Multiscale Problems

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depen

Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the most successful domain decomposition solvers for partial differential equations. The purpose of this book is to gi

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 Mul

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 perio

The aim of this volume that presents lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework f

Physical phenomena can be modeled at varying degrees of complexity and at different scales. Multiscale modeling provides a framework, based on fundamental principles, for constructing mathematical and computational models of such phenomena, by examining the connection between models at different scales. This book, by a leading contributor to the field, is the first to provide a unified treatment of the subject, covering, in a systematic way, the general principles of multiscale models, algorithms and analysis. After discussing the basic techniques and introducing the fundamental physical models, the author focuses on the two most typical applications of multiscale modeling: capturing macroscale behavior and resolving local events. The treatment is complemented by chapters that deal with more specific problems. Throughout, the author strikes a balance between precision and accessibility, providing sufficient detail to enable the reader to understand the underlying principles without all

In many physical problems several scales present either in space or in time, caused by either inhomogeneity of the medium or complexity of the mechanical process. A fundamental approach is to first co

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

This book offers unique insight on structural safety and reliability by combining computational methods that address multiphysics problems, involving multiple equations describing different physical p

An original comprehensive guide on computational nanomechanics discussing basic concepts and implications in areas such as computational physics, materials, mechanics and engineering as well as several other interdisciplinary avenues. This book makes the underlying theory accessible to readers without specialised training or extensive background in quantum physics, statistical mechanics, or theoretical chemistry. It combines a careful treatment of theoretical concepts with a detailed tutorial on computer software and computing implementation, including multiscale simulation and computational statistical theory. Multidisciplinary perspectives are provided, yielding a true insight on the applications of computational nanomechanics across diverse engineering fields. The book can serve as a practical guide with step-by-step discussion of coding, example problems and case studies. This book will be essential reading for students new to the subject, as well as an excellent reference for gra

Focusing Mesoscales of Multiscale Problems in Chemical Engineering, a volume in the Advances in Chemical Engineering series provides readers with the personal views of recognized authorities who prese

The book is an introduction to the methods that deal with problems raised in using multiscale mathematical/statistical models such as wavelets and other multiscale systems. Special emphasis is given t

Ubiquitous and fundamental in cell mechanics, multiscale problems can arise in the growth of tumors, embryogenesis, tissue engineering, and more. Cell Mechanics: From Single Scale-Based Models to Mult

Complex fluid flows are encountered widely in nature, in living beings and in engineering practice. These flows often involve both geometric and dynamic complexity and present problems that are difficult to analyse because of their wide range of length and time scales, as well as their geometric configuration. This book describes some computational techniques and modelling strategies for analysing and predicting complex transport phenomena. It summarizes advances in the context of a pressure-based algorithm. Among methods discussed are discretization schemes for treating convection and pressure, parallel computing, multigrid methods, and composite, multiblock techniques. With respect to physical modelling, the book addresses issues of turbulence closure and multiscale, multiphase transport from an engineering viewpoint. Both fundamental and practical issues are considered, along with the relative merits of competing approaches. Numerous examples are given throughout the text. Mechanica

Complex fluid flows are encountered widely in nature, in living beings and in engineering practice. These flows often involve both geometric and dynamic complexity and present problems that are difficult to analyse because of their wide range of length and time scales, as well as their geometric configuration. This book describes some computational techniques and modelling strategies for analysing and predicting complex transport phenomena. It summarizes advances in the context of a pressure-based algorithm. Among methods discussed are discretization schemes for treating convection and pressure, parallel computing, multigrid methods, and composite, multiblock techniques. With respect to physical modelling, the book addresses issues of turbulence closure and multiscale, multiphase transport from an engineering viewpoint. Both fundamental and practical issues are considered, along with the relative merits of competing approaches. Numerous examples are given throughout the text. Mechanica

Many computionally challenging problems omnipresent in science and engineering exhibit multiscale phenomena so that the task of computing or even representing all scales of action is computationally v