Lecture notes in computational science and engineering ;
مشخصه جلد
123
يادداشت کلی
متن يادداشت
Selected papers from the conference.
یادداشتهای مربوط به کتابنامه ، واژه نامه و نمایه های داخل اثر
متن يادداشت
Includes bibliographical references.
یادداشتهای مربوط به مندرجات
متن يادداشت
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.
متن يادداشت
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.
متن يادداشت
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.
متن يادداشت
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.
متن يادداشت
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.
بدون عنوان
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بدون عنوان
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بدون عنوان
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بدون عنوان
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یادداشتهای مربوط به خلاصه یا چکیده
متن يادداشت
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.--