Avoiding recurrence in multiscale environments

On the Consistency Restoring in SPH

François Le Lionnais and the Oulipo. The Unexpected Role of Mathematics in Literature

“The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry” (Bertrand Russel, Mysticism and Logic, 1910). This sentence, quoted by François Le Lionnais in his work La Beauté en Mathématiques in [1], reflects his conception of a deep bond between mathematics and literature. He had a multifaceted education and was an erudite and founder of the Oulipo with Raymond Queneau. Even though he was neither a “professional” mathematician nor a “professional” man of letters but only an épicurien passionné as he defined himself [2],1 while alive, he channelled his interests in the the…

Wavelet-like bases for thin-wire integral equations in electromagnetics

AbstractIn this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis trans…

Admissible perturbations of alpha-psi-pseudocontractive operators: convergence theorems

In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we …

Black hole accretion discs and jets at super-Eddington luminosity

Super-Eddington accretion discs with 3 and 15 dot M_E around black holes with mass 10 M_sun are examined by two-dimensional radiation hydrodynamical calculations extending from the inner disc edge to 5*10^4 r_g and lasting up to \sim 10^6 r_g/c. The dominant radiation-pressure force in the inner region of the disc accelerates the gas vertically to the disc plane, and jets with 0.2 -- 0.4$c$ are formed along the rotational axis. In the case of the lower accretion rate, the initially anisotropic high-velocity jet expands outward and becomes gradually isotropic flow in the distant region. The mass-outflow rate from the outer boundary is as large as \sim 10^{19} -- 10^{23} g s^{-1}, but it is v…

An advanced variant of an interpolatory graphical display algorithm

In this paper an advanced interpolatory graphical display algorithm based on cardinal B-spline functions is provided. It is well-known that B-spline functions are a flexible tool to design various scale rapresentations of a signal. The proposed method allows to display without recursion a function at any desiderable resolution so that only initial data and opportune vectors weight are involved. In this way the structure of the algorithm is independent across the scale and a computational efficiency is reached. In this paper mono and bi-dimensional vectors weight generated by means of centered cubic cardinal B-spline functions have been supplied. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Wei…

Finite difference time domain simulation of soil ionization in grounding systems under lightning surge conditions

This paper proposes a Maxwell’s equations finite difference time domain (FDTD) approach for electromagnetic transients in ground electrodes in order to take into account the non linear effects due to soil ionization. A time variable soil resistivity method is used in order to simulate the soil breakdown, without the formulation of an initial hypothesis about the geometrical shape of the ionized zone around the electrodes. The model has been validated by comparing the computed results with available data found in technical literature referred to concentrated earths. Some application examples referred to complex grounding systems are reported to show the computational capability of the propos…

Iterative Reconstruction of Signals on Graph

We propose an iterative algorithm to interpolate graph signals from only a partial set of samples. Our method is derived from the well known Papoulis-Gerchberg algorithm by considering the optimal value of a constant involved in the iteration step. Compared with existing graph signal reconstruction algorithms, the proposed method achieves similar or better performance both in terms of convergence rate and computational efficiency.

A Smoothed Particle Interpolation Scheme for Transient Electromagnetic Simulation

In this paper, the fundamentals of a mesh-free particle numerical method for electromagnetic transient simulation are presented. The smoothed particle interpolation methodology is used by considering the particles as interpolation points in which the electromagnetic field components are computed. The particles can be arbitrarily placed in the problem domain: No regular grid, nor connectivity laws among the particles, have to be initially stated. Thus, the particles can be thickened only in distinct confined areas, where the electromagnetic field rapidly varies or in those regions in which objects of complex shape have to be simulated. Maxwell’s equations with the assigned boundary and initi…

Luminosity oscillations in accretion discs around compact objects

Multiscale Particle Method in Solving Partial Differential Equations

A novel approach to meshfree particle methods based on multiresolution analysis is presented. The aim is to obtain numerical solutions for partial differential equations by avoiding the mesh generation and by employing a set of particles arbitrarily placed in problem domain. The elimination of the mesh combined with the properties of dilation and translation of scaling and wavelets functions is particularly suitable for problems governed by hyperbolic partial differential equations with large deformations and high gradients.

