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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Review and analysis of dense linear system solver package for distributed memory machines

A dense linear system solver package recently developed at the University of Texas at Austin for distributed memory machine (e.g. Intel Paragon) has been reviewed and analyzed. The package contains about 45 software routines, some written in FORTRAN, and some in C-language, and forms the basis for parallel/distributed solutions of systems of linear equations encountered in many problems of scientific and engineering nature. The package, being studied by the Computer Applications Branch of the Analysis and Computation Division, may provide a significant computational resource for NASA scientists and engineers in parallel/distributed computing. Since the package is new and not well tested or documented, many of its underlying concepts and implementations were unclear; our task was to review, analyze, and critique the package as a step in the process that will enable scientists and engineers to apply it to the solution of their problems. All routines in the package were reviewed and analyzed. Underlying theory or concepts which exist in the form of published papers or technical reports, or memos, were either obtained from the author, or from the scientific literature; and general algorithms, explanations, examples, and critiques have been provided to explain the workings of these programs. Wherever the things were still unclear, communications were made with the developer (author), either by telephone or by electronic mail, to understand the workings of the routines. Whenever possible, tests were made to verify the concepts and logic employed in their implementations. A detailed report is being separately documented to explain the workings of these routines.

Narang, H. N.↗
DOE OSTI2025

Limitations of Fault-Tolerant Quantum Linear System Solvers for Quantum Power Flow

Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for solving such a problem using a classical algorithm exceeds that required by a quantum algorithm. Reducing the power flow (PF) problem into a linear system of equations allows for the formulation of quantum PF (QPF) algorithms, which are based on solving methods for quantum linear systems such as the Harrow-Hassidim-Lloyd (HHL) algorithm. Speedup from using QPF algorithms is often claimed to be exponential when compared to classical PF solved by state-of-the-art algorithms. Here, we investigate the potential for practical quantum advantage in solving QPF compared to classical methods on gate-based quantum computers. Notably, this paper does not present a new QPF solving algorithm but scrutinizes the end-to-end complexity of the QPF approach, providing a nuanced evaluation of the purported quantum speedup in this problem. Our analysis establishes a best-case bound for the HHL-based quantum power flow complexity, conclusively demonstrating that the HHL-based method has higher runtime complexity compared to the classical algorithm for solving the direct current power flow (DCPF) and fast decoupled load flow (FDLF) problem. Notably, our analysis and conclusions can be extended to any quantum linear system solver with rigorous performance guarantees, based on the known complexity lower bounds for this problem. Additionally, we establish that for potential practical quantum advantage (PQA) to exist it is necessary to consider DCPF-type problems with a very narrow range of condition number values and readout requirements.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1994

Using parallel banded linear system solvers in generalized eigenvalue problems

Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speedup is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.

DISTRIBUTED MEMORY MULTIPROCES↗
NASA NTRS1993

Using parallel banded linear system solvers in generalized eigenvalue problems

Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.

Zhang, Hong↗
DOE OSTI2021

EKAT v.1.0

E3SM Kokkos Application Toolkit (EKAT) is a collection of C++, Fortran, and CMake utilities for providing a single implementation of common kernels based on the Kokkos programming model. The library contains utilities for vectorization, tridiagonal linear system solvers, and linear interpolation as well as some general-purpose utilities such as testing utilities, parameter lists, representation of physical units, and additional interfaces. The goal is to provide a centralized implementation for high-performance computing structures and common utilities that reduce code duplication and streamline maintenance efforts. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. SAND2022-1327 O

Bertagna, Luca↗
DOE OSTI2022

kynema-fmb [SWR-23-07]

