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On the multi-grid iteration for the eigenvalue problem and the degree of interpolation wich it requires (I). (English) Zbl 1084.65532
Summary: In [Bull. for Applied Math., 1560/’98-LXXXVI-A, Hungary, 449-456],[On bidimensional Higher Order Interpolation. Application] we presented an approach method to realise a third and fourth order interpolation in two dimensions. In [Bull. for Applied Math., 1560/’98-LXXXVI-A, Hungary, 449-456] we showed that interpolations of these type can be used as prolongation operator in the multi-grid method and we proved that the accuracy of the multi-grid method can be increased in this way. We study the optimal degree of the prolongation operator which the second order elliptic eigenvalue problem requires in the point of view of the accuracy. We realise the implementation in Matlab of the multi-grid method with finite difference discretization. Numerical results are also given.
MSC:
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
Software:
Matlab
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