The adaptive immersed interface finite element method for elliptic and Maxwell interface problems
Journal of Computational Physics
An adaptive inverse iteration for Maxwell eigenvalue problem based on edge elements
Journal of Computational Physics
An Optimal Iterative Solver for Symmetric Indefinite Systems Stemming from Mixed Approximation
ACM Transactions on Mathematical Software (TOMS)
General Constrained Energy Minimization Interpolation Mappings for AMG
SIAM Journal on Scientific Computing
An Adaptive Finite Element Method for the Eddy Current Model with Circuit/Field Couplings
SIAM Journal on Scientific Computing
Journal of Scientific Computing
Analysis and Computation of Compatible Least-Squares Methods for div-curl Equations
SIAM Journal on Numerical Analysis
Algebraic Multigrid for Linear Systems Obtained by Explicit Element Reduction
SIAM Journal on Scientific Computing
Parallel numerical solution of the time-harmonic maxwell equations
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
Computers & Mathematics with Applications
A Decoupled Preconditioning Technique for a Mixed Stokes---Darcy Model
Journal of Scientific Computing
| Hi-index | 0.01 |
In this paper, we develop and analyze a general approach to preconditioning linear systems of equations arising from conforming finite element discretizations of H(curl, )- and H(div, )-elliptic variational problems. The preconditioners exclusively rely on solvers for discrete Poisson problems. We prove mesh-independent effectivity of the preconditioners by using the abstract theory of auxiliary space preconditioning. The main tools are discrete analogues of so-called regular decomposition results in the function spaces H(curl, ) and H(div, ). Our preconditioner for H(curl, ) is similar to an algorithm proposed in [R. Beck, Algebraic Multigrid by Component Splitting for Edge Elements on Simplicial Triangulations, Tech. rep. SC 99-40, ZIB, Berlin, Germany, 1999].