Search results for "Particle method"
showing 10 items of 12 documents
A Mesh-free Particle Method for Transient Full-wave Simulation
2007
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
2007
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 Consistency Restoring in SPH
2009
On the use of a meshless solver for PDEs governing electromagnetic transients
2009
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.
Multiscale Particle Method in Solving Partial Differential Equations
2007
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 Smoothed Particle Image Reconstruction method
2010
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…
A velocity–diffusion method for a Lotka–Volterra system with nonlinear cross and self-diffusion
2009
The aim of this paper is to introduce a deterministic particle method for the solution of two strongly coupled reaction-diffusion equations. In these equations the diffusion is nonlinear because we consider the cross and self-diffusion effects. The reaction terms on which we focus are of the Lotka-Volterra type. Our treatment of the diffusion terms is a generalization of the idea, introduced in [P. Degond, F.-J. Mustieles, A deterministic approximation of diffusion equations using particles, SIAM J. Sci. Stat. Comput. 11 (1990) 293-310] for the linear diffusion, of interpreting Fick's law in a deterministic way as a prescription on the particle velocity. Time discretization is based on the …
A numerical meshless particle method in solving the magnetoencephalography forward problem
2012
In this paper, a numerical meshless particle method is presented in order to solve the magnetoencephalography forward problem for analyzing the complex activation patterns in the human brain. The forward problem is devoted to compute the scalp potential and magnetic field distribution generated by a set of current sources representing the neural activity, and in this paper, it has been approached by means of the smoothed particle hydrodynamics method suitably handled. The Poisson equation generated by the quasi-stationary Maxwell’s curl equations, by assuming Neumann boundary conditions has been considered, and the current sources have been simulated by current dipoles. The adopted meshless…
Smoothed Particle ElectroMagnetics: A mesh-free solver for transients
2006
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…