<p>The process of computational engineering analysis includes the discretization of geometric models and the solution of partial differential equations using numerical methods. In the popular finite element method, a geometric model is discretized into a mesh of elements of simple geometries (trianges and quadrilaterals in 2D, and tetrahedrons and hexahedrons in 3D). With increasingly affordable computer power, the human effort required in mesh generation becomes increasingly critical in terms of both cost and time. Furthermore, geometric models in digital image, STL format and point clouds are becoming more and more popular in engineering applications and present challenges to well-established numerical methods.
This presentation covers the development of the scaled boundary finite element method, aiming to fully automate the process of engineering analysis directly from common formats of geometric models. The scaled boundary finite elements require the discretization of boundary only and can have any number of faces, edges and vortices, leading to a much higher degree of flexibility in mesh generation than standard finite elements. This allows the use of simple and efficient quatree/octree algorithm for fully automatic mesh generation of digital images, STL models, point clouds</p>