Hybrid Density Functional Theory (DFT) has recently gained popularity as an accurate model of electronic interactions in chemistry and materials science applications. The most computationally expensive part of hybrid DFT simulations is the calculation of exchange integrals between pairs of electrons. We present strategies to achieve improved load balancing and scalability for the parallel computation of these integrals. First, we develop a cost model for the calculation, and utilize random search algorithms to optimize the data distribution and calculation schedule. Second, we further improve performance using partial data-replication to increase data availability across cores. We demonstrate these improvements using an implementation in the Qbox Density Functional Theory code on the Mira Blue Gene/Q computer at Argonne National Laboratory. We perform calculations in the range of 8k to 128k cores on two representative simulation samples from materials science and chemistry applications: liquid water and a metal-water interface.

In serial computation, program profiling is often helpful for optimization of key sections of code. When moving to parallel computation, not only does the code execution need to be considered but also communication between the different processes which can induce delays that are detrimental to performance. As the number of processes increases, so does the impact of the communication delays on performance. For large-scale parallel applications, it is critical to understand how the communication impacts performance in order to make the code more efficient. There are several tools available for visualizing program execution and communications on parallel systems. These tools generally provide either views which statistically summarize the entire program execution or process-centric views. However, process-centric visualizations do not scale well as the number of processes gets very large. In particular, the most common representation of parallel processes is a Gantt char t with a row for each process. As the number of processes increases, these charts can become difficult to work with and can even exceed screen resolution. We propose a new visualization approach that affords more scalability and then demonstrate it on systems running with up to 16,384 processes.

First-principles simulations of high-Z metallic systems using the Qbox code on the BlueGene/L supercomputer demonstrate unprecedented performance and scaling for a quantum simulation code. Specifically designed to take advantage of massively-parallel systems like BlueGene/L, Qbox demonstrates excellent parallel efficiency and peak performance. A sustained peak performance of 207.3 TFlop/s was measured on 65,536 nodes, corresponding to 56.5% of the theoretical full machine peak using all 128k CPUs.

Blue Gene/L represents a new way to build supercomputers, using a large number of low power processors, together with multiple integrated interconnection networks. Whether real applications can scale to tens of thousands of processors (on a machine like Blue Gene/L) has been an open question. In this paper, we describe early experience with several physics and material science applications on a 32,768 node Blue Gene/L system, which was installed recently at the Lawrence Livermore National Laboratory. Our study shows some problems in the applications and in the current software implementation, but overall, excellent scaling of these applications to 32K nodes on the current Blue Gene/L system. While there is clearly room for improvement, these results represent the first proof point that MPI applications can effectively scale to over ten thousand processors. They also validate the scalability of the hardware and software architecture of Blue Gene/L.

We demonstrate that the Qbox code supports unprecedented large-scale First-Principles Molecular Dynamics (FPMD) applications on the BlueGene/L supercomputer. Qbox is an FPMD implementation specifically designed for large-scale parallel platforms such as BlueGene/L. Strong scaling tests for a Materials Science application show an 86% scaling efficiency between 1024 and 32,768 CPUs. Measurements of performance by means of hardware counters show that 36% of the peak FPU performance can be attained.