Premium
Time‐domain vector potential technique for the meshless radial point interpolation method
Author(s) -
Shaterian Zahra,
Kaufmann Thomas,
Fumeaux Christophe
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4864
Subject(s) - interpolation (computer graphics) , convergence (economics) , node (physics) , mathematics , divergence (linguistics) , radial basis function , finite element method , domain (mathematical analysis) , mathematical analysis , magnetic potential , mathematical optimization , algorithm , computer science , physics , artificial neural network , artificial intelligence , motion (physics) , linguistics , philosophy , quantum mechanics , economics , thermodynamics , economic growth
Summary A time‐domain meshless algorithm based on vector potentials is introduced for the analysis of transient electromagnetic fields. The proposed numerical algorithm is a modification of the radial point interpolation method, where radial basis functions are used for local interpolation of the vector potentials and their derivatives. In the proposed implementation, solving the second‐order vector potential wave equation intrinsically enforces the divergence‐free property of the electric and magnetic fields. Furthermore, the computational effort associated with the generation of a dual node distribution (as required for solving the first‐order Maxwell's equations) is avoided. The proposed method is validated with several examples of 2D waveguides and filters, and the convergence is empirically demonstrated in terms of node density or size of local support domains. It is further shown that inhomogeneous node distributions can provide increased convergence rates, that is, the same accuracy with smaller number of nodes compared with a solution for homogeneous node distribution. A comparison of the magnetic vector potential technique with conventional radial point interpolation method is performed, highlighting the superiority of the divergence‐free formulation. Copyright © 2015 John Wiley & Sons, Ltd.