Multiscale Problems and Methods in Numerical Simulations - Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 9-15, 2001

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.

List of contents

Preface.- A. Cohen: Theoretical Applied and Computational Aspects of Nonlinear Approximation.- W. Dahmen: Multiscale and Wavelet Methods for Operator Equations.- J. H. Bramble: Multilevel Methods in Finite Elements.

About the author

Albert Cohen geboren 1895 auf Korfu, starb 1981 in Genf. Er gilt als einer der wichtigsten französischsprachigen Autoren des 20. Jahrhunderts.

Summary

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.

Product details

• Authors: James H. Bramble, Albert Cohen, Wolfgang Dahmen
• Assisted by: Claudio Canuto (Editor), Claudio G Canuto (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2004
• EAN: 9783540200994
• ISBN: 978-3-540-20099-4
• No. of pages: 163
• Weight: 280 g
• Series: Lecture Notes in Mathematics; C.I.M.E. Foundation Subseries; Lecture Notes in Mathematics; C.I.M.E. Foundation Subseries
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; C, Differentialrechnung und -gleichungen, Numerische Mathematik, Mathematics and Statistics, Numerical analysis, Fourier Analysis, Approximations and Expansions, Approximation theory, Differential calculus and equations