-scale modeling of components and cells. It also discusses the major scientific challenges of this field, such as that of lithium-ion batteries. This book demonstrates how fuel cells and batteries can be brought together to take advantage of well-established multi-scale physical modeling methodologies to advance research in this area. This book also highlights promising capabilities of such approaches for inexpensive virtual experimentation. In recent years, electrochemical systems such as polymer electrolyte membrane fuel cells, solid oxide fuel cells, water electrolyzers, lithium-ion batteries and supercapacitors have attracted much attention due to their potential for clean energy conversion and as storage devices. This has resulted in tremendous technological progress, such as the development of new electrolytes and new engineering designs of electrode structures. However, these technologies do not yet possess all the necessary characteristics, especially in terms of cost and durability, to compete within the most attractive markets. Physical multiscale modeling approaches bridge the gap between materials’ atomistic and structural properties and the macroscopic behavior of a device. They play a crucial role in optimizing the materials and operation in real-life conditions, thereby enabling enhanced cell performance and durability at a reduced cost. This book provides a valuable resource for researchers, engineers and students interested in physical modelling, numerical simulation, electrochemistry and theoretical chemistry.

Author: Grigoris Pavliotis
Publisher: Springer Science & Business Media
ISBN: 0387738290
Category : Mathematics
Languages : en
Pages : 314

View

Book Description
This introduction to multiscale methods gives you a broad overview of the methods’ many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter.With the exception of Chapter One, all chapters are supplemented with exercises.

Author: Ivan G. Graham
Publisher: Springer Science & Business Media
ISBN: 3642220614
Category : Mathematics
Languages : en
Pages : 376

View

Book Description
The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

Author: Jacob Fish
Publisher: John Wiley & Sons
ISBN: 1118534859
Category : Science
Languages : en
Pages : 420

View

Book Description
Practical Multiscaling covers fundamental modelling techniques aimed at bridging diverse temporal and spatial scales ranging from the atomic level to a full-scale product level. It focuses on practical multiscale methods that account for fine-scale (material) details but do not require their precise resolution. The text material evolved from over 20 years of teaching experience at Rensselaer and Columbia University, as well as from practical experience gained in the application of multiscale software. This book comprehensively covers theory and implementation, providing a detailed exposition of the state-of-the-art multiscale theories and their insertion into conventional (single-scale) finite element code architecture. The robustness and design aspects of multiscale methods are also emphasised, which is accomplished via four building blocks: upscaling of information, systematic reduction of information, characterization of information utilizing experimental data, and material optimization. To ensure the reader gains hands-on experience, a companion website hosting a lite version of the multiscale design software (MDS-Lite) is available. Key features: Combines fundamental theory and practical methods of multiscale modelling Covers the state-of-the-art multiscale theories and examines their practical usability in design Covers applications of multiscale methods Accompanied by a continuously updated website hosting the multiscale design software Illustrated with colour images Practical Multiscaling is an ideal textbook for graduate students studying multiscale science and engineering. It is also a must-have reference for government laboratories, researchers and practitioners in civil, aerospace, pharmaceutical, electronics, and automotive industries, and commercial software vendors.