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8960 Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation

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Nechaev, O.V. and Shurina, E.P. and Botchev, M.A. (2006) Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation. Memorandum 1806, Department of Applied Mathematics, University of Twente, Enschede. ISSN 0169-2690

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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 [1] 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.

[1] R. Hiptmair. Multigrid method for Maxwell's equations. SIAM J. Numer. Anal., 36(1):204-225, 1999.

Item Type:	Internal Report (Memorandum)
Research Group:	EWI-MACS: Mathematics of Computational Science
Research Program:	IMPACT-Mechanics of Fluids and Solids, IMPACT-General, MESA-General
Research Project:	NWO-RFBR: Dutch-Russian research project, BRICKS/MSV1.5: Hp-Adaptive Finite Element Methods for the Maxwell Equations
Additional Information:	Please note different possible spellings of the last author's name: "Botchev" or "Bochev"
Uncontrolled Keywords:	Nédélec vector finite elements; kernel of the rotor operator; multilevel iterative solvers; hierarchical preconditioners; domain decomposition
ID Code:	8960
Deposited On:	25 January 2007
More Information:	statistics metis

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Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation (deposited 25 January 2007)
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- Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation (deposited 16 June 2008)

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