External facelist calculation on three-dimensional unstructured meshes is used in scientific visualization libraries to efficiently render the results of operations such as clipping, interval volumes, and material boundaries. With this study, we consider the external facelist algorithm on many-core architectures. We introduce four different approaches: three based on hashing and one based on sorting. Each of the algorithms consists entirely of data-parallel primitive operations, in an effort to achieve portable performance across different architectures. We study the performance of the algorithms via experiments varying over algorithm, data set, hardware, and other factors. Overall, we observe that a hashing-based implementation achieves better runtime performance for the majority of configurations, while also achieving the most-stable performance on highly unstructured data sets.