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＜電子ブック＞
Adaptive Multiscale Schemes for Conservation Laws / by Siegfried Müller
(Lecture Notes in Computational Science and Engineering. ISSN:21977100 ; 27)

版	1st ed. 2003.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2003
本文言語	英語
大きさ	XIV, 188 p. 1 illus : online resource
著者標目	*Müller, Siegfried author SpringerLink (Online service)
件　名	LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Mathematical physics LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 FREE:Computational Mathematics and Numerical Analysis FREE:Theoretical, Mathematical and Computational Physics FREE:Mathematical and Computational Engineering Applications
一般注記	1 Model Problem and Its Discretization -- 1.1 Conservation Laws -- 1.2 Finite Volume Methods -- 2 Multiscale Setting -- 2.1 Hierarchy of Meshes -- 2.2 Motivation -- 2.3 Box Wavelet -- 2.4 Change of Stable Completion -- 2.5 Box Wavelet with Higher Vanishing Moments -- 2.6 Multiscale Transformation -- 3 Locally Refined Spaces -- 3.1 Adaptive Grid and Significant Details -- 3.2 Grading -- 3.3 Local Multiscale Transformation -- 3.4 Grading Parameter -- 3.5 Locally Uniform Grids -- 3.6 Algorithms: Encoding, Thresholding, Grading, Decoding -- 3.7 Conservation Property -- 3.8 Application to Curvilinear Grids -- 4 Adaptive Finite Volume Scheme -- 4.1 Construction -- 4.2 A gorithms: Initial data, Prediction, Fluxes and Evolution -- 5 Error Analysis -- 5.1 Perturbation Error -- 5.2 Stability of Approximation -- 5.3 Reliability of Prediction -- 6 Data Structures and Memory Management -- 6.1 Algorithmic Requirements and Design Criteria -- 6.2 Hashing -- 6.3 Data Structures -- 7 Numerical Experiments -- 7.1 Parameter Studies -- 7.2 Real World Application -- A Plots of Numerical Experiments -- B The Context of Biorthogonal Wavelets -- B.1 General Setting -- B.1.1 Multiscale Basis -- B.1.2 Stable Completion -- B.1.3 Multiscale Transformation -- B.2 Biorthogonal Wavelets of the Box Function -- B.2.1 Haar Wavelets -- B.2.2 Biorthogonal Wavelets on the Real Line -- References -- List of Figures -- List of Tables -- Notation During the last decade enormous progress has been achieved in the field of computational fluid dynamics. This became possible by the development of robust and high-order accurate numerical algorithms as well as the construc­ tion of enhanced computer hardware, e. g. , parallel and vector architectures, workstation clusters. All these improvements allow the numerical simulation of real world problems arising for instance in automotive and aviation indus­ try. Nowadays numerical simulations may be considered as an indispensable tool in the design of engineering devices complementing or avoiding expen­ sive experiments. In order to obtain qualitatively as well as quantitatively reliable results the complexity of the applications continuously increases due to the demand of resolving more details of the real world configuration as well as taking better physical models into account, e. g. , turbulence, real gas or aeroelasticity. Although the speed and memory of computer hardware are currently doubled approximately every 18 months according to Moore's law, this will not be sufficient to cope with the increasing complexity required by uniform discretizations. The future task will be to optimize the utilization of the available re­ sources. Therefore new numerical algorithms have to be developed with a computational complexity that can be termed nearly optimal in the sense that storage and computational expense remain proportional to the "inher­ ent complexity" (a term that will be made clearer later) problem. This leads to adaptive concepts which correspond in a natural way to unstructured grids HTTP:URL=https://doi.org/10.1007/978-3-642-18164-1

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