A renormalized formulation of SPH method

Black-Hole Accretion Discs and Jets at Super-Eddington Luminosity

Super-Eddington accretion discs with 3 and 15 dot M_E around black holes with mass 10 M_sun are examined by two-dimensional radiation hydrodynamical calculations extending from the inner disc edge to 5*10^4 r_g and lasting up to \sim 10^6 r_g/c. The dominant radiation-pressure force in the inner region of the disc accelerates the gas vertically to the disc plane, and jets with 0.2 -- 0.4$c$ are formed along the rotational axis. In the case of the lower accretion rate, the initially anisotropic high-velocity jet expands outward and becomes gradually isotropic flow in the distant region. The mass-outflow rate from the outer boundary is as large as \sim 10^{19} -- 10^{23} g s^{-1}, but it is v…

A MESHLESS PARTICLE FORMULATION FOR ELECTROMGNETIC PROBLEMS

Radiative Shocks in Rotating Accretion Flows around Black Holes

It is well known that the rotating inviscid accretion flows with adequate injection parameters around black holes could form shock waves close to the black holes, after the flow passes through the outer sonic point and can be virtually stopped by the centrifugal force. We examine numerically such shock waves in 1D and 2D accretion flows, taking account of cooling and heating of the gas and radiation transport. The numerical results show that the shock location shifts outward compared with that in the adiabatic solutions and that the more rarefied ambient density leads to the more outward shock location. In the 2D-flow, we find an intermediate frequency QPO behavior of the shock location as …

WITHDRAWN: An efficient multiscale algorithm

The publisher regrets that this article has been temporarily removed. The reason for the overturn of the decision on ACHA-16-25 from Acceptance to Rejection is: One of the colleagues of the authors, Elisa Francomano, claims that the authors submitted the manuscript to ACHA without her knowledge and omitting her as one of the authors. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy .

A Mesh-free Particle Method for Transient Full-wave Simulation

A mesh-free particle method is presented for electromagnetic (EM) transient simulation. The basic idea is to obtain numerical solutions for the partial differential equations describing the EM problem in time domain, by using a set of particles, considered as spatial interpolation points of the field variables, arbitrarily placed in the problem domain and by avoiding the use of a regular mesh. Irregular problems geometry with diffused non-homogeneous media can be modeled only with an initial set of arbitrarily distributed particles. The time dependence is accounted for with an explicit finite difference scheme. Moreover the particle discretization can be improved during the process time ste…

Corrective meshless particle formulations for time domain Maxwell's equations

AbstractIn this paper a meshless approximation of electromagnetic (EM) field functions and relative differential operators based on particle formulation is proposed. The idea is to obtain numerical solutions for EM problems by passing up the mesh generation usually required to compute derivatives, and by employing a set of particles arbitrarily placed in the problem domain. The meshless Smoothed Particle Hydrodynamics method has been reformulated for solving the time domain Maxwell's curl equations. The consistency of the discretized model is investigated and improvements in the approximation are obtained by modifying the numerical process. Corrective algorithms preserving meshless consiste…

On the use of a meshless solver for PDEs governing electromagnetic transients

In this paper some key elements of the Smoothed Particle Hydrodynamics methodology suitably reformulated for analyzing electromagnetic transients are investigated. The attention is focused on the interpolating smoothing kernel function which strongly influences the computational results. Some issues are provided by adopting the polynomial reproducing conditions. Validation tests involving Gaussian and cubic B-spline smoothing kernel functions in one and two dimensions are reported.

Iterative Methods for Signal Reconstruction on Graphs

In applications such as social, energy, transportation, sensor, and neuronal networks, big data naturally reside on the vertices of graphs. Each vertex stores a sample, and the collection of these samples is referred to as a graph signal. The product of the network graph with the time series graph is considered as underlying structure for the evolution through time of graph signal “snapshots”. The framework of signal processing on graphs [4] extends concepts and methodologies from classical discrete signal processing. The task of sampling and recovery is one of the most critical topics in the signal processing community. In this talk, we present some localized iterative methods, obtained by…

Modelli numerici meshfree per l’analisi di problemi elettromagnetici.

