0000000000861996
AUTHOR
Francomano Elisa
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.
Detection of the human brain activity with fundamental solution method
Human brain activity mapping is a fundamental task for the neurophysiological research and for the diagnostic purposes too. Non-invasive techniques such as Electroencephalography (EEG) and magnetoencephalography (MEG) allow the reconstruction of the cerebral electrical currents providing useful information on the neuronal activity in the human brain. Based on a typical inverse problem the M/EEG imaging techniques require to solve more times a forward one. In this paper we discuss on a numerical tool based on the Method of the Fundamental Solutions(MFS) to efficiently solve the M/EEG forward problem going over the BEM state-of-the-art procedure. Inspired by the Leave-One-Out Cross Validation…
Advanced numerical treatment of an accurate SPH method
The summation of Gaussian kernel functions is an expensive operation frequently encountered in scientific simulation algorithms and several methods have been already proposed to reduce its computational cost. In this work, the Improved Fast Gauss Transform (IFGT) [1] is properly applied to the Smoothed Particle Hydrodynamics (SPH) method [2] in order to speed up its efficiency. A modified version of the SPH method is considered in order to overcome the loss of accuracy of the standard formulation [3]. A suitable use of the IFGT allows us to reduce the computational effort while tuning the desired accuracy into the SPH framework. This technique, coupled with an algorithmic design for exploit…
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 …