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In this work, we report on strategies and results of our initial approach for modernization of Titan2D code. Titan2D is a geophysical mass flow simulation code designed for modeling of volcanic flows, debris avalanches and landslides over a realistic terrain model. It solves an underlying hyperbolic system of partial differential equations using parallel adaptive mesh Godunov scheme. The following work was done during code refactoring and modernization. To facilitate user input two level python interface was developed. Such design permits large changes in C++ and Python low-level while maintaining stable high-level interface exposed to the end user. Multiple diverged forks implementing different material models were merged back together. Data storage layout was changed from a linked list of structures to a structure of arrays representation for better memory access and in preparation for further work on better utilization of vectorized instruction. Existing MPI parallelization was augmented with OpenMP parallelization. The performance of a hash table used to store mesh elements and nodes references was improved by switching from a linked list for overflow entries to dynamic arrays allowing the implementation of the binary search algorithm. The introduction of the new data layout made possible to reduce the number of hash table look-ups by replacing them with direct use of indexes from the storage class. The modifications lead to 8-9 times performance improvement for serial execution., Comment: First International Workshop on Legacy Software Refactoring for Performance (REFAC'19) in conjunction with ISC'19

Motivated by recent computational models for redistricting and detection of gerrymandering, we study the following problem on graph partitions. Given a graph $G$ and an integer $k\geq 1$, a $k$-district map of $G$ is a partition of $V(G)$ into $k$ nonempty subsets, called districts, each of which induces a connected subgraph of $G$. A switch is an operation that modifies a $k$-district map by reassigning a subset of vertices from one district to an adjacent district; a 1-switch is a switch that moves a single vertex. We study the connectivity of the configuration space of all $k$-district maps of a graph $G$ under 1-switch operations. We give a combinatorial characterization for the connectedness of this space that can be tested efficiently. We prove that it is NP-complete to decide whether there exists a sequence of 1-switches that takes a given $k$-district map into another; and NP-hard to find the shortest such sequence (even if a sequence of polynomial length is known to exist). We also present efficient algorithms for computing a sequence of 1-switches that takes a given $k$-district map into another when the space is connected, and show that these algorithms perform a worst-case optimal number of switches up to constant factors.

Given a point set $S=\{s_1,\ldots , s_n\}$ in the unit square $U=[0,1]^2$, an anchored square packing is a set of $n$ interior-disjoint empty squares in $U$ such that $s_i$ is a corner of the $i$th square. The reach $R(S)$ of $S$ is the set of points that may be covered by such a packing, that is, the union of all empty squares anchored at points in $S$. It is shown that area$(R(S))\geq \frac12$ for every finite set $S\subset U$, and this bound is the best possible. The region $R(S)$ can be computed in $O(n\log n)$ time. Finally, we prove that finding a maximum area anchored square packing is NP-complete. This is the first hardness proof for a geometric packing problem where the size of geometric objects in the packing is unrestricted., Comment: 20 pages, 13 figures. A 15-page extended abstract appears in the Proceedings of the 43rd International Symposium on Mathematical Foundations of Computer Science (Liverpool, UK, 2018)

In this work we examine how the updates addressing Meltdown and Spectre vulnerabilities impact the performance of HPC applications. To study this we use the application kernel module of XDMoD to test the performance before and after the application of the vulnerability patches. We tested the performance difference for multiple application and benchmarks including: NWChem, NAMD, HPCC, IOR, MDTest and IMB. The results show that although some specific functions can have performance decreased by as much as 74%, the majority of individual metrics indicates little to no decrease in performance. The real-world applications show a 2-3% decrease in performance for single node jobs and a 5-11% decrease for parallel multi node jobs.

Workload characterization is an integral part of performance analysis of high performance computing (HPC) systems. An understanding of workload properties sheds light on resource utilization and can be used to inform performance optimization both at the software and system configuration levels. It can provide information on how computational science usage modalities are changing that could potentially aid holistic capacity planning for the wider HPC ecosystem. Here, we report on the results of a detailed workload analysis of the portfolio of supercomputers comprising the NSF Innovative HPC program in order to characterize its past and current workload and look for trends to understand the nature of how the broad portfolio of computational science research is being supported and how it is changing over time. The workload analysis also sought to illustrate a wide variety of usage patterns and performance requirements for jobs running on these systems. File system performance, memory utilization and the types of parallelism employed by users (MPI, threads, etc) were also studied for all systems for which job level performance data was available., Comment: 93 pages, 82 figures, 19 tables

Blue Waters is a Petascale-level supercomputer whose mission is to enable the national scientific and research community to solve "grand challenge" problems that are orders of magnitude more complex than can be carried out on other high performance computing systems. Given the important and unique role that Blue Waters plays in the U.S. research portfolio, it is important to have a detailed understanding of its workload in order to guide performance optimization both at the software and system configuration level as well as inform architectural balance tradeoffs. Furthermore, understanding the computing requirements of the Blue Water's workload (memory access, IO, communication, etc.), which is comprised of some of the most computationally demanding scientific problems, will help drive changes in future computing architectures, especially at the leading edge. With this objective in mind, the project team carried out a detailed workload analysis of Blue Waters., Comment: 107 pages, >100 figures (figure sizes reduced to save space, contact authors for version with full resolution)