An adaptive Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) method for multi-patch structured Kirchhoff--Love plates
Abstract
We present a novel adaptive isogeometric method for solving the Kirchhoff-Love plate problem for plates whose mid-surface is defined by a planar multi-patch domain with possibly extraordinary vertices, parametrized by an analysis-suitable G1 multi-patch geometry. The proposed technique relies on the concept of Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP), which enforces the required C1-smoothness of the solution across a common edge of two neighboring patches by imposing appropriate continuity conditions by means of Lagrange multipliers. The resulting saddle point problem is solved using a dual-primal formulation, first by a small linear problem for the Lagrange multipliers and then by local, parallelizable linear problems on the individual patches for the coefficients of the numerical solution. While for the local problems on the single patches standard diagonally scaling is used as preconditioner, a suitable preconditioner for the problem of finding the Lagrange multipliers is introduced. To perform adaptive refinement, the solution of the Kirchhoff-Love plate problem on the single patches of the multi-patch domain is discretized by employing (truncated) hierarchical B-splines, and an appropriate refinement strategy of the underlying mesh is presented. Finally, the potential of the developed adaptive IETI-DP method for solving the Kirchhoff-Love plate problem on planar multi-patch geometries is numerically tested on the basis of several numerical examples. Thereby, the numerical results show on the one hand optimal convergence behavior with respect to adaptive refinement, and on the other hand a good performance of the proposed preconditioner for the linear problem of determining the Lagrange multipliers.
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BibTeX
@misc{kapl2026adaptive,
title = {{An adaptive Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) method for multi-patch structured Kirchhoff--Love plates}},
author = {Mario Kapl and Aljaž Kosmač and Vito Vitrih},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.07220},
eprint = {2606.07220},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.07220},
}
RIS
TY - UNPB
TI - An adaptive Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) method for multi-patch structured Kirchhoff--Love plates
AU - Mario Kapl
AU - Aljaž Kosmač
AU - Vito Vitrih
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2606.07220
UR - https://arxiv.org/abs/2606.07220
AB - We present a novel adaptive isogeometric method for solving the Kirchhoff-Love plate problem for plates whose mid-surface is defined by a planar multi-patch domain with possibly extraordinary vertices, parametrized by an analysis-suitable G^1 multi-patch geometry. The proposed technique relies on the concept of Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP), which enforces the required C^1-smoothness of the solution across a common edge of two neighboring patches by imposing appropriate continuity conditions by means of Lagrange multipliers. The resulting saddle point problem is solved using a dual-primal formulation, first by a small linear problem for the Lagrange multipliers and then by local, parallelizable linear problems on the individual patches for the coefficients of the numerical solution. While for the local problems on the single patches standard diagonally scaling is used as preconditioner, a suitable preconditioner for the problem of finding the Lagrange multipliers is introduced. To perform adaptive refinement, the solution of the Kirchhoff-Love plate problem on the single patches of the multi-patch domain is discretized by employing (truncated) hierarchical B-splines, and an appropriate refinement strategy of the underlying mesh is presented. Finally, the potential of the developed adaptive IETI-DP method for solving the Kirchhoff-Love plate problem on planar multi-patch geometries is numerically tested on the basis of several numerical examples. Thereby, the numerical results show on the one hand optimal convergence behavior with respect to adaptive refinement, and on the other hand a good performance of the proposed preconditioner for the linear problem of determining the Lagrange multipliers.
ER -