A High-Order Isogeometric Collocation Method with Adaptive Refinement and Multi-patch Geometric Modeling

Abstract

Purpose

Isogeometric analysis (IGA) seamlessly integrates computer-aided design (CAD) with finite element analysis (FEA), streamlining the transition from geometric modeling to structural analysis.

Methods

This paper introduces a high-order isogeometric collocation method (IGA-C) specifically designed for analyzing complex multi-patch geometric structures. The method effectively resolves two primary challenges: the optimal selection of collocation points in high-order elements and ensuring stability in computations under complex geometric boundary conditions.

Results

Our contributions are threefold: first, we develop high-order basis function elements featuring local adaptive refinement tailored for IGA-C. Second, we investigate the optimal placement of collocation points across elements of varying orders, emphasizing their strategic distribution within non-uniform grids. Third, we present the Gaussian collocation method (IGA-GC) that employs advanced PHT-spline elements to facilitate the analysis of intricate multipatch structures.

Conclusions

Additionally, this work expands the algorithm to support elements of arbitrarily high order within the IGA-GC framework. Our numerical experiments validate that the proposed method not only achieves optimal convergence rates but also adeptly navigates the complexities associated with multi-patch geometric structures.