Search results for "Meshless method"

A marching-on in time meshless kernel based solver for full-wave electromagnetic simulation

2012

A meshless particle method based on an unconditionally stable time domain numerical scheme, oriented to electromagnetic transient simulations, is presented. The proposed scheme improves the smoothed particle electromagnetics method, already developed by the authors. The time stepping is approached by using the alternating directions implicit finite difference scheme, in a leapfrog way. The proposed formulation is used in order to efficiently overcome the stability relation constraint of explicit schemes. In fact, due to this constraint, large time steps cannot be used with small space steps and vice-versa. The same stability relation holds when the meshless formulation is applied together w…

A regular variational boundary model for free vibrations of magneto-electro-elastic structures

2011

In this paper a regular variational boundary element formulation for dynamic analysis of two-dimensional magneto-electro-elastic domains is presented. The method is based on a hybrid variational principle expressed in terms of generalized magneto-electro-elastic variables. The domain variables are approximated by using a superposition of weighted regular fundamental solutions of the static magneto-electro-elastic problem, whereas the boundary variables are expressed in terms of nodal values. The variational principle coupled with the proposed discretization scheme leads to the calculation of frequency-independent and symmetric generalized stiffness and mass matrices. The generalized stiffne…

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

2011

Evolutionary design optimization with Nash games and hybridized mesh/meshless methods in computational fluid dynamics

2012

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

2012

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.

ON THE UNIT CELL BOUNDARY VALUE PROBLEM WITH MESHLESS FORMULATION FOR MASONRY STRUCTURES

2017

In a generic multi-scale computational homogenization (CH) procedure, the crucial point is the definition and the solution of the Unit Cell (UC) Boundary Value Problem (BVP). The main aspects to be chosen for the formulation of the UC BVP are: (i) geometry; (ii) bound- ary conditions (BCs); (iii) material models; (iv) numerical approximation techniques. All these components play a key-role in the efficiency of the multi-scale procedure. In the present study, the UC BVP is formulated for running bond masonry according to a dis- placement based variational formulation, where the material of the blocks is considered indefi- nitely elastic and the mortar joints are simulated by zero-thickness e…

Free vibrations of anisotropic panels

2004

A meshfree approach, called Displacement Boundary Method, for the analysis of in-plane and out-of-plane free vibrations of anisotropic plates is presented. The discretization process is based on the use of a modified variational principle and the static fundamental solutions of the problem operators. The stiffness and mass matrices are frequencyindependent, symmetric and positive definite and their computation requires boundary integrations of regular kernels only. Thus, the final resolving system can be solved with classical approaches by using standard numerical procedures. Numerical results are presented to show the accuracy and effectiveness of the method.

Numerical Investigations of an Implicit Leapfrog Time-Domain Meshless Method

2014

Numerical solution of partial differential equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes in time. A predefined grid in the problem domain and a stability step size restriction need. Recently, the authors have reformulated the meshless framework based on smoothed particle hydrodynamics, in order to be applied for time domain electromagnetic simulation. Despite the good spatial properties, the numerical explicit time integration introduces, also in a meshless context, a severe constraint. In this paper, at first, the stability condition is addressed in a general way by allowing the time step inc…

Exponential convergence andH-c multiquadric collocation method for partial differential equations

2003

The radial basis function (RBF) collocation method uses global shape functions to interpolate and collocatethe approximate solution of PDEs. It is a truly meshless method as compared to some of the so-calledmeshless or element-free finite element methods. For the multiquadric and Gaussian RBFs, there are twoways to make the solution converge—either by refining the mesh size