On a programming language for graph algorithms
Computer language for implementation of graphic theoretical algorithms
Basili, V. R.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Advances in Structure Prediction of Lanthanides and Actinides with Genetic Algorithms
Computationally guided materials discovery has advanced significantly in the past two decades. Recent developments of widely available genetic algorithm-based structure prediction software in the past 10+ years has led to increased use of this methodology in the discovery and design of new materials. Owing to the computational challenges of treating f-block elements and computationally expensive methods for structure prediction, the discovery of new phases of lanthanide and actinide materials has been particularly challenging. With advancements in the development of genetic algorithms for structure prediction and the continuing improvement of high-performance computing resources, genetic algorithms provide a tractable method to find new stable phases of materials at high pressure or to search a large phase space for unknown compounds. Genetic algorithms have already been applied to the successful identification of novel lanthanide and actinide materials, as well as the prediction of unusual material properties in new phases that make promising synthetic targets.
Shields, Ashley↗
Matrix-based, finite-difference algorithms for computational acoustics
A compact numerical algorithm is introduced for simulating multidimensional acoustic waves. The algorithm is expressed in terms of a set of matrix coefficients on a three-point spatial grid that approximates the acoustic wave equation with a discretization error of O(h exp 5). The method is based on tracking a local phase variable and its implementation suggests a convenient coordinate splitting along with natural intermediate boundary conditions. Results are presented for oblique plane waves and compared with other procedures. Preliminary computations of acoustic diffraction are also considered.
Davis, Sanford↗
Computationally efficient algorithm for the dynamics of multi-link mechanisms
A computationally efficient algorithm for the dynamics of multi-rigid-link mechanisms is presented which is applicable to on-board processing for robotic manipulator control systems. A formulation of the equations of motion for such systems is presented which results in a solution algorithm of the order the number of system degrees of freedom. The formulation is presented for tree topology systems, where the chain topology of typical manipulators is a subset. Comparison of this algorithm is made with existing multibody simulation programs to illustrate the increased computational efficiency.
Singh, R. P.↗
An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids
An implicit, Navier-Stokes solution algorithm is presented for the computation of turbulent flow on unstructured grids. The inviscid fluxes are computed using an upwind algorithm and the solution is advanced in time using a backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with a point-implicit relaxation scheme. This methodology provides a viable and robust algorithm for computing turbulent flows on unstructured meshes. Results are shown for subsonic flow over a NACA 0012 airfoil and for transonic flow over a RAE 2822 airfoil exhibiting a strong upper-surface shock. In addition, results are shown for 3 element and 4 element airfoil configurations. For the calculations, two one equation turbulence models are utilized. For the NACA 0012 airfoil, a pressure distribution and force data are compared with other computational results as well as with experiment. Comparisons of computed pressure distributions and velocity profiles with experimental data are shown for the RAE airfoil and for the 3 element configuration. For the 4 element case, comparisons of surface pressure distributions with experiment are made. In general, the agreement between the computations and the experiment is good.
Anerson, W. Kyle↗
Faster Algorithm For Computation Of Incompressible Flow
Improved algorithm yields faster numerical solutions of Navier-Stokes equations of steady or unsteady three-dimensional flow of incompressible fluid. In artificial-compressibility method, unsteady flow treated as incompressible in advancing from one time step to next, but at each time step (or in steady state), fluid treated as having variable compressibility enabling propagation of flow field, and subiterations performed in increments of pseudotime until effects of compressibility subside. Directly couples pressure and velocity fields at same time step and converts elliptic incompressible Navier-Stokes equations to hyperbolic form more amenable to numerical integration.
Rogers, S. E.↗
Fast algorithm for computing complex number-theoretic transforms
A high-radix FFT algorithm for computing transforms over FFT, where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional FFT.
Reed, I. S.↗
A test of a modified algorithm for computing spherical harmonic coefficients using an FFT
The Dilts (1985) algorithm for computing the spherical harmonic expansion coefficients for a function on a sphere, on the basis of a two-dimensional FFT, is presently modified, tested, and found to eliminate problems of overflow and large storage requirements associated with the encounter of harmonic degree values greater than 16. Results from timing tests show the Dilts program to be impractical, however, for the computation of spherical harmonic expansion coefficients for large harmonic degree values.
