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Model reduction of parametrized systems / Peter Benner [and four others], editors
(MS&A ; v. 17)

データ種別	電子ブック
出版者	Cham, Switzerland : Springer
出版年	[2017]
大きさ	1 online resource : ill

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URL	配架場所	巻　次	請求記号	登録番号	状　態	コメント	ISBN	刷　年	利用注記	予約	複写取寄	指定図書
URL	研究室		510/M17	1181000046			9783319587868		禁帯出特別本

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一般注記	Includes bibliographical referneces 4 A Reduced Basis Method with an Exact Solution Certificate and Spatio-Parameter Adaptivity: Application to LinearElasticity4.1 Introduction; 4.2 Preliminaries; 4.2.1 Problem Statement; 4.2.2 Abstract Error Bounds: Energy Norm and Compliance Output; 4.3 Upper Bound of the Dual Norm of the Residual; 4.3.1 Bound Form; 4.3.2 Minimum-Bound Solutions and Approximations; 4.4 Stability Constant; 4.4.1 Transformation of the Stability Constant; 4.4.2 A Residual-Based Lower Bound of the Minimum Eigenvalue; 4.4.3 FE Approximation of Bounds of t(u) 4.4.4 Offline-Online Efficient SCM and RB Bounds of t(u)4.5 Error Bounds; 4.6 Spatio-Parameter Adaptation; 4.7 Numerical Results; 4.7.1 Problem Description; 4.7.2 Uniform Spatio-Parameter Refinement; 4.7.3 Spatio-Parameter Adaptive SCM and RB Refinement; References; 5 A Reduced Basis Method for Parameter Functions Using Wavelet Approximations; 5.1 Introduction; 5.2 Reduced Basis Method; 5.3 Space-Time Variational Formulation for Parabolic Problems; 5.4 Reduced Basis Method for Parameter Functions; 5.4.1 Using the Initial Value as Parameter in a Space-Time Setting Preface; Contents; About the Editors; 1 Two Ways to Treat Time in Reduced Basis Methods; 1.1 Introduction; 1.2 Variational Formulations of Parabolic Problems; 1.2.1 Semi-variational Formulation; 1.2.2 Space-Time Variational Formulation; 1.3 Parametrized Problems and the RBM; 1.4 Reduced Basis Methods with POD-Greedy; 1.5 Space-Time Reduced Basis Methods; 1.6 Numerical Results; 1.6.1 Data; 1.6.2 Results; 1.7 Conclusions; References; 2 Simultaneous Empirical Interpolation and Reduced Basis Method: Application to Non-linear Multi-Physics Problem; 2.1 Introduction 2.2 A Simultaneous EIM-RB Method2.2.1 Preliminaries; 2.2.1.1 Empirical Interpolation Method; 2.2.1.2 Reduced Basis Method; 2.2.2 ser Method; 2.2.2.1 Error Estimation; 2.2.2.2 Some ser Variants; 2.3 Numerical Experiments; 2.4 Application to Multi-Physics Model; 2.4.1 Electro-Thermal Model; 2.4.2 Application to Bitter Magnet; 2.4.3 Application to Polyhelix Magnet; 2.5 Conclusion; References; 3 A Certified Reduced Basis Approach for Parametrized Optimal Control Problems with Two-Sided Control Constraints; 3.1 Introduction; 3.2 General Problem Statement and Finite Element Discretization 3.2.1 Preliminaries3.2.2 Abstract Formulation of Linear-Quadratic Optimal Control Problems and the First-Order Optimality Conditions; 3.3 Reduced Basis Method for the Primal Problem; 3.3.1 Reduced Basis Approximation; 3.3.2 Primal Error Bound; 3.4 Slack Problem and the Primal-Slack Error Bound; 3.4.1 FE and RB Slack Problem; 3.4.2 Primal-Slack Error Bound; 3.5 Greedy Sampling Procedure; 3.6 Numerical Results: Graetz Flow with Parametrized Geometry and Lower and Upper Control Constraints; 3.7 Conclusions; References Master record variable field(s) change: 050, 072, 082, 650 HTTP:URL=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1589459 Information=EBSCOhost
著者標目	Benner, Peter editor
件　名	LCSH:Mathematical models LCSH:Mathematical optimization LCSH:Computational complexity FREE:MATHEMATICS / General FREE:Electronic books LCSH:Electronic books
分　類	LCC:QA401 DC23:511.3/4
書誌ID	EB00003523
ISBN	9783319587868