Related papers: Radial Basis Function Approximations: Comparison a…
The popularity of local meshless methods in the field of numerical simulations has increased greatly in recent years. This is mainly due to the fact that they can operate on scattered nodes and that they allow a direct control over the…
In this study,a new method was presented by developing Reduced differential transform method in order to find approximate solution of partial differential equations. Here, RDTM with fixed grid size algorithm was developed for the first time…
Accurate and compact representation of signed distance functions (SDFs) of implicit surfaces is crucial for efficient storage, computation, and downstream processing of 3D geometry. In this work, we propose a general learning method for…
In this paper, we deal with the challenging computational issue of interpolating large data sets, with eventually non-homogeneous densities. To such scope, the Radial Basis Function Partition of Unity (RBF-PU) method has been proved to be a…
We study the numerical evaluation of the integral fractional Laplacian and its application in solving fractional diffusion equations. We derive a pseudo-spectral formula for the integral fractional Laplacian operator based on fractional…
In solving the variational problem, the key is to efficiently find the target function that minimizes or maximizes the specified functional. In this paper, by using the Pade approximant, we suggest a methods for the variational problem. By…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
This work introduces the nested-set Hessian approximation, a second-order approximation method that can be used in any derivative-free optimization routine that requires such information. It is built on the foundation of the generalized…
Radial basis function generated finite difference (RBF-FD) methods for PDEs require a set of interpolation points which conform to the computational domain $\Omega$. One of the requirements leading to approximation robustness is to place…
The Radial Basis Function-generated finite differences became a popular variant of local meshless strong form methods due to its robustness regarding the position of nodes and its controllable order of accuracy. In this paper, we present a…
This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted…
In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals, including…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can…
In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural…
In this paper two common collocation approaches based on radial basis functions have been considered; one be computed through the integration process (IRBF) and one be computed through the differentiation process (DRBF). We investigated the…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
In this paper, Bayesian optimisation is used to simultaneously search the optimal values of the shape parameter and the radius in radial basis function partition of unity interpolation problem. It is a probabilistic iterative approach that…
The reciprocal function, 1/x, is important for many real-time algorithms. It is used in a large variety of algorithms from areas ranging from iterative estimation to machine learning. Many of these algorithms are iterative in nature and…