Data Structure for Supporting Patch Refinement in Adaptive Isogeometric Analysis

摘要

Isogeometric Analysis (IGA) is relatively young computational method built on the assumption that Non-Uniform Rational B-Splines (NURBS) are used both for modelling curved objects and as the base functions for approximating unknown fields. While single patch IGA implementation is relatively easy, implementation of multi-patch IGA with local patch refinement is more difficult, especially with respect to providing flexible data structures. This paper describes the use of generic framework for handling mesh data (MOAB) to build flexible data structure supporting adaptive, multipatch version of IGA. The key issue of such data structure is an appropriate numbering of mesh vertices to help building projection operator between patches, that ensures continuity of geometry parametrisation. The paper presents the idea of special tagging of vertices and specific order of their enumeration that serves well this purpose.