## Martin BerzinsParallel ComputingGPUs |
## Mike KirbyFinite Element MethodsUncertainty Quantification GPUs |
## Valerio PascucciScientific Data Management |
## Chris JohnsonProblem Solving Environments |

## Ross WhitakerGPUs |
## Chuck HansenGPUs |

Improving accuracy in the MPM method using a null space filterC. Gritton, M. Berzins. In Computational Particle Mechanics, pp. 1--12. 2016. ISSN: 2196-4386 DOI: 10.1007/s40571-016-0134-3 The material point method (MPM) has been very successful in providing solutions to many challenging problems involving large deformations. Nevertheless there are some important issues that remain to be resolved with regard to its analysis. One key challenge applies to both MPM and particle-in-cell (PIC) methods and arises from the difference between the number of particles and the number of the nodal grid points to which the particles are mapped. This difference between the number of particles and the number of grid points gives rise to a non-trivial null space of the linear operator that maps particle values onto nodal grid point values. In other words, there are non-zero particle values that when mapped to the grid point nodes result in a zero value there. Moreover, when the nodal values at the grid points are mapped back to particles, part of those particle values may be in that same null space. Given positive mapping weights from particles to nodes such null space values are oscillatory in nature. While this problem has been observed almost since the beginning of PIC methods there are still elements of it that are problematical today as well as methods that transcend it. The null space may be viewed as being connected to the ringing instability identified by Brackbill for PIC methods. It will be shown that it is possible to remove these null space values from the solution using a null space filter. This filter improves the accuracy of the MPM methods using an approach that is based upon a local singular value decomposition (SVD) calculation. This local SVD approach is compared against the global SVD approach previously considered by the authors and to a recent MPM method by Zhang and colleagues. |

An Overview of Performance Portability in the Uintah Runtime System Through the Use of KokkosD. Sunderland, B. Peterson, J. Schmidt, A. Humphrey, J. Thornock,, M. Berzins. In Proceedings of the Second Internationsl Workshop on Extreme Scale Programming Models and Middleware, Salt Lake City, Utah, ESPM2, IEEE Press, Piscataway, NJ, USA pp. 44--47. 2016. ISBN: 978-1-5090-3858-9 DOI: 10.1109/ESPM2.2016.10 The current diversity in nodal parallel computer architectures is seen in machines based upon multicore CPUs, GPUs and the Intel Xeon Phi's. A class of approaches for enabling scalability of complex applications on such architectures is based upon Asynchronous Many Task software architectures such as that in the Uintah framework used for the parallel solution of solid and fluid mechanics problems. Uintah has both an applications layer with its own programming model and a separate runtime system. While Uintah scales well today, it is necessary to address nodal performance portability in order for it to continue to do. Incrementally modifying Uintah to use the Kokkos performance portability library through prototyping experiments results in improved kernel performance by more than a factor of two. |

Packing Configurations of PBX-9501 Cylinders to Reduce the Probability of a Deflagration to Detonation Transition (DDT)J. Beckvermit, T. Harman, C. Wight,, M. Berzins. In Propellants, Explosives, Pyrotechnics, 2016. ISSN: 1521-4087 DOI: 10.1002/prep.201500331 The detonation of hundreds of explosive devices from either a transportation or storage accident is an extremely dangerous event. This paper focuses on identifying ways of packing/storing arrays of explosive cylinders that will reduce the probability of a Deflagration to Detonation Transition (DDT). The Uintah Computational Framework was utilized to predict the conditions necessary for a large scale DDT to occur. The results showed that the arrangement of the explosive cylinders and the number of devices packed in a "box" greatly effects the probability of a detonation. |

TOD-Tree: Task-Overlapped Direct send Tree Image Compositing for Hybrid MPI Parallelism and GPUsA. V. P. Grosset, M. Prasad, C. Christensen, A. Knoll, C. Hansen. In IEEE Transactions on Visualization and Computer Graphics, IEEE, pp. 1--1. 2016. DOI: 10.1109/tvcg.2016.2542069 Modern supercomputers have thousands of nodes, each with CPUs and/or GPUs capable of several teraflops. However, the network connecting these nodes is relatively slow, on the order of gigabits per second. For time-critical workloads such as interactive visualization, the bottleneck is no longer computation but communication. In this paper, we present an image compositing algorithm that works on both CPU-only and GPU-accelerated supercomputers and focuses on communication avoidance and overlapping communication with computation at the expense of evenly balancing the workload. The algorithm has three stages: a parallel direct send stage, followed by a tree compositing stage and a gather stage. We compare our algorithm with radix-k and binary-swap from the IceT library in a hybrid OpenMP/MPI setting on the Stampede and Edison supercomputers, show strong scaling results and explain how we generally achieve better performance than these two algorithms. We developed a GPU-based image compositing algorithm where we use CUDA kernels for computation and GPU Direct RDMA for inter-node GPU communication. We tested the algorithm on the Piz Daint GPU-accelerated supercomputer and show that we achieve performance on par with CPUs. Lastly, we introduce a workflow in which both rendering and compositing are done on the GPU. |

