Sparse grids and applications : Miami 2016 /: Miami 2016. ([2018])

• Record Type: Book
• Further Information: Note: Jochen Garcke, Dirk Pflüger, Clayton G. Webster, Guannan Zhang, editors.
• Editors: Garcke, Jochen; Pflüger, Dirk; Webster, Clayton G (Clayton Garrett), 1978-; Zhang, Guannan, 1984-
• Other Names: Workshop on Sparse Grids and Applications, 4th
• Contents: 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 4.1 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 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 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
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Copyright Date: 2018
• Extent: 1 online resource
• Subjects: 004.36; Mathematics; Sparse matrices -- Congresses; Numerical analysis -- Congresses; Numerical grid generation (Numerical analysis) -- Congresses; COMPUTERS / Computer Literacy; COMPUTERS / Computer Science; COMPUTERS / Data Processing; COMPUTERS / Hardware / General; COMPUTERS / Information Technology; COMPUTERS / Machine Theory; COMPUTERS / Reference; Numerical analysis; Numerical grid generation (Numerical analysis); Sparse matrices; Mathematics; Computational Mathematics and Numerical Analysis; Mathematics of Computing; Simulation and Modeling; Approximations and Expansions; Computers -- Data Processing; Computers -- Computer Simulation; Mathematics -- Mathematical Analysis; Mathematical theory of computation; Computer modelling & simulation; Differential calculus & equations; Computer science_xMathematics; Computer science; Computer simulation; Mathematics -- Counting & Numeration; Numerical analysis; Electronic books; Conference papers and proceedings
• Languages: English
• ISBNs: 9783319754260; 3319754262
• Related ISBNs: 9783319754253; 3319754254
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (EBSCO, viewed June 25, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.