Corrective meshless particle formulations for time domain Maxwell's equations

Authors:
G. Ala;E. Francomano;A. Tortorici;E. Toscano;F. Viola
Affiliations:
Dipartimento di Ingegneria Elettrica, Elettronica e delle Telecomunicazioni, Universití degli Studi di Palermo, Viale delle Scienze, I-90128 Palermo, Italy;Dipartimento di Ingegneria Informatica, Universití degli Studi di Palermo, Viale delle Scienze, I-90128 Palermo, Italy;Dipartimento di Ingegneria Informatica, Universití degli Studi di Palermo, Viale delle Scienze, I-90128 Palermo, Italy;Dipartimento di Ingegneria Informatica, Universití degli Studi di Palermo, Viale delle Scienze, I-90128 Palermo, Italy;Dipartimento di Ingegneria Elettrica, Elettronica e delle Telecomunicazioni, Universití degli Studi di Palermo, Viale delle Scienze, I-90128 Palermo, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

In this paper a meshless approximation of electromagnetic (EM) field functions and relative differential operators based on particle formulation is proposed. The idea is to obtain numerical solutions for EM problems by passing up the mesh generation usually required to compute derivatives, and by employing a set of particles arbitrarily placed in the problem domain. The meshless Smoothed Particle Hydrodynamics method has been reformulated for solving the time domain Maxwell's curl equations. The consistency of the discretized model is investigated and improvements in the approximation are obtained by modifying the numerical process. Corrective algorithms preserving meshless consistency are presented and successfully used. Test problems, dealing with even and uneven particles distribution, are simulated to validate the proposed methodology, also by introducing a comparison with analytical solution.