A Parallel Geometric Multigrid Method for Finite Elements on Octree Meshes

Abstract. In this article, we present a parallel geometric multigrid algorithm for solving elliptic partial differential equations (PDEs) on octree based conforming finite element discretizations. We describe an algorithm for constructing the coarser multigrid levels starting with an arbitrary 2:1 balanced fine-grid octree discretization. We also describe matrix-free implementations for the discretized finite element operators and the intergrid transfer operations. The key component of our scheme is an octree meshing algorithm, which handles “hanging” vertices in a manner that naturally supports conforming trilinear shape functions. Our MPI-based implementation has scaled to billions of elements on thousands of processors on the Cray XT3 MPP system “Bigben” at the Pittsburgh Supercomputing Center (PSC) and the Intel 64 Linux Cluster “Abe” at the National Center for Supercomputing Applications (NCSA). Although we do not discuss adaptive mesh refinement here, the propose...

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Rahul S. Sampath, George Biros
• Keywords: Algorithms, Geometric Multigrid Algorithm, Multigrid, SIAMSC 2010