The Isogeometric Segmentation Pipeline

Abstract

We present a pipeline for the conversion of 3D models into a form suitable for isogeometric analysis (IGA). The input into our pipeline is a boundary represented 3D model, either as a triangulation or as a collection of trimmed nonuniform rational B-spline (NURBS) surfaces. The pipeline consists of three stages: computer aided design (CAD) model reconstruction from a triangulation (if necessary); segmentation of the boundary-represented solid into topological hexahedra; and volume parameterization. The result is a collection of volumetric NURBS patches. In this paper we discuss our methods for the three stages, and demonstrate the suitability of the result for IGA by performing stress simulations with examples of the output.

Discontinuous Galerkin isogeometric analysis for segmentations generating overlapping regions

“…This type of overlapping regions are discussed in the numerical Example 3. It is clear that through a segmentation and parametrization procedure, overlapping regions with more complicated shapes than the shapes in the examples shown here can exist, e.g., more than two overlapping patches, T-joint faces on the boundary, see, e.g., [27]. In an ongoing work we are extending the present methodology to treat these cases.…”

“…more than two overlapping patches, T-joint faces on the boundary, see, e.g. [ 10 ]. In an ongoing work, we are extending the present methodology to treat these cases.…”

“…It is important to obtain a curve that splits Ω into new simple domains with good shapes being suitable for IGA. During the computation of the multipatch representation, errors can occur when defining the corresponding control points, see [ 10 , 14 , 19 ]. A consequence of this is non-conforming parametrizations of the patches in the sense that the images of the patch interfaces under the parametrizations are not identical.…”

Isogeometric segmentation: Construction of auxiliary curves

“…For our purposes, a solid is represented by a collection of trimmed surfaces, together with incidence [2,3], a segmentation of the solid into topological hexahedra was given in [19] and shown to be suitable for isogeometric analysis. For the examples of that paper, a preliminary version of the present paper's method was used to produce the auxiliary curves.…”

Parallelization of continuous and discontinuous Galerkin dual–primal isogeometric tearing and interconnecting methods

“…The obtained patch parametrizations and the original geometry may not be identical. The result are small gaps and overlaps occurring at the interfaces of the patches, called segmentation crimes, see [26], [42] and [24] for a comprehensive analysis. Nevertheless, one still wants to solve PDEs on such domains.…”