General-Purpose Sparse Matrix Building Blocks using the NVIDIA CUDA Technology Platform

We report on our experience with integrating and using graphics processing units (GPUs) as fast parallel floa tingpoint co-processors to accelerate two fundamental computa tional scientific kernels on the GPU: sparse direct factorization a nd nonlinear interior-point optimization. Since a full re-imple mentation of these complex kernels is typically not feasible, we ident ify e.g. the matrix-matrix multiplication as a first natural entry-p oint for a minimally invasive integration of GPUs. We investigate the performance on the NVIDIA GeForce 8800 multicore chip. We exploit the architectural features of the GeForce 8800 GPU t o design an efficient GPU-parallel sparse matrix solver. A prototype approach to leverage the bandwidth and computing power of GPUs for these matrix kernel operation is demonstrated resu lting in an overall performance of over110 GFlops/s on the desktop for large matrices. We use our GPU algorithm for PDE-constrained optimization problems and demonstrate that the commodity GPU is a useful co-processor for scientific applications.