Overlaying surface meshes: Extension and parallelization

Many computational applications involve multiple physical components and require exchanging data across the interface between them, often on parallel computers. The interface is typically represented by surface meshes that are non-matching, with differing connectivities and geometry. To transfer data accurately and conservatively, it is important to construct a common refinement (or common tessellation) of these surface meshes. Previously, Jiao and Heath developed an algorithm for constructing a common refinement by overlaying the surface meshes. The original algorithm was efficient and robust but unfortunately was complex and difficult to implement and parallelize. In this paper, we present a modified algorithm for overlaying surface meshes. Our algorithm employs a higher-level primitive, namely face-face intersection, to facilitate easy parallelization of mesh overlay while retaining the robustness of the original algorithm. We also introduce a safeguarded projection primitives to improve the robustness against non-matching features and potential topological inconsistencies. We present numerical examples to demonstrate the robustness and effectiveness of the new method on parallel computers.