An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
On a parallel multilevel preconditioned Maxwell eigensolver
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Applied Numerical Mathematics
Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Algebraic Multigrid for Linear Systems Obtained by Explicit Element Reduction
SIAM Journal on Scientific Computing
Algebraic Multigrid for High-Order Hierarchical $H(curl)$ Finite Elements
SIAM Journal on Scientific Computing
Numerical Study of the Plasma-Lorentz Model in Metamaterials
Journal of Scientific Computing
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Computers & Mathematics with Applications
A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
Journal of Computational Physics
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We propose two improvements to the Reitzinger and Schöberl algebraic multigrid (AMG) method for solving the eddy current approximations to Maxwell's equations. The main focus in the Reitzinger/Schöberl method is to maintain null space properties of the weak $\nabla \times \nabla \times$ operator on coarse grids. While these null space properties are critical, they are not enough to guarantee h-independent convergence of the overall multigrid method. We illustrate how the Reitzinger/Schöberl AMG method loses h-independence due to the somewhat limited approximation property of the grid transfer operators. We present two improvements to these operators that not only maintain the important null space properties on coarse grids but also yield significantly improved multigrid convergence rates. The first improvement is based on smoothing the Reitzinger/Schöberl grid transfer operators. The second improvement is obtained by using higher order nodal interpolation to derive the corresponding AMG interpolation operators. While not completely h-independent, the resulting AMG/CG method demonstrates improved convergence behavior while maintaining low operator complexity.