Numerical reproducibility and stability of large scale scientific simulations, especially climate modeling, on distributed memory parallel computers are becoming critical issues. In particular, global summation of distributed arrays is most susceptible to rounding errors, and their propagation and accumulation cause uncertainty in final simulation results. We analyzed several accurate summation methods and found that two methods are particularly effective to improve (ensure) reproducibility and stability -- Kahan's self-compensated summation and Bailey's double-double precision summation. We provide an MPI operator MPI_SUMMDD to work with MPI collective operations to ensure a scalable implementation on a large number of processors. The final methods are particularly simple to adopt in practical codes.

We investigate the OpenMP parallelization and optimization of two novel data classification algorithms. The new algorithms are based on graph and PDE solution techniques and provide significant accuracy and performance advantages over traditional data classification algorithms in serial mode. The methods leverage the Nystrom extension to calculate eigenvalue/eigenvectors of the graph Laplacian and this is a self-contained module that can be used in conjunction with other graph- Laplacian based methods such as spectral clustering.We use performance tools to collect the hotspots and memory access of the serial codes and use OpenMP as the parallelization language to parallelize the most timeconsuming parts. Where possible, we also use library routines. We then optimize the OpenMP implementations and detail the performance on traditional supercomputer nodes (in our case a Cray XC30), and test the optimization steps on emerging testbed systems based on Intel’s Knights Corner and Landing processors. We show both performance improvement and strong scaling behavior. A large number of optimization techniques and analyses are necessary before the algorithm reaches almost ideal scaling.