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NASA NTRS1990

Non-oscillatory central differencing for hyperbolic conservation laws

Many of the recently developed high resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block for these schemes is the averaging of an appropriate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the direction of the wind. Instead, the use of the more robust Lax-Friedrichs (LxF) solver is proposed. The main advantage is simplicity: no Riemann problems are solved and hence field-by-field decompositions are avoided. The main disadvantage is the excessive numerical viscosity typical to the LxF solver. This is compensated for by using high-resolution MUSCL-type interpolants. Numerical experiments show that the quality of results obtained by such convenient central differencing is comparable with those of the upwind schemes.

Nessyahu, Haim↗

NASA NTRS1986

Multi-color incomplete Cholesky conjugate gradient methods for vector computers

In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems.

Poole, E. L.↗

NASA NTRS1993

Efficient partitioning and assignment on programs for multiprocessor execution

The general problem studied is that of segmenting or partitioning programs for distribution across a multiprocessor system. Efficient partitioning and the assignment of program elements are of great importance since the time consumed in this overhead activity may easily dominate the computation, effectively eliminating any gains made by the use of the parallelism. In this study, the partitioning of sequentially structured programs (written in FORTRAN) is evaluated. Heuristics, developed for similar applications are examined. Finally, a model for queueing networks with finite queues is developed which may be used to analyze multiprocessor system architectures with a shared memory approach to the problem of partitioning. The properties of sequentially written programs form obstacles to large scale (at the procedure or subroutine level) parallelization. Data dependencies of even the minutest nature, reflecting the sequential development of the program, severely limit parallelism. The design of heuristic algorithms is tied to the experience gained in the parallel splitting. Parallelism obtained through the physical separation of data has seen some success, especially at the data element level. Data parallelism on a grander scale requires models that accurately reflect the effects of blocking caused by finite queues. A model for the approximation of the performance of finite queueing networks is developed. This model makes use of the decomposition approach combined with the efficiency of product form solutions.

Standley, Hilda M.↗

NASA NTRS1987

Catalytic Layer Makes Aircraft Seats More Fire Retardant

Specially constructed cushion retards fires in aircraft seats through action of catalytic matrix that cracks flammable gaseous decomposition products to less flammable species. Improved cushion contributes substantially to fire safety without adding significantly to weight or to manufacturing cost. In this fire-blocking covering for an aircraft seat cushion, flammable pyrolysis products cracked to less flammable species by catalytic layer covering foam core of cushion. Aluminum foil holds in pyrolysis vapors to promote catalysis and prevent spread of fire by ignition of released vapors.

