Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes
Thông tin tác giả: TS. Timon Rabczuk, Trưởng nhóm Nhóm nghiên cứu cơ học tính toán thuộc Trường đại học Tôn Đức Thắng (DCM)
Tên bài báo: Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes
Thông tin tạp chí: Bài báo được công bố trên tạp chí ISI Computer Methods in Applied Mechanics and Engineering (impact factor là 3.949 theo ISI và chỉ số H-index là 155 theo SJR).
Tóm tắt: An adaptive higher-order method based on a generalization of polynomial/rational splines over hierarchical T-meshes (PHT/RHT-splines) is introduced. While most problems considered in isogeometric analysis can be solved efficiently when the solution is smooth, many non-trivial simulations have rough solutions. This can be caused, for example, by the presence of re-entrant corners in the domain. For such problems, a tensor-product basis is less suitable for resolving the singularities that appear, as refinement propagates throughout the computational domain. Hierarchical bases and adaptivity allow for a more efficient way of dealing with singularities, by adding more degrees of freedom only where they are necessary to improve the approximation. In order to drive the adaptive refinement, an efficient recovery-based error estimator is proposed in this work. The estimator produces a “recovered solution” which is a more accurate approximation than the computed numerical solution. Several 2D and 3D numerical investigations with PHT-splines of higher order and greater continuity show good performance compared to uniform refinement in terms of degrees of freedom and computational cost.
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