Delaunay-based optimization in CFD leveraging multivariate adaptive polyharmonic splines (MAPS)

2017 ◽  
Author(s):  
Shahrouz Alimo ◽  
Pooriya Beyhaghi ◽  
Gianluca Meneghello ◽  
Thomas Bewley
Keyword(s):  
Polyharmonic Splines

A Spline Framework for Estimating the EEG Surface Laplacian Using the Euclidean Metric

2011 ◽  
Vol 23 (11) ◽  
pp. 2974-3000 ◽  
Author(s):  
Claudio G. Carvalhaes ◽  
Patrick Suppes
Keyword(s):  
Basic Problem ◽  
Algebraic Surfaces ◽  
Eeg Analysis ◽  
Sphere Model ◽  
Surface Laplacian ◽  
Three Sphere ◽  
Euclidean Metric ◽  
Low Degree ◽  
Euclidean Setting ◽  
Polyharmonic Splines

This letter develops a framework for EEG analysis and similar applications based on polyharmonic splines. This development overcomes a basic problem with the method of splines in the Euclidean setting: that it does not work on low-degree algebraic surfaces such as spherical and ellipsoidal scalp models. The method’s capability is illustrated through simulations on the three-sphere model and using empirical data.

scholarly journals A stabilized well-balanced RBF-FD meshless method for shallow-water equations

2019 ◽  
Author(s):  
Joel Antonio Godoy de Moraes ◽  
Eduardo Cardoso de Abreu ◽  
Luis Guilherme Cunha Santos
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Bottom Topography ◽  
Point Clouds ◽  
General Criterion ◽  
Modified Method ◽  
Modified Method Of Characteristics ◽  
Polyharmonic Splines ◽  
Convection Dominated ◽  
Careful Design

In this work, we are concerned with the study and computing of stabilized radial basis function-generated finite difference (RBF-FD) approximations for shallow-water equations. In order to obtain both stable and highly accurate numerical approximations of convection-dominated shallow-water equations, we use stabilized flat Gaussians (RBFSGA-FD) and polyharmonic splines with supplementary polynomials (RBFPHS-FD) as basis functions, combined with modified method of characteristics. These techniques are combined with careful design for the spatial derivative operators in the momentum flux equation, according to a general criterion for the exact preservation of the “lake at rest” solution in general mesh-based and meshless numerical schemes for the strong form of the shallow-water equations with bottom topography. Both structured and unsructured point clouds are employed for evaluating the influence of cloud refinement, size of local supports and maximal permissible degree of the polynomials in RBFPHS-FD.

Comparing RBF-FD approximations based on stabilized Gaussians and on polyharmonic splines with polynomials

2018 ◽  
Vol 115 (4) ◽  
pp. 462-500 ◽  
Author(s):  
L. G. C. Santos ◽  
N. Manzanares-Filho ◽  
G. J. Menon ◽  
E. Abreu
Keyword(s):  
Polyharmonic Splines

Fast evaluation of polyharmonic splines in three dimensions

2006 ◽  
Vol 27 (3) ◽  
pp. 427-450 ◽  
Author(s):  
R. K. Beatson ◽  
M. J. D. Powell ◽  
A. M. Tan
Keyword(s):  
Three Dimensions ◽  
Fast Evaluation ◽  
Polyharmonic Splines
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