相关论文: Mixing Sinc kernels to improve interpolations in s…

The numerical convergence of smoothed particle hydrodynamics (SPH) can be severely restricted by random force errors induced by particle disorder, especially in shear flows, which are ubiquitous in astrophysics. The increase in the number…

A set of interpolating functions of the type f(v)={(sin[v pi/2])/(v pi/2)}^n is analyzed in the context of the smoothed-particle hydrodynamics (SPH) technique. The behaviour of these kernels for several values of the parameter n has been…

We present a set of new smoothing kernels for smoothed particle hydrodynamics (SPH) that improve the convergence of the method without any additional computational cost. These kernels are generated through a linear combination of other SPH…

The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy,…

We study the problem of the appropriate choice of the interpolating kernel to be used in the evaluation of gradients of functions. Such interpolation technique is often used in applications, e.g. it is typical for Smoothed Particle…

Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…

In the class of immersed boundary (IB) methods, the choice of the delta function plays a crucial role in transferring information between fluid and solid domains. Most prior work has used isotropic kernels that do not preserve the…

The error of smoothed particle hydrodynamics (SPH) using kernel for particle-based approximation mainly comes from smoothing and integration errors. The choice of kernels has a significant impact on the numerical accuracy, stability and…

We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…

Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…

Tensile instability, often observed in smoothed particle hydrodynamics (SPH), is a numerical artifact that manifests itself by unphysical clustering or separation of particles. The instability originates in estimating the derivatives of the…

We present a formulation of smoothed particle hydrodynamics (SPH) that utilizes a first-order consistent reproducing kernel, a smoothing function that exactly interpolates linear fields with particle tracers. Previous formulations using…

Smoothed Particle Hydrodynamics (SPH) is plagued by the phenomenon of tensile instability, which is the occurrence of short wavelength zero energy modes resulting in unphysical clustering of particles. The root cause of the instability is…

There has been great interest recently in applying nonparametric kernel mixtures in a hierarchical manner to model multiple related data samples jointly. In such settings several data features are commonly present: (i) the related samples…

We discuss capability of Smooth Particle Hydrodynamics to represent adequately the dynamics of self-gravitating systems, in particular for what regards the quality of approximation of force fields in the motion equations. When cubic spline…

We propose and study a new quasi-interpolation method on spheres featuring the following two-phase construction and analysis. In Phase I, we analyze and characterize a large family of zonal kernels (e.g., the spherical version of Poisson…

Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…

We present and explore a new shock-capturing particle hydrodynamics approach. Our starting point is a commonly used discretization of smoothed particle hydrodynamics. We enhance this discretization with Roe's approximate Riemann solver, we…

In this relation I present a technique of construction and fast evaluation of a family of cubic polynomials for analytic smoothing and graphical rendering of particles trajectories for flows in a generic geometry. The principal result of…

In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…