1,720,999 research outputs found
Inverse and saturation theorems for radial basis function interpolation
No full textWhile direct theorems for interpolation with radial basis functions are intensively investigated, little is known about inverse theorems so far. This paper deals with both inverse and saturation theorems. For an inverse theorem we especially show that a function that can be approximated sufficiently fast must belong to the native space of the basis function in use. In case of thin plate spline interpolation we also give certain saturation theorems
Inverse and saturation theorems for radial basis function interpolation
No full textWhile direct theorems for interpolation with radial basis functions are intensively investigated, little is known about inverse theorems so far. This paper deals with both inverse and saturation theorems. For an inverse theorem we especially show that a function that can be approximated sufficiently fast must belong to the native space of the basis function in use. In case of thin plate spline interpolation we also give certain saturation theorems
Local polynomial reproduction and moving least squares approximation
No full textLocal polynomial reproduction is a key ingredient in providing error estimates for several approximation methods. To bound the Lebesgue constants is a hard task especially in a multivariate setting. We provide a result which allows us to bound the Lebesgue constants uniformly and independently of the space dimension by oversampling. We get explicit and small bounds for the Lebesgue constants. Moreover, we use these results to establish error estimates for the moving least squares approximation scheme, also with special emphasis on the involved constants. We discuss the numerical treatment of the method and analyse its effort. Finally, we give large scale examples
On the convergence of a general class of finite volume methods
No full textIn this paper we investigate numerical methods for solving hyperbolic conservation laws based on finite volumes and optimal recovery. These methods can, for example, be applied in certain ENO schemes. Their approximation properties depend in particular on the reconstruction from cell averages. Hence, this paper is devoted to prove convergence results for such reconstruction processes from cell averages
On the convergence of the rescaled localized radial basis function method
Full text linkThe rescaled localized RBF method was introduced in Deparis, Forti, and Quarteroni (2014) for scattered data interpolation. It is a rational approximation method based on interpolation with compactly supported radial basis functions. It requires the solution of two linear systems with the same sparse matrix, which has a small condition number, due to the scaling of the basis function. Hence, it can be computed using an unpreconditioned conjugate gradient method in linear time. Numerical evidence provided in Deparis, Forti, and Quarteroni (2014) shows that the method produces good approximations for many examples but no theoretical results were provided. In this paper, we discuss the convergence of the rescaled localized RBF method in the case of quasi-uniform data and stationary scaling. As the method is not only interpolatory but also reproduces constants exactly, linear convergence is expected. We can show this linear convergence up to a certain conjecture
A meshless spatial coupling scheme for large-scale fluid-structure-interaction problems
No full textWe present a new efficient scheme for loose coupling in fluid-structure-interaction problems as they typically appear in the context of aircraft design. This coupling scheme is based upon a multivariate scattered data interpolation approach, based on radial basis functions and partition of unity methods. It allows us to couple arbitrary meshes on fluid and structure side. It conserves virtual work and forces. It is designed for large scale problems and allows the coupling of entire aircraft meshes
A meshless spatial coupling scheme for large-scale fluid-structure-interaction problems
No full textWe present a new efficient scheme for loose coupling in fluid-structure-interaction problems as they typically appear in the context of aircraft design. This coupling scheme is based upon a multivariate scattered data interpolation approach, based on radial basis functions and partition of unity methods. It allows us to couple arbitrary meshes on fluid and structure side. It conserves virtual work and forces. It is designed for large scale problems and allows the coupling of entire aircraft meshes
Adaptive greedy techniques for approximate solution of large rbf systems
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