Spectral element multigrid. I. Formulation and numerical results
Journal of Scientific Computing
To overlap or not to overlap: a note on a domain decomposition method for elliptic problems
SIAM Journal on Scientific and Statistical Computing
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
An Algebraic Convergence Theory for Restricted Additive Schwarz Methods Using Weighted Max Norms
SIAM Journal on Numerical Analysis
Convergence Theory of Restricted Multiplicative Schwarz Methods
SIAM Journal on Numerical Analysis
Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method
Journal of Scientific Computing
Schwarz Iterations for Symmetric Positive Semidefinite Problems
SIAM Journal on Matrix Analysis and Applications
Schwarz methods for quasi stationary distributions of Markov chains
Calcolo: a quarterly on numerical analysis and theory of computation
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J. Lottes and P. Fischer (J. Sci. Comput. 24:45---78, [2005]) studied many smoothers or preconditioners for hybrid Multigrid-Schwarz algorithms for the spectral element method. The behavior of several of these smoothers or preconditioners are analyzed in the present paper. Here it is shown that the Schwarz smoother that best performs in the above reference, is equivalent to a special case of the weighted restricted additive Schwarz, for which convergence analysis is presented. For other preconditioners which do not perform as well, examples and explanations are presented illustrating why this behavior may occur.