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Fast multigrid solvers for conforming and non-conforming multi-patch Isogeometric Analysis. (arXiv:1902.01818v1 [math.NA])

Isogeometric Analysis allows high-order discretizations of boundary value problems using a number of degrees of freedom which is as small as for a low-order method. To be able to choose high spline degrees in practice, suitable numerical solvers are required. In non-trivial cases, the computational domain is typically decomposed into several patches, where for each patch a separate isogeometric discretization is chosen. If the discretization agrees on the interfaces between the patches, the coupling can be done in a conforming way. Otherwise, non-conforming discretizations (utilizing discontinuous Galerkin approaches) are required. The author and his coworkers have previously introduced multigrid solvers for Isogeometric Analysis. In the present paper, these results are extended to the non-conforming case. Moreover, it is shown that the solves get even more powerful if the proposed smoother is combined with a (standard) Gauss-Seidel smoother.查看全文

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