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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.
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.
High-speed, low-power, reconfigurable electronic hardware has been developed to implement ICER-3D, an algorithm for compressing hyperspectral-image data. The algorithm and parts thereof have been the topics of several NASA Tech Briefs articles, including Context Modeler for Wavelet Compression of Hyperspectral Images (NPO-43239) and ICER-3D Hyperspectral Image Compression Software (NPO-43238), which appear elsewhere in this issue of NASA Tech Briefs. As described in more detail in those articles, the algorithm includes three main subalgorithms: one for computing wavelet transforms, one for context modeling, and one for entropy encoding. For the purpose of designing the hardware, these subalgorithms are treated as modules to be implemented efficiently in field-programmable gate arrays (FPGAs). The design takes advantage of industry- standard, commercially available FPGAs. The implementation targets the Xilinx Virtex II pro architecture, which has embedded PowerPC processor cores with flexible on-chip bus architecture. It incorporates an efficient parallel and pipelined architecture to compress the three-dimensional image data. The design provides for internal buffering to minimize intensive input/output operations while making efficient use of offchip memory. The design is scalable in that the subalgorithms are implemented as independent hardware modules that can be combined in parallel to increase throughput. The on-chip processor manages the overall operation of the compression system, including execution of the top-level control functions as well as scheduling, initiating, and monitoring processes. The design prototype has been demonstrated to be capable of compressing hyperspectral data at a rate of 4.5 megasamples per second at a conservative clock frequency of 50 MHz, with a potential for substantially greater throughput at a higher clock frequency. The power consumption of the prototype is less than 6.5 W. The reconfigurability (by means of reprogramming) of the FPGAs makes it possible to effectively alter the design to some extent to satisfy different requirements without adding hardware. The implementation could be easily propagated to future FPGA generations and/or to custom application-specific integrated circuits.
Java Architecture for Detect-And-Avoid (DAA) Extensibility and Modeling (JADEM) was developed at NASA Ames Research Center as a research and modeling tool for Unmanned Aircraft Systems (UAS) Integration in the National Airspace System (NAS). UAS will be required to have DAA systems in order to fulfill the regulatory requirement to remain well clear'' of other traffic. JADEM supports research on technological requirements and Minimum Operational Performance Standards (MOPS) for UAS DAA systems by providing a flexible and extensible software platform that includes models and algorithms for all major DAA functions. This paper describes one of these algorithms, the Generic Resolution Advisor and Conflict Evaluator (GRACE). GRACE supports two core DAA functions: threat evaluation and guidance. GRACE is generic in the sense that it is designed to work with any aircraft or sensor type (both cooperative and non-cooperative), and to be used in various applications and DAA guidance concepts, thus supporting evolving MOPS requirements and research. GRACE combines flexibility, robustness, and computational efficiency. It has modest memory requirements and can handle multiple cooperative and noncooperative intruders. GRACE has been used as a core JADEM component in several real-time and fast-time experiments, including human-in-the-loop simulations and live flight tests.
A memory system is provided, of the type that includes an error-correcting circuit that detects and corrects, that more efficiently utilizes the capacity of a memory formed of groups of binary cells whose states can be inadvertently switched by ionizing radiation. Each memory cell has an asymmetric geometry, so that ionizing radiation causes a significantly greater probability of errors in one state than in the opposite state (e.g., an erroneous switch from '1' to '0' is far more likely than a switch from '0' to'1'. An asymmetric error correcting coding circuit can be used with the asymmetric memory cells, which requires fewer bits than an efficient symmetric error correcting code.
Scientific and engineering applications often involve structured meshes. These meshes may be nested (for multigrid codes) and/or irregularly coupled (called multiblock or irregularly coupled regular mesh problems). A combined runtime and compile-time approach for parallelizing these applications on distributed memory parallel machines in an efficient and machine-independent fashion was described. A runtime library which can be used to port these applications on distributed memory machines was designed and implemented. The library is currently implemented on several different systems. To further ease the task of application programmers, methods were developed for integrating this runtime library with compilers for HPK-like parallel programming languages. How this runtime library was integrated with the Fortran 90D compiler being developed at Syracuse University is discussed. Experimental results to demonstrate the efficacy of our approach are presented. A multiblock Navier-Stokes solver template and a multigrid code were experimented with. Our experimental results show that our primitives have low runtime communication overheads. Further, the compiler parallelized codes perform within 20 percent of the code parallelized by manually inserting calls to the runtime library.
