A new family of mixed finite elements in IR3
Numerische Mathematik
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Inner and Outer Iterations for the Chebyshev Algorithm
SIAM Journal on Numerical Analysis
Multigrid Method for Maxwell's Equations
SIAM Journal on Numerical Analysis
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Analysis of a Multigrid Algorithm for Time Harmonic Maxwell Equations
SIAM Journal on Numerical Analysis
A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
SIAM Journal on Scientific Computing
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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 [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.