Isogeometric computation reuse method for complex objects with topology-consistent volumetric parameterization

TL;DR

This paper introduces a computation reuse framework for isogeometric analysis on similar 3D models, significantly improving efficiency by precomputing and reusing key calculations, especially for complex geometries.

Contribution

It proposes a novel framework combining volumetric parameterization and a quadrature-free method for efficient IGA on models with similar features.

Findings

Achieves finite element analysis-like efficiency for IGA on complex models.

Pre-computation and reuse reduce computational cost significantly.

Effective for models with similar semantic features and complex geometries.

Abstract

Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with similar semantic features. Given a template domain, B-spline based consistent volumetric parameterization is first constructed for a set of models with similar semantic features. An efficient quadrature-free method is investigated in our framework to compute the entries of stiffness matrix by Bezier extraction and polynomial approximation. In our approach, evaluation on the stiffness matrix and imposition of the boundary conditions can be pre-computed and reused during IGA on a set of CAD models. Examples with complex geometry are presented to show the effectiveness of our methods, and efficiency similar to the computation in linear finite element analysis can be achieved for IGA taken on a set of models.