Parallel Triangular Mesh Refinement by Longest Edge Bisection

Abstract

Longest edge bisection based refinement, which is also known as Rivara refinement, is a well-known technique for adaptive refinement of unstructured triangular meshes. Our work contributes a fine grain parallel adaptive refinement algorithm. Refinements can propagate in an irregular fashion to neighboring triangles. Once propagations are done, refinement templates can be applied. Since elements are created and deleted in an irregular fashion, dynamic data structures need to be designed and concurrency issues need to be resolved. Unlike the previous approaches that solved an independent set problem to resolve concurrent updates, our algorithm instead makes use of prefix computations. Tests carried out on an NVIDIA Tesla M2070 GPU show that running time on a 32 million element mesh is overall roughly 25 times faster than the sequential run on an Intel Xeon system. Our refinement code is available at http://code.google.com/p/gpu-mesh-refine.