Efficient r-Adaptive Multipatch Isogeometric Method in Arbitrary Dimension

Abstract

We introduce an r-adaptive (or r-refinement) multi-patch isogeometric method that applies to parametric curves or surfaces embedded in two or three dimensions as well as to volumetric domains. The proposed approach preserves C 0 continuity across patch interfaces. Moreover, if the underlying geometric parameterization is G 1 -compatible, then the resulting moving mesh mapping also preserves G 1 regularity across the interfaces. The global adaptive mesh is constructed by iteratively solving a Laplace equation in the computational domain, through a fast diagonalization solver that exploits the Kronecker-product structure of the matrices. Mesh adaptation is driven by a moving-mesh partial differential equation with a density function derived from either an arc-length monitor or a posteriori error indicator. Numerical experiments are carried out using an analytic density function, with additional applications to singular solutions and to the highly anisotropic diffusion equation.

On the Hadamard form of hierarchical spline Galerkin matrices and their efficient assembly in isogeometric analysis
Carlotta Giannelli, Angelos Mantzaflaris, Mattia Matucci
Computer Methods in Applied Mechanics and Engineering26 Oct 2026Peer-reviewedCC BY 4.0Full textNumerical analysis & scientific computingHAL
Cahn-Hilliard phase-field modeling of tumor growth via locally adaptive isogeometric analysis with THB-splines
Dhiraj S. Bombarde, Carlotta Giannelli, Alessandro Reali +1
arXiv2 Oct 2026PreprintCC BY-NC-SA 4.0Full textNumerical analysis & scientific computingarXiv
An adaptive Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) method for multi-patch structured Kirchhoff--Love plates
Mario Kapl, Aljaž Kosmač, Vito Vitrih
arXiv2 Oct 2026PreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
Irreducibility of the Bloch variety for periodic Schrödinger operators in arbitrary dimension
Wencai Liu
arXiv15 Sep 2026PreprintarXiv licenceFull textAnalysis & PDEs Mathematical physicsarXiv
A construction of Kakeya Sets in Arbitrary Dimension
Rafael J. Fernández-Delgado, Mikael de la Salle
arXiv17 Sep 2026PreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeX RIS

BibTeX

@misc{bahari2026efficient,
  title = {{Efficient r-Adaptive Multipatch Isogeometric Method in Arbitrary Dimension}},
  author = {Mustapha Bahari and Blaise Faugeras and Bernard Mourrain and Francesca Rapetti},
  howpublished = {HAL},
  year = {2026},
  month = jun,
  url = {https://hal.science/hal-05761930v1},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Efficient r-Adaptive Multipatch Isogeometric Method in Arbitrary Dimension
AU  - Mustapha Bahari
AU  - Blaise Faugeras
AU  - Bernard Mourrain
AU  - Francesca Rapetti
PY  - 2026
DA  - 2026/06/02
PB  - HAL
UR  - https://hal.science/hal-05761930v1
AB  - We introduce an r-adaptive (or r-refinement) multi-patch isogeometric method that applies to parametric curves or surfaces embedded in two or three dimensions as well as to volumetric domains. The proposed approach preserves C 0 continuity across patch interfaces. Moreover, if the underlying geometric parameterization is G 1 -compatible, then the resulting moving mesh mapping also preserves G 1 regularity across the interfaces. The global adaptive mesh is constructed by iteratively solving a Laplace equation in the computational domain, through a fast diagonalization solver that exploits the Kronecker-product structure of the matrices. Mesh adaptation is driven by a moving-mesh partial differential equation with a density function derived from either an arc-length monitor or a posteriori error indicator. Numerical experiments are carried out using an analytic density function, with additional applications to singular solutions and to the highly anisotropic diffusion equation.
ER  -

Abstract

Related

Cite