Search results for "Meshless method"
showing 10 items of 30 documents
On the use of SPH for Mechanical Engineering structural analyses: an elastic linear case
2011
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…
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…
Unconditionally stable meshless integration of time-domain Maxwell’s curl equations
2015
Grid based methods coupled with an explicit approach for the evolution in time are traditionally adopted in solving PDEs in computational electromagnetics. The discretization in space with a grid covering the problem domain and a stability step size restriction, must be accepted. Evidence is given that efforts need for overcoming these heavy constraints. The connectivity laws among the points scattered in the problem domain can be avoided by using meshless methods. Among these, the smoothed particle electromagnetics, gives an interesting answer to the problem, overcoming the limit of the grid generation. In the original formulation an explicit integration scheme is used providing, spatial a…
A brief overview on the numerical behavior of an implicit meshless method and an outlook to future challenges
2015
In this paper recent results on a leapfrog ADI meshless formulation are reported and some future challenges are addressed. The method benefits from the elimination of the meshing task from the pre-processing stage in space and it is unconditionally stable in time. Further improvements come from the ease of implementation, which makes computer codes very flexible in contrast to mesh based solver ones. The method requires only nodes at scattered locations and a function and its derivatives are approximated by means of a kernel representation. A perceived obstacle in the implicit formulation is in the second order differentiations which sometimes are eccesively sensitive to the node configurat…
Estimating the temperature evolution of foodstuffs during freezing with a 3D meshless numerical method
2015
Abstract Freezing processes are characterised by sharp changes in specific heat capacity and thermal conductivity for temperatures close to the freezing point. This leads to strong nonlinearities in the governing PDE that may be difficult to resolve using traditional numerical methods. In this work we present a meshless numerical method, based on a local Hermite radial basis function collocation approach in finite differencing mode, to allow the solution of freezing problems. By introducing a Kirchhoff transformation and solving the governing equations in Kirchhoff space, the strength of nonlinearity is reduced while preserving the structure of the heat equation. In combination with the hig…
On a regularized approach for the method of fundamental solution
2018
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.
A 3D Meshless Approach for Transient Electromagnetic PDEs
2012
A full wave three dimensional meshless approach for electromagnetic transient simulations is presented. The smoothed particle hydrodynamic (SPH) method is used by considering the particles as interpolation points, arbitrarily placed in the computational domain. Maxwell’s equations in time domain with the assigned boundary and initial conditions are numerically solved by means of the proposed method. The computational tool is assessed and, for the first time, a 3D test problem is simulated in order to validate the proposed approach.
A preliminary comparison between finite element and meshless simulations of extrusion
2009
In this paper the extrusion process of a cross-shaped profile was investigated. In particular, the study was focused on the distortion of extruding profiles when the workpiece and die axis are not aligned. The process was simulated using the finite element method (FEM) and the natural element method (NEM), both implemented in an updated-Lagrangian formulation, in order to avoid the burden associated with the description of free surfaces in ALE or Eulerian formulations. Furthermore, an experimental equipment was developed in order to obtain reliable data in terms of deformed entity, required process load and calculated pressure. At the end, a comparison between the numerical predictions and …