عنوان
پدید آورنده
موضوع
رده
QA188
QA188
کتابخانه
محل استقرار
3319754262
9783319754260
3319754254
9783319754253
Sparse grids and applications :
[Book]
Miami 2016 /
Jochen Garcke, Dirk Pflüger, Clayton G. Webster, Guannan Zhang, editors.
Cham, Switzerland :
Springer,
[2018]
©2018
1 online resource
Lecture notes in computational science and engineering ;
123
Selected papers from the conference.
Includes bibliographical references.
Intro; Preface; Contents; Contributors; Comparing Nested Sequences of Leja and PseudoGauss Points to Interpolate in 1D and Solve the Schroedinger Equation in 9D; 1 Introduction; 2 Interpolation; 3 The Importance of Nesting; 3.1 PseudoGauss Nested Points; 3.2 Leja Nested Points; 4 Lebesgue Constants; 5 Comparison Between Leja Points and PseudoGauss Points in Collocation Calculations; 6 Conclusion; References; On the Convergence Rate of Sparse Grid Least Squares Regression; 1 Introduction; 2 Least-Squares Regression; 3 Full Grids and Sparse Grids; 4 Error Analysis.
4 Numerical Results4.1 Second-Order Linear Oscillator with External Forcing; 4.2 A simple Fluid-Structure Interaction Example; 5 Conclusions and Outlook; References; Limiting Ranges of Function Values of Sparse Grid Surrogates; 1 Introduction; 2 Sparse Grids; 2.1 Hierarchical Ancestors and the Fundamental Property; 2.2 Interpolation on Sparse Grids; 3 Limiting Ranges of Sparse Grid Function Values; 3.1 Limitation from Above and Below; 3.2 Minimal Extension Set; 3.3 Computing Coefficients of the Extension Set; 3.4 Intersection Search; 4 Approximation of Gaussians with Extended Sparse Grids.
4.1 Intersection Search and Candidate Sets for Regular Sparse Grids4.2 Extension Sets and Convergence for Regular Grids; 4.3 Extension Sets for Adaptively Refined Grids; 5 Conclusions; References; Scalable Algorithmic Detection of Silent Data Corruption for High-Dimensional PDEs; 1 Introduction; 1.1 High-Dimensional PDEs in High-Performance Computing; 2 Theory of the Classical Combination Technique; 3 The Combination Technique in Parallel; 4 Dealing with System Faults; 5 Detecting and Recovering from SDC; 5.1 Method 1: Comparing Combination Solutions Pairwise via a Maximum Norm.
4.1 Well-Posedness and Error Decay4.2 Application to Sparse Grids; 5 Numerical Experiments; 5.1 Error Decay; 5.2 Balancing the Error; 6 Conclusion; References; Multilevel Adaptive Stochastic Collocation with Dimensionality Reduction; 1 Introduction; 2 Adaptivity with Sparse Grids; 2.1 Interpolation on Spatially-Adaptive Sparse Grids; 2.2 Interpolation with Dimension-Adaptive Sparse Grids; 3 Multilevel Stochastic Collocation with Dimensionality Reduction; 3.1 Generalized Polynomial Chaos; 3.2 Multilevel Approaches for Generalized Polynomial Chaos; 3.3 Stochastic Dimensionality Reduction.
5.2 Method 2: Comparing Combination Solutions via their Function Values Directly5.3 Cost and Parallelization; 5.4 Detection Rates; 6 Numerical Tests; 6.1 Experimental Setup; 6.2 SDC Injection; 6.3 Results: Detection Rates and Errors; 6.4 Results: Scaling; 6.5 Dealing with False Positives; 7 Extensions to Quantities of Interest; 8 Conclusion; References; Sparse Grid Quadrature Rules Based on Conformal Mappings; 1 Introduction and Background; 2 Transformed Quadrature Rules; 2.1 Standard One-Dimensional Quadrature Rules; 2.2 Sparse Quadrature for High Dimensional Integrals.
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Sparse grids are a popular tool for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different flavors, are frequently the method of choice. This volume of LNCSE presents selected papers from the proceedings of the fourth workshop on sparse grids and applications, and demonstrates once again the importance of this numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including computational chemistry, computational fluid dynamics, and big data analytics, to name but a few.--
Springer Nature
com.springer.onix.9783319754260
Sparse grids and applications.
9783319754253
Numerical analysis, Congresses.
Numerical grid generation (Numerical analysis), Congresses.
Sparse matrices, Congresses.
Computer modelling & simulation.
COMPUTERS-- Computer Literacy.
COMPUTERS-- Computer Science.
COMPUTERS-- Data Processing.
COMPUTERS-- Hardware-- General.
COMPUTERS-- Information Technology.
COMPUTERS-- Machine Theory.
COMPUTERS-- Reference.
Differential calculus & equations.
Mathematical theory of computation.
Numerical analysis.
Numerical analysis.
Numerical grid generation (Numerical analysis)
Sparse matrices.
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COM-- 014000
COM-- 018000
COM-- 032000
COM-- 037000
COM-- 052000
COM-- 067000
PBKS
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QA188
Garcke, Jochen
Pflüger, Dirk
Webster, Clayton G., (Clayton Garrett),1978-
Zhang, Guannan,1984-
Workshop on Sparse Grids and Applications(4th :2016 :, Miami, Fla.)
20200823105914.0
pn
مطالعه متن کتاب [Book]
Y