Radiative Heat Transfer Calculation on 16384 GPUs Using a Reverse Monte Carlo Ray Tracing Approach with Adaptive Mesh RefinementA. Humphrey, D. Sunderland, T. Harman, M. Berzins. In 2016 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), pp. 1222-1231. May, 2016. DOI: 10.1109/IPDPSW.2016.93 Modeling thermal radiation is computationally challenging in parallel due to its all-to-all physical and resulting computational connectivity, and is also the dominant mode of heat transfer in practical applications such as next-generation clean coal boilers, being modeled by the Uintah framework. However, a direct all-to-all treatment of radiation is prohibitively expensive on large computers systems whether homogeneous or heterogeneous. DOE Titan and the planned DOE Summit and Sierra machines are examples of current and emerging GPUbased heterogeneous systems where the increased processing capability of GPUs over CPUs exacerbates this problem. These systems require that computational frameworks like Uintah leverage an arbitrary number of on-node GPUs, while simultaneously utilizing thousands of GPUs within a single simulation. We show that radiative heat transfer problems can be made to scale within Uintah on heterogeneous systems through a combination of reverse Monte Carlo ray tracing (RMCRT) techniques combined with AMR, to reduce the amount of global communication. In particular, significant Uintah infrastructure changes, including a novel lock and contention-free, thread-scalable data structure for managing MPI communication requests and improved memory allocation strategies were necessary to achieve excellent strong scaling results to 16384 GPUs on Titan. |

Approximating the Generalized Voronoi Diagram of Closely Spaced ObjectsJ. Edwards, E. Daniel, V. Pascucci, C. Bajaj. In Computer Graphics Forum, Vol. 34, No. 2, Wiley-Blackwell, pp. 299-309. May, 2015. DOI: 10.1111/cgf.12561 Generalized Voronoi Diagrams (GVDs) have far-reaching applications in robotics, visualization, graphics, and simulation. However, while the ordinary Voronoi Diagram has mature and efficient algorithms for its computation, the GVD is difficult to compute in general, and in fact, has only approximation algorithms for anything but the simplest of datasets. Our work is focused on developing algorithms to compute the GVD efficiently and with bounded error on the most difficult of datasets -- those with objects that are extremely close to each other. |

Paint and Click: Unified Interactions for Image BoundariesB. Summa, A. A. Gooch, G. Scorzelli, V. Pascucci. In Computer Graphics Forum, Vol. 34, No. 2, Wiley-Blackwell, pp. 385--393. May, 2015. DOI: 10.1111/cgf.12568 Image boundaries are a fundamental component of many interactive digital photography techniques, enabling applications such as segmentation, panoramas, and seamless image composition. Interactions for image boundaries often rely on two complementary but separate approaches: editing via painting or clicking constraints. In this work, we provide a novel, unified approach for interactive editing of pairwise image boundaries that combines the ease of painting with the direct control of constraints. Rather than a sequential coupling, this new formulation allows full use of both interactions simultaneously, giving users unprecedented flexibility for fast boundary editing. To enable this new approach, we provide technical advancements. In particular, we detail a reformulation of image boundaries as a problem of finding cycles, expanding and correcting limitations of the previous work. Our new formulation provides boundary solutions for painted regions with performance on par with state-of-the-art specialized, paint-only techniques. In addition, we provide instantaneous exploration of the boundary solution space with user constraints. Finally, we provide examples of common graphics applications impacted by our new approach. |

Reducing overhead in the Uintah framework to support short-lived tasks on GPU-heterogeneous architecturesB. Peterson, H. K. Dasari, A. Humphrey, J.C. Sutherland, T. Saad, M. Berzins. In Proceedings of the 5th International Workshop on Domain-Specific Languages and High-Level Frameworks for High Performance Computing (WOLFHPC'15), ACM, pp. 4:1-4:8. 2015. DOI: 10.1145/2830018.2830023 |

Developing Uintah’s Runtime System For Forthcoming Architectures,Subtitled “Refereed paper presented at the RESPA 15 Workshop at SuperComputing 2015 Austin Texas,” B. Peterson, N. Xiao, J. Holmen, S. Chaganti, A. Pakki, J. Schmidt, D. Sunderland, A. Humphrey, M. Berzins.
SCI Institute, 2015. |

Spectral and High Order Methods for Partial Differential Equations,Subtitled “Selected Papers from the ICOSAHOM'14 Conference, June 23-27, 2014, Salt Lake City, UT, USA.,” R.M. Kirby, M. Berzins, J.S. Hesthaven (Editors).
In Lecture Notes in Computational Science and Engineering, Springer, 2015. |

Improving Accuracy In Particle Methods Using Null Spaces and FiltersC. Gritton, M. Berzins, R. M. Kirby. In Proceedings of the IV International Conference on Particle-Based Methods - Fundamentals and Applications, Barcelona, Spain, Edited by E. Onate and M. Bischoff and D.R.J. Owen and P. Wriggers and T. Zohdi, CIMNE, pp. 202-213. September, 2015. ISBN: 978-84-944244-7-2 While particle-in-cell type methods, such as MPM, have been very successful in providing solutions to many challenging problems there are some important issues that remain to be resolved with regard to their analysis. One such challenge relates to the difference in dimensionality between the particles and the grid points to which they are mapped. There exists a non-trivial null space of the linear operator that maps particles values onto nodal values. In other words, there are non-zero particle values values that when mapped to the nodes are zero there. Given positive mapping weights such null space values are oscillatory in nature. The null space may be viewed as a more general form of the ringing instability identified by Brackbill for PIC methods. It will be shown that it is possible to remove these null-space values from the solution and so to improve the accuracy of PIC methods, using a matrix SVD approach. The expense of doing this is prohibitive for real problems and so a local method is developed for doing this. |