A discontinuous Galerkin method with block cyclic reduction solver for simulating compressible flows on GPUs

Abstract

An optimized implementation of a block tridiagonal solver based on the block cyclic reduction (BCR) algorithm is introduced and its portability to graphics processing units (GPUs) is explored. The computations are performed on the NVIDIA GTX480 GPU. The results are compared with those obtained on a single core of Intel Core i7-920 (2.67 GHz) in terms of calculation runtime. The BCR linear solver achieves the maximum speedup of 5.84x with block size of 32 over the CPU Thomas algorithm in double precision. The proposed BCR solver is applied to discontinuous Galerkin (DG) simulations on structured grids via alternating direction implicit (ADI) scheme. The GPU performance of the entire computational fluid dynamics (CFD) code is studied for different compressible inviscid flow test cases. For a general mesh with quadrilateral elements, the ADI-DG solver achieves the maximum total speedup of 7.45x for the piecewise quadratic solution over the CPU platform in double precision.

Keywords:

• block cyclic reduction
• GPU
• discontinuous Galerkin
• compressible flow
• alternating direction implicit
• speedup

2010 AMS Subject Classifications::

• 76N15
• 74S05
• 65Y05
• 68W10

Acknowledgements

The authors thank the Vehicle, Fuel and Environment Research Institute (VFERI) of University of Tehran for general support during this study.