1. Robust optimal multilevel preconditioners for non-conforming finite element systems<FNR></FNR><FN>Dedicated to Professor Owe Axelsson on the occasion of his 70th birthday, with respect and appreciation </FN>. Author Blaheta, R., Margenov, S., and Neytcheva, M. Subjects *FINITE element method, *NUMERICAL analysis, *MATHEMATICAL analysis, *MATHEMATICS, *LINEAR systems Abstract We consider strategies to construct optimal order two- and multilevel hierarchical preconditioners for linear systems as arising from the finite element discretization of self-adjoint second order elliptic problems using non-conforming Crouzeix–Raviart linear elements. In this paper we utilize the hierarchical decompositions, derived in a previous work by the same authors (Numerical Linear Algebra with Applications 2004; 11:309–326) and provide a further analysis of these decompositions in order to assure robustness with respect to anisotropy. Finally, we show how to construct both multiplicative and additive versions of the algebraic multilevel iteration preconditioners and show robustness and optimal order convergence estimates. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR] Published 2005 Full Text View/download PDF
2. Substitutive divergent bases for FEM modelling of field singularities near a wedge. Author Masoni, Juri, Pelosi, Giuseppe, and Selleri, Stefano Subjects *FINITE element method, *NUMERICAL analysis, *MATHEMATICAL analysis, *MATHEMATICAL singularities, *MATHEMATICS Abstract A finite-element implementation for the analysis of propagation constants and fields in a guiding structure is presented in this paper. The solution explicitly takes into account the field divergence on the edges of the internal wedges by exploiting substitutive divergent bases. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 327–328, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20624 [ABSTRACT FROM AUTHOR] Published 2005 Full Text View/download PDF