Title :
Dendro: Parallel algorithms for multigrid and AMR methods on 2:1 balanced octrees
Author :
Sampath, Rahul S. ; Adavani, Santi S. ; Sundar, Hari ; Lashuk, Ilya ; Biros, George
Author_Institution :
Georgia Inst. of Technol., Atlanta, GA, USA
Abstract :
In this article, we present Dendro, a suite of parallel algorithms for the discretization and solution of partial differential equations (PDEs) involving second-order elliptic operators. Dendro uses trilinear finite element discretizations constructed using octrees. Dendro, comprises four main modules: a bottom-up octree generation and 2:1 balancing module, a meshing module, a geometric multiplicative multigrid module, and a module for adaptive mesh refinement (AMR). Here, we focus on the multigrid and AMR modules. The key features of Dendro are coarsening/refinement, inter-octree transfers of scalar and vector fields, and parallel partition of multilevel octree forests. We describe a bottom-up algorithm for constructing the coarser multigrid levels. The input is an arbitrary 2:1 balanced octree-based mesh, representing the fine level mesh. The output is a set of octrees and meshes that are used in the multigrid sweeps. Also, we describe matrix-free implementations for the discretized PDE operators and the intergrid transfer operations. We present results on up to 4096 CPUs on the Cray XT3 (ldquoBigBenrdquo), the Intel 64 system (ldquoAberdquo), and the Sun Constellation Linux cluster (ldquoRangerrdquo).
Keywords :
elliptic equations; finite element analysis; octrees; parallel algorithms; partial differential equations; AMR method; Dendro; PDE operator; adaptive mesh refinement; balanced octrees; bottom-up octree generation; fine level mesh; geometric multiplicative multigrid module; intergrid transfer operation; interoctree transfer; matrix-free implementation; meshing module; multilevel octree forest; parallel algorithm; partial differential equation; second-order elliptic operator; trilinear finite element discretizations; Adaptive mesh refinement; Finite element methods; Iterative algorithms; Linux; Mesh generation; Multigrid methods; Parallel algorithms; Partial differential equations; Partitioning algorithms; Sun;
Conference_Titel :
High Performance Computing, Networking, Storage and Analysis, 2008. SC 2008. International Conference for
Conference_Location :
Austin, TX
Print_ISBN :
978-1-4244-2834-2
Electronic_ISBN :
978-1-4244-2835-9
DOI :
10.1109/SC.2008.5218558