Solving the triharmonic equation over multi-patch planar domains using isogeometric analysis

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:358

Article

Kapl, Mario¹  Vitrih, Vito^2,3,4 

[1] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, Linz, Austria

[2] Univ Primorska, IAM, Koper, Slovenia

[3] Univ Primorska, FAMNIT, Koper, Slovenia

[4] Inst Math Phys & Mech, Ljubljana, Slovenia

关键词: Isogeometric analysis;    Triharmonic equation;    Geometric continuity;    C-2-continuity;    Multi-patch domain;   

DOI  :  10.1016/j.cam.2019.03.020

来源: Elsevier

【 摘 要 】

We present a framework for solving the triharmonic equation over bilinearly parameterized planar multi-patch domains by means of isogeometric analysis. Our approach is based on the construction of a globally C-2-smooth isogeometric spline space which is used as discretization space. The generated C-2-smooth space consists of three different types of isogeometric functions called patch, edge and vertex functions. All functions are entirely local with a small support, and numerical examples indicate that they are well-conditioned. The construction of the functions is simple and works uniformly for all multi-patch configurations. While the patch and edge functions are given by a closed form representation, the vertex functions are obtained by computing the null space of a small system of linear equations. Several examples demonstrate the potential of our approach for solving the triharmonic equation. (C) 2019 Elsevier B.V. All rights reserved.

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