Meshless Vector Radial Basis Functions With Weak Forms

Meshless methods construct their shape functions based on scattered nodes in the domain. One drawback of this approach is the presence of nonphysical modes in the numerical solution when dealing with vector problems due to the lack of the divergence free condition, in a similar way that occurs with...

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Bibliographic Details
Published in:IEEE transactions on magnetics 2017-06, Vol.53 (6), p.1-4
Main Authors: Lima, Naisses Z., Mesquita, Renato C.
Format: Article
Language:English
Subjects:
Basis functions
Construction methods
Divergence
Divergence free
eigenvalue problem
Eigenvalues and eigenfunctions
Electric fields
Electromagnetic waveguides
Finite element analysis
Finite element method
Magnetism
Mathematical analysis
meshless method
Meshless methods
Neural networks
Propagation
Shape
Shape functions
vector radial basis function (VRBF)
Wave propagation
weak form
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Summary:Meshless methods construct their shape functions based on scattered nodes in the domain. One drawback of this approach is the presence of nonphysical modes in the numerical solution when dealing with vector problems due to the lack of the divergence free condition, in a similar way that occurs with the node-based finite-element method. On the other hand, vector radial basis functions were developed to produce numerical approximations that satisfy the divergence free condition. This paper presents the usage of those functions in conjunction with weak forms to solve vector electromagnetic problems. Numerical tests involving the Maxwell eigenvalue problem and the wave propagation in a waveguide are solved to demonstrate that the numerical solution is not corrupted with spurious modes.
ISSN:0018-9464
1941-0069
DOI:10.1109/TMAG.2017.2652728