Abstract: Numerical methods of PDEs are mostly "compactly supported",say finite element,and finite difference methods etc. Due to the compact support, the global matrix associated with those numerical methods for scientific and engineering are sparse and very often also band shaped. We proposed and developed a high performance spMV algorithm for this specific but widely used sparse matrix type. The new algorithm, termed "bDIA (banded diagnal)", is implemented on NVIDIA GTX 285. Detailed comparisons with the five other mostly used sparse matrix formats/algorithms supported in the open source cuda linear algebra library (CUSP) show that bDIA doubles the best performance of the other five algorithms, breaking the float point efficiency limit of 4 0 o for single precision and 22.2% for double-precision. The conjugate gradient (CG) and the bi-conjugate gradient stabilized (BiCGStab) solvers both gain a speedup of around 1.5 using the proposed "bDIA" format/algorithm.

Key words: Banded sparse matrix-vector multiplication, bDIA, GFEM, GPU, CG solver optimization