Isotropic treatment of EMF effects in advanced photomasks
Jaione Tirapu Azpiroz, Alan E. Rosenbluth, et al.
SPIE Photomask Technology + EUV Lithography 2009
Multigrid methods are analyzed in the style of standard iterative methods. A basic error bound is derived in terms of residuals on neighboring levels. The terms in this bound derive from the iterative methods used as smoothers on each level and the operators used to go from a level to the next coarser level. This bound is correct whether the underlying operator is symmetric or nonsymmetric, definite or indefinite, and singular or nonsingular. This paper allows any iterative method as a smoother (or rougher) in the multigrid cycle. While standard multigrid error analysis typically assumes a specific multigrid cycle (e.g., a V, W, or F cycle), analysis for arbitrary multigrid cycles, including adaptively chosen ones, is provided. This theory applies directly to aggregation-disaggregation methods used to solve systems of linear equations.
Jaione Tirapu Azpiroz, Alan E. Rosenbluth, et al.
SPIE Photomask Technology + EUV Lithography 2009
M. Tismenetsky
International Journal of Computer Mathematics
R.A. Brualdi, A.J. Hoffman
Linear Algebra and Its Applications
Sankar Basu
Journal of the Franklin Institute