Local multigrid on adaptively refined meshes and multilevel preconditioning with applications to problems in electromagnetism and acoustics

  • We consider local multigrid methods for adaptive finite element and adaptive edge element discretized boundary value problems as well as multilevel preconditioned iterative solvers for the finite element discretization of a special class of saddle point problems. The local multigrid methods feature local smoothing processes on adaptively refined meshes and are applied to adaptive P1 conforming finite element discretizations of linear second order elliptic boundary value problems and to adaptive curl-conforming edge element approximations of H(curl)-elliptic problems and the time-harmonic Maxwell equations. On the other hand, the multilevel preconditioned iterative schemes feature block-diagonal or upper block-triangular preconditioned GMRES or BiCGStab applied to the resulting algebraic saddle point problems and preconditioned CG applied to the associated Schur complement system. As technologically relevant applications of the above methods, we consider the numerical simulation ofWe consider local multigrid methods for adaptive finite element and adaptive edge element discretized boundary value problems as well as multilevel preconditioned iterative solvers for the finite element discretization of a special class of saddle point problems. The local multigrid methods feature local smoothing processes on adaptively refined meshes and are applied to adaptive P1 conforming finite element discretizations of linear second order elliptic boundary value problems and to adaptive curl-conforming edge element approximations of H(curl)-elliptic problems and the time-harmonic Maxwell equations. On the other hand, the multilevel preconditioned iterative schemes feature block-diagonal or upper block-triangular preconditioned GMRES or BiCGStab applied to the resulting algebraic saddle point problems and preconditioned CG applied to the associated Schur complement system. As technologically relevant applications of the above methods, we consider the numerical simulation of Logging-While-Drilling tools in oil exploration and the numerical simulation of piezoelectrically actuated surface acoustic waves.show moreshow less

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Metadaten
Author:Ronald H. W. HoppeGND, Xuejun Xu, Huangxin Chen
URN:urn:nbn:de:bvb:384-opus4-11489
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1388
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2010-05)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Contributing Corporation:University of Houston, Chinese Academy of Sciences
Release Date:2010/04/26
Tag:local multigrid methods; adaptively refined meshes; multilevel preconditioners; Logging-While-Drilling; surface acoustic waves
GND-Keyword:Mehrgitterverfahren; Akustische Oberflächenwelle; Elliptisches Randwertproblem
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand