Performance enhancement of the multi-p preconditioner

Guo, Xian-Zhong; Katz, Irving

doi:10.1016/s0898-1221(98)00136-9

Cited by 3 publications

(1 citation statement)

References 3 publications

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“…In the context of elastostatic examples in 2D and 3D, they proved convergence with condition number O(1+log( p) 2 ), and gave numerical evidence of pindependent convergence rates in both 2D and 3D. Further work by this team is found in [16,17].…”

Section: Historymentioning

confidence: 93%

The hp‐multigrid method applied to hp‐adaptive refinement of triangular grids

Mitchell

2010

Numerical Linear Algebra App

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SUMMARYRecently the hp version of the finite element method, in which adaptivity occurs in both the size, h, of the elements and in the order, p, of the approximating piecewise polynomials, has received increasing attention. It is desirable to combine this optimal order discretization method with an optimal order algebraic solution method like multigrid. An intriguing notion is to use the values of p as the levels of a multilevel method. In this paper we present such a method, known as hp-multigrid, for high-order finite elements and hp-adaptive grids. We present a survey of the development of p-multigrid and hp-multigrid, define an hp-multigrid algorithm based on the p-hierarchical basis for the p levels and h-hierarchical basis for an h-multigrid solution of the p = 1 'coarse grid' equations, and present numerical convergence results using hp-adaptive grids. The numerical results suggest that the method has a convergence rate of

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Section: Historymentioning

confidence: 93%

The hp‐multigrid method applied to hp‐adaptive refinement of triangular grids

Mitchell

2010

Numerical Linear Algebra App

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A parallel multi-p method

Guo

Katz

2000

Computers & Mathematics with Applications

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Efficient Distributed Matrix-free Multigrid Methods on Locally Refined Meshes for FEM Computations

Münch

Heister

Saavedra

et al. 2023

ACM Trans. Parallel Comput.

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This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening (both h -multigrid), and polynomial global coarsening (a variant of p -multigrid). We have integrated the algorithms into the same framework—the open-source finite-element library deal.II —, which allows us to make fair comparisons regarding their implementation complexity, computational efficiency, and parallel scalability as well as to compare the measurements with theoretically derived performance metrics. Serial simulations and parallel weak and strong scaling on up to 147,456 CPU cores on 3,072 compute nodes are presented. The results obtained indicate that global-coarsening algorithms show a better parallel behavior for comparable smoothers due to the better load balance, particularly on the expensive fine levels. In the serial case, the costs of applying hanging-node constraints might be significant, leading to advantages of local smoothing, even though the number of solver iterations needed is slightly higher. When using p - and h -multigrid in sequence ( hp -multigrid), the results indicate that it makes sense to decrease the degree of the elements first from a performance point of view due to the cheaper transfer.

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Performance enhancement of the multi-p preconditioner

Cited by 3 publications

References 3 publications

The hp‐multigrid method applied to hp‐adaptive refinement of triangular grids

The hp‐multigrid method applied to hp‐adaptive refinement of triangular grids

A parallel multi-p method

Efficient Distributed Matrix-free Multigrid Methods on Locally Refined Meshes for FEM Computations

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