scholarly journals A fast summation method for oscillatory lattice sums

2017 ◽  
Vol 58 (2) ◽  
pp. 023511 ◽  
Author(s):  
Ryan Denlinger ◽  
Zydrunas Gimbutas ◽  
Leslie Greengard ◽  
Vladimir Rokhlin
Keyword(s):  
Summation Method ◽  
Lattice Sums ◽  
Fast Summation

A PPPM fast summation method for fluids and beyond

2014 ◽  
Vol 33 (6) ◽  
pp. 1-11 ◽  
Author(s):  
Xinxin Zhang ◽  
Robert Bridson
Keyword(s):  
Summation Method ◽  
Fast Summation

scholarly journals Viscous Vortex Particle Method Coupling with Computational Structural Dynamics for Rotor Comprehensive Analysis

2021 ◽  
Vol 11 (7) ◽  
pp. 3149
Author(s):  
Wenguo Zhu ◽  
Marco Morandini ◽  
Shu Li
Keyword(s):  
Particle Method ◽  
Summation Method ◽  
Comprehensive Analysis ◽  
Particle Interactions ◽  
Vortex Particle Method ◽  
Fast Summation ◽  
Computational Structural Dynamics ◽  
Induced Velocity ◽  
Far Wake ◽  
Vortex Particle

A panel/vortex particle hybrid method is coupled with a computational structure dynamics code to predict helicopter rotor loads. The rotor blade surfaces and near wakes are modeled by the panel method, while the far wake is modeled by resorting to the vortex particles method. A fast summation method is introduced to accelerate the evolution of particle–particle-induced velocity and its derivative as well as panel–particle interactions. The developed vortex particle method code is coupled with the multibody code MBDyn to predict the rotor airloads. Numerical validations are carried, out and the results are compared with the experiments and simulation results in the literature.

Partial Summation Method for XANES Calculation

1997 ◽  
Vol 7 (C2) ◽  
pp. C2-99-C2-102
Author(s):  
T. Fujikawa ◽  
R. Yanagisawa ◽  
N. Yiwata
Keyword(s):  
Summation Method ◽  
Partial Summation

scholarly journals Optimization Analysis of Settlement Parameters for Postgrouting Piles in Loess Area of Shaanxi, China

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Zhijun Zhou ◽  
Shanshan Zhu ◽  
Xiang Kong ◽  
Jiangtao Lei ◽  
Tong Liu
Keyword(s):  
Compression Modulus ◽  
Summation Method ◽  
Cone Penetration ◽  
Optimization Analysis ◽  
Loess Area ◽  
Elastic Compression ◽  
Settlement Calculation ◽  
Side Resistance ◽  
Load Tests ◽  
The Relationship

The settlement calculation of postgrouting piles is complex and depends on the calculation method and parameters. Static load tests were conducted to compare the settlement characteristics of nongrouting and postgrouting piles, and three vital parameters in the layer-wise summation method were revised to predict the settlement of postgrouting piles. The elastic compression coefficient was deduced based on the Mindlin–Geddes method by considering the influence of the change in the pile side resistance distribution and end resistance ratio on the elastic compression after grouting. The relationship between the compression modulus and soil gravity stress and cone penetration resistance were established, respectively, using experimental data. The optimum value of the settlement empirical coefficient was determined using regional data. Finally, we used the postgrouting pile of the Wuqi–Dingbian expressway as a practical example. The results obtained from the layer-wise summation method after parametric optimization were close to the measured values. The results of this study provide reference data and guidance for the settlement calculation of postgrouting piles in this area.

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