Improving the Mixed Formulation for Meshless Local Petrov–Galerkin Method

Fonseca, Adelaida Pallavicini; Correa, Bruno; Silva, Élson J.; Mesquita, Renato C.

doi:10.1109/tmag.2010.2043513

Cited by 14 publications

(17 citation statements)

References 4 publications

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“…The radial point interpolation method with polynomial terms (RPIMp) will lead to a shape function that indeed obeys the Kronecker delta property. Hence, this paper uses the MLS method for interior nodes and the RPIMp method to impose the essential boundary conditions directly [2].…”

Section: Improvements To the Mlpg Methodsmentioning

confidence: 99%

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Complex problem domain based local Petrov-Galerkin meshless method for electromagnetic problems

Liu

Hutchcraft

et al. 2013

JAE

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In this paper, an improved MLPG method has been introduced to simplify the algorithm and thus make it more suitable for dealing with engineering problems with complex domains. In the case of a complex domain with an irregular global boundary, it can be very hard to determine the intersections between the local sub-domains and the global boundary. The improvements of the MLPG method make the MLPG method only require the domain integrations. The intersections between local sub-domains and the global boundary as well as boundary integrations have been avoided. A rectangular problem domain and a circular problem domain with exact solutions have been studied in this paper to investigate the accuracy of the improved MLPG method. The results show that compared to the regular MLPG method, the improved MLPG method can have the same accuracy, but the improved method is much easier to deal with irregular boundaries or complex problem domains.

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Section: Improvements To the Mlpg Methodsmentioning

confidence: 99%

“…The FEM requires the solution domain to be meshed, and the accuracy of the FEM depends on the quality of the mesh. The meshless methods have received a lot of attention in recent years; this is mainly because the meshless methods do not need any connectivity structure among nodes [2,3].…”

Section: Introductionmentioning

confidence: 99%

Complex problem domain based local Petrov-Galerkin meshless method for electromagnetic problems

Liu

Hutchcraft

et al. 2013

JAE

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“…There are many types of test functions that can be chosen [12]. The Heaviside function is adopted in this paper [9]:…”

Section: The Mlpg Formulationmentioning

confidence: 99%

A simple and efficient local Petrov-Galerkin meshless method and its application

Liu

Yang

et al. 2014

JAE

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In the MLPG method of this paper, only the boundary integrations over local subdomains is involved, which make the MLPG method is very easy to carry out because the local sub-domains are chosen in MLPG method as simple circular or rectangular ranges. In order to simplify the MLPG method, the radius of local sub-domains has been adjusted for the nodes close to the global boundary but not exactly on the boundary. In addition, the boundary conditions including the essential and natural boundary are imposed directly by the nodes which are exactly on the global boundary. Two electromagnetic models have been studied in this paper to investigate the accuracy and computational efficiency of the MLPG method. The results, which are compared with the solutions obtained from the MLPG in the reference and the FEM, show that the MLPG method in this paper can obtain more accurate results by using fewer nodes.

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“…Since some of the shape functions used in the conventional meshless methods do not satisfy the Kronecker delta property (Belytschko et al, 1996), the imposition of essential boundary conditions is another problem in these methods. A mixed formulation has been presented in Fonseca et al (2010) which combines Shepard's shape functions for inner nodes to reduce the computational time and RPIM shape functions for boundary nodes to impose the essential boundary conditions. But, it is interesting to note that for the suggested direct shape function, smaller the overhang radius of the shape function using correct set of a, closer to zero the value of the shape COMPEL 33,1/2 function in the other nodes.…”

Section: Direct Shape Functionmentioning

confidence: 99%

Unconditionally stable improved meshless methods for electromagnetic time-domain modeling

Razmjoo

Movahhedi

2013

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose -In this paper, a modified meshless method, as one of the numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to solving time-domain wave equation. The paper aims to discuss these issues. Design/methodology/approach -In space domain, the fields at the collocation points are expanded into a series of new Shepard's functions which have been suggested recently and are treated with a meshless method procedure. For time discretization of the second-order time-derivative, two finite-difference schemes, i.e. backward difference and Newmark-b techniques, are proposed. Findings -Both schemes are implicit and always stable and have unconditional stability with different orders of accuracy and numerical dispersion. The unconditional stability of the proposed methods is analytically proven and numerically verified. Moreover, two numerical examples for electromagnetic field computation are also presented to investigate characteristics of the proposed methods. Originality/value -The paper presents two unconditionally stable schemes for meshless methods in time-domain electromagnetic problems.

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Improving the Mixed Formulation for Meshless Local Petrov–Galerkin Method

Cited by 14 publications

References 4 publications

Complex problem domain based local Petrov-Galerkin meshless method for electromagnetic problems

Complex problem domain based local Petrov-Galerkin meshless method for electromagnetic problems

A simple and efficient local Petrov-Galerkin meshless method and its application

Unconditionally stable improved meshless methods for electromagnetic time-domain modeling

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