On Full Multigrid Schemes for Isogeometric Analysis

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)


We investigate a geometric full multigrid method for solving the large sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. We observe that the full multigrid approach performs much better than the V-cycle multigrid method in many cases, in particular in higher dimensions with increased spline degrees. Often, a single cycle of the full multigrid process is sufficient to obtain a quasi-optimal solution in the L 2-norm. A modest increase in the number of smoothing steps suffices to restore optimality in cases where the V-cycle performs badly.



This work was supported by the National Research Network “Geometry + Simulation” (NFN S117, 2012–2016), funded by the Austrian Science Fund (FWF). The first author was also supported by the project AComIn “Advanced Computing for Innovation”, grant 316087, funded by the FP7 Capacity Programme “Research Potential of Convergence Regions”.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Computational MathematicsJohannes Kepler University LinzLinzAustria

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