Element-free Galerkin method for electromagnetic field computations

Čingoski, Vlatko; Miyamoto, Naoki; Yamashita, Hideo

doi:10.1109/20.717759

Cited by 96 publications

(43 citation statements)

References 7 publications

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“…The weak form functional corresponding to the above boundary value problem is (4) Owing to the non-Kronecker delta function property of the shape functions of meshless methods, an additional term representing contributions of normal derivatives of the solution variable on essential boundaries that corresponds to that for the finite element method, is introduced in the formulations of (4). It should be pointed out that this term is commonly neglected by most fellow researchers in their related works.…”

Section: A Governing Equation and Weak Form Functionalmentioning

confidence: 99%

“…To determine the unknown parameters , the difference between the local approximation given by (5) and the nodal parameters , i.e., the weighted, discrete norm as given by (6), is minimized. Moreover, (6) where is a compactly supported weighting function with center at node and is the number of nodes in the neighborhood of for which the weighting function [3], [4]. The weighting functions used in this paper are the tensor products of one dimensional ones.…”

Section: B Moving Least Square Approximationsmentioning

confidence: 99%

“…In simulation studies in electrical engineering, it is common to have geometrical deformations for optimization and nondestructive evaluation problems, and many researchers have found the meshless method very promising for the study of electromagnetics [4]- [6]. This paper describes in details the discretization procedures and the associated discrete formulations of a meshless method based on the Moving Least Square (MLS) approximant that are required when using meshless methods to study electromagnetic problems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of a meshless method in electromagnetics

Yang

Machado

et al. 2001

IEEE Trans. Magn.

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Abstract-An improved meshless method is presented with an emphasis on the detailed description of this new computational technique and its numerical implementations by investigating the usefulness of a commonly neglected parameter in this paper. Two approaches to enforce essential boundary conditions are also thoroughly investigated. Numerical tests on a mathematical function is carried out as a means of validating the proposed method. It will be seen that the proposed method is more robust than the conventional ones. Applications in solving electromagnetic problems are also presented.Index Terms-Lagrange multiplier method, least squares method, meshless method, moving-least square approximants.

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Section: A Governing Equation and Weak Form Functionalmentioning

confidence: 99%

Section: B Moving Least Square Approximationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of a meshless method in electromagnetics

Yang

Machado

et al. 2001

IEEE Trans. Magn.

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“…The EFGM has been used to model a variety of physics, e.g. 2D linear elasticity [8][9][10], static and dynamic fracture mechanics [11,12], plate and shell analysis [13][14][15], vibration [7,16,17], electromagnetics [18], heat transfer [8,[19][20][21], metal forming [22,23], biomechanics [24,25] and geomechanics [26]. While the EFGM is superior to the FEM in terms of accuracy and convergence, and there are no issues of volumetric locking [27], MLS shape functions are computationally more expensive and complicate the imposition of essential boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Finite deformation elasto-plastic modelling using an adaptive meshless method

Ullah

Augarde

2013

Computers & Structures

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'Finite deformation elasto-plastic modelling using an adaptive meshless method. ', Computers and structures., Further information on publisher's website:http://dx.doi.org/10. 1016/j.compstruc.2012.04.001 Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Computers and structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version will be subsequently published in Computers and structures, 2012Computers and structures, , 10.1016Computers and structures, /j.compstruc.2012 Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Problems including both material and geometric nonlinearities are of practical engineering importance in many applications. Efficient computational modelling of these problems with minimum computer resources remains challenging. Often these problems are modelled with the finite element method (FEM) with adaptive analysis, in which an error estimation procedure automatically determines regions for coarse and fine discretization. Meshless methods offer the attractive possibility of simpler adaptive procedures involving no remeshing, simply insertion or deletion of nodes. However, as meshless methods are computationally more expensive than the FEM, the use of the minimum possible number and proper distribution of nodes are important issues. In this study an adaptive meshless approach for nonlinear solid mechanics is developed based on the element free Galerkin method. An existing error estimation procedure for linear elasto-static problems, is extended here for nonlinear problems including finite deformation and elasto-plasticity, and a new adaptive procedure is described and demonstrated.

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“…Therefore, it is highly desirable to explore methods which will alleviate, at least partly, the onerous mesh generation or adaptive updating process. Accordingly, many meshless methods, all of which originate from computational mechanics, have been proposed and proved to be very promising in the study of electromagnetic field problems [2]- [5]. Since the interpolation of meshless methods is based on a set of nodes, and a connectivity of elements is not required, they offer the flexibility of additions and deletions of a set of nodes, which may be distributed in the solution domain irregularly, with relative ease.…”

Section: Introductionmentioning

confidence: 99%

Refinement computations of electromagnetic fields using FE and meshless methods

Yang

Wong

et al. 2005

IEEE Trans. Magn.

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A refinement algorithm for electromagnetic field computations using a combination of finite element and meshless methods is introduced. Bridging scales are used to separate the finite element and meshless shape functions to make the refinement hierarchical and to uphold the mathematical properties such as consistency and linear independence for all the bases. To facilitate the application of the proposed algorithm, details about the node addition, requirements for the node distribution, and relationships between the finite element and meshless shape functions, as well as the determination of the stop criterion are also fully addressed. Primary numerical results are reported to demonstrate and validate the applicability and advantages of the proposed algorithm over traditional ones.

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Element-free Galerkin method for electromagnetic field computations

Cited by 96 publications

References 7 publications

Application of a meshless method in electromagnetics

Application of a meshless method in electromagnetics

Finite deformation elasto-plastic modelling using an adaptive meshless method

Refinement computations of electromagnetic fields using FE and meshless methods

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