Pyop2: Framework For Performance-Portable Parallel Computations On Unstructured Meshes

Rathgeber, Florian; Dearman, Hector; gbts,; Bercea, Gheorghe-Teodor; Sato, Kosei; Funke, Simon W.; Mitchell, Lawrence; Homolya, Miklós; Russell, Francis P.; Jacobs, Christian T.; Ham, David A.; McRae, Andrew T. T.; Markall, Graham; Luporini, Fabio

doi:10.5281/zenodo.49281

Cited by 3 publications

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“…The Zenodo system was used to archive all packages used to perform the experiments: Firedrake , PETSc [Smith et al 2016], petsc4py [Firedrake 2016], FIAT , UFL , FFC , PyOP2 [Rathgeber et al 2016b] and COFFEE . The experiments can be reproduced using a publicly available benchmark suite [Rathgeber et al 2016a].…”

Section: Methodsmentioning

confidence: 99%

An algorithm for the optimization of finite element integration loops

Luporini,

Ham,

Kelly

2016

Preprint

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We present an algorithm for the optimization of a class of finite element integration loop nests. This algorithm, which exploits fundamental mathematical properties of finite element operators, is proven to achieve a locally optimal operation count. In specified circumstances the optimum achieved is global. Extensive numerical experiments demonstrate significant performance improvements over the state of the art in finite element code generation in almost all cases. This validates the effectiveness of the algorithm presented here, and illustrates its limitations.

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Section: Methodsmentioning

confidence: 99%

An algorithm for the optimization of finite element integration loops

Luporini,

Ham,

Kelly

2016

Preprint

Self Cite

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Automated optimization of numerical methods for partial differential equations

Luporini¹

2016

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A numbering algorithm for finite elements on extruded meshes which avoids the unstructured mesh penalty

Bercea

McRae

Ham

et al. 2016

Preprint

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Abstract. We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells. Applications of extruded meshes include, but are not limited to, the representation of 3D high aspect ratio domains employed by geophysical finite element simulations. These meshes are structured in the extruded direction. The algorithm presented here exploits this structure to avoid the performance penalty traditionally associated with unstructured meshes. We evaluate our algorithm on a range of low compute intensity operations which constitute worst cases for data layout performance exploration. The experiments show that having structure along the extruded direction enables the cost of the indirect data accesses to be amortized after 10–20 layers as long as the underlying mesh is well-ordered. We characterise the resulting spatial and temporal reuse in a representative set of both continuous-Galerkin and discontinuous-Galerkin discretisations. On meshes with realistic numbers of layers the performance achieved is between 70 % and 90 % of a theoretical hardware-specific limit.

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Pyop2: Framework For Performance-Portable Parallel Computations On Unstructured Meshes

Cited by 3 publications

References 0 publications

An algorithm for the optimization of finite element integration loops

An algorithm for the optimization of finite element integration loops

Automated optimization of numerical methods for partial differential equations

A numbering algorithm for finite elements on extruded meshes which avoids the unstructured mesh penalty

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