5 Parallel Geometric Multigrid

A geometric data structure for parallel finite elements and the application to multigrid methods with block smoothing

We present a parallel data structure which is directly linked to geometric quantities of an underlying mesh and which is well adapted to the requirements of a general finite element realization. In addition, we define an abstract linear algebra model which supports multigrid methods (extending our previous work in Comp. Vis. Sci. 1 (1997) 27-40). Finally, we apply the parallel multigrid precond...

Parallel Geometric Multigrid

Multigrid methods are among the fastest numerical algorithms for the solution of large sparse systems of linear equations. While these algorithms exhibit asymptotically optimal computational complexity, their efficient parallelisation is hampered by the poor computation-to-communication ratio on the coarse grids. Our contribution discusses parallelisation techniques for geometric multigrid meth...

Large-scale Simulations of 3D Groundwater Flow using Parallel Geometric Multigrid Method

The multigrid method used with OpenMP/MPI hybrid parallel programming models is expected to play an important role in large-scale scientific computing on post-peta/exa-scale supercomputer systems. In the present work, the effect of sparse matrix storage formats on the performance of parallel geometric multigrid solvers was evaluated, and a new data structure for the Ellpack-Itpack (ELL) format ...

A Parallel AMG Solver for An Electromagnetic Finite Element Analysis

The algebraic multigrid (AMG) method is not only efficient in solving for linear systems arising in finite element analyses, but also applicable at a matrix level without geometric information on the domain, different from the geometric multigrid solvers. The present paper proposes a combination of the parallel processing technique and the AMG method as a fast solver for electromagnetic field a...

A Full-Depth Amalgamated Parallel 3D Geometric Multigrid Solver for GPU Clusters