A fast GPU based bidiagonal solver for computational aeroacoustics

In this work a computational aeroacoustic (CAA) solver used for sound propagation in engineering practice is accelerated on Graphics Processing Units (GPUs). The high-fidelity CAA solver is based on linearized Euler equations (LEE) which features high order prefactored compact schemes. Solving the prefactored compact scheme is the dominant computational cost and results in a bidiagonal matrix. Multiple methods to solve the bidiagonal matrix are investigated on GPUs. The numerical methods achieve different performance in the different directions. A new hybrid method is proposed and a strategy is concluded in solving the bidiagonal matrix in 3D computations. To the authors’ knowledge, this is the first time of investigation of bidiagonal matrix on GPUs. It is found that the anisotropic memory access pattern results in performance gap in different directions. Consequently, different numerical methods are employed in different directions in 3D computations. Based on a comparison of the elapsed time on the same amount of CPU cores and GPUs, speed-ups of 40–80 are achieved in double precision.