数値シミュレーションにおけるウェーブレット<br>Wavelets in Numerical Simulation : Problem Adapted Construction and Applications (Lecture Notes in Computational Science and Engineering, 22)

個数:

数値シミュレーションにおけるウェーブレット
Wavelets in Numerical Simulation : Problem Adapted Construction and Applications (Lecture Notes in Computational Science and Engineering, 22)

  • 提携先の海外書籍取次会社に在庫がございます。通常2週間で発送いたします。
    重要ご説明事項
    1. 納期遅延や、ご入手不能となる場合が若干ございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。
  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 181 p.
  • 言語 ENG
  • 商品コード 9783540430551
  • DDC分類 515.2433

Full Description


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.

Table of Contents

Preface                                            vii
Wavelet Bases 1 (82)
Wavelet Bases in L2(Ω) 1 (11)
General Setting 2 (3)
Characterization of Soboley-Spaces 5 (2)
Riesz Basis Property in L2(Ω) 7 (1)
Norm Equivalences 8 (1)
General Setting Continued 9 (1)
Further Wavelet Features 10 (1)
A Program for Constructing Wavelets 11 (1)
Wavelets on the Real Line 12 (5)
Orthonormal Wavelets 13 (1)
Biorthogonal B-Spline Wavelets 14 (1)
Interpolatory Wavelets 15 (2)
Wavelets on the Interval 17 (29)
Boundary Scaling Functions 19 (1)
Biorthogonal Scaling Functions 19 (6)
Biorthogonalization 25 (5)
Refinement Matrices 30 (3)
Biorthogonal Wavelets on (0, 1) 33 (8)
Quantitative Aspects of the 41 (3)
Biorthogonalization
Boundary Conditions 44 (1)
Other Bases 45 (1)
Tensor Product Wavelets 46 (1)
Wavelets on General Domains 47 (34)
Domain Decomposition and Parametric 51 (2)
Mappings
Multiresolution and Wavelets on the 53 (1)
Subdomains
Multiresolution on the Global Domain 54 (1)
Ω
Wavelets on the Global Domain 55 (1)
Univariate Matched Wavelets and Other 56 (6)
Functions
Bivariate Matched Wavelets 62 (11)
Trivariate Matched Wavelets 73 (5)
Characterization of Sobolev Spaces 78 (3)
Vector Wavelets 81 (2)
Wavelet Bases for H(div) and H(curl) 83 (26)
Differentiation and Integration 84 (6)
Differentiation and Integration on the 84 (1)
Real Line
Differentiation and Integration on (0, 1) 85 (1)
Assumptions for General Domains 86 (3)
Norm Equivalences 89 (1)
The Spaces H(div) and H (curl) 90 (2)
Stream Function Spaces 91 (1)
Flux Spaces 91 (1)
Hodge Decompositions 92 (1)
Wavelet Systems for H (curl) 92 (6)
Wavelets in H0(curl; Ω) 93 (2)
Curl-Free Wavelet Bases 95 (3)
Wavelet Bases for H (div) 98 (2)
Wavelet Bases in H (div; Ω) 98 (1)
Divergence-Free Wavelet Bases 99 (1)
Helmholtz and Hodge Decompositions 100(2)
A Biorthogonal Helmholtz Decomposition 100(1)
Interrelations and Hodge Decompositions 101(1)
General Domains 102(3)
Tensor Product Domains 102(1)
Parametric Mappings 103(1)
Fictitions Domain Method 104(1)
Examples 105(4)
Applications 109(52)
Robust and Optimal Preconditioning 109(9)
Wavelet-Galerkin Discretizations 109(3)
The Lame Equations for Almost 112(4)
Incompressible Material
The Maxwell Equations 116(1)
Preconditioning in H (div; Ω) 117(1)
Analysis and Simulation of Turbulent Flows 118(20)
Numerical Simulation of Turbulence 118(1)
Divergence-Free Wavelet Analysis of 119(1)
Turbulence
Proper Orthogonal Decomposition (POD) 120(2)
Numerical Implementation and Validation 122(2)
Numerical Results I: Data Analysis 124(4)
Numerical Results II: Complexity of 128(10)
Turbulent Flows
Hardening of an Elastoplastic Rod 138(23)
The Physical Problem 138(4)
Numerical Treatment 142(3)
Stress Correction and Wavelet Bases 145(1)
Numerical Results I: Variable Order 146(8)
Discretizations
Numerical Results II: Plastic Indicators 154(7)
References 161(8)
List of Figures 169(4)
List of Tables 173(2)
List of Symbols 175(4)
Index 179