A high order multivariate approximation scheme for scattered data sets

2010 ◽  
Vol 229 (18) ◽  
pp. 6343-6361 ◽  
Author(s):  
Qiqi Wang ◽  
Parviz Moin ◽  
Gianluca Iaccarino
Keyword(s):  
Approximation Scheme ◽  
Scattered Data ◽  
High Order ◽  
Multivariate Approximation ◽  
Data Sets

Multi-Variable, High Order, Performance Models (2005C)

2005 ◽  
Author(s):  
David Japikse ◽  
Oleg Dubitsky ◽  
Kerry N. Oliphant ◽  
Robert J. Pelton ◽  
Daniel Maynes ◽  
...  
Keyword(s):  
Data Processing ◽  
Large Data ◽  
High Order ◽  
Large Data Sets ◽  
Data Sets ◽  
Performance Models ◽  
Statistical Accuracy ◽  
Evaluation Methodologies ◽  
New Models ◽  
The Impact

In the course of developing advanced data processing and advanced performance models, as presented in companion papers, a number of basic scientific and mathematical questions arose. This paper deals with questions such as uniqueness, convergence, statistical accuracy, training, and evaluation methodologies. The process of bringing together large data sets and utilizing them, with outside data supplementation, is considered in detail. After these questions are focused carefully, emphasis is placed on how the new models, based on highly refined data processing, can best be used in the design world. The impact of this work on designs of the future is discussed. It is expected that this methodology will assist designers to move beyond contemporary design practices.

Verification, Validation, and Best Practices for a High-Order, Potential-Flow Boundary Element Method

2015 ◽  
Author(s):  
W. James Doyle ◽  
Lauren S. Schambach ◽  
Marc V. Smith ◽  
Charles Field ◽  
Christopher J. Hart
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Potential Flow ◽  
Best Practice ◽  
High Order ◽  
Data Sets ◽  
Design Environment ◽  
Best Practice Guidelines ◽  
Physical Experiments ◽  
Element Method

Aegir is a medium-fidelity potential flow code that uses a high-order, non-uniform rational B-Spline (NURBS) based boundary-element method for the computation of steady and unsteady ship hydrodynamics. This paper documents verification and validation for Aegir in its steady-state wave resistance prediction mode and Aegir’s LEAPS to Aegir function. A set of best practice guidelines has been created to aid the user in selecting initial input parameters, which reduces the necessary time for verification. This paper also presents validation of the numerical solution versus physical experiments from publically available ship data sets. Aegir has become more prevalent in the naval ship design community and is now a part of the US Navy’s Integrated Hydrodynamic Design Environment (IHDE).

Efficient Fitting and Rendering of Large Scattered Data Sets Using Subdivision Surfaces

2002 ◽  
Vol 21 (3) ◽  
pp. 353-362 ◽  
Author(s):  
Vincent Scheib ◽  
Jorg Haber ◽  
Ming C. Lin ◽  
Hans-Peter Seidel
Keyword(s):  
Scattered Data ◽  
Subdivision Surfaces ◽  
Data Sets

scholarly journals The Hong Kong/AAO/Strasbourg Hα (HASH) Planetary Nebula Database

2016 ◽  
Vol 12 (S323) ◽  
pp. 327-328
Author(s):  
Ivan S. Bojičić ◽  
Quentin A. Parker ◽  
David J. Frew
Keyword(s):  
Hong Kong ◽  
Observational Data ◽  
Planetary Nebula ◽  
Scattered Data ◽  
Easy Access ◽  
Online Research ◽  
Data Sets ◽  
Main Motivation ◽  
Research Platform ◽  
Imaging And Spectroscopy

AbstractThe Hong Kong/AAO/Strasbourg Hα (HASH) planetary nebula database is an online research platform providing free and easy access to the largest and most comprehensive catalogue of known Galactic PNe and a repository of observational data (imaging and spectroscopy) for these and related astronomical objects. The main motivation for creating this system is resolving some of long standing problems in the field e.g. problems with mimics and dubious and/or misidentifications, errors in observational data and consolidation of the widely scattered data-sets. This facility allows researchers quick and easy access to the archived and new observational data and creating and sharing of non-redundant PN samples and catalogues.

Structures of copper(II) and manganese(II) di(hydrogen malonate) dihydrate; effects of intensity profile truncation and background modelling on structure models

2001 ◽  
Vol 57 (4) ◽  
pp. 497-506 ◽  
Author(s):  
A. T. H. Lenstra ◽  
O. N. Kataeva
Keyword(s):  
Crystal Structures ◽  
Truncation Error ◽  
High Order ◽  
Data Sets ◽  
Data Set ◽  
Background Modelling ◽  
Local Background ◽  
Model Robustness ◽  
Selection Of ◽  
Low Order

The crystal structures of the title compounds were determined with net intensities I derived via the background–peak–background procedure. Least-squares optimizations reveal differences between the low-order (0 < s < 0.7 Å−1) and high-order (0.7 < s < 1.0 Å−1) structure models. The scale factors indicate discrepancies of up to 10% between the low-order and high-order reflection intensities. This observation is compound independent. It reflects the scan-angle-induced truncation error, because the applied scan angle (0.8 + 2.0 tan θ)° underestimates the wavelength dispersion in the monochromated X-ray beam. The observed crystal structures show pseudo-I-centred sublattices for three of its non-H atoms in the asymmetric unit. Our selection of observed intensities (I > 3σ) stresses that pseudo-symmetry. Model refinements on individual data sets with (h + k + l) = 2n and (h + k + l) = 2n + 1 illustrate the lack of model robustness caused by that pseudo-symmetry. To obtain a better balanced data set and thus a more robust structure we decided to exploit background modelling. We described the background intensities B(\displaystyle\mathrel{\mathop H^{\rightharpoonup}}) with an 11th degree polynomial in θ. This function predicts the local background b at each position \displaystyle\mathrel{\mathop H^{\rightharpoonup}} and defines the counting statistical distribution P(B), in which b serves as average and variance. The observation R defines P(R). This leads to P(I) = P(R)/P(B) and thus I = R − b and σ2(I) = I so that the error σ(I) is background independent. Within this framework we reanalysed the structure of the copper(II) derivative. Background modelling resulted in a structure model with an improved internal consistency. At the same time the unweighted R value based on all observations decreased from 10.6 to 8.4%. A redetermination of the structure at 120 K concluded the analysis.

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