A massively parallel geometric multigrid solver on hierarchically distributed grids

Abstract

A parallel geometric multigrid solver on hierarchically distributed grids is presented. Using a tree-structure for grid distribution onto the processing entities, the multigrid cycle is performed similarly to the serial algorithm, using additional vertical communication during transfer operations. The workload is gathered to fewer processes on coarser levels. Involved parallel structures are described in detail and the multigrid algorithm is formulated, discussing parallelization details. A performance study is presented that shows close to optimal efficiency for weak scaling up to 262k processes in 2 and 3 space dimensions.

Parallel geometric-algebraic multigrid on unstructured forests of octrees

“…Based on a new version of the unstructured grids (UG) package [14], recent work [15] presents formidable weak and strong scalability results for a Laplace equation on Blue Gene/P in Jülich on up to 262K cores. These results are for uniformly refined unit cubes, but, in principle, the framework also supports non-uniform meshes and different element types.…”

Iterative Solution of Large Sparse Systems of Equations

“…Reiter et al[320]). However, even the global (undiscretised) problem may be divided into subproblems which are discretely coupled in very weak form (see, e.g., the mortar method in[100, §7] or Quarteroni-Valli[315, §2.5.1]).3 The use of parallel computers and the construction of the iterative method are in principle independent.…”

Scalable shape optimization methods for structured inverse modeling in 3D diffusive processes

“…3 was implemented as a plugin in the software toolbox UG4 [14]. This software is known to be scalable and features parallel multigrid solvers [15]. Numerical experiments were conducted on the HER-MIT 1 supercomputer.…”