Parker, John A.↗

NASA NTRS1998

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

A code trellis is a graphical representation of a code, block or convolutional, in which every path represents a codeword (or a code sequence for a convolutional code). This representation makes it possible to implement Maximum Likelihood Decoding (MLD) of a code with reduced decoding complexity. The most well known trellis-based MLD algorithm is the Viterbi algorithm. The trellis representation was first introduced and used for convolutional codes [23]. This representation, together with the Viterbi decoding algorithm, has resulted in a wide range of applications of convolutional codes for error control in digital communications over the last two decades. There are two major reasons for this inactive period of research in this area. First, most coding theorists at that time believed that block codes did not have simple trellis structure like convolutional codes and maximum likelihood decoding of linear block codes using the Viterbi algorithm was practically impossible, except for very short block codes. Second, since almost all of the linear block codes are constructed algebraically or based on finite geometries, it was the belief of many coding theorists that algebraic decoding was the only way to decode these codes. These two reasons seriously hindered the development of efficient soft-decision decoding methods for linear block codes and their applications to error control in digital communications. This led to a general belief that block codes are inferior to convolutional codes and hence, that they were not useful. Chapter 2 gives a brief review of linear block codes. The goal is to provide the essential background material for the development of trellis structure and trellis-based decoding algorithms for linear block codes in the later chapters. Chapters 3 through 6 present the fundamental concepts, finite-state machine model, state space formulation, basic structural properties, state labeling, construction procedures, complexity, minimality, and sectionalization of trellises. Chapter 7 discusses trellis decomposition and subtrellises for low-weight codewords. Chapter 8 first presents well known methods for constructing long powerful codes from short component codes or component codes of smaller dimensions, and then provides methods for constructing their trellises which include Shannon and Cartesian product techniques. Chapter 9 deals with convolutional codes, puncturing, zero-tail termination and tail-biting.Chapters 10 through 13 present various trellis-based decoding algorithms, old and new. Chapter 10 first discusses the application of the well known Viterbi decoding algorithm to linear block codes, optimum sectionalization of a code trellis to minimize computation complexity, and design issues for IC (integrated circuit) implementation of a Viterbi decoder. Then it presents a new decoding algorithm for convolutional codes, named Differential Trellis Decoding (DTD) algorithm. Chapter 12 presents a suboptimum reliability-based iterative decoding algorithm with a low-weight trellis search for the most likely codeword. This decoding algorithm provides a good trade-off between error performance and decoding complexity. All the decoding algorithms presented in Chapters 10 through 12 are devised to minimize word error probability. Chapter 13 presents decoding algorithms that minimize bit error probability and provide the corresponding soft (reliability) information at the output of the decoder. Decoding algorithms presented are the MAP (maximum a posteriori probability) decoding algorithm and the Soft-Output Viterbi Algorithm (SOVA) algorithm. Finally, the minimization of bit error probability in trellis-based MLD is discussed.

Lin, Shu↗

NASA NTRS1990

Reliable and Efficient Parallel Processing Algorithms and Architectures for Modern Signal Processing

Least-squares (LS) estimations and spectral decomposition algorithms constitute the heart of modern signal processing and communication problems. Implementations of recursive LS and spectral decomposition algorithms onto parallel processing architectures such as systolic arrays with efficient fault-tolerant schemes are the major concerns of this dissertation. There are four major results in this dissertation. First, we propose the systolic block Householder transformation with application to the recursive least-squares minimization. It is successfully implemented on a systolic array with a two-level pipelined implementation at the vector level as well as at the word level. Second, a real-time algorithm-based concurrent error detection scheme based on the residual method is proposed for the QRD RLS systolic array. The fault diagnosis, order degraded reconfiguration, and performance analysis are also considered. Third, the dynamic range, stability, error detection capability under finite-precision implementation, order degraded performance, and residual estimation under faulty situations for the QRD RLS systolic array are studied in details. Finally, we propose the use of multi-phase systolic algorithms for spectral decomposition based on the QR algorithm. Two systolic architectures, one based on triangular array and another based on rectangular array, are presented for the multiphase operations with fault-tolerant considerations. Eigenvectors and singular vectors can be easily obtained by using the multi-pase operations. Performance issues are also considered.

Liu, Kuojuey Ray↗

NASA NTRSDate not supplied

Aeroacoustic Analysis using Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements

In this paper, we present a new method for the diagnosis and analysis of aeroacoustic phenomena. Taking advantage of the well-known property that the measurements of the Unsteady Pressure-Sensitive Paint (uPSP) have much higher spatial resolution compared to those of the conventional pressure transducers, the method is based on the visualization and analysis of the outputs of the Dynamic Mode Decomposition (DMD) of the uPSP measurements. The uPSP measurements were collected with four Phantom high-speed cameras in the Ascent Transient Aerodynamics Test (ATAT) of the Space Launch System (SLS) Block 1 cargo vehicle in the 11-by-11-foot transonic test section of the Unitary Plan Wind Tunnel (UPWT) at NASA Ames Research Center in September 2019. The method presented in this paper is demonstrated by investigating an interesting phenomenon observed in the SLS ATAT – the vortex shedding tone generated by the forward attachment of the Solid Rocket Booster (SRB). As examples, the DMD outputs of the uPSP measurements in a subsonic test in the SLS ATAT are presented. It is shown the information retrieved from the DMD outputs of the uPSP measurements can be effectively used in the identification and diagnosis of the aeroacoustic phenomena. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding was provided by the NASA Aerosciences Evaluation and Test Capabilities Portfolio Office.

