Periodic Boundary Conditions in the Natural Element Method

Gonçalves, Bárbara; Afonso, Márcio Matias; Coppoli, Eduardo H. R.; Schroeder, Marco Aurélio O.; Alípio, Rafael; Ramdane, Brahim; Maréchal, Yves

doi:10.1109/tmag.2015.2485958

Cited by 4 publications

(1 citation statement)

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“…where K is an N x N sparse and symmetric global matrix, and X and F are, respectively, the unknown and the source vectors of dimension N . The elements of the matrix K and vector F are given respectively by:

K_{ij} = \int_{Ω} \frac{1}{μ} \nabla ϕ_{j} \nabla ϕ_{i} dΩ

…”

Section: The Natural Element Methodsmentioning

confidence: 99%

Comparison of natural and finite element interpolation functions behavior

Gonçalves

Afonso

Coppoli

et al. 2017

Int J Numerical Modelling

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International audienceIn this paper, the interpolation functions behavior of the natural element method (NEM) and the finite element method (FEM) are compared. It is discussed how the unknown in both methods affects the stiffness matrix and contributes to NEM better accuracy. The visibility criterion and the constrained NEM are also addressed, and a pseudoalgorithm is proposed to implement the constrained Voronoï diagram, which is the base for the constrained NEM. A complex heterogeneous magnetic problem is solved by both FEM and NEM methods and their solutions are compared. It is shown that for the same discretization, the number of contributions for NEM is in general bigger than those related to the FEM and better accuracy results for NEM

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