Communication-Avoiding Krylov Techniques on Graphic Processing Units

May 11th, 2013


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])