acoustics↗

NASA NTRSDate not supplied

Aeroacoustic Analysis using Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements

acoustics↗

DOE OSTI2025

A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems

This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2004

Making Carbon-Nanotube Arrays Using Block Copolymers: Part 2

Some changes have been incorporated into a proposed method of manufacturing regular arrays of precisely sized, shaped, positioned, and oriented carbon nanotubes. Such arrays could be useful as mechanical resonators for signal filters and oscillators, and as electrophoretic filters for use in biochemical assays. A prior version of the method was described in Block Copolymers as Templates for Arrays of Carbon Nanotubes, (NPO-30240), NASA Tech Briefs, Vol. 27, No. 4 (April 2003), page 56. To recapitulate from that article: As in other previously reported methods, carbon nanotubes would be formed by decomposition of carbon-containing gases over nanometer-sized catalytic metal particles that had been deposited on suitable substrates. Unlike in other previously reported methods, the catalytic metal particles would not be so randomly and densely distributed as to give rise to thick, irregular mats of nanotubes with a variety of lengths, diameters, and orientations. Instead, in order to obtain regular arrays of spaced-apart carbon nanotubes as nearly identical as possible, the catalytic metal particles would be formed in predetermined regular patterns with precise spacings. The regularity of the arrays would be ensured by the use of nanostructured templates made of block copolymers.

Bronikowski, Michael↗

NASA NTRS2021

Fast Near-Optimal Heterogeneous Task Allocation via Flow Decomposition

Multi-robot systems are uniquely well-suited to perform complex tasks such as patrolling and tracking, infor- mation gathering, and pick-up and delivery problems, offering significantly higher performance than single-robot systems. A fundamental building block in most multi-robot systems is dynamic task allocation: assigning robots to tasks (e.g., patrolling an area, or servicing a transportation request) as they appear based on the robots’ states to maximize reward. In many practical situations, the allocation must account for potentially heteroge- neous capabilities (e.g., availability of appropriate sensors or actuators) to ensure the feasibility of execution, and exploit predictive information concerning the likelihood of future tasks to promote a higher reward over a long time horizon. To this end, we present an efficient algorithm for predictive heterogeneous task- allocation achieving an approximation factor of at least 1/2 of the optimal reward. Our approach demonstrates that the problem can be decomposed into several homogeneous subproblems that can be solved efficiently using min-cost flow. Through simulation experiments, we show that our algorithm is faster by several orders of magnitude than a MILP-based approach.

Pavone, Marco↗

DOE OSTI2025

Classical Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics

In quantum dynamics, symmetries are vital for identifying and assessing conserved quantities that govern the evolution of a quantum system. When promoted to the open quantum system setting, dynamical symmetries can be negatively altered by system-environment interactions, thus, complicating their analysis. Previous work on noisy symmetric quantum dynamics has focused on the Markovian setting, despite the ubiquity of non-Markovian noise in a number of widely used quantum technologies. Here, in this Letter, we develop a framework for quantifying the impact of non-Markovian noise on symmetric quantum evolution via root space decompositions and the filter function formalism. We demonstrate analytically that symmetry-preserving noise maintains the symmetric subspace, while nonsymmetric noise leads to highly specific leakage errors that are block diagonal in the symmetry representation. We support our findings with numerical studies of a transverse-field Ising model and a quantum error detecting code subject to spatiotemporally correlated multiaxis noise. Our results are broadly applicable, providing new analytic insights into the control and characterization of open quantum system dynamics.

