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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

User's guide to the Fault Inferring Nonlinear Detection System (FINDS) computer program

Described are the operation and internal structure of the computer program FINDS (Fault Inferring Nonlinear Detection System). The FINDS algorithm is designed to provide reliable estimates for aircraft position, velocity, attitude, and horizontal winds to be used for guidance and control laws in the presence of possible failures in the avionics sensors. The FINDS algorithm was developed with the use of a digital simulation of a commercial transport aircraft and tested with flight recorded data. The algorithm was then modified to meet the size constraints and real-time execution requirements on a flight computer. For the real-time operation, a multi-rate implementation of the FINDS algorithm has been partitioned to execute on a dual parallel processor configuration: one based on the translational dynamics and the other on the rotational kinematics. The report presents an overview of the FINDS algorithm, the implemented equations, the flow charts for the key subprograms, the input and output files, program variable indexing convention, subprogram descriptions, and the common block descriptions used in the program.

Caglayan, A. K.↗
NASA NTRS1991

Rectilinear partitioning of irregular data parallel computations

New mapping algorithms for domain oriented data-parallel computations, where the workload is distributed irregularly throughout the domain, but exhibits localized communication patterns are described. Researchers consider the problem of partitioning the domain for parallel processing in such a way that the workload on the most heavily loaded processor is minimized, subject to the constraint that the partition be perfectly rectilinear. Rectilinear partitions are useful on architectures that have a fast local mesh network. Discussed here is an improved algorithm for finding the optimal partitioning in one dimension, new algorithms for partitioning in two dimensions, and optimal partitioning in three dimensions. The application of these algorithms to real problems are discussed.

Nicol, David M.↗
NASA NTRS2003

Applications of Space-Filling-Curves to Cartesian Methods for CFD

The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.

Aftosmis, Michael J.↗
NASA NTRS2003

Applications of Space-Filling-Curves to Cartesian Methods for CFD

This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.

Aftosmis, M. J.↗
NASA NTRS1991

Fast, efficient lossless data compression

This paper presents lossless data compression and decompression algorithms which can be easily implemented in software. The algorithms can be partitioned into their fundamental parts which can be implemented at various stages within a data acquisition system. This allows for efficient integration of these functions into systems at the stage where they are most applicable. The algorithms were coded in Forth to run on a Silicon Composers Single Board Computer (SBC) using the Harris RTX2000 Forth processor. The algorithms require very few system resources and operate very fast. The performance of the algorithms with the RTX enables real time data compression and decompression to be implemented for a wide range of applications.

Ross, Douglas↗
NASA NTRS1987

A dual-processor multi-frequency implementation of the FINDS algorithm

This report presents a parallel processing implementation of the FINDS (Fault Inferring Nonlinear Detection System) algorithm on a dual processor configured target flight computer. First, a filter initialization scheme is presented which allows the no-fail filter (NFF) states to be initialized using the first iteration of the flight data. A modified failure isolation strategy, compatible with the new failure detection strategy reported earlier, is discussed and the performance of the new FDI algorithm is analyzed using flight recorded data from the NASA ATOPS B-737 aircraft in a Microwave Landing System (MLS) environment. The results show that low level MLS, IMU, and IAS sensor failures are detected and isolated instantaneously, while accelerometer and rate gyro failures continue to take comparatively longer to detect and isolate. The parallel implementation is accomplished by partitioning the FINDS algorithm into two parts: one based on the translational dynamics and the other based on the rotational kinematics. Finally, a multi-rate implementation of the algorithm is presented yielding significantly low execution times with acceptable estimation and FDI performance.

Godiwala, Pankaj M.↗
NASA NTRS1987

Performance studies of the multigrid algorithms implemented on hypercube multiprocessor systems

In this paper, we analyze and compare the performance on a hypercube multiprocessor of some of the major multigrid techniques used in practice. The model problem considered here is that of solving the 2-D incompressible Navier-Stokes equations representing the flow between two parallel plates. Results obtained by implementing the different multigrid schemes on an iPSC are presented. Effects on the overall performance of various parameters of the algorithms, of the partitioning strategies employed, and of some of the characteristics of the underlying architecture are discussed.

Naik, Vijay K.↗
NASA NTRS2006

Compressing Image Data While Limiting the Effects of Data Losses

ICER is computer software that can perform both lossless and lossy compression and decompression of gray-scale-image data using discrete wavelet transforms. Designed for primary use in transmitting scientific image data from distant spacecraft to Earth, ICER incorporates an error-containment scheme that limits the adverse effects of loss of data and is well suited to the data packets transmitted by deep-space probes. The error-containment scheme includes utilization of the algorithm described in "Partitioning a Gridded Rectangle Into Smaller Rectangles " (NPO-30479), NASA Tech Briefs, Vol. 28, No. 7 (July 2004), page 56. ICER has performed well in onboard compression of thousands of images transmitted from the Mars Exploration Rovers.

