0000000000861997
AUTHOR
Paliaga Marta
SPH method: numerical investigations and applications
In this paper we discuss on the enhancements in accuracy and computational demanding in approx- imating a function and its derivatives via Smoothed Particle Hydrodynamics. The standard method is widely used nowadays in various physics and engineering applications [1],[2],[3]. However it suffers of low approximation accuracy at boundaries or when scattered data distributions are con- sidered. In this paper we discuss on some numerical behaviors of the method. Some variants of the process are analyzed and results on the accuracy and the computational demanding, dealing with different sets of data and bivariate functions, are proposed.
On a regularized approach for the method of fundamental solution
The method of fundamental solution is a boundary meshless method recently adopted in the framework of non-invasive neu- roimaging techniques. The method approximates the solution of a BVP by a linear combination of fundamental solutions of the governing PDE. A crucial feature of the method is the placement of the fictitious boundary to avoid the singularities of fundamental solutions. In this paper we report on our experiences with a regularized MFS method in the neuroimaging context.
Numerical insights of an improved SPH method
In this paper we discuss on the enhancements in accuracy and computational demanding in approximating a function and its derivatives via Smoothed Particle Hydrodynamics. The standard method is widely used nowadays in various physics and engineering applications [1],[2],[3]. However it suffers of low approximation accuracy at boundaries or when scattered data distributions is considered. Here we reformulate the original method by means of the Taylor series expansion and by employing the kernel function and its derivatives as projection functions and integrating over the problem domain [3]. In this way, accurate estimates of the function and its derivatives are simultaneously provided and no …