An Immersed Boundary Approach for the Numerical Analysis of Objects Represented by Oriented Point Clouds

Abstract

This contribution presents a method for numerical analysis of solids whose boundaries are represented by oriented point clouds. In contrast to standard finite elements that require a boundary-conforming discretization of the domain of interest, our approach works directly on the point cloud representation of the geometry. This is achieved by combining the inside-outside information that is inferred from the members of the point cloud with a high order immersed boundary technique. This allows for avoiding the challenging task of surface fitting and mesh generation, simplifying the image-based analysis pipeline drastically. We demonstrate by a numerical example how the proposed method can be applied in the context of linear elastostatic analysis of solids.