Multilevel preconditioners for isogeometric collocation methods based on generalized B-splines

초록

We propose a new class of additive and multiplicative multilevel methods for isogeometric collocation methods based on generalized B-splines (GB-splines). To our knowledge, this represents the first systematic development of multilevel solvers for isogeometric collocation schemes based on GB-splines. We provide numerical evidence supporting the optimality of our proposed preconditioners, accelerated by GMRES, with respect to the number of levels. Furthermore, we conduct a comprehensive numerical study to assess the robustness of the proposed preconditioners with respect to isogeometric discretization parameters. Particular attention is devoted to investigating the effectiveness of the multilevel solvers in the presence of domain deformations. © 2026 Elsevier B.V.

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