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