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.
In this paper, a multi-grid solver for the discretisation of partial differential equations on complicated domains is developed. The algorithm requires as input the given discretisation only instead of a hierarchy of discretisations on coarser grids. Such auxiliary grids and discretisations are generated in a black-box fashion and are employed to define purely algebraic intergrid transfer operators. The geometric interpretation of the algorithm allows one to use the framework of geometric multigrid methods to prove its convergence. The focus of this paper is on the formulation of the algorithm and the demonstration of its efficiency by numerical experiments, while the analysis is carried out for some model problems.
AbstractIn this paper, a multi-grid solver for the discretisation of partial differential equations on complicated domains will be developed. The algorithm requires as input only the given discretisation instead of a hierarchy of discretisations on coarser grids. Such auxiliary grids and discretisations will be generated in a black-box fashion and will be employed to define purely algebraic intergrid transfer operators. The geometric interpretation of the algorithm allows to use the framework of geometric multigrid methods to prove its convergence.The focus of this paper is on the formulation of the algorithm and the demonstration of its efficiency by numerical experiments while the analysis is carried out for some model problems.
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