Numerical Methods and Analysis of Multiscale Problems

Alexandre L. Madureira

ISBN 10: 3319508644 / ISBN 13: 9783319508641

Published by Springer International Publishing, Springer International Publishing Feb 2017, 2017

About this Item

Neuware -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 depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics ¿ or researchers seeking a no-nonsense approach ¿, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods.The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 136 pp. Englisch.

Seller Inventory # 9783319508641

Bibliographic Details

• Title: Numerical Methods and Analysis of Multiscale Problems
• Publisher: Springer International Publishing, Springer International Publishing Feb 2017
• Publication Date: 2017
• Language: English
• ISBN 10: 3319508644
• ISBN 13: 9783319508641
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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 depend on different physical scales.  Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses  examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods.

The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.

About the Author

Alexandre L. Madureira is a senior researcher at the National Laboratory for Scientific Computing (LNCC), Brazil, and also works at the Brazilian School of Economics and Finance (EPGE) at the Fundação Getúlio Vargas (FGV). He holds a PhD from Penn State University, USA, and served as a visiting professor at the Istituto di Analisi Numerica (IAN), Italy, University of Colorado at Denver, USA, and Brown University, USA. His main field of interest is numerical analysis, more specifically modeling and analysis of multiscale problems from PDE and numerical points of view.