Nechaev, O.V. and Shurina, E.P. and Botchev, M.A.
Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation.
Department of Applied Mathematics, University of Twente, Enschede.
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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  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.
 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|
|Deposited On:||25 January 2007|
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