A Cartesian grid approach for the solution of the Euler equations within the framework of a patched, embedded Cartesian field mesh is described. As Cartesian grids are not necessarily body-aligned, an accurate representation for the surface boundary is important. In this paper a gridless boundary treatment using a cloud of nodes in the vicinity of the body combined with the multiquadric radial ...

A large-eddy simulation (LES) based meshless model is developed for the three-dimensional (3D) problem of continuous casting (CC) steel billet. The local collocation method on radial basis functions (RBF) applied in 3D. applies scaled multiquadric (MQ) RBF with a shape parameter seven nodded sub-domains. incompressible turbulent fluid flow described using mass, energy, and momentum conservation...

The innovation of the present paper is analytical study Brownian motion effects on nanofluid flow and electromagnetic force between parallel disks with a heat source. Nanoparticle nondimensional temperature field velocity fluid were analyzed using Akbari-Ganji’s Method radial basis function approximation based Hardy multiquadric function. (AGM) strong method that solves any linear nonlinear dif...

The total variation (TV) denoising method is a PDE-based technique that preserves the edges well but has undesirable staircase effect in some cases, namely, the translation of smooth regions (ramps) into piecewise constant regions (stairs). This paper introduces a novel mesh-free approach using TV (ROFmodel) regularization and radial basis function (RBF) for the numerical approximation of TV-ba...

In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. Thus, the number of nodes in the stencils can be relatively large compared to the resulting accuracy. The generalization of mehrstellenverfahren (compact) FD (CFD) formu...

In our previous work, an effective preconditioning scheme that is based upon constructing least-squares approximation cardinal basis functions (ACBFs) from linear combinations of the RBF-PDE matrix elements has shown very attractive numerical results. The preconditioner costs O(N2) flops to set up and O(N) storage. The preconditioning technique is sufficiently general that it can be applied to ...

It’s well-known that there is a so-called high-level error bound for multiquadric and inverse multiquadric interpolations, which was put forward by Madych and Nelson in 1992. It’s of the form |f(x)− s(x)| ≤ λ 1 d ‖f‖h where 0 < λ < 1 is a constant, d is the fill distance which roughly speaking measures the spacing of the data points, s(x) is the interpolating function of f(x), and h denotes the...

In this note a local thinning of the data locations is proposed, in order to construct a least squares multiquadric approximant stable and close to the multiquadric interpolant

This note concerns density properties of the general multiquadric, (x + c2)k−1/2, where k is a fixed natural number. We establish that scattered translates of the general multiquadric are dense in C([a, b]), where a and b are finite. As a corollary, we show that scattered translated of the general multiquadric are dense in the function spaces L([a, b]), for 1 ≤ p <∞.

As a kernel independent algorithm, multilevel Green’s function interpolation method (MLGFIM) [1] [2] has been developed for electromagnetic problems from low frequency to fullwave simulation. This method inherits the multilevel tree structure of multilevel fast multipole algorithm (MLFMA) and adopts the interpolation technique of pre-corrected fast Fourier transform (PFFT). Compare with other f...