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Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions

Varun Shankar, Grady B. Wright
2018 Journal of Computational Physics  
The three new methods are based on interpolation using 1) global RBFs, 2) local RBF stencils, and 3) RBF partition of unity.  ...  artificial singularities associated with surface-based coordinate systems.  ...  Indeed, recent work on Euclidean geometries [13, 42] has demonstrated that it is more beneficial to use the finitely-smooth polyharmonic spline (PHS) kernels in the context of RBF-FD methods, augmented  ... 
doi:10.1016/j.jcp.2018.04.007 fatcat:y2k5axawmvgbdct3vsve6rgzou

Radial basis functions: Developments and applications to planetary scale flows

Natasha Flyer, Bengt Fornberg
2011 Computers & Fluids  
Spectral accuracy becomes now easily available also when using completely unstructured node layouts, permitting local node refinements in critical areas.  ...  The first major PDE applications for which RBFs have been shown to compete successfully against the best currently available numerical approaches can be found in the geosciences.  ...  These implementations are in 2D and 3D spherical geometries, using 1000s to over half million degrees of freedom in space.  ... 
doi:10.1016/j.compfluid.2010.08.005 fatcat:cwsxigwkmvcjlnsitoxzzteomq

Solving 3-D Gray–Scott Systems with Variable Diffusion Coefficients on Surfaces by Closest Point Method with RBF-FD

Marzieh Raei, Salvatore Cuomo, Giovanni Colecchia, Gerardo Severino
2021 Mathematics  
In this way, we solve the GS problem with a radial basis function–finite difference (RBF-FD) algorithm combined with the closest point method (CPM).  ...  In this paper, we discuss a numerical scheme for solving the GS system. The diffusion coefficients of the model are on surfaces and they depend on space and time.  ...  We thank Rosanna Campagna for useful discussions that helped improve the manuscript.  ... 
doi:10.3390/math9090924 fatcat:qotdcmn3hjfcbb5xges272llva

Robust Node Generation for Meshfree Discretizations on Irregular Domains and Surfaces [article]

Varun Shankar, Robert M. Kirby, Aaron L. Fogelson
2018 arXiv   pre-print
We explore the influence of Poisson disk sampling parameters on both quasi-uniformity in the node sets and errors in an RBF-FD discretization of the heat equation.  ...  Spherical Radial Basis Function (SBF)-based geometric modeling of irregular domain boundaries.  ...  The RBF-FD discretization is achieved by us- ing PHS RBFs in conjunction with high-degree polynomials, where the convergence rates are dictated purely by the polynomial degree [12, 11, 1].  ... 
arXiv:1806.02972v1 fatcat:gm2jjslh2zdvpogszcugosuhvy

The Direct Radial Basis Function Partition of Unity (D-RBF-PU) Method for Solving PDEs [article]

Davoud Mirzaei
2020 arXiv   pre-print
Alternatively, the new method is an RBF-generated finite difference (RBF-FD) method in a PU setting which is much faster and in some situations more accurate than the original RBF-FD.  ...  The polyharmonic splines are used for local approximations, and the error and stability issues are considered.  ...  Special thanks go to Behnam Hashemi (Shiraz University of Technology) for his helpful comments about sparse matrix manipulation in MATLAB and a careful proofreading.  ... 
arXiv:2009.07175v2 fatcat:dyemriobsrailjm55aawnpfoae

A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds

Varun Shankar, Grady B. Wright, Akil Narayan
2020 SIAM Journal on Scientific Computing  
Our hyperviscosity formulation is independent of RBF-LOI and can be used straightforwardly with other RBF-FD methods based on the projection approach [38, 40] , the closest-point approach [28, 29] , or  ...  In the context of global stability, the augmenting of polyharmonic spline (PHS) RBFs with polynomials also appears to enhance global stability for elliptic operators on Euclidean domains [3] , though this  ...  In other words, each interpolant in the family is given by varying \bfity , with the n RBF-FD weights for that interpolant given by (w x ) j (\bfity ). 1 In the standard RBF-FD method, \bfity \equiv  ... 
doi:10.1137/19m1288747 fatcat:4wa3foqvhrgp7ao2hxoj3ewtem

A High-Order Accurate Meshless Method for Solution of Incompressible Fluid Flow Problems [article]

Shantanu Shahane, Anand Radhakrishnan, Surya Pratap Vanka
2021 arXiv   pre-print
Meshless solution to differential equations using radial basis functions (RBF) is an alternative to grid based methods commonly used.  ...  Recently, Polyharmonic splines (PHS) with appended polynomials have been shown to solve the above issues and give rapid convergence of discretization errors with the degree of appended polynomials.  ...  Fornberg and colleagues [45] [46] [47] [48] [49] The PHS-RBF Method In this research, we use a cloud based PHS-RBF approach with appended polynomials to obtain numerical estimates of the differential  ... 
arXiv:2010.01702v2 fatcat:aejx27kq3zcfnlwywh6hjj4i2m

A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds [article]

Varun Shankar, Grady B. Wright, Akil Narayan
2020 arXiv   pre-print
Our surface discretizations use the recently-developed RBF-LOI method, and with the addition of hyperviscosity, are now empirically high-order accurate, stable, and free of stagnation errors.  ...  We present a new hyperviscosity formulation for stabilizing radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion-reaction equations on manifolds M⊂R^3 of co-dimension  ...  Our hyperviscosity formulation is independent of RBF-LOI, and can be used straightforwardly with other RBF-FD methods based on the projection approach [38, 40] , the closest-point approach [28, 29] ,  ... 
arXiv:1910.07059v2 fatcat:xsxefxqx6nejnln34pmaup5mye

Papers published in Journal of Computer Science and Cybernetics: 1984-2014

2015 Journal of Computer Science and Cybernetics  
(Projection-iteractive method is used for Carleman problem.)  ...  (MCA method in information storage and retrieval.) 29 Nguyễn Chí Công, Trần Xuân Thuận -Hệ phát triển vi tính FT 68K.  ...  (Control with uncertainty problems on the basis of fuzzy logic and the use of the hedge algebras in the knowledge -based system control.) 222 Nguyễn Xuân Huy, Nguyễn Xuân Hoàng, Vũ Mạnh Xuân, Nguyễn Văn  ... 
doi:10.15625/1813-9663/30/4/5854 fatcat:2k5lfinqmfelng2vb2rsjmxd5a

CARS 2016—Computer Assisted Radiology and Surgery Proceedings of the 30th International Congress and Exhibition Heidelberg, Germany, June 21–25, 2016

2016 International Journal of Computer Assisted Radiology and Surgery  
We would like to thank the Spanish company BQ for the donation of the 3D printing hardware for clinical use.  ...  ., for providing valuable computing resources through an ''AWS in Education Research'' grant.  ...  In addition to comparing the radiomic RF-based and DCNN-based ML-EC schemes, we also evaluated the performance of a single RF-based ML-EC scheme which only used features of the single-energy 140 kVp CTC  ... 
doi:10.1007/s11548-016-1412-5 pmid:27206418 fatcat:uk5r46n2xvhedkfjzmeiweyneq

Simulations of Nanoparticle Synthesis in Laminar Stagnation Flames

Eric Bringley, Apollo-University Of Cambridge Repository, Markus Kraft
2021
First, the growth of particles was described with a spherical particle model fully coupled to the conservation equations of chemically reacting flow.  ...  Detailed chemical source terms and transport coefficients are used to close the equations.  ...  The most recent application of RBM-FD to micro-combustion was for reactive flows in complex geometries [22] .  ... 
doi:10.17863/cam.78775 fatcat:uvtbzddis5byjdkkcnudmsfusq

High-resolution imaging beneath the Santorini volcano

Kajetan Marcin Chrapkiewicz, Joanna Morgan, Michele Paulatto, Leverhulme Trust
2022
Constraining the geometry and physical properties of these systems, in particular detecting high melt fraction (magma) reservoirs, is key to managing a volcanic hazard and understanding fundamental processes  ...  Unfortunately, unambiguous evidence of magma reservoirs has not yet been provided due to the limited resolving power of the geophysical methods used so far.  ...  Hooft for numerous pieces of useful advice, enthusiasm and constant encouragement to complete this study.  ... 
doi:10.25560/96427 fatcat:vkyhjumylrgufm4g4jfv4bstsy

Endoscopic low coherence interferometry applied to tri-dimensional contouring of upper airways

Yves Delacrétaz
2008
It is based on an interferometric setup, using a reduced coherence light source, and is fully adaptable to endoscopic procedure commonly in used in ear-nose-throat (ENT) medicine.  ...  Simulated results have been carefully compared with measurements, both in the spatial domain and in the Fourier domain (spatial frequencies response), which has permitted to better understand the processes  ...  In case of compactly supported RBF, interpolation with RBF can be approximated by the use of two-scale B-Splines [80; 81].  ... 
doi:10.5075/epfl-thesis-4287 fatcat:jtkzmc44njbuxgrajvewlnajbq

Design Optimization of a High-speed Vac-train with an Axial Flow Air Compressor, an Aerodynamic Bearing Levitation and a Linear Synchronous Electromagnetic Motor

Ahmed Hodaib
2017 unpublished
With the exception of such quotations, this thesis is entirely our own work.  We have acknowledged all main sources of help.  Where the thesis is based on work done by ourselves jointly with others,  ...  " and the work presented in it are our own.  ...  Implicit density-based coupled solver and Roe's flux difference scheme (Roe's FDS) are used. Absolute velocity formulation is used because the flow domain is not rotating.  ... 
doi:10.13140/rg.2.2.13071.12966 fatcat:sngla6aybrhptmvtghgucxs66q

Development of Particle Image Velocimetry for In-Vitro Studies of Arterial Haemodynamics [article]

Nicolas Buchmann, University Of Canterbury
2010
The arterial geometries are reproduced in optically clear silicone and the flowing blood is modelled with a refractive index matched [...]  ...  In particular, this research develops and uses state-of-the-art Particle Image Velocimetry (PIV) techniques to measure three-dimensional velocity and WSS fields in scaled models of the human carotid artery  ...  Therefore, to achieve high accuracy and to avoid loss of information, higher order reconstruction schemes, such as biquatratic or bicubic, B-spline functions or Gaussian and FFT based schemes should be  ... 
doi:10.26021/1526 fatcat:vttaudkeineodkirizhppikvui
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