ix Resumé xi Remerciements xiii Abbréviations xv I General Introduction 1 0.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.2 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 0.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 0.4 Outline . . . . . . . . . . . . . . . . . . . . ...

The Hermite Radial Basis Functions (HRBF) Implicits reconstruct an implicit function which interpolates or approximates scattered multivariate Hermite data (i.e., unstructured points and their corresponding normals). Experiments suggest that HRBF Implicits allow the reconstruction of surfaces rich in details and behave better than previous related methods under coarse and/or nonuniform sampling...

In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable wit...

A Bayesian framework for the analysis of radial basis functions (RBF) is proposed which readily accommodates uncertainty in the dimension of the model. A distribution is deened over the space of all RBF models of a given basis function and posteriors are computed using reversible jump Markov chain Monte Carlo samplers (Green, 1995). This alleviates the need to select one particular architecture...

In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $nu$ ($1< nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. ...

This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any str...

The paper discusses the numerical solution of large-eddy formulation for modelling turbulent fluid flow with solidification in continuous casting steel. This industrially relevant problem is solved by a meshless method first time. solid-liquid system formulated within continuum mixture governing, mass momentum and energy equations. Darcy porous media model describes mushy region. based on Smago...

Several radial basis function based methods contain a free shape parameter which has  a crucial role in the accuracy of the methods. Performance evaluation of this parameter in different  functions with various data has always been a topic of study. In the present paper, we consider studying the methods which determine an optimal value for the shape parameter in interpolations of radial basis  ...

Abstract. Radial basis function (RBF) interpolation can be very effective for scattered data in any number of dimensions. As one of their many applications, RBFs can provide highly accurate collocation-type numerical solutions to several classes of PDEs. To better understand the accuracy that can be obtained, we survey here derivative approximations based on RBFs using a similar Fourier analysi...

The collocation method with multiquadrics basis functions and a first-order shear deformation theory are used to find natural flexural frequencies of a square plate with various material symmetries and subjected to different boundary conditions. Computed results are found to agree well with the literature values obtained by the solution of the three-dimensional elasticity equations using the fi...