decoherence↗

NASA NTRS1975

Hypermatrix scheme for finite element systems on CDC STAR-100 computer

A study is made of the adaptation of the hypermatrix (block matrix) scheme for solving large systems of finite element equations to the CDC STAR-100 computer. Discussion is focused on the organization of the hypermatrix computation using Cholesky decomposition and the mode of storage of the different submatrices to take advantage of the STAR pipeline (streaming) capability. Consideration is also given to the associated data handling problems and the means of balancing the I/Q and cpu times in the solution process. Numerical examples are presented showing anticipated gain in cpu speed over the CDC 6600 to be obtained by using the proposed algorithms on the STAR computer.

Noor, A. K.↗

NASA NTRS1984

Hydrolytic properties of phenylalanyl- and N-acetylphenylalanyl adenylate anhydrides

The hydrolysis of phenylalynyl- and N-acetylephenylalanyl adenylate anhydrides (AcPhe-AMP) is studied experimentally using a new spectrophotometric method. The hydrolysis process was analyzed at low concentrations (0.0001 M), constant temperature of 25 C, constant buffer concentration (0.05 M), and as a function of pH. It is found that while Phe-AMP is susceptible to attack by OH(-), AcPhe-AMP is susceptible to acid decomposition as well. At a pH of 4 to 8, Phe-AMP hydolyzes faster than AcPhe-AMP, but at pH less than four or greater than eight, the blocked form hydrolyzes faster. Both forms are attacked by H2O at the same rate. The rate laws for the various hydrolytic mechanisms and the activation energies for the hydrolyses at pH 7.1 are given in a table, and the possible relevance of the findings to the origin and evolution of the process of protein synthesis is discussed.

Lacey, J. C., Jr.↗

DOE OSTI2024

Progressive Hedging Decomposition for Solutions of Large-Scale Process Family Design Problems

Rapid, wide-scale deployment of green process systems, such as carbon capture or water desalination systems, is essential for combatting climate change. Methods relying on traditional design or modularity fail to capture the benefits of both economies of numbers and economies of scale. We have proposed process family design, which designs a family of processes simultaneously exploiting opportunities for common elements. In previous work, we explored different optimization formulations to solve this problem. In this work, we develop a decomposition approach to tackle larger problems efficiently. We solve a water desalination case study, which is too large to solve within a reasonable timeframe with the discretization formulation. We exploit the block angular structure of the discretization problem to decompose and solve using Progressive Hedging (PH). We use the open-source Python package mpi-sppy to execute PH which allows us to leverage parallelization and a HPC cluster to further improve solution time.

Stinchfield, Georgia↗

DOE OSTI2025

Personalized Tucker Decomposition: Modeling Commonality and Peculiarity on Tensor Data

In this paper, we propose a personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global components and personalized local components. We introduce an order orthogonality assumption and develop a proximal gradient regularized block coordinate descent algorithm guaranteed to converge to a stationary point. The unique and common representations learned by perTucker reveal intrinsic statistical patterns in data and provide valuable information for a wide range of downstream analytics, including anomaly detection, source classification, and clustering. We demonstrate perTucker’s effectiveness through a simulation study and two case studies on solar flare detection and tonnage signal classification.

14 SOLAR ENERGY↗

NASA NTRS1993

Canonical forms of multidimensional steady inviscid flows

Canonical forms and canonical variables for inviscid flow problems are derived. In these forms the components of the system governed by different types of operators (elliptic and hyperbolic) are separated. Both the incompressible and compressible cases are analyzed, and their similarities and differences are discussed. The canonical forms obtained are block upper triangular operator form in which the elliptic and non-elliptic parts reside in different blocks. The full nonlinear equations are treated without using any linearization process. This form enables a better analysis of the equations as well as better numerical treatment. These forms are the analog of the decomposition of the one dimensional Euler equations into characteristic directions and Riemann invariants.

Taasan, Shlomo↗

NASA NTRS1990

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

Janus, J. Mark↗