GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
SIAM Journal on Matrix Analysis and Applications
Multigrid Method for Maxwell's Equations
SIAM Journal on Numerical Analysis
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Matrix algorithms
A Krylov--Schur Algorithm for Large Eigenproblems
SIAM Journal on Matrix Analysis and Applications
Parallel multigrid smoothing: polynomial versus Gauss--Seidel
Journal of Computational Physics
An Improved Algebraic Multigrid Method for Solving Maxwell's Equations
SIAM Journal on Scientific Computing
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Toward an h-Independent Algebraic Multigrid Method for Maxwell's Equations
SIAM Journal on Scientific Computing
Conformal FDTD-methods to avoid time step reduction with and without cell enlargement
Journal of Computational Physics
Consistent boundary conditions for the Yee scheme
Journal of Computational Physics
An Algebraic Multigrid Approach Based on a Compatible Gauge Reformulation of Maxwell's Equations
SIAM Journal on Scientific Computing
Anasazi software for the numerical solution of large-scale eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
Application of Dey-Mittra conformal boundary algorithm to 3D electromagnetic modeling
Journal of Computational Physics
Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
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For embedded boundary electromagnetics using the Dey-Mittra (Dey and Mittra, 1997) [1] algorithm, a special grad-div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwell's curl-curl matrix. Efficient curl-curl inversions are demonstrated within a shift-and-invert Krylov-subspace eigensolver (open-sourced at [ofortt]https://github.com/bauerca/maxwell[cfortt]) on the spherical cavity and the 9-cell TESLA superconducting accelerator cavity. The accuracy of the Dey-Mittra algorithm is also examined: frequencies converge with second-order error, and surface fields are found to converge with nearly second-order error. In agreement with previous work (Nieter et al., 2009) [2], neglecting some boundary-cut cell faces (as is required in the time domain for numerical stability) reduces frequency convergence to first-order and surface-field convergence to zeroth-order (i.e. surface fields do not converge). Additionally and importantly, neglecting faces can reduce accuracy by an order of magnitude at low resolutions.