ALBERT

Description: We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.

Description: The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.

Description: Earth science applications of the future will stress the capabilities of even the highest performance supercomputers in the areas of raw compute power, mass storage management, and software environments. These NASA mission critical problems demand usable multi-petaflops and exabyte-scale systems to fully realize their science goals. With an exciting vision of the technologies needed, NASA has established a comprehensive program of advanced research in computer architecture, software tools, and device technology to ensure that, in partnership with US industry, it can meet these demanding requirements with reliable, cost effective, and usable ultra-scale systems. NASA will exploit, explore, and influence emerging high end computing architectures and technologies to accelerate the next generation of engineering, operations, and discovery processes for NASA Enterprises. This article captures this vision and describes the concepts, accomplishments, and the potential payoff of the key thrusts that will help meet the computational challenges in Earth science applications.

Description: We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.

Description: This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.

Description: NASA has increasingly relied on high-performance computing (HPC) re- sources for computational modeling, simulation, and data analysis to meet the science and engineering goals of its missions in space exploration, aeronautics, and Earth and space science. The NASA Advanced Supercomputing (NAS) Division at Ames Research Center in Silicon Valley, Calif., hosts NASAs premier supercomputing resources, integral to achieving and enhancing the success of the agencys missions. NAS provides a balanced environment, funded under the High-End Computing Capability (HECC) project, comprised of world-class supercomputers, including its flagship distributed-memory cluster, Pleiades; high-speed networking; and massive data storage facilities, along with multi-disciplinary support teams for user support, code porting and optimization, and large-scale data analysis and scientific visualization. However, as scientists have increased the fidelity of their simulations and engineers are conducting larger parameter-space studies, the requirements for supercomputing resources have been growing by leaps and bounds. With the facility housing the HECC systems reaching its power and cooling capacity, NAS undertook a prototype project to investigate an alternative approach for housing supercomputers. Modular supercomputing, or container-based computing, is an innovative concept for expanding NASAs HPC capabilities. With modular supercomputing, additional containerssimilar to portable storage podscan be connected together as needed to accommodate the agencys ever-increasing demand for computing resources. In addition, taking advantage of the local weather permits the use of cooling technologies that would additionally save energy and reduce annual water usage. The first stage of NASAs Modular Supercomputing Facility (MSF) prototype, which resulted in a 1,000 square-foot module on a concrete pad with room for 16 compute racks, was completed in Fall 2016 and an SGI (now HPE) computer system, named Electra, was deployed there in early 2017. Cooling is performed via an evaporative system built into the module, and preliminary experience shows a Power Usage Effectiveness (PUE) measurement of 1.03. Electra achieved over a petaflop on the LINPACK benchmark, sufficient to rank number 96 on the November 2016 TOP500 list [14]. The system consists of 1,152 InfiniBand-connected Intel Xeon Broadwell-based nodes. Its users access their files on a facility-wide file system shared by all HECC compute assets via Mellanox MetroX InfiniBand extenders, which connect the Electra fabric to Lustre routers in the primary facility over fiber-optic links about 900 feet long. The MSF prototype has exceeded expectations and is serving as a blueprint for future expansions. In the remainder of this chapter, we detail how modular data center technology can be used to expand an existing compute resource. We begin by describing NASAs requirements for supercomputing and how resources were provided prior to the integration of the Electra module-based system.

Description: This paper examines the applications most commonly run on the supercomputers at the Numerical Aerospace Simulation (NAS) facility. It analyzes the extent to which such applications are fundamentally oriented to vector computers, and whether or not they can be efficiently implemented on hierarchical memory machines, such as systems with cache memories and highly parallel, distributed memory systems.

Description: The increasing gap between processor and memory performance has lead to new architectural models for memory-intensive applications. In this paper, we explore the performance of a set of memory-intensive benchmarks and use them to compare the performance of conventional cache-based microprocessors to a mixed logic and DRAM processor called VIRAM. The benchmarks are based on problem statements, rather than specific implementations, and in each case we explore the fundamental hardware requirements of the problem, as well as alternative algorithms and data structures that can help expose fine-grained parallelism or simplify memory access patterns. The benchmarks are characterized by their memory access patterns, their basic control structures, and the ratio of computation to memory operation.

Description: Space-filling curves is a popular approach based on a geometric embedding for linearizing computational meshes. We present a new O(n log n) combinatorial algorithm for constructing a self avoiding walk through a two dimensional mesh containing n triangles. We show that for hierarchical adaptive meshes, the algorithm can be locally adapted and easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the runtime partitioning and load balancing of adaptive unstructured grids.

Description: In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the adaption phase of FE applications oil triangular meshes and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments oil EARTH-SP2, on implementation of EARTH on the IBM SP2 with different load balancing strategies that are built into the runtime system.