Communication-Avoiding Krylov Techniques on Graphic Processing Units

May 11th, 2013

Abstract:

Communicating data within the graphic processing unit (GPU) memory system and between the CPU and GPU are major bottlenecks in accelerating Krylov solvers on GPUs. Communication-avoiding techniques reduce the communication cost of Krylov subspace methods by computing several vectors of a Krylov subspace “at once,” using a kernel called “matrix powers.” The matrix powers kernel is implemented on a recent generation of NVIDIA GPUs and speedups of up to 5.7 times are reported for the communication-avoiding matrix powers kernel compared to the standards prase matrix vector multiplication (SpMV) implementation.

(M. Mehri Dehnavi, Y. El-Kurdi, J. Demmel and D. Giannacopoulos: “Communication-Avoiding Krylov Techniques on Graphic Processing Units”, IEEE Transactions on Magnetics 49(5):1749-1752, May 2013. [DOI])