Elowitz, Mark↗
Addendum to 'A new hybrid algorithm for computing a fast discrete Fourier transform'
The reported investigation represents a continuation of a study conducted by Reed and Truong (1979), who proposed a hybrid algorithm for computing the discrete Fourier transform (DFT). The proposed technique employs a Winograd-type algorithm in conjunction with the Mersenne prime-number theoretic transform to perform a DFT. The implementation of the technique involves a considerable number of additions. The new investigation shows an approach which can reduce the number of additions significantly. It is proposed to use Winograd's algorithm for computing the Mersenne prime-number theoretic transform in the transform portion of the hybrid algorithm.
Reed, I. S.↗
Euler-Rodrigues Parameters: A Quantum Circuit to Calculate Rigid-Body Rotations
The use of vectorial parameterization to create geometrical representations in computational models has a large number of applications. One particular application is the calculation of the 3D rotational motion of rigid bodies, that could be used for the spatial location estimation from objects. Provided the algebraic nature of this problem, it could benefit from Quantum Computing, in particular several vectors could be superposed to be transformed with a single operation, providing a quantum processing advantage. In this article, we propose an implementation of a Quantum Computing algorithm to compute Euler-Rodrigues Parameters to model rigid body rotations to transform arbitrary functions, rotating multiple vectors in superposition. We developed this algorithm using Qiskit, taking into account the limitations imposed by the current Noisy Intermediate Scale Quantum (NISQ) devices, such as the reduced number of qubits available and the limited coherence time.
Pelaez, Emilio↗
A greedy algorithm for computing eigenvalues of a symmetric matrix with localized eigenvectors
Here, we present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy manner, and obtains approximations to the desired eigenpairs of $H$ by computing eigenpairs of a submatrix extracted from the corresponding rows and columns of $H$. Even when the eigenvector is not completely localized, the approximate eigenvectors obtained by the greedy algorithm can be used as good starting guesses to accelerate the convergence of an iterative eigensolver applied to $H$. We discuss a few possibilities for selecting important rows and columns of $H$ and techniques for constructing good initial guesses for an iterative eigensolver using the approximate eigenvectors returned from the greedy algorithm. We demonstrate the effectiveness of this approach with examples from nuclear quantum many-body calculations and many-body localization studies of quantum spin chains.
97 MATHEMATICS AND COMPUTING↗
NASA and Blue Origin Collaborative Assessment of Precision Landing Algorithms and Computing
NASA’s Safe and Precise Landing Integrated Capabilities Evolution (SPLICE) project is developing sensor, algorithm, and compute technologies for precision landing and hazard avoidance. These technologies are being tested as an integrated Precision Landing and Hazard Avoidance (PL&HA) system on Blue Origin’s New Shephard suborbital vehicle. A key goal for the computing element of this technology development is to characterize the performance of the SPLICE software workloads on the project’s Descent and Landing Computer (DLC). The DLC is a multi-core processor designed as a surrogate for NASA’s High-Performance Space Computer (HPSC). Measurements of the SPLICE workload performance on the DLC provides NASA insight on how PL&HA capabilities will perform on the HPSC, and guidance on how the SPLICE algorithms can be implemented to best utilize the DLC platform. This insight can also be used to derive requirements to guide trade studies on candidate computing architectures, for use on platforms like Blue Moon. NASA and Blue Origin are collaborating under an agreement to pursue this mutual benefit. Performance metrics collected are based on measurement of common compute resources such as percentage used of memory bandwidth, I/O utilization, interrupt latency, and kernel vs. user space code residency. Where possible existing performance counters and metrics that are part of the operating system kernel are used. As the design has a significant FPGA component, performance counters are identified and instantiated in the fabric to measure DMA performance and interface metrics. Collection of metrics is performed on the DLC with a representative workload that simulates a full landing cycle of the Blue Origin New Shepard vehicle. Consideration is given to the other compute implementations and whether they can run SPLICE algorithms at the same rate and with the same latency as the DLC. One option being considered is the use of a RISC-V soft core instantiated in a radiation resilient FPGA fabric such as the Xilinx KU60. Select algorithms from the SPLICE code will be run for comparison with the DLC. This paper describes how the DLC is instrumented to collect performance measurements of the SPLICE workloads, preliminary results from these measurements, and their implications on SPLICE algorithm implementation. The results of experimentation to derive candidate requirements for architecture trades on a PL&HA computing system are also presented.
