Sparse Matrix-vector Multiplication on GPGPU Clusters: A New Storage Format and a Scalable Implementation - Kreutzer, M.; Hager, G.; Wellein, G.; Fehske, H.; Basermann, A.; Bishop, A. R. (2012 26th IEEE International Parallel and Distributed Processing Symposium Workshops, 2012)
Sparse matrix-vector multiplication (spMVM) is the dominant operation in many sparse solvers. We investigate performance properties of spMVM with matrices of various sparsity patterns on the nVidia "Fermi" class of GPGPUs. A new "padded jagged diagonals storage" (pJDS) format is proposed which may substantially reduce the memory overhead intrinsic to the widespread ELLPACK-R scheme while making no assumptions about the matrix structure. In our test scenarios the pJDS format cuts the overall spMVM memory footprint on the GPGPU by up to 70%, and achieves 91% to 130% of the ELLPACK-R performance. Using a suitable performance model we identify performance bottlenecks on the node level that invalidate some types of matrix structures for efficient multi-GPGPU parallelization. For appropriate sparsity patterns we extend previous work on distributed-memory parallel spMVM to demonstrate a scalable hybrid MPI-GPGPU code, achieving efficient overlap of communication and computation.