1,721,068 research outputs found
Some numerical modelings beyond the mesh
No full textIn recent years meshless methods have gained much attention in several application areas of science. These methods benefit of savings due to the elimination of meshing process and are suite to handle changes in the geometry of the domain of interest. Further advantages come from the ease of implementation, which makes computer codes very flexible. We present some numerical experiences lying in the meshless framework dealing with domain and boundary-type methods
The smoothed particle hydrodynamics method via residual iteration
Full text linkIn this paper we propose for the first time an iterative approach of the Smoothed Particle Hydrodynamics (SPH) method. The method is widespread in many areas of science and engineering and despite its extensive application it suffers from several drawbacks due to inaccurate approximation at boundaries and at irregular interior regions. The presented iterative process improves the accuracy of the standard method by updating the initial estimates iterating on the residuals. It is appealing preserving the matrix-free nature of the method and avoiding to modify the kernel function. Moreover the process refines the SPH estimates and it is not affected by disordered data distribution. We discuss on the numerical scheme and experiments with a bivariate test function and different sets of data validate the adopted approach
SPH method: numerical investigations and applications
No full textIn 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
Highlighting numerical insights of an efficient SPH method
No full textIn this paper we focus on two sources of enhancement in accuracy and computational de manding in approximating a function and its derivatives by means of the Smoothed Particle Hydrodynamics method. The approximating power of the standard method is perceived to be poor and improvements can be gained making use of the Taylor series expansion of the kernel approximation of the function and its derivatives. The modified formulation is appealing providing more accurate results of the function and its derivatives simultaneously without changing the kernel function adopted in the computation. The request for greater accuracy needs kernel function derivatives with order up to the desidered accuracy order in approximating the function or higher for the derivatives. In this paper we discuss on the scheme dealing with the infinitely differentiable Gaussian kernel function. Studies on the accuracy, convergency and computational efforts with various sets of data sites are provided. Moreover, to make large scale problems tractable the improved fast Gaussian transform is considered picking up the computational cost at an acceptable level preserving the accuracy of the computation
A normalized iterative Smoothed Particle Hydrodynamics method
Full text linkIn this paper we investigate on a normalized iterative approach to improve the Smoothed Particle Hydrodynamics (SPH) estimate of a function. The method iterates on the residuals of an initial SPH approximation to obtain a more accurate solution. The iterative strategy preserves the matrix-free nature of the method, does not require changes on the kernel function and it is not affected by disordered data distribution. The iterative refinement is further improved by ensuring a linear approximation order to the starting iterative values. We analyze the accuracy and the convergence of the method with the standard and normalized formulation giving evidence of the improvements obtained with both uniform and non-uniform data density. Numerical experiments in 2D domain with different data sets are presented to validate the iterative approac
Numerical insights of an improved SPH method
Full text linkIn 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 lower order derivatives are inherent in approximating the higher order derivatives. Moreover, high order of accuracy can be obtained without changes on the kernel function avoiding to lead unphysical results such as negative density or negative energy that can lead to breakdown of the entire computation in simulating some problems [1]. The modified scheme obtains the required accuracy, but the high computational effort makes the procedure rather expensive and not easily approachable in the applications. To this aim we make use of fast summations to generate a more efficient procedure, allowing to tune the desired accuracy. Working with the Gaussian function we proceed by applying the improved fast Gaussian transform as valid alternative to efficiently com- pute the summations of the kernel and its derivatives [4]. We discuss about the accuracy and the computational demanding of the improved method dealing with different sets of data and bivariate functions
Detecting tri-stability of 3D models with complex attractors via meshfree reconstruction of invariant manifolds of saddle points
No full textIn mathematical modeling it is often required the analysis of the vector field topology in order to predict the evolution of the variables involved. When a dynamical system is multi-stable the trajectories approach different stable states, depending on the initialmconditions. The aim of this work is the detection of the invariant manifolds of thesaddle points to analyze the boundaries of the basins of attraction. Once that a sufficient number of separatrix points is found a Moving Least Squares meshfree method is involved to reconstruct the separatrix manifolds. Numerical results are presented to assess the method referring to tri-stable models with complex attractors such as limit cycles or limit tori
Detection of the human brain activity with fundamental solution method
No full textHuman 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 (LOOCV) strategy we improve the accuracy of the numerical solver gaining promising results
On the Numerical Solution of Some Elliptic PDEs with Neumann Boundary Conditions through Multinode Shepard Method
No full textIn this talk, the multinode Shepard method is proposed to solve elliptic partial differential equations with Neumann boundary conditions. The method has been opportunely handled to solve different equations with various boundary conditions dealing with scattered distribution of points [1, 2]. The particular feature of the method, based on local polynomial interpolants on opportunely choosen nearby nodes [3], is a collocation matrix which is reduced in size with many zero entrances and a small condition number. Experiments in 2d domains have been performed with Neumann boundary conditions. Comparisons with the analytic solutions and the results generated with the RBF method proposed by Kansa are presented referring to different distribution of points
Computational Issues of an Electromagnetics Transient Meshless Method
No full textIn this paper we refer to the computational issues in solving Maxwell’ s curl equations without using any connectivity among the points in which the problem domain is discretized. The adopted procedure is able to approximate the electric and magnetic vector fields making use of the derivatives of a kernel function at points arranged in the computational domain. In order to improve the numerical accuracy, dealing with irregular data distribution or data located near the boundary, a suitable strategy is considered. The computational core of the overall process requires elementary linear algebra operations. In the paper the method is presented and the discussion is revolved to the computational issues. Moreover, some numerical simulations are presented to validate the numerical process
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