computer performance↗
A computational approach to complex junctions and interfaces
Molecular- and nano- junctions, surfaces, interfaces, and interfacial processes have been the subjects of this DOE supported program for about 20 years. We have investigated electronic and magnetic structure, spin-dependent charge transport, and emerging phenomena at surfaces and interfaces in a number of physical systems ranging from nano-clusters, to nanowires, to two-dimensional (2D) crystals and their interactions, to bulk matter. Eighty-four refereed papers were published [1-84], with a majority effort from the group led by the PI, and over a hundred presentations were made at international conferences. We use first-principles methods in the framework of density functional theory in conjunction with nano-equilibrium Green function techniques, semi-empirical Boltzmann transport theory, tight-binding models, and the Hubbard model and many-body wavefunction approaches. In pursuing our scientific goals, we have also developed a number of computational algorithms and computational packages.
2D materials↗
An algorithm for real-time computer control of a tracking system with a nonlinearity
Real time computer algorithm for achieving optimal position of tracking antenna with nonlinear control system
Tabak, D.↗
On the inherent intractability of finding good codes
The problem of computing the minimum distance of an arbitrary binary linear code is non-polynomial complete. This strongly suggests, but does not imply, that it is impossible to design a computer algorithm for computing the minimum distance of an arbitrary code whose running time is bounded by a polynomial in the number of inputs.
Mceliece, R. J.↗
Inertial attitude determination for a dual-spin planetary spacecraft
Design and performance evaluations of an onboard inertial attitude determination system for a dual-spin planetary spacecraft are presented. A quaternion integration algorithm and a rate estimator sequentially determine the scan platform's inertial attitude and rate from the drift and misalignment compensated gyro outputs. A least-squares estimator algorithm processes the star transit data from a rotor-mounted star scanner, and provides periodic updates of the scan platform's attitude as a means of correcting the drift of the quaternion integration algorithm. Computer simulated algorithm performance in the presence of nutation and sensor noise are presented.
Wong, E. C.↗
Field lines and magnetic surfaces in a two-component slab/2D model of interplanetary magnetic fluctuations
A two-component model for the spectrum of interplanetary magnetic fluctuations was proposed on the basis of ISEE observations, and has found an intriguing level of application in other solar wind studies. The model fluctuations consist of a fraction of 'slab' fluctuations, varying only in the direction parallel to the locally uniform mean magnetic field B(0) and a complement of 2D (two-dimensional) fluctuations that vary in the directions transverse to B(0). We have developed an spectral method computational algorithm for computing the magnetic flux surfaces (flux tubes) associated with the composite model, based upon a precise analogy with equations for ideal transport of a passive scalar in planar two dimensional geometry. Visualization of various composite models will be presented, including the 80 percent 2D/ 20 percent slab model with delta B/B(0) approximately equals 1 and a minus 5/3 spectral law, that is thought to approximately represent a snapshot of solar wind turbulence. Characteristically, the visualizations show that flux tubes, even when defined as regular on some plane, shred and disperse rapidly as they are viewed along the parallel direction. This diffusive process, which generalizes the standard picture of field line random walk, will be discussed in detail. Evidently, the traditional picture that flux tubes randomize like strands of spaghetti with a uniform tangle along the axial direction is in need of modification.
Matthaeus, W. H.↗
A Computational Fluid Dynamics Algorithm on a Massively Parallel Computer
The discipline of computational fluid dynamics is demanding ever-increasing computational power to deal with complex fluid flow problems. We investigate the performance of a finite-difference computational fluid dynamics algorithm on a massively parallel computer, the Connection Machine. Of special interest is an implicit time-stepping algorithm; to obtain maximum performance from the Connection Machine, it is necessary to use a nonstandard algorithm to solve the linear systems that arise in the implicit algorithm. We find that the Connection Machine ran achieve very high computation rates on both explicit and implicit algorithms. The performance of the Connection Machine puts it in the same class as today's most powerful conventional supercomputers.
Jespersen, Dennis C.↗