Abstract
The parallel CPU+multiGPU implementation of the Implicitly Restarted Arnoldi method (IRA) is presented in the paper. We focus on the problem of implementing an efficient method for large scale non-symmetric eigenvalue problems arising in linear stability and Floquet theory analysis in fluid dynamics problems. We give brief details about the problem in both cases. We use and cross-compare different methods to implement QR shifts with polynomial filtering. Then we conduct a benchmark on standard non-symmetric matrices. The presented results give insight on the best choice of the method of polynomial filters. It turns out that a polynomial filter is essential to accelerate computations in fluid dynamics stability problems as well as to increase the Krylov space dimension. However, some knowledge about the spectral radius of the problem is required. Further, we investigate the parallel efficiency of the method for single-GPU and multi-GPU modes using the problems previously considered. It is shown that the implementation of Givens rotations on one GPU for QR computations (of a Hessenberg matrix) is essential in order to achieve high speed for a considerable Krylov subspace dimension. In the final part we present some results regarding the application of the IRA polynomial filtered method to linear stability and Floquet analysis for large fluid dynamics problem with parallel efficiency comparison on multi-GPU architecture.
The work is supported by the Russian Foundation for Basic Research (grant RFBR 14-07-00123).
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Evstigneev, N.M. (2017). Implementation of Implicitly Restarted Arnoldi Method on MultiGPU Architecture with Application to Fluid Dynamics Problems. In: Sokolinsky, L., Zymbler, M. (eds) Parallel Computational Technologies. PCT 2017. Communications in Computer and Information Science, vol 753. Springer, Cham. https://doi.org/10.1007/978-3-319-67035-5_22
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