Kynema-FMB (FKA: Kynema) is an open-source performance portable flexible multibody (FMB) dynamics solver designed for time-domain simulations. While originally tailored for wind turbine structural dynamics, the formulation and implementation are those of a general flexible-multidbody dynamics solver that can readily be applied to a wide range of systems. Kynema was designed with a narrow focus, namely to provide a lightweight, fast, accurate FMD solver for coupling to computational-fluid-dynamics (CFD) codes, especially the CFD codes in the Kynema suite, for fluid-structure-interaction (FSI) simulations. Kynema-FMB is equipped to model systems that can be represented as a collection of beams and rigid bodies that are connected through constraints. Degrees of freedom are defined in the inertial/global frame of reference and include displacements and rotations (formally as rotation matrices, but stored as quaternions). The underlying formulation is built on a Lie-group time integrator designed for index-3 differential-algebraic equations, which is second-order accurate in time (Bruls et al., 2012). Beam models are based on geometrically exact beam theory and are discretized as high-order spectral finite elements similar to those in BeamDyn (Wang et al., 2017). The governing equations for a FMD system like a wind turbine constitute a highly nonlinear system of constrained partial-differential equations. Kynema-FMB uses analytical Jacobians in the nonlinear-system solves in each time step. Linear systems use sparse storage and several third-party sparse-linear-system solvers are enabled. Ill conditioning of linear systems is mitigated with preconditioning described in Bottasso et al, 2008. Kynema-FMB is integrated with a simple open-source controller (ROSCO). There is an application programming interface (API) for coupling to geometry-resolved CFD (like that in Sharma et al., 2023) and actuator-force CFD (like that in Kuhn et al., 2025). In the latter, for actuator-line models, Kynema-FMB includes an internal blade-element solver that depends on user-provided lookup tables for coefficients of lift and drag, i.e., aerodynamic polars. Kynema-FMB is written in C++ and leverages Kokkos and Kokkos-Kernels (KokkosEcosystem) as its performance portability layer enabling simulations on both CPU and GPU systems. The repository is equipped with extensive automated testing at the unit and regression/system levels. The following describes the high-level development objectives conceived for Kynema: *Kynema will follow modern software development best practices, including test-driven development (TDD), version control, hierarchical automated testing, and continuous integration (CI) for a robust development environment. *The core data structures are memory efficient and enable vectorization and parallelization at multiple levels. *Data structures are data-oriented to exploit methods for accelerated computing including high utilization of chip resources (e.g., single instruction multiple data (SIMD) instruction sets) and parallelization using GP-GPUs. *The computational algorithms incorporate robust open-source libraries for mathematical operations, resource allocation, and data management. *The API design considers multiple stakeholder needs and ensure integration with existing and future ecosystems for data science, machine learning, and AI. *Kynema-FMB is written in modern C++ and leverages Kokkos as its performance-portability library with inspiration from the kynema stack.

Sprague, MichaelA.↗
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↗
DOE OSTI2024

Low Precision and Efficient Programming Languages for Sustainable AI: Final Report for the Summer Project of 2024

This document contains all relevant material generated during the authors' summer internship at NREL in 2024. This report shows how to improve energy efficiency of a few code samples by using low-precision data types combined with mixed-precision algorithms. The main applications considered here are (i) linear system solvers using mixed precision, and (ii) neural networks using mixed precision. This report also discusses how programming languages affect energy consumption of algorithms, energy metrics for a code and tools, and the available current software and hardware infrastructure.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2002

Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving ~he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required to obtain usable convergence from an iterative solver. The authors have examined the use of an Incomplete LU Threshold (ILUT) preconditioner . to solver linear systems stemming from higher order BEM/FEM formulations in 2D scattering problems. Although the resulting preconditioner provided aD excellent approximation to the system inverse, its size in terms of non-zero entries represented only a modest improvement when compared with the fill-in associated with a sparse direct solver. Furthermore, the fill-in of the preconditioner could not be substantially reduced without the occurrence of instabilities. In addition to the results for these 2D problems, the authors will present iterative solution data from the application of the ILUT preconditioner to 3D problems.

Fink, P. W.↗
DOE OSTI2022

FY2022 Q4: Demonstrate multi-turbine simulation with hybrid-structured/unstructured-moving-grid software stack running primarily on GPUs and propose improvements for successful KPP-2 [Poster]

Milestone accomplishments staged the ExaWind team for successful completion of KPP-2 challenge problem in FY23, which requires the simulation on Frontier of at least four MW-scale turbines in an atmospheric boundary layer with at least 20B gridpoints. The ExaWind project and software stack is many faceted, with team members working on multiple areas, including linear-system solvers (Trilinos, hypre, AMReX), overset meshes, turbulence modeling, and in situ visualization, all with an aim for high fidelity predictions and performance portability. This milestone marks significant improvements on many fronts and provides the team with a pathway to exascale wind farm simulations in FY23.

17 WIND ENERGY↗
NASA NTRS1987

Principles for problem aggregation and assignment in medium scale multiprocessors

One of the most important issues in parallel processing is the mapping of workload to processors. This paper considers a large class of problems having a high degree of potential fine grained parallelism, and execution requirements that are either not predictable, or are too costly to predict. The main issues in mapping such a problem onto medium scale multiprocessors are those of aggregation and assignment. We study a method of parameterized aggregation that makes few assumptions about the workload. The mapping of aggregate units of work onto processors is uniform, and exploits locality of workload intensity to balance the unknown workload. In general, a finer aggregate granularity leads to a better balance at the price of increased communication/synchronization costs; the aggregation parameters can be adjusted to find a reasonable granularity. The effectiveness of this scheme is demonstrated on three model problems: an adaptive one-dimensional fluid dynamics problem with message passing, a sparse triangular linear system solver on both a shared memory and a message-passing machine, and a two-dimensional time-driven battlefield simulation employing message passing. Using the model problems, the tradeoffs are studied between balanced workload and the communication/synchronization costs. Finally, an analytical model is used to explain why the method balances workload and minimizes the variance in system behavior.

