Multilevel methods for PHT-splines

doi:10.1016/j.cma.2025.118251

Multilevel methods for PHT-splines

2025-07-26

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DOI：10.1016/j.cma.2025.118251

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Abstract

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This paper presents the development of efficient multilevel solvers, including BPX preconditioners and multigrid methods, for isogeometric discretizations of second-order elliptic PDEs based on (polynomial splines over hierarchical T-meshes) PHT-splines. Exploiting the inherent hierarchical structure of PHT-splines, we construct a stable subspace decomposition and establish convergence results that are uniform with respect to both the mesh level and mesh size. A central contribution of this work lies in the design of novel block smoothers specifically constructed for PHT-splines, wherein each block is associated with four basis functions sharing a common basis vertex. Furthermore, to enhance convergence, we incorporate correction steps in the smoothing procedure for both boundary and truncated basis functions. Numerical experiments confirm the robustness and optimality of the proposed multilevel solvers.

Keywords:

isogeometric analysis

PHT-splines

multilevel solvers

BPX preconditioners

multigrid methods

Multilevel methods for PHT-splines

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