Optimal Cache-Oblivious Mesh Layouts

Michael A. Bender, Bradley C. Kuszmaul, Shang-Hua Teng, Kebin Wang

Abstract: A mesh is a graph that divides physical space into regularly-shaped regions. Meshes computations form the basis of many applications, including finite-element methods, image rendering, collision detection, and N-body simulations. In one important mesh primitive, called a mesh update, each mesh vertex stores a value and repeatedly updates this value based on the values stored in all neighboring vertices. The performance of a mesh update depends on the layout of the mesh in memory. Informally, if the mesh layout has good data locality (most edges connect a pair of nodes that are stored near each other in memory), then a mesh update runs quickly.