Nicol, David M.↗
NASA NTRS1989

Krylov methods preconditioned with incompletely factored matrices on the CM-2

The performance is measured of the components of the key interative kernel of a preconditioned Krylov space interative linear system solver. In some sense, these numbers can be regarded as best case timings for these kernels. Sweeps were timed over meshes, sparse triangular solves, and inner products on a large 3-D model problem over a cube shaped domain discretized with a seven point template. The performance of the CM-2 is highly dependent on the use of very specialized programs. These programs mapped a regular problem domain onto the processor topology in a careful manner and used the optimized local NEWS communications network. The rather dramatic deterioration in performance was documented when these ideal conditions no longer apply. A synthetic workload generator was developed to produce and solve a parameterized family of increasingly irregular problems.

Berryman, Harry↗
NASA NTRS1995

Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis

An aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three-dimensional geometries. The function of sensitivity analysis is to directly couple computational fluid dynamics (CFD) with numerical optimization techniques, which facilitates the construction of efficient direct-design methods. The development of a practical three-dimensional design procedures entails many challenges, such as: (1) the demand for significant efficiency improvements over current design methods; (2) a general and flexible three-dimensional surface representation; and (3) the efficient solution of very large systems of linear algebraic equations. It is demonstrated that each of these challenges is overcome by: (1) employing fully implicit (Newton) methods for the CFD analyses; (2) adopting a Bezier-Bernstein polynomial parameterization of two- and three-dimensional surfaces; and (3) using preconditioned conjugate gradient-like linear system solvers. Whereas each of these extensions independently yields an improvement in computational efficiency, the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficient design strategies in current use. The new aerodynamic shape optimization procedure is demonstrated in the design of both two- and three-dimensional inviscid aerodynamic problems including a two-dimensional supersonic internal/external nozzle, two-dimensional transonic airfoils (resulting in supercritical shapes), three-dimensional transport wings, and three-dimensional supersonic delta wings. Each design application results in realistic and useful optimized shapes.

Burgreen, Gregory W.↗
DOE OSTI2024

Linear Solvers for Collector Systems of Generalized Large-scale Inverter-Based Resources

Collector systems for inverter-based resources (IBRs) are typically represented by equivalent circuits for electromagnetic transient (EMT) simulations. Recent studies have revealed that modeling a detailed collector system is essential to accurately represent the behavior of IBRs, especially when dealing with partial tripping during external disturbances. However, there are several challenges in simulating a detailed EMT model of a collector system due to the time required to simulate such systems. Thus, this paper investigates the modeling of a detailed collector system, taking into account its configuration and components as defined in IEEE standard 2800. The configurations include the collector systems of generalized large-scale IBR plants. The components include the main IBR transformer, collector bus, and feeders with lines and/or cables. The EMT model of the collector system is represented by differential algebraic equations (DAEs) that are discretized to form linear equations that are solved using linear solvers. In this paper, linear solvers are proposed based on the Schur complement method, which are utilized for simulation of the EMT model of collector systems of generalized large-scale IBRs to accelerate simulation speed while maintaining the accuracy of the results. The proposed solvers are verified by comparing the performance to that of linear solvers provided in MATLAB.

Choi, Jongchan↗
NASA NTRS1977

A block iterative LU solver for weakly coupled linear systems

A hybrid technique, called the block iterative LU solver, is proposed for solving the linear equations resulting from a finite element numerical analysis of certain fluid dynamics problems where the equations are weakly coupled between distinct sets of variables. Either the block Jacobi iterative method or the block Gauss-Seidel iterative solver is combined with LU decomposition.

Cooke, C. H.↗
DOE OSTI2022

MAPPRAISER: A massively parallel map-making framework for multi-kilo pixel CMB experiments

Forthcoming cosmic microwave background (CMB) polarized anisotropy experiments have the potential to revolutionize our understanding of the Universe and fundamental physics. The sought-after, tale-telling signatures will be however distributed over voluminous data sets which these experiments will collect. These data sets will need to be efficiently processed and unwanted contributions due to astrophysical, environmental, and instrumental effects characterized and efficiently mitigated in order to uncover the signatures. This poses a significant challenge to data analysis methods, techniques, and software tools which will not only have to be able to cope with huge volumes of data but to do so with unprecedented precision driven by the demanding science goals posed for the new experiments. A keystone of efficient CMB data analysis is solvers of very large linear systems of equations. Such systems appear in very diverse contexts throughout CMB data analysis pipelines, however they typically display similar algebraic structures and can therefore be solved using similar numerical techniques. Linear systems arising in the so-called map-making problem are one of the most prominent and common ones. In this work we present a massively parallel, flexible and extensible framework, comprised of a numerical library, MIDAPACK, and a high level code, MAPPRAISER, which provide tools for solving efficiently such systems. Here, the framework implements iterative solvers based on conjugate gradient techniques: enlarged and preconