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At least 1,099 records · Page 61

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NASA NTRS1984

Algorithms for solving large sparse systems of simultaneous linear equations on vector processors

Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.

David, R. E.↗

NASA NTRS1992

An unsymmetric Lanczos algorithm for damped structural dynamics systems

A one-sided, unsymmetric block Lanczos algorithm is proposed for the model reduction of structural dynamics systems with unsymmetric damping and/or stiffness matrices. The algorithm is a three-term iteration scheme, which transforms the system matrix into an almost skew-symmetric, block-tridiagonal form. The Lanczos reduced-order model is guaranteed to be stable if the full-order system is stable. For unstable systems, a shifting method is available. Also, the algorithm offers flexibility in the choice of starting vectors and thus can yield more accurate reduced-order models. A linear system example and a plane truss structure example are used to show the efficacy of the proposed method.

Su, Tzu-Jeng↗

NASA NTRS1988

Domain decomposition methods for the parallel computation of reacting flows

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

Keyes, David E.↗

DOE OSTI2012

Axisymmetric boundary integral formulation for a two fluid system

A 3D axisymmetric Galerkin boundary integral formulation for modeling the motion of one inviscid fluid enclosed inside another is described. The interface variables are the velocity potential and the normal velocity, and they can be solved for separately, the second linear system being symmetric. The algorithm is validated by comparing with the analytic solutions for a static interior spherical drop, over a range of values for the relative densities D=rho_E/rho_I of exterior and interior fluids, and various boundary conditions. For time dependent simulations utilizing a Level Set method for the interface tracking, the accuracy has been checked by comparing against the known oscillation frequency of the sphere. Pinch-off profiles corresponding to an initial two lobe geometry drop and D=6 are also presented.

42 ENGINEERING↗

DOE OSTI2021

Climatology of Linear Mesoscale Convective System Morphology in the United States based on Random Forests Method

This study uses machine learning methods, specifically the random forest (RF), on a radar-based mesoscale convective system (MCS) tracking dataset to classify the five types of linear MCS morphology in the contiguous United States during the period 2004-2016. The algorithm is trained using radar- and satellite-derived spatial and morphological parameters, and reanalysis environmental information from 5-26yr manually identified nonlinear and five linear MCS modes. The algorithm is then used to automate the classification of linear MCSs over 8 years with high accuracy, providing a systematic, long-term climatology of linear MCSs. Results reveal that nearly 40% of MCSs are classified as linear MCSs, in which half of the linear events belong to the type of system having a leading convective line. The occurrence of linear MCSs shows large annual and seasonal variations. On average, 113 linear MCSs occur annually during the warm season (through March to October), with most of these events clustered from May through August in the central eastern Great Plains. MCS characteristics, including duration, propagation speed, orientation, and system cloud size, have large variability among the different linear modes. The systems having a trailing convective line and the systems having a back-building area of convection typically move more slowly and have higher precipitation rate, and thus have higher potential in producing extreme rainfall and flash flooding. Analysis of the environmental conditions associated with linear MCSs show that the storm-relative flow is of most importance in determining the organization mode of linear MCSs.

Cui, Wenjun↗

DOE OSTI2017

A Full-Height Axial P 3 Solver for the 2D/1D Method in MPACT

This report encompasses the efforts to complete L3:RTM.PRT.P15.04, which relates to improvements to the axial solvers in MPACT. Over the past few years, a number of convergence issues have been encountered throughout the 2D/1D calculation. While many of these were related to transport-corrected stability, which has been much improved through the development of multigroup MOC kernels, there are still some instabilities that are more directly related to the 1D axial nodal solvers. The primary focus of this milestone is on the development of a full-height P 3 solver, which solves for a single linear system for the entire rod, compared to the one- and two-node solvers previously available in MPACT. To provide an efficient full-height solver, the SuperLU direct linear solver was leveraged and an alternative rod decomposition scheme is used in favor over the typically employed axial decomposition. In addition to the full-height solver, a number of stability observations are discussed pertaining to (1) cases with thin planes in the axial reflectors, (2) quadratic radial leakage interpolation, (3) the reset sol capability, which reinitializes the solution before continuing the calculation, and (4) the flux threshold used in the radial transverse leakage splitting logic. The last of these was improved by identifying an acceptable threshold, which greatly help provide stability to the default one-node P 3 solver approach. Results demonstrating the full-height solver are presented for (1) a single assembly case from the AP1000 reactor design, (2) VERA Progression Problem 5a, and (3) a Watts Bar Unit 1, Cycle 1 case that demonstrated convergence issues due to thin planes in the axial reflector. In total, the full-height solver appears to be 3–5× slower for the nodal solve time, yield a roughly 10–20% increase in total problem run time, and requires ~5% more memory. However, these increases may be justifiable if the solver is proven to be more stable than the current default. Additionally, the VERA Progression Problem 4a case with the 252-group library is shown for the one-node P 3 solver with the updated threshold for radial transverse leakage splitting. This case also previous failed very early in the calculation, but is now able to run to completion. Brief details are also included related to the refactoring the nodal sweeper design. Previously, all nodal sweeper options were available in one large module, which was cumbersome and difficult to extend. Before the work here began, the design was refactored to include a number of abstract and extended types, which will help make future extensions easier. All-in-all, this milestone successfully implemented a new axial solver and improved the stability of the current default axial solver. However, additional testing will be necessary on new cases that demonstrate convergence issues before a decision can be made to change the current default in MPACT.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1974

Multilevel control optimization using subsystem relative performance index sensitivity

A method is presented for the design of optimal feedback controllers for large multivariable systems with subsystem sensitivity constraints. The weighted sum of subsystem and/or operational mode relative performance index sensitivities is defined as the overall performance index. The method is developed for linear systems with quadratic performance criteria and either full or partial state feedback. An example concerning the design of a stability augmentation system for a VTOL aircraft in the transition mode demonstrates the effectiveness of the design method.

Leininger, G. G.↗

DOE OSTI2021

Porting hypre to heterogeneous computer architectures: Strategies and experiences

We report that linear systems are occurring in many applications, and solving them can take a large amount of the total simulation time. The high performance library hypre provides a variety of interfaces and linear solvers, including various multigrid methods, that have achieved good scalability on a variety of homogeneous parallel computer architectures. Heterogeneous architectures with nodes that have both CPUs and accelerators provide new challenges, since they require more fine-grained parallelism and reduced data movement between different memories on a single node as well as across nodes. We will discuss our experiences and strategies to port hypre to heterogeneous computers with accelerators, including the design of a new memory model, the use of abstractions, the BoxLoop macros in the structured and semi-structured interfaces, and the restructuring of algebraic multigrid (AMG) into modular components. We present numerical experiments comparing CPU and GPU performance for several test problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Regions of stability with unequal saturation limits and non-zero set point

Constraints on the magnitudes of control variables limit the region where open-loop unstable systems can be stabilized using feedback control. Variations in regions of stability with unequal control saturation limits and non-zero set points are illustrated for single-input unstable linear systems which have one or two unstable eigenvalues. The regions of stability for saddle-point- and unstable-node-type singularities increase with the increase in one of the saturation limits, but they become invariant when the larger control limit exceeds a certain value; the stability regions vanish for non-zero set-points that saturate the controls. The unstable-focus-type singularity exhibits strikingly different characteristics. These results suggest guidelines for obtaining desired stability regions for different types of singularities.

Stengel, R. F.↗

NASA NTRS1986

Multidisciplinary analysis of actively controlled large flexible spacecraft

The control of Flexible Structures (COFS) program has supported the development of an analysis capability at the Langley Research Center called the Integrated Multidisciplinary Analysis Tool (IMAT) which provides an efficient data storage and transfer capability among commercial computer codes to aid in the dynamic analysis of actively controlled structures. IMAT is a system of computer programs which transfers Computer-Aided-Design (CAD) configurations, structural finite element models, material property and stress information, structural and rigid-body dynamic model information, and linear system matrices for control law formulation among various commercial applications programs through a common database. Although general in its formulation, IMAT was developed specifically to aid in the evaluation of the structures. A description of the IMAT system and results of an application of the system are given.

Cooper, Paul A.↗

NASA NTRS1987

Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

NASA NTRS1989

Galerkin/Runge-Kutta discretizations for parabolic equations with time-dependent coefficients

Keeling, Stephen L.↗

DOE OSTI2024

Early Exploration of a Flexible Framework for Efficient Quantum Linear Solvers in Power Systems

The rapid integration of renewable energy resources presents formidable challenges in managing power grids. While advanced computing and machine learning techniques offer some solutions for accelerating grid modeling and simulation, there remain complex problems that classical computers cannot effectively address. Quantum computing, a promising technology, has the potential to fundamentally transform how we manage power systems, especially in scenarios with a higher proportion of renewable energy sources. One critical aspect is solving linear systems of equations, crucial for power system applications like power flow analysis, for which the Harrow-Hassidim-Lloyd (HHL) algorithm is a well-known quantum solution. However, HHL quantum circuits often exhibit excessive depth, making them impractical for current Noisy-Intermediate-Scale-Quantum (NISQ) devices. In this paper, we introduce a versatile framework, powered by NWQSim, that bridges the gap between power system applications and quantum linear solvers available in Qiskit. This framework empowers researchers to efficiently explore power system applications using quantum linear solvers. Through innovative gate fusion strategies, reduced circuit depth, and GPU acceleration, our simulator significantly enhances resource efficiency. Power flow case studies have demonstrated up to a eight-fold speedup compared to Qiskit Aer, all while maintaining comparable levels of accuracy.

quantum computing, Harrow-Hassidim-Lloyd, high-per↗

NASA NTRS2004

Development of a high stability microstrip-based L-band radiometer for ocean salinity measurements.

The development of a microstrip-based L-band Dicke radiometer with the long-term stability required for future ocean salinity measurements to an accuracy of 0.1 psu is presented. This will require the L-band radiometer requirements and configuration to achieve this objective. System configuration and component performance have been evaluated with radiometer test beds at both JPL and GSFC. The GSFC testbed uses a cryogenic chamber that al-lows long-term characterization at radiometric temperatures in the range of 70 - 120 K. The research has addressed several areas including component characterization as a function of temperature and bias, system linearity, optimum noise diode injection calibration and precision temperature control of components. A breadboard radiometer, utilizing microstrip-based technologies, has been built to demonstrate this long-term stability. This system is partially polarimetric providing V, H, -45 and +45 signals. Test results are compared to current and future ocean salinity radiometer requirements to show that the desire performance is possible.

Tanner, Alan B.↗

NASA NTRS1956

An Optimum Switching Criterion for a Third-order Contactor Acceleration Control System

A switching criterion for optimum performance of a third-order contractor acceleration control system having complex roots is presented. Analytical and analog-computer methods are utilized to determine this criterion. The resulting optimum transient responses are presented and compared with those of an equivalent linear system.

CONTROL, AUTOMATIC↗

DOE OSTI2022

Cascaded Control for Building HVAC Systems in Practice

Actuator hunting is a widespread and often neglected problem in the HVAC field. Hunting is typically characterized by sustained or intermittent oscillations, and can result in decreased efficiency, increased actuator wear, and poor setpoint tracking. Cascaded control loops have been shown to effectively linearize system dynamics and reduce the prevalence of hunting. This paper details the implementation of cascaded control architectures for Air Handling Unit chilled water valves at three university campus buildings. A framework for implementation the control in existing Building Automation software is developed that requires only a single line of additional code. Results gathered for more than a year show that cascaded control not only eliminates hunting in control loops with documented hunting issues, but provides better tracking and more consistent performance during all seasons. A discussion of efficiency losses due to hunting behavior is presented and illustrated with comparative data. Furthermore, an analysis of cost savings from implementing cascaded chilled water valve control is presented. Field tests show 2.2–4.4% energy savings, with additional potential savings from reduced operational costs (i.e., maintenance and controller retuning).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Magnetically Coupled Broadband Dual Magnetic Mass/Spring Vibrational Energy Harvesting Design

Self-powering sensors and networks are a reality. The ability to extract ambient energy from the surroundings to power electronic devices has a profound impact on the realization of smart adaptable sensor networks. In this study, a magnetically coupled dual spring and magnet design has been investigated to improve the efficiency and performance bandwidth of vibration energy harvesting (VEH) sensors. Using numerical models based on traditional systems of coupled ordinary differential equations (ODE), an optimized design was developed and compared to experimental measurements. Numerical and empirical results show good agreement. Results show improvement in the bandwidth over an equivalent linear system and corresponding improvement in output power conversion efficiency. The increased bandwidth allows improved conversion sensitivity and enhanced power harvesting capabilities. This operational bandwidth coincides with the expected input spectrum for in situ applications.

42 ENGINEERING↗

NASA NTRS1992

Controls and guidance research

The objectives of the control group are concentrated on research and education. The control problem of the hypersonic space vehicle represents an important and challenging issue in aerospace engineering. The work described in this report is part of our effort in developing advanced control strategies for such a system. In order to achieve the objectives stated in the NASA-CORE proposal, the tasks were divided among the group based upon their educational expertise. Within the educational component we are offering a Linear Systems and Control course for students in electrical and mechanical engineering. Also, we are proposing a new course in Digital Control Systems with a corresponding laboratory.

Homaifar, Abdollah↗