Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation

Nechaev, O.V. and Shurina, E.P. and Botchev, M.A. (2008) Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation. Computers & Mathematics with Applications, 55 (10). pp. 2346-2362. ISSN 0898-1221

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Abstract:	In the edge vector finite element solution of the frequency domain Maxwell equations, the presence of a large kernel of the discrete rotor operator is known to ruin convergence of standard iterative solvers. We extend the approach of [R. Hiptmair, Multigrid method for Maxwell’s equations, SIAM J. Numer. Anal. 36 (1) (1999) 204–225] and, using domain decomposition ideas, construct a multilevel iterative solver where the projection with respect to the kernel is combined with the use of a hierarchical representation of the vector finite elements. The new iterative scheme appears to be an efficient solver for the edge finite element solution of the frequency domain Maxwell equations. The solver can be seen as a variable preconditioner and, thus, accelerated by Krylov subspace techniques (e.g. GCR or FGMRES). We demonstrate the efficiency of our approach on a test problem with strong jumps in the conductivity.
Item Type:	Article
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Mathematics of Computational Science (MaCS)
Link to this item:	http://purl.utwente.nl/publications/62360
Official URL:	http://dx.doi.org/10.1016/j.camwa.2007.11.003
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