A Meshless Method for Image Reconstruction

Consistency Restoring in SPH for Trigonometric Functions Approximation

Admissible perturbations of alpha-psi-pseudocontractive operators: convergence theorems

In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we …

SPH simulations of Shakura-Sunyaev instability at intermediate accretion rates

We show that a standard Shakura-Sunyaev accretion disc around a black hole with an accretion rate lower than the critical Eddington limit does show the instability in the radiation pressure dominated zone. We obtain this result performing time-dependent simulations of accretion disks for a set of values of the viscosity parameter and accretion rate. In particular we always find the occurrence of the collapse of the disc: the instability develops always towards a collapsed gas pressure dominated disc and not towards the expansion. This result is valid for all initial configurations we tested. We find significant convective heat flux that increases the instability development time, but is not…

The Poisson problem: A comparison between two approaches based on SPH method

Abstract In this paper two approaches to solve the Poisson problem are presented and compared. The computational schemes are based on Smoothed Particle Hydrodynamics method which is able to perform an integral representation by means of a smoothing kernel function by involving domain particles in the discrete formulation. The first approach is derived by means of the variational formulation of the Poisson problem, while the second one is a direct differential method. Numerical examples on different domain geometries are implemented to verify and compare the proposed approaches; the computational efficiency of the developed methods is also studied.

BourbOulipo. Relazioni tra Oulipo e Bourbaki

Il tema dell’influenza delle idee e delle metodologie bourbakiste su discipline che trascendono l’ambito matematico è stato frequentemente affrontato e, in particolare, la riflessione sul rapporto tra Bourbaki e Oulipo ha animato un appassionato dibattito in seno alla critica letteraria. Lo scopo di questo contributo è quello di investigare le relazioni tra Le Lionnais, Queneau e Roubaud - e più in generale l’Oulipo - e Bourbaki. Attraverso un esame comparativo tra i due gruppi si è evidenziata l’esistenza di un innegabile carisma del “matematico policefalo” sul movimento artistico-letterario. The theme of the influence of Bourbaki's ideas and methodologies on disciplines that transcend the…

Smoothed Particle Interpolation for electromagnetic simulations

A meshless approach solving time domain Maxwell’s equations

On the use of SPH for Mechanical Engineering structural analyses: an elastic linear case

Smoothed Particle ElectroMagnetics: A mesh-free solver for transients

AbstractIn this paper an advanced mesh-free particle method for electromagnetic transient analysis, is presented. The aim is to obtain efficient simulations by avoiding the use of a mesh such as in the most popular grid-based numerical methods. The basic idea is to obtain numerical solutions for partial differential equations describing the electromagnetic problem by using a set of particles arbitrarily placed in the problem domain. The mesh-free smoothed particle hydrodynamics method has been adopted to obtain numerical solution of time domain Maxwell's curl equations. An explicit finite difference scheme has been employed for time integration. Details about the numerical treatment of elec…

Un metodo meshfree particellare per la risoluzione delle equazioni di Maxwell: sviluppo di un codice in ambiente GRID

APPROCCIO "MESHFREE" PARTICELLARE PER L'ANALISI ELETTROMAGNETICA IN DOMINI TRIDIMENSIONALI

Radiative 2D Shocks, Super-Eddington Disks and Jets around Black Holes

It is well known that rotating inviscid accretion flows with adequate injection parameters around black holes could form shock waves close to the black holes, after the flow passes through the outer sonic point and can be virtually stopped by the centrifugal force. Such shock waves in 2D accretion flows are examined by 2D radiation hydrodynamical calculations. We also examine super‐Eddington accretion disks with 15 ṀE around black holes, focusing on a small collimation degree of the jet and a large mass‐outflow rate observed in the X‐ray source SS 433.

An Advanced Numerical Method for Recovering Image Velocity Vectors Field

Mauro Picone, Sandro Faedo, and the numerical solution of partial differential equations in Italy (1928-1953)

In this paper we revisit the pioneering work on the numerical analysis of partial differential equations (PDEs) by two Italian mathematicians, Mauro Picone (1885-1977) and Sandro Faedo (1913-2001). We argue that while the development of constructive methods for the solution of PDEs was central to Picone's vision of applied mathematics, his own work in this area had relatively little direct influence on the emerging field of modern numerical analysis. We contrast this with Picone's influence through his students and collaborators, in particular on the work of Faedo which, while not the result of immediate applied concerns, turned out to be of lasting importance for the numerical analysis of …

Numerical Simulations of the Thermal Instability Collapse in Radiation Pressure Dominated Disks

We show that accretion disks, both in the subcritical and supercritical accretion rate regime, may exhibit significant amplitude luminosity oscillations. The luminosity time behavior has been obtained by performing a set of time‐dependent 2D SPH simulations of accretion disks with different values of α and accretion rate. An explanation of this luminosity behavior is proposed in terms of limit‐cycle instability: the disk oscillates between a radiation pressure dominated configuration (with a high luminosity value) and a gas pressure dominated one (with a low luminosity value). The origin of this instability is the difference between the heat produced by viscosity and the energy emitted as r…

Exploiting Numerical Behaviors in SPH.

