Wavelets in Numerical Simulation: Problem Adapted Construction And Applications: 22 (Lecture Notes in Computational Science and Engineering, 22) - Softcover

Urban, Karsten

Softcover

ISBN 10: 3540430555 ISBN 13: 9783540430551

Verlag: Springer, 2013

Inhaltsangabe

Sapere aude! Immanuel Kant (1724-1804) Numerical simulations playa key role in many areas of modern science and technology. They are necessary in particular when experiments for the underlying problem are too dangerous, too expensive or not even possible. The latter situation appears for example when relevant length scales are below the observation level. Moreover, numerical simulations are needed to control complex processes and systems. In all these cases the relevant problems may become highly complex. Hence the following issues are of vital importance for a numerical simulation: - Efficiency of the numerical solvers: Efficient and fast numerical schemes are the basis for a simulation of ’real world’ problems. This becomes even more important for realtime problems where the runtime of the numerical simulation has to be of the order of the time span required by the simulated process. Without efficient solution methods the simulation of many problems is not feasible. ’Efficient’ means here that the overall cost of the numerical scheme remains proportional to the degrees of freedom, i. e. , the numerical approximation is determined in linear time when the problem size grows e. g. to upgrade accuracy. Of course, as soon as the solution of large systems of equations is involved this requirement is very demanding.

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This research monograph addresses recent developments of wavelet concepts in the context of large scale numerical simulation. It offers a systematic attempt to exploit the sophistication of wavelets as a numerical tool by adapting wavelet bases to the problem at hand. This includes both the construction of wavelets on fairly general domains and the adaptation of wavelet bases to the particular structure of function spaces governing certain variational problems. Those key features of wavelets that make them a powerful tool in numerical analysis and simulation are clearly pointed out. The particular constructions are guided by the ultimate goal to ensure the key features also for general domains and problem classes. All constructions are illustrated by figures and examples are given.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2013
• Sprache: Englisch
• ISBN 10: 3540430555
• ISBN 13: 9783540430551
• Einband: Tapa blanda
• Anzahl der Seiten: 204
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland