Creating higher order vector shape functions based on H(curl) for the edge meshless method

ABSTRACT

The goal of this work is to extend the Edge Meshless Method (EMM) presenting a new way to build the vector shape functions based on the H(curl) space. These vector shape functions allow the use of four, five and six edges in the support domain. For this, the basis functions polynomial order is increased. The new EMM vector shape functions are applied to eigenvalues problems with different media. The numerical solution is not corrupted by spurious modes, field singularities generated by corners are correctly overcome and the continuity of tangential components across the interface between two different media is satisfied. The shape function with six edges in the support domain present the best results, where the majority of the eigenvalues double their convergence rate. Also, approximations of different polynomial orders can be used in the same problem.

Keywords:

• Edge meshless method
• high order vectorial shape functions
• H(curl) space
• vector shape functions

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was funded by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001, Conselho Nacional de Desenvolvimento Científico e TecnológicoResolved (CNPq) and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG).

Notes on contributors

Luilly A. G. Ortiz

Luilly Alejandro Garcia Ortiz was bor in Cúcuta, Colombia, in 1992. He received the B.S in Electronic Engineering in 2015 from the Francisco University of Paula Santander of Cúcuta, Colombia, where he developed his degree project in the Telecommunications Research and Development Group. He received the M.S. degrees in electrical engineering from the Federal University of Minas Gerais, Belo Horizonte, Brazil in 2016. He is currently a Ph.D. Candidate at the Federal University of Minas Gerais, Belo Horizonte, Brazil.

Renato C. Mesquita

Renato Cardoso Mesquita was born in Belo Horizonte, Brazil, in 1959. He received the B.S. and M.S. degrees in electrical engineering from the Federal University of Minas Gerais, Belo Horizonte, Brazil, in 1982 and 1986, respectively, and the Dr. degree in electrical engineering from the Federal University of Santa Catarina, Florianópolis, Brazil, in 1990. Since 1983, he has been with the Department of Electrical Engineering, Federal University of Minas Gerais, where he is currently a Professor. His main research interest is in the area of electromagnetic field computation. He has authored or coauthored over 200 journal and conference papers in this area.

Naísses Z. Lima

Naísses Zoia Lima was born in Raul Soares, Brazil, in 1983. He received the B.S. degree in Control and Automation Engineering in 2008, the M.S and Dr. degrees in 2011 and 2016, respectively, from the Federal University of Minas Gerais, Belo Horizonte, Brazil. Since 2013, he has been with the Polytechnic Institute at Una Center University, where he is currently a Professor.