Smoothed Particle Hydrodynamics is a meshless particle method able to evaluate unknown field functions and relative differential operators. This evaluation is done by performing an integral representation based on a suitable smoothing kernel function which, in the discrete formulation, involves a set of particles scattered in the problem domain. Two fundamental aspects strongly characterizing the development of the method are the smoothing kernel function and the particle distribution. Their choice could lead to the so-called particle inconsistency problem causing a loose of accuracy in the approximation; several corrective strategies can be adopted to overcome this problem. This paper focu…

Fixed point iterative schemes for variational inequality problems

In a wide class of evolutionary processes, the problem of computing the solutions of an initial value problem is encountered. Here, we consider projected dynamical systems in the sense of \cite{Daniele} and references therein. Precisely, a projected dynamical system is an operator which solves the initial value problem: \begin{equation}\label{PDS}\frac{dx(t)}{dt}= \Pi_{\mathbb{K}}\left(x(t),-F(x(t))\right), \quad x(0)=x_0 \in \mathbb{K}, \, t \in [0,+\infty[,\tag{P}\end{equation} where $\mathbb{K}$ is a convex polyhedral set in $\mathbb{R}^n$, $F: \mathbb{K} \to \mathbb{R}^n$ and $\Pi_{\mathbb{K}}: \mathbb{R} \times \mathbb{K} \to \mathbb{R}^n$ is given as follows $\Pi_{\mathbb{K}}(x,-F(x))…

Hardware and Software Platforms for Distributed Computing on Resource Constrained Devices

The basic idea of distributed computing is that it is possible to solve a large problem by using the resources of various computing devices connected in a network. Each device interacts with each other in order to process a part of a problem, contributing to the achievement of a global solution. Wireless sensor networks (WSNs) are an example of distributed computing on low resources devices. WSNs encountered a considerable success in many application areas. Due to the constraints related to the small sensor nodes capabilities, distributed computing in WSNs allows to perform complex tasks in a collaborative way, reducing power consumption and increasing battery life. Many hardware platforms …

An efficient solver for electromagnetic transient simulationi

A Smoothed Particle Image Reconstruction method

Many image processing techniques work with scattered data distribution usually employing grid based methods leading to numerical problems. To address this issue, a numerical method avoiding mesh generation can be used. Such a method performs an integral representation by means of a smoothing kernel function and, in the discrete formulation, involves domain particles. In this paper the meshless Smoothed Particle Hydrodynamics method is proposed in the Image Reconstruction context and a new computational strategy called Smoothed Particle Image Reconstruction is presented; the new method is based on a scatter approach and several innovative ideas are introduced in order to improve the computat…

Ab initiosimulations of accretion disc instability

We show that accretion disks, both in the subcritical and supercritical accretion rate regime, may exhibit significant amplitude luminosity oscillations. The luminosity time behavior has been obtained by performing a set of time-dependent 2D SPH simulations of accretion disks with different values of alpha and accretion rate. In this study, to avoid any influence of the initial disk configuration, we produced the disks injecting matter from an outer edge far from the central object. The period of oscillations is 2 - 50 s respectively for the two cases, and the variation amplitude of the disc luminosity is 10^38 - 10^39 erg/s. An explanation of this luminosity behavior is proposed in terms o…

Properties determining parameters choice in meshless solver for electromagnetic transients

Modeling of Electronic Devices using Radial Basis Functions for EMC Evaluation

Impiego di metodi numerici meshfree per l’analisi elettromagnetica

Exploring parallel capabilities of an innovative numerical method for recovering image velocity vectors field

In this paper an efficient method devoted to estimate the velocity vectors field is investigated. The method is based on a quasi-interpolant operator and involves a large amount of computation. The operations characterizing the computational scheme are ideal for parallel processing because they are local, regular and repetitive. Therefore, the spatial parallelism of the process is studied to rapidly proceed in the computation on distributed multiprocessor systems. The process has shown to be synchronous, with good task balancing and requiring a small amount of data transfer.

The thermal instability collapse in radiation pressure dominated discs