Discrete-event simulation programs make heavy use of dynamic memory allocation in order to support simulation's very dynamic space requirements. When programming in C one is likely to use the malloc() routine. However, a parallel simulation which uses the standard Unix System V malloc() implementation may achieve an overly optimistic speedup, possibly superlinear. An alternate implementation provided on some (but not all systems) can avoid the speedup anomaly, but at the price of significantly reduced available free space. This is especially severe on most parallel architectures, which tend not to support virtual memory. It is shown how a simply implemented user-constructed interface to malloc() can both avoid artificially inflated speedups, and make efficient use of the dynamic memory space. The interface simply catches blocks on the basis of their size. The problem is demonstrated empirically, and the effectiveness of the solution is shown both empirically and analytically.
A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. Universal reconstructions are obtained by distributing unknowns in a geometrically similar manner for all unstructured cells. Placements of the unknown and flux points with various order of accuracy are given for the line, triangular and tetrahedral elements. The data structure of the new method permits an optimum use of cache memory, resulting in further computational efficiency on modern computers. A new pointer system is developed that reduces memory requirements and simplifies programming for any order of accuracy. Numerical solutions are presented and compared with the exact solutions for wave propagation problems in both two and three dimensions to demonstrate the capability of the method. Excellent agreement has been found. The method is simpler and more efficient than previous discontinuous Galerkin and spectral volume methods for unstructured grids.
Convolutional coding coupled with 16-PSK modulation is investigated for bandwidth efficient transmission. Rate 3/4, small memory codes are found which are optimized in the free-distance sense on the Gaussian channel. These codes provide up to 4.8 dB of coding gain with 32 states over uncoded 8-PSK, a scheme having the same spectral efficiency as the codes described. The performance is compared with earlier findings of Ungerboeck and some recent results on R = 2/3 coded 8-PSK. In addition, results of a channel transmission study to assess the performance of the four-state code on the band-limited nonlinear channel are presented, and it is found that performance of the coded scheme degrades comparably with uncoded 8-PSK, i.e., coding gain is roughly preserved.
A three-dimensional unstructured mesh Reynolds averaged Navier-Stokes solver is described. Turbulence is simulated using a single field-equation model. Computational overheads are minimized through the use of a single edge-based data-structure, and efficient multigrid solution technique, and the use of multi-tasking on shared memory multi-processors. The accuracy and efficiency of the code are evaluated by computing two-dimensional flows in three dimensions and comparing with results from a previously validated two-dimensional code which employs the same solution algorithm. The feasibility of computing three-dimensional flows on grids of several million points in less than two hours of wall clock time is demonstrated.
A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense of additional memory usage. The solver is cache efficient and fully vectorizable, and is parallelized using a two-level hybrid MPI-OpenMP implementation suitable for shared and/or distributed memory architectures, as well as clusters of shared memory machines. Convergence and scalability results are illustrated for various high-lift cases.
Computational performance of the FUN3D unstructured-grid computational fluid dynamics (CFD) application on massively parallel GPU environments is memory-bound and highly dependent upon efficient reads from and atomic updates to the irregular cell-, edge-, and node-based data structures. In this talk, we present recent efforts into optimizing select performance-critical kernels on NVIDIA Tesla V100 and A100 GPUs and AMD CDNA MI100 GPUs. A novel use of L2 cache residency controls and asynchronous loads into on-chip shared memory are explored on the A100 GPU for the sparse iterative solver, which is dominated by mixed-precision, sparse matrix vector multiplication. Demonstrations show that these methods improve global memory bandwidth utilization by 13.5% on the A100 GPU. Several techniques are also presented that use registers and/or shared memory to facilitate array transposition and aggregation which combine to reduce the frequency and increase the cache efficiency of floating-point atomic updates to the irregular data structures. These methods are demonstrated to improve the kernel throughput by nearly 500% on select kernels on the AMD MI100 over atomic updates directly to global memory. Overall, both V100 and A100 GPUs outperformed the MI100 GPU on kernels dominated by double-precision atomic updates; however, the techniques demonstrated here reduced the performance gap and improved the MI100 performance.
The results are summarized of a multiprocessor systems design review. The systems were reviewed against use in a space station environment. The proposed designs were evaluated from a systems viewpoint in general and from the systems software in particular. The recommendations resulting from this evaluation are anticipated to be considered for the design of a multiprocessing system built around a SUMC. Two multiprocessing system designs were reviewed. The designs reviewed were highly functional and many questions could not be answered. However, several major issues were uncovered which could be evaluated to some detail, and which could greatly impact the SUMC-MP design. The major issues relevant to a multiprocessing system design revolve around the following functions: (1) Storage Management, (2) Processor Management, (3) Intermodule Communication, (4) Memory Access Interference, (5) System Efficiency, and (6) System Recovery/Reliability.
Device's voltage amplitude distribution is similar to that of standing waves on transmission line. It can be used for fast, efficient information encoding, decoding, and memory. Device operates in response to brief tone burst setting up standing-wave mode of oscillation which is unique for each possible burst frequency.
Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.
We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.
Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.
An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.