Kiely, Aaron↗
NASA NTRS1993

Experience with parametric binary dissection

Parametric Binary Dissection (PBD) is a new algorithm that can be used for partitioning graphs embedded in 2- or 3-dimensional space. It partitions explicitly on the basis of nodes + (lambda)x(edges cut), where lambda is the ratio of time to communicate over an edge to the time to compute at a node. The new algorithm is faster than the original binary dissection algorithm and attempts to obtain better partitions than the older algorithm, which only takes nodes into account. The performance of parametric dissection with plain binary dissection on 3 large unstructured 3-d meshes obtained from computational fluid dynamics and on 2 random graphs were compared. It was showm that the new algorithm can usually yield partitions that are substantially superior, but that its performance is heavily dependent on the input data.

Bokhari, Shahid H.↗
NASA NTRS1993

Parametric binary dissection

Binary dissection is widely used to partition non-uniform domains over parallel computers. This algorithm does not consider the perimeter, surface area, or aspect ratio of the regions being generated and can yield decompositions that have poor communication to computation ratio. Parametric Binary Dissection (PBD) is a new algorithm in which each cut is chosen to minimize load + lambda x(shape). In a 2 (or 3) dimensional problem, load is the amount of computation to be performed in a subregion and shape could refer to the perimeter (respectively surface) of that subregion. Shape is a measure of communication overhead and the parameter permits us to trade off load imbalance against communication overhead. When A is zero, the algorithm reduces to plain binary dissection. This algorithm can be used to partition graphs embedded in 2 or 3-d. Load is the number of nodes in a subregion, shape the number of edges that leave that subregion, and lambda the ratio of time to communicate over an edge to the time to compute at a node. An algorithm is presented that finds the depth d parametric dissection of an embedded graph with n vertices and e edges in O(max(n log n, de)) time, which is an improvement over the O(dn log n) time of plain binary dissection. Parallel versions of this algorithm are also presented; the best of these requires O((n/p) log(sup 3)p) time on a p processor hypercube, assuming graphs of bounded degree. How PBD is applied to 3-d unstructured meshes and yields partitions that are better than those obtained by plain dissection is described. Its application to the color image quantization problem is also discussed, in which samples in a high-resolution color space are mapped onto a lower resolution space in a way that minimizes the color error.

Bokhari, Shahid H.↗
NASA NTRS1977

An application of the square root information filter to large scale linear interconnected systems

It is demonstrated that use of the square root information filter (SRIF) can reduce the storage and computation required for estimation of certain classes of large-scale interconnected systems. The SRIF uses an information array that is related to the Kalman filter covariance and estimate. The SRIF algorithm, which is optimal, is a direct application of matrix partitioning to some optimal filtering algorithms described in the literature. The SRIF algorithm is able to reduce the storage requirements of a 40-subsystem 10-state problem by a full order of magnitude.

Bierman, G. J.↗
NASA NTRS1993

Multiphase complete exchange: A theoretical analysis

Complete Exchange requires each of N processors to send a unique message to each of the remaining N-1 processors. For a circuit switched hypercube with N = 2(sub d) processors, the Direct and Standard algorithms for Complete Exchange are optimal for very large and very small message sizes, respectively. For intermediate sizes, a hybrid Multiphase algorithm is better. This carries out Direct exchanges on a set of subcubes whose dimensions are a partition of the integer d. The best such algorithm for a given message size m could hitherto only be found by enumerating all partitions of d. The Multiphase algorithm is analyzed assuming a high performance communication network. It is proved that only algorithms corresponding to equipartitions of d (partitions in which the maximum and minimum elements differ by at most 1) can possibly be optimal. The run times of these algorithms plotted against m form a hull of optimality. It is proved that, although there is an exponential number of partitions, (1) the number of faces on this hull is Theta(square root of d), (2) the hull can be found in theta(square root of d) time, and (3) once it has been found, the optimal algorithm for any given m can be found in Theta(log d) time. These results provide a very fast technique for minimizing communication overhead in many important applications, such as matrix transpose, Fast Fourier transform, and ADI.

Bokhari, Shahid H.↗
NASA NTRSDate not supplied

Molecular dynamics simulation of effects of solutes on dislocation propagation in Ni-based superalloys

Ni-based superalloys are used in the hot sections of jet turbine engines because of their high strength, stability and resistance to oxidation. The properties of these alloys can be further optimized by adding alloying elements. Therefore, a fundamental knowledge on the effect of different elements on properties of Ni-based superalloys is required. Molecular dynamics simulation could shed light here but its application is hindered by the absence of reliable and computationally cheap semi-empirical potential of the interatomic interaction for 4 and more element alloys. We will present a new Ni-Al-Cr-Nb Finnis-Sinclair (FS) potential specially designed to simulate the dislocation propagation from to  phase. In order to construct this potential, we designed a special algorithm to incorporate the data on element partitioning in the potential development procedure. For example, it is known from experiment, that Cr is mostly present in the gamma phase. Figure 1 shows a snapshot obtained after equilibration of the model of the Ni68Al17Cr15 alloy at T=1000 K using the hybrid Monte-Carlo (MC)/molecular dynamics (MD) simulation with the developed semi-empirical potential. One can clearly see that the Cr partitioning is in agreement with the experimental data. We will discuss the developed algorithm to incorporate the solute partition data in details. Using the developed semi-empirical potential, we first investigated the effect of anti-site defects in the  phase on the single dislocation propagation. It was found that the dislocation velocity increases with the increasing of the anti-site defect concentration. This effect was attributed to smaller number of Al-Al pairs forming during the dislocation migration in the presence of the anti-site defects. Next, we investigated the effect of Nb on the dislocation pair propagation in the Kolbe mechanism. It was found that the addition of Nb leads to considerable decrease in the dislocation propagation rate. This is in agreement with the experimental data on the effect of Nb on the creep resistance of the Ni-based superalloys. We will discuss the origin of this effect.

Mikhail I. Mendelev↗
NASA NTRS1993

A new clustering algorithm applicable to multispectral and polarimetric SAR images

We describe an application of a scale-space clustering algorithm to the classification of a multispectral and polarimetric SAR image of an agricultural site. After the initial polarimetric and radiometric calibration and noise cancellation, we extracted a 12-dimensional feature vector for each pixel from the scattering matrix. The clustering algorithm was able to partition a set of unlabeled feature vectors from 13 selected sites, each site corresponding to a distinct crop, into 13 clusters without any supervision. The cluster parameters were then used to classify the whole image. The classification map is much less noisy and more accurate than those obtained by hierarchical rules. Starting with every point as a cluster, the algorithm works by melting the system to produce a tree of clusters in the scale space. It can cluster data in any multidimensional space and is insensitive to variability in cluster densities, sizes and ellipsoidal shapes. This algorithm, more powerful than existing ones, may be useful for remote sensing for land use.

Wong, Yiu-Fai↗
NASA NTRS2010

Multiscale Simulations of Magnetic Island Coalescence

We describe a new interactive parallel Adaptive Mesh Refinement (AMR) framework written in the Python programming language. This new framework, PyAMR, hides the details of parallel AMR data structures and algorithms (e.g., domain decomposition, grid partition, and inter-process communication), allowing the user to focus on the development of algorithms for advancing the solution of a systems of partial differential equations on a single uniform mesh. We demonstrate the use of PyAMR by simulating the pairwise coalescence of magnetic islands using the resistive Hall MHD equations. Techniques for coupling different physics models on different levels of the AMR grid hierarchy are discussed.

Dorelli, John C.↗
NASA NTRS2019

Partition-based Feasible Integer Solution Pre-computation for Hybrid Model Predictive Control

For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a static map from the current parameter to a suboptimal integer solution such that the remaining convex program is feasible. Convergence is proved with a new insight that the overlap among the feasible parameter sets of each integer solution governs the partition complexity. The partition is stored as a tree which makes querying the feasible solution efficient. The algorithm can be used to warm start a mixed integer solver with a real-time guarantee or to provide a reference integer solution in several suboptimal MPC schemes. The algorithm is tested on randomly generated systems with up to six states, demonstrating the effectiveness of the approach.

Bayard, David S.↗
NASA NTRS1997

An Adaptive Flow Solver for Air-Borne Vehicles Undergoing Time-Dependent Motions/Deformations

This report describes a concurrent Euler flow solver for flows around complex 3-D bodies. The solver is based on a cell-centered finite volume methodology on 3-D unstructured tetrahedral grids. In this algorithm, spatial discretization for the inviscid convective term is accomplished using an upwind scheme. A localized reconstruction is done for flow variables which is second order accurate. Evolution in time is accomplished using an explicit three-stage Runge-Kutta method which has second order temporal accuracy. This is adapted for concurrent execution using another proven methodology based on concurrent graph abstraction. This solver operates on heterogeneous network architectures. These architectures may include a broad variety of UNIX workstations and PCs running Windows NT, symmetric multiprocessors and distributed-memory multi-computers. The unstructured grid is generated using commercial grid generation tools. The grid is automatically partitioned using a concurrent algorithm based on heat diffusion. This results in memory requirements that are inversely proportional to the number of processors. The solver uses automatic granularity control and resource management techniques both to balance load and communication requirements, and deal with differing memory constraints. These ideas are again based on heat diffusion. Results are subsequently combined for visualization and analysis using commercial CFD tools. Flow simulation results are demonstrated for a constant section wing at subsonic, transonic, and a supersonic case. These results are compared with experimental data and numerical results of other researchers. Performance results are under way for a variety of network topologies.

Singh, Jatinder↗