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A higher-order finite element method with an explicit higher-order time integration scheme

David Degerfeldt (Institutionen för signaler och system, Signalbehandling) ; Thomas Rylander (Institutionen för signaler och system, Signalbehandling)
EMB07 Computational Electromagnetics Methods and Applications, Lund, Sweden, Oct 18-19, 2007 p. 91-98. (2007)
[Konferensbidrag, refereegranskat]

We formulate and analyze a FEM that exploits higher-order approximations of the fields for both space and time. An explicit leap-frog type scheme is used to update Faraday's and Ampére's law, and we present a stability and error analysis for this time-stepping scheme. Our formulation exploits a matrix free representation of Maxwell's equations, which reduces the memory requirements significantly. The scheme is tested by solving eigenvalue problems in a cubic cavity with metal walls. The tests demonstrate that the method yields exponential convergence with respect to spatial order p and polynomial convergence, h2p, with respect to the cell size h. Analogous convergence is achieved for the time-stepping scheme. The method reduces to the standard FDTD method for lowest order of approximation with respect to space and time. The technique presented is useful for computational studies of reverberation chambers and similar applications.

Nyckelord: FEM, FDTD, higher-order methods, explicit schemes



Denna post skapades 2007-10-16. Senast ändrad 2007-10-23.
CPL Pubid: 54235

 

Institutioner (Chalmers)

Institutionen för signaler och system, Signalbehandling

Ämnesområden

Elektroteknik

Chalmers infrastruktur

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A hybrid finite element method for electromagnetics with applications in time-domain