Isogeometric collocation on planar multi-patch domains

08/02/2019
by   Mario Kapl, et al.
0

We present an isogeometric framework based on collocation for solving the Poisson's equation over planar bilinearly parameterized multi-patch domains. As a discretization space for the partial differential equation a globally C^2-smooth isogeometric spline space is used, whose construction is simple and works uniformly for all possible multi-patch configurations. The basis of the C^2-smooth space can be described as the span of three different types of locally supported functions corresponding to the single patches, edges and vertices of the multi-patch domain. For the selection of the collocation points, which is important for the stability and convergence of the collocation problem, two different choices are numerically investigated. The first approach employs the tensor-product Greville abscissae as collocation points, and shows for the multi-patch case the same convergence behavior as for the one-patch case [2], which is suboptimal in particular for odd spline degrees. The second approach generalizes the concept of superconvergent points from the one-patch case (cf. [1,14,31]) to the multi-patch case. Again, these points possess better convergence properties than Greville abscissae in case of odd spline degrees.

READ FULL TEXT
research
08/14/2020

C^s-smooth isogeometric spline spaces over planar multi-patch parameterizations

The design of globally C^s-smooth (s ≥ 1) isogeometric spline spaces ove...
research
01/02/2021

C^1 isogeometric spline space for trilinearly parameterized multi-patch volumes

We study the space of C^1 isogeometric spline functions defined on trili...
research
09/14/2022

Isogeometric analysis for multi-patch structured Kirchhoff-Love shells

We present an isogeometric method for the analysis of Kirchhoff-Love she...
research
03/13/2023

Isogeometric multi-patch C^1-mortar coupling for the biharmonic equation

We propose an isogeometric mortar method to fourth order elliptic proble...
research
04/21/2022

Adaptive isogeometric methods with C^1 (truncated) hierarchical splines on planar multi-patch domains

Isogeometric analysis is a powerful paradigm which exploits the high smo...
research
05/02/2016

Isogeometric analysis using manifold-based smooth basis functions

We present an isogeometric analysis technique that builds on manifold-ba...
research
03/04/2021

Construction of approximate C^1 bases for isogeometric analysis on two-patch domains

In this paper, we develop and study approximately smooth basis construct...

Please sign up or login with your details

Forgot password? Click here to reset