

Preprint 72/2003
Multi-Grid Methods for FEM and BEM Applications
Wolfgang Hackbusch
Contact the author: Please use for correspondence this email.
Submission date: 30. Jul. 2003
Pages: 23
published in: Encyclopedia of computational mechanics. Vol 1 : Fundamentals / E. Stein (ed.)
Chichester : Wiley, 2004. - P. 577 - 595
Bibtex
Keywords and phrases: multi-grid method, fem, bem, systems of linear equations, systems of nonlinear equations, integral equations, eigenvalue problems
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Abstract:
After discretisation of the partial differential equations from mechanics one
usually obtains large systems of (non)linear equations. Their efficient
solution requires the use of fast iterative methods. Multi-grid iterations are
able to solve linear and nonlinear systems with a rather fast rate of
convergence, provided the problem is of elliptic type. The contribution
describes the basic construction of multigrid methods, their ingredients,
related methods, and their application to various problem classes.
Although most of the applications concern FEM discretisations of partial
differential equations, there are also applications to integral equations as
they occur in boundary element methods (BEM).