Solving the triharmonic equation over multi-patch domains using isogeometric analysis
Abstract
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 -smooth isogeometric spline space which is used as discretization space. The generated -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.
Keywords
Cite
@article{arxiv.1801.05669,
title = {Solving the triharmonic equation over multi-patch domains using isogeometric analysis},
author = {Mario Kapl and Vito Vitrih},
journal= {arXiv preprint arXiv:1801.05669},
year = {2018}
}