Vectorization of high-order DG in Ateles for the NEC SX-ACE

Harald Klimach (Univ. of Siegen)

Discontinuos Galerkin methods combine a solution representation by functions with non-overlapping elements that interact via fluxes, like finite volume methods. They, thereby, offer high accuracy with a high locality, as only relatively small amounts of data need to be exchanged between elements. The arising meshes for this scheme may be unstructured and adapted to the geometry of the problem to solve. Within the elements however, we find a highly structured representation of the solution. Thus, the scheme provides a rigid data structure on the one hand and on the other hand a flexible geometry representation.

Ateles is a implementation in Fortran of a high-order discontinuous Galerkin scheme that uses Legendre polynomials to represent the solution within cubical elements. In this presentation we look at some experiences from porting and running this code on the NEC SX-ACE vector system. We explore how the scheme can be vectorized for high-order representations, where large blocks of structured data exist within elements. As Ateles uses several Fortran 2003 features, all observations are reported for the new sxf03 compiler.