Analysis of a finite element method for Maxwell's equations
SIAM Journal on Numerical Analysis
A preconditioned iterative method for saddlepoint problems
SIAM Journal on Matrix Analysis and Applications
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions
Mathematics of Computation
Multigrid Method for Maxwell's Equations
SIAM Journal on Numerical Analysis
Some Nonoverlapping Domain Decomposition Methods
SIAM Review
An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations
Mathematics of Computation
An iterative substructuring method for Maxwell's equations in two dimensions
Mathematics of Computation
An Iterative Method with Variable Relaxation Parameters for Saddle-Point Problems
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Numerical Analysis
Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations
Mathematics of Computation
A Nonoverlapping Domain Decomposition Method for Maxwell's Equations in Three Dimensions
SIAM Journal on Numerical Analysis
An adaptive inverse iteration for Maxwell eigenvalue problem based on edge elements
Journal of Computational Physics
Modified block preconditioners for the discretized time-harmonic Maxwell equations in mixed form
Journal of Computational and Applied Mathematics
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This paper is concerned with the saddle-point problems arising from edge element discretizations of Maxwell's equations in a general three dimensional nonconvex polyhedral domain. A new augmented technique is first introduced to transform the problems into equivalent augmented saddle-point systems so that they can be solved by some existing preconditioned iterative methods. Then some substructuring preconditioners are proposed, with very simple coarse solvers, for the augmented saddle-point systems. With the preconditioners, the condition numbers of the preconditioned systems are nearly optimal; namely, they grow only as the logarithm of the ratio between the subdomain diameter and the finite element mesh size.