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At least 181 records · Page 10

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NASA NTRS2021

Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering

Estimation of unknown noise covariances in a Kalman filter is a problem of significant practical interest in a wide array of applications. Although this problem has a long history, reliable algorithms for their estimation were scant, and necessary and sufficient conditions for identifiability of the covariances were in dispute until recently. Necessary and sufficient conditions for covariance estimation and a batch estimation algorithm were presented in our previous study. This paper presents stochastic gradient descent algorithms for noise covariance estimation in adaptive Kalman filters that are an order of magnitude faster than the batch method for similar or better root mean square error. More significantly, these algorithms are applicable to non-stationary systems where the noise covariances can occasionally jump up or down by an unknown magnitude. The computational efficiency of the new algorithms stems from adaptive thresholds for convergence, recursive fading memory estimation of the sample cross-correlations of the innovations, and accelerated stochastic gradient descent algorithms. The comparative evaluation of the proposed methods on a number of test cases demonstrates their computational efficiency and accuracy.

Adaptive Kalman filtering↗

NASA NTRSDate not supplied

Efficient Preconditioning of a High-Order Solver for Multiple Physics

This work addresses preconditioning approaches for an implicit high-order solver frame-work applied to multiple physics. The solver is based on a space-time spectral element method and matrix-free Newton-Krylov solver developed at NASA over the recent years. Within this context, most preconditioning methods are impractical, as the computational time and memory requirements scale poorly with increasing polynomial orders. To improve computational efficiency, we first describe a novel entity-based Block Jacobi preconditioner for the continuous-Galerkin solution of the linear-elasticity and linear-shell equations. Second, we introduce a multigrid algorithm to further reduce time-to-solution on stiff cases arising from continuous-and discontinuous-Galerkin discretizations. Results obtained on relevant single-physics reference solutions, demonstrate the feasibility of the methods, paving the way for high-order solutions of fully coupled multi-physics problems.

STMD↗

NASA NTRS1988

Eigenvalue computation of large symmetric tridiagonal matrices on concurrent processors

Symmetric tridiagonal eigenvalue problems may arise indirectly in structural dynamic analysis. An algorithm for eigenvalue computation of large symmetric tridiagonal matrices on concurrent processors to meet the challenge of the new emerging computer hardware technology is presented. A standard bisection method in conjunction with Sylvester's Theorem is chosen to be converted into a parallel N-section algorithm. This parallel algorithm takes advantage of the multi-processor environment by carrying out N (number of processors) triangular factorizations of chosen shifted matrices in all processors concurrently and by minimizing communication between processors. The algorithm is designed for local-memory concurrent processors, i.e. message passing type processors. The efficiency and speed-up are given in terms of problem and machine parameters. The algorithm is very efficient when both the number of processors and the number of eigenvalues to be extracted are much smaller than the order of the tridiagonal matrix.

Chang, H. Y.↗

NASA NTRS1992

An efficient and robust algorithm for time dependent viscous incompressible Navier-Stokes equations

A recently developed finite difference algorithm is presented for steady incompressible Navier-Stokes calculations. The algorithm is extremely robust with respect to Reynolds number, and has been used to directly compute incompressible flows with smoothly resolved streamfunction, kinetic energy and vorticity contours for Reynolds numbers as high as Re = 100,000 without requiring any subscale modelling. The algorithm is second order accurate in both time and space, with Crank-Nicolson differencing for the diffusion terms, with a lagged second order Adams-Basforth differencing for the convection terms, and with central differencing for all space derivatives. The algorithm is extremely efficient with respect to both computing time and physical memory. Solutions are shown for cavity and channel flows at various Reynolds numbers.

Goodrich, John W.↗

NASA NTRS1992

PARTI primitives for unstructured and block structured problems

Described here is a set of primitives (PARTI) developed to efficiently execute unstructured and block structured problems on distributed memory parallel machines. We present experimental data from a 3-D unstructured Euler solver run on the Intel Touchstone Delta to demonstrate the usefulness of our methods.

Sussman, Alan↗

NASA NTRS1992

PARTI primitives for unstructured and block structured problems

Sussman, A.↗

NASA NTRS1992

Address tracing of parallel systems via TRAPEDS

Trace-driven simulation is an important aid in performance analysis of computer systems. Capturing address traces to use in these simulations, however, is a difficult problem for parallel processor architectures. A technique termed TRAPEDS modifies executable code (at the assembly language level) to dynamically collect the address trace from executing code. TRAPEDS has recently been implemented on both a hypercube multicomputer and a shared-memory multiprocessor. Particular attention is focused on strategies for efficiently and accurately collecting traces from both classes of parallel machines. The iPSC/2 hypercube multicomputer implementation traces both user and system code, and performs simulation on-the-fly to avoid large storage costs. Strategies are detailed for mitigating address trace distortion when collecting operating system traces. The Encore Multimax multiprocessor implementation uses a timer-based approach to reflect the interleaving of the processor traces and stores the traces to disc. Time and space overhead results are presented for both TRAPEDS implementations. Experimental cache simulation results derived from iPSC/2 address traces are presented to illustrate the importance of tracing operating system references.

