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.
|Place of Publication||Enschede|
|Publisher||University of Twente, Department of Applied Mathematics|
|Number of pages||23|
|Publication status||Published - Jul 2006|
|Name||Applied Mathematics Memoranda|
|Publisher||Department of Applied Mathematics, University of Twente|
- Nédélec vector finite elements
- hierarchical preconditioners
- kernel of the rotor operator
- Domain decomposition
- multilevel iterative solvers
Nechaev, O. V., Shurina, E. P., & Bochev, M. A. (2006). Multilevel iterative solvers for the edge finite element solution of the 3D Maxwell equation. (Applied Mathematics Memoranda; No. 1806). Enschede: University of Twente, Department of Applied Mathematics.