Spectral Analysis of Geometric Multigrid Methods for Isogeometric Analysis

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8962)

Abstract

We investigate geometric multigrid methods for solving the large, sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. We observe that the performance of standard V-cycle iteration is highly dependent on the spatial dimension as well as the spline degree of the discretization space. Conjugate gradient iteration preconditioned with one V-cycle mitigates this dependence, but does not eliminate it. We perform both classical local Fourier analysis as well as a numerical spectral analysis of the two-grid method to gain better understanding of the underlying problems and observe that classical smoothers do not perform well in the isogeometric setting.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Computational MathematicsJohannes Kepler University LinzLinzAustria

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