Numerical Methods and Analysis of Multiscale Problems
Springer International Publishing (Verlag)
978-3-319-50864-1 (ISBN)
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.
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.
Introductory Material and Finite Element Methods.- A One-dimensional Singular Perturbed Problem.- An Application in Neuroscience: Heterogeneous Cable Equation.- Two-Dimensional Reaction-Diffusion Equations.- Modeling PDEs in Domains with Rough Boundaries.- Partial Differential Equations with Oscillatory Coefficients.
"This book is a tutorial on numerical methods for multiscale problems accompanied by the corresponding numerical analysis. It is well studied as introductory material for graduate students at the master's level. ... All proofs are given in detail and results of instructive numerical experiments are demonstrated." (Karsten Urban, Mathematical Reviews, May, 2018)
"This monograph is concerned with the asymptotic analysis and numerical methods for multiscale problems. ... the book is orientated toward advanced undergraduate and graduate students." (Rolf Dieter Grigorieff, zbMATH, Vol. 1366.65108, 2017)
| Erscheinungsdatum | 03.03.2017 |
|---|---|
| Reihe/Serie | SpringerBriefs in Mathematics |
| Zusatzinfo | X, 123 p. 31 illus., 9 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Applications of Mathematics • Applied mathematics • asymptotic analysis • Differential calculus and equations • Elliptic equations • finite elements • Mathematics • mathematics and statistics • multiscale • Numerical analysis • Partial differential equations • Singular Perturbed Problems |
| ISBN-10 | 3-319-50864-4 / 3319508644 |
| ISBN-13 | 978-3-319-50864-1 / 9783319508641 |
| Zustand | Neuware |
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