405 research outputs found
Reconstruction of density functions by sk-splines
Reconstruction of density functions and their characteristic functions by
radial basis functions with scattered data points is a popular topic in the
theory of pricing of basket options. Such functions are usually entire or admit
an analytic extension into an appropriate tube and "bell-shaped" with rapidly
decaying tails. Unfortunately, the domain of such functions is not compact
which creates various technical difficulties. We solve interpolation problem on
an infinite rectangular grid for a wide range of kernel functions and calculate
explicitly their Fourier transform to obtain representations for the respective
density functions
Enhancing SPH using moving least-squares and radial basis functions
In this paper we consider two sources of enhancement for the meshfree
Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving
the accuracy of the particle approximation. Namely, we will consider shape
functions constructed using: moving least-squares approximation (MLS); radial
basis functions (RBF). Using MLS approximation is appealing because polynomial
consistency of the particle approximation can be enforced. RBFs further appeal
as they allow one to dispense with the smoothing-length -- the parameter in the
SPH method which governs the number of particles within the support of the
shape function. Currently, only ad hoc methods for choosing the
smoothing-length exist. We ensure that any enhancement retains the conservative
and meshfree nature of SPH. In doing so, we derive a new set of
variationally-consistent hydrodynamic equations. Finally, we demonstrate the
performance of the new equations on the Sod shock tube problem.Comment: 10 pages, 3 figures, In Proc. A4A5, Chester UK, Jul. 18-22 200
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