This chapter presents a graphics processing unit (GPU)-based implementation of a derivative-free optimization method. The utility of derivative-free optimization is demonstrated in a mesh optimization algorithm that improves the element quality of a surface mesh. One can formalize the mesh optimization problem as having three components-the quality metric, the objective function, and the optimization algorithm. The quality metric is a continuous function that measures one or more geometric properties of an element and provides a measure of how "good" the shape of an element is. This specifically focuses on triangulated surface meshes, meaning the mesh elements are triangles embedded in three-dimensional space. It uses the minimum angle in a triangle as the quality metric, with larger minimum angles indicating higher element quality. Although minimum angle is not necessarily the best quality metric available, it is reasonably effective and has the benefit of being very intuitive and widely used in engineering practice.
|Original language||English (US)|
|Title of host publication||GPU Computing Gems Jade Edition|
|Number of pages||10|
|State||Published - 2012|
ASJC Scopus subject areas
- Computer Science(all)