A wide class of geometry processing and PDE resolution methods needs to solve a linear system, where the non-zero pattern of the matrix is dictated by the connectivity matrix of the mesh. The advent of GPUs with their ever-growing amount of parallel horsepower makes them a tempting resource for such numerical computations. This can be helped by new APIs (CTM from ATI and CUDA from NVIDIA) which give a direct access to the multithreaded computational resources and associated memory bandwidth of GPUs; CUDA even provides a BLAS implementation but only for dense matrices (CuBLAS). However, existing GPU linear solvers are restricted to specific types of matrices, or use non-optimal compressed row storage strategies. By combining recent GPU programming techniques with supercomputing strategies (namely block compressed row storage and register blocking), we implement a sparse generalpurpose linear solver which outperforms leading-edge CPU counterparts (MKL / ACML).