Optimizing scientific applications on today's accelerator-based high performance computing systems can be challenging, especially when multiple GPUs and CPUs with heterogeneous memories and persistent non-volatile memories are present. An example is Summit, an accelerator-based system at the Oak Ridge Leadership Computing Facility (OLCF) that is rated as the world's fastest supercomputer to-date. New strategies are thus needed to expose the parallelism in legacy applications, while being amenable to efficient mapping to the underlying architecture. In this paper we discuss our experiences and strategies to port a scientific application, DCA++, to Summit. DCA++ is a high-performance research application that solves quantum many-body problems with a cutting edge quantum cluster algorithm, the dynamical cluster approximation. Our strategies aim to synergize the strengths of the different programming models in the code. These include: a) streamlining the interactions between the CPU threads and the GPUs, b) implementing computing kernels on the GPUs and decreasing CPU-GPU memory transfers, c) allowing asynchronous GPU communications, and d) increasing compute intensity by combining linear algebraic operations. Full-scale production runs using all 4600 Summit nodes attained a peak performance of 73.5 PFLOPS with a mixed precision implementation. We observed a perfect strong and weak scaling for the quantum Monte Carlo solver in DCA++, while encountering about 2x input/output (I/O) and MPI communication overhead on the time-to-solution for the full machine run. Our hardware agnostic optimizations are designed to alleviate the communication and I/O challenges observed, while improving the compute intensity and obtaining optimal performance on a complex, hybrid architecture like Summit.

We present a new quantum cluster algorithm to simulate models of high-Tc superconductors. This algorithm extends current methods with continuous lattice self-energies, thereby removing artificial long-range correlations. This cures the fermionic sign problem in the underlying quantum Monte Carlo solver for large clusters and realistic values of the Coulomb interaction in the entire temperature range of interest. We find that the new algorithm improves time-to-solution by nine orders of magnitude compared to current, state of the art quantum cluster simulations. An efficient implementation is given, which ports to multi-core as well as hybrid CPU-GPU systems. Running on 18,600 nodes on ORNL's Titan supercomputer enables us to compute a converged value of Tc/t = 0.053 ± 0.0014 for a 28 site cluster in the 2D Hubbard model with U/t = 7 at 10% hole doping. Typical simulations on Titan sustain between 9.2 and 15.4 petaflops (double precision measured over full run), depending on configuration and parameters used.

Staggering computational and algorithmic advances in recent years now make possible systematic Quantum Monte Carlo (QMC) simulations of high temperature (high-Tc) superconductivity in a microscopic model, the two dimensional (2D) Hubbard model, with parameters relevant to the cuprate materials. Here we report the algorithmic and computational advances that enable us to study the effect of disorder and nano-scale inhomogeneities on the pair-formation and the superconducting transition temperature necessary to understand real materials. The simulation code is written with a generic and extensible approach and is tuned to perform well at scale. Significant algorithmic improvements have been made to make effective use of current supercomputing architectures. By implementing delayed Monte Carlo updates and a mixed single-/double precision mode, we are able to dramatically increase the efficiency of the code. On the Cray XT4 systems of the Oak Ridge National Laboratory (ORNL), for example, we currently run production jobs on 31 thousand processors and thereby routinely achieve a sustained performance that exceeds 200 TFlop/s. On a system with 49 thousand processors we achieved a sustained performance of 409 TFlop/s. We present a study of how random disorder in the effective Coulomb interaction strength affects the superconducting transition temperature in the Hubbard model.