Multi-Grid Methods for FEM and BEM Applications
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Submission date: 30. Jul. 2003
published in: Encyclopedia of computational mechanics. Vol 1 : Fundamentals / E. Stein (ed.)
Chichester : Wiley, 2004. - P. 577 - 595
Keywords and phrases: multi-grid method, fem, bem, systems of linear equations, systems of nonlinear equations, integral equations, eigenvalue problems
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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).