Stunkel, Craig B.↗

NASA NTRS1997

Parametric State Space Structuring

Structured approaches based on Kronecker operators for the description and solution of the infinitesimal generator of a continuous-time Markov chains are receiving increasing interest. However, their main advantage, a substantial reduction in the memory requirements during the numerical solution, comes at a price. Methods based on the "potential state space" allocate a probability vector that might be much larger than actually needed. Methods based on the "actual state space", instead, have an additional logarithmic overhead. We present an approach that realizes the advantages of both methods with none of their disadvantages, by partitioning the local state spaces of each submodel. We apply our results to a model of software rendezvous, and show how they reduce memory requirements while, at the same time, improving the efficiency of the computation.

Ciardo, Gianfranco↗

NASA NTRS1997

Tolerant (parallel) Programming

In order to be truly portable, a program must be tolerant of a wide range of development and execution environments, and a parallel program is just one which must be tolerant of a very wide range. This paper first defines the term "tolerant programming", then describes many layers of tools to accomplish it. The primary focus is on F-Nets, a formal model for expressing computation as a folded partial-ordering of operations, thereby providing an architecture-independent expression of tolerant parallel algorithms. For implementing F-Nets, Cooperative Data Sharing (CDS) is a subroutine package for implementing communication efficiently in a large number of environments (e.g. shared memory and message passing). Software Cabling (SC), a very-high-level graphical programming language for building large F-Nets, possesses many of the features normally expected from today's computer languages (e.g. data abstraction, array operations). Finally, L2(sup 3) is a CASE tool which facilitates the construction, compilation, execution, and debugging of SC programs.

DiNucci, David C.↗

NASA NTRS2011

Freeing Space for NASA: Incorporating a Lossless Compression Algorithm into NASA's FOSS System

NASA's Fiber Optic Strain Sensing (FOSS) system can gather and store up to 1,536,000 bytes (1.46 megabytes) per second. Since the FOSS system typically acquires hours - or even days - of data, the system can gather hundreds of gigabytes of data for a given test event. To store such large quantities of data more effectively, NASA is modifying a Lempel-Ziv-Oberhumer (LZO) lossless data compression program to compress data as it is being acquired in real time. After proving that the algorithm is capable of compressing the data from the FOSS system, the LZO program will be modified and incorporated into the FOSS system. Implementing an LZO compression algorithm will instantly free up memory space without compromising any data obtained. With the availability of memory space, the FOSS system can be used more efficiently on test specimens, such as Unmanned Aerial Vehicles (UAVs) that can be in flight for days. By integrating the compression algorithm, the FOSS system can continue gathering data, even on longer flights.

Fiechtner, Kaitlyn↗

NASA NTRS2005

Collaboration: It Is Much More Than the Technology

A joint study conducted with the University of Central Florida and the National Aeronautics and Space Agency's (NASA) Kennedy Space Center (KSC) resulted in a new approach to the collaboration issues that had troubled the Agency. We believe in teams. We believe in the concept of collaboration. We never doubted Douglas Engelbart's thesis-- "Our very survival depends on our ability to work together, more effectively, to get collectively smarter. Computers -- when used properly -- can help us do that". It was not lack of trying. Predictably, NASA engineers had worked as if better and better technology would resolve the matter. It had not. The study itself provided an insight, an "aha! moment that pointed us toward the problems of collaboration we had to solve. People quickly saw that we had to remove barriers and make it easier to share data, coordinate efficiently, work together to add value and create corporate memory. This paper describes what happened.

Elfrey, Priscilla↗

NASA NTRS1996

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

Dynamic mesh adaption on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load imbalance among processors on a parallel machine. This paper describes the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution cost is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35% of the mesh is randomly adapted. For large-scale scientific computations, our load balancing strategy gives almost a sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remapper yields processor assignments that are less than 3% off the optimal solutions but requires only 1% of the computational time.

Biswas, Rupak↗

NASA NTRS1996

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

Dynamic mesh adaptation on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load inbalances among processors on a parallel machine. This paper described the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution coast is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35 percent of the mesh is randomly adapted. For large scale scientific computations, our load balancing strategy gives an almost sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remappier yields processor assignments that are less than 3 percent of the optimal solutions, but requires only 1 percent of the computational time.

Biswas, Rupak↗

NASA NTRS1992

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗

NASA NTRS2000

Incremental Parallelization of Non-Data-Parallel Programs Using the Charon Message-Passing Library

Message passing is among the most popular techniques for parallelizing scientific programs on distributed-memory architectures. The reasons for its success are wide availability (MPI), efficiency, and full tuning control provided to the programmer. A major drawback, however, is that incremental parallelization, as offered by compiler directives, is not generally possible, because all data structures have to be changed throughout the program simultaneously. Charon remedies this situation through mappings between distributed and non-distributed data. It allows breaking up the parallelization into small steps, guaranteeing correctness at every stage. Several tools are available to help convert legacy codes into high-performance message-passing programs. They usually target data-parallel applications, whose loops carrying most of the work can be distributed among all processors without much dependency analysis. Others do a full dependency analysis and then convert the code virtually automatically. Even more toolkits are available that aid construction from scratch of message passing programs. None, however, allows piecemeal translation of codes with complex data dependencies (i.e. non-data-parallel programs) into message passing codes. The Charon library (available in both C and Fortran) provides incremental parallelization capabilities by linking legacy code arrays with distributed arrays. During the conversion process, non-distributed and distributed arrays exist side by side, and simple mapping functions allow the programmer to switch between the two in any location in the program. Charon also provides wrapper functions that leave the structure of the legacy code intact, but that allow execution on truly distributed data. Finally, the library provides a rich set of communication functions that support virtually all patterns of remote data demands in realistic structured grid scientific programs, including transposition, nearest-neighbor communication, pipelining, gather/scatter, and redistribution. At the end of the conversion process most intermediate Charon function calls will have been removed, the non-distributed arrays will have been deleted, and virtually the only remaining Charon functions calls are the high-level, highly optimized communications. Distribution of the data is under complete control of the programmer, although a wide range of useful distributions is easily available through predefined functions. A crucial aspect of the library is that it does not allocate space for distributed arrays, but accepts programmer-specified memory. This has two major consequences. First, codes parallelized using Charon do not suffer from encapsulation; user data is always directly accessible. This provides high efficiency, and also retains the possibility of using message passing directly for highly irregular communications. Second, non-distributed arrays can be interpreted as (trivial) distributions in the Charon sense, which allows them to be mapped to truly distributed arrays, and vice versa. This is the mechanism that enables incremental parallelization. In this paper we provide a brief introduction of the library and then focus on the actual steps in the parallelization process, using some representative examples from, among others, the NAS Parallel Benchmarks. We show how a complicated two-dimensional pipeline-the prototypical non-data-parallel algorithm- can be constructed with ease. To demonstrate the flexibility of the library, we give examples of the stepwise, efficient parallel implementation of nonlocal boundary conditions common in aircraft simulations, as well as the construction of the sequence of grids required for multigrid.

VanderWijngaart, Rob F.↗

NASA NTRS1993

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics, part 2

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallellize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet and perhaps will never be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient than explicit codes when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗

NASA NTRS1973

NASTRAN postprocessor program for transient response to input accelerations

The description of a transient analysis program for computing structural responses to input base accelerations is presented. A hybrid modal formulation is used and a procedure is demonstrated for generating and writing all modal input data on user tapes via NASTRAN. Use of several new Level 15 modules is illustrated along with a problem associated with reading the postprocessor program input from a user tape. An example application of the program is presented for the analysis of a spacecraft subjected to accelerations initiated by thrust transients. Experience with the program has indicated it to be very efficient and economical because of its simplicity and small central memory storage requirements.

Wingate, R. T.↗

NASA NTRS1981

SAR processing on the MPP

The processing of synthetic aperture radar (SAR) signals using the massively parallel processor (MPP) is discussed. The fast Fourier transform convolution procedures employed in the algorithms are described. The MPP architecture comprises an array unit (ARU) which processes arrays of data; an array control unit which controls the operation of the ARU and performs scalar arithmetic; a program and data management unit which controls the flow of data; and a unique staging memory (SM) which buffers and permutes data. The ARU contains a 128 by 128 array of bit-serial processing elements (PE). Two-by-four surarrays of PE's are packaged in a custom VLSI HCMOS chip. The staging memory is a large multidimensional-access memory which buffers and permutes data flowing with the system. Efficient SAR processing is achieved via ARU communication paths and SM data manipulation. Real time processing capability can be realized via a multiple ARU, multiple SM configuration.

Batcher, K. E.↗