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Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.


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TL;DR: In this paper, a time-domain meshless algorithm based on vector potentials is introduced for the analysis of transient electromagnetic fields, where radial basis functions are used for local interpolation of the vector potential and their derivatives.
Abstract: Summary A time-domain meshless algorithm based on vector potentials is introduced for the analysis of transient electromagnetic fields. The proposed numerical algorithm is a modification of the radial point interpolation method, where radial basis functions are used for local interpolation of the vector potentials and their derivatives. In the proposed implementation, solving the second-order vector potential wave equation intrinsically enforces the divergence-free property of the electric and magnetic fields. Furthermore, the computational effort associated with the generation of a dual node distribution (as required for solving the first-order Maxwell's equations) is avoided. The proposed method is validated with several examples of 2D waveguides and filters, and the convergence is empirically demonstrated in terms of node density or size of local support domains. It is further shown that inhomogeneous node distributions can provide increased convergence rates, that is, the same accuracy with smaller number of nodes compared with a solution for homogeneous node distribution. A comparison of the magnetic vector potential technique with conventional radial point interpolation method is performed, highlighting the superiority of the divergence-free formulation. Copyright © 2015 John Wiley & Sons, Ltd.

5 citations

Journal ArticleDOI
TL;DR: In this article, the Generalized Multiscale Finite Element Method (GMsFEM) was proposed to handle complex heterogeneities in piezoelectric mesh.
Abstract: In this paper, we study multiscale methods for piezocomposites. We consider a model of static piezoelectric problem that consists of deformation with respect to components of displacements and a function of electric potential. This problem includes the equilibrium equations, the quasi-electrostatic equation for dielectrics, and a system of coupled constitutive relations for mechanical and electric fields. We consider a model problem that consists of coupled differential equations. The first equation describes the deformations and is given by the elasticity equation and includes the effect of the electric field. The second equation is for the electric field and has a contribution from the elasticity equation. In previous findings, numerical homogenization methods are proposed and used for piezocomposites. We consider the Generalized Multiscale Finite Element Method (GMsFEM), which is more general and is known to handle complex heterogeneities. The main idea of the GMsFEM is to develop additional degrees of freedom and can go beyond numerical homogenization. We consider both coupled and split basis functions. In the former, the multiscale basis functions are constructed by solving coupled local problems. In particular, coupled local problems are solved to generate snapshots. Furthermore, in the snapshot space, a local spectral decomposition is performed to identify multiscale basis functions. Our approaches share some common concepts with meshless methods as they solve the underlying problem on a coarse mesh, which does not conform heterogeneities and contrast. We discuss this issue in the paper. We show that with a few basis functions per coarse element, one can achieve a good approximation of the solution. Numerical results are presented.

5 citations

Journal ArticleDOI
TL;DR: This study presents a method of formulating the FCM equations such that they allow for the specification of varying material properties and is applied to the heat transfer equation.

5 citations

Journal ArticleDOI
TL;DR: In this paper, the sensitivity coefficients are determined on the basis of partial derivatives of the homogenized elasticity tensor calculated using the response function method with respect to all composite components' elastic characteristics.

5 citations

Posted Content
TL;DR: A wide array of meshless methods to reliably simulate materials undergoing large deformations is benchmarked and the complete source code of all methods considered is made public in the interest of reproducibility.
Abstract: Meshless methods are a promising candidate to reliably simulate materials undergoing large deformations. Unlike mesh based methods like the FEM, meshless methods are not limited in the amount of deformation they can reproduce since there are no mesh regularity constraints to consider. However, other numerical issues like zero energy modes, the tensile instability and disorder of the discretization points due to the deformation may impose limits on the deformations possible. It is thus worthwhile to benchmark a wide array of these methods since a proper review to this end has been missing from the literature so far. In the interest of reproducibility, the complete source code of all methods considered is made public.

5 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202355
2022112
2021102
202092
201996
201897