A Least Squares Radial Basis Function Finite Difference Method with Improved Stability Properties

نویسندگان

چکیده

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 6 March 2020Accepted: 08 February 2021Published online: 26 April 2021Keywordsradial basis function, least squares, partial differential equation, elliptic problem, Neumann condition, RBF-FDAMS Subject Headings65N06, 65N12, 65N35Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society for Industrial and Applied MathematicsCODEN: sjoce3

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Numerical comparison of least square-based finite-difference (LSFD) and radial basis function-based finite-difference (RBFFD) methods

1. I N T R O D U C T I O N In the past decade, the so-called mesh-free methods have become one of the hot tes t research areas in computa t ional mechanics. The te rm mesh-free or meshless is used to describe the special ways of constructing the approximation or interpolation scheme for the spatial discretization. Tha t is, the function and its derivatives at one central node are approximated e...

متن کامل

On the efficiency of the orthogonal least squares training method for radial basis function networks

The efficiency of the orthogonal least squares (OLS) method for training approximation networks is examined using the criterion of energy compaction. We show that the selection of basis vectors produced by the procedure is not the most compact when the approximation is performed using a nonorthogonal basis. Hence, the algorithm does not produce the smallest possible networks for a given approxi...

متن کامل

The overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD

We present a generalization of the RBF-FD method that allows full control of the overlap between RBF-FD stencils. We accomplish this by introducing a continuous overlap parameter δ ∈ [0, 1] such that δ = 1 recovers the standard RBF-FD method and δ = 0 results in a full decoupling of the RBF-FD stencils. We show with a simple example that global interpolation with both RBFs and RBFs augmented wi...

متن کامل

A least-squares preconditioner for radial basis functions collocation methods

Although meshless radial basis function (RBF) methods applied to partial differential equations (PDEs) are not only simple to implement and enjoy exponential convergence rates as compared to standard mesh-based schemes, the system of equations required to find the expansion coefficients are typically badly conditioned and expensive using the global Gaussian elimination (G-GE) method requiring O...

متن کامل

The Overlapped Radial Basis Function-Finite Difference (RBF-FD) Method for the Numerical Solution of PDEs

We present a generalization of the RBF-FD method that allows full control of the overlap between RBF-FD stencils. We accomplish this by introducing a continuous overlap parameter δ ∈ [0, 1] such that δ = 1 recovers the standard RBF-FD method and δ = 0 results in a full decoupling of the RBF-FD stencils. We show with a simple example that global interpolation with both RBFs and RBFs augmented wi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: SIAM Journal on Scientific Computing

سال: 2021

ISSN: ['1095-7197', '1064-8275']

DOI: https://doi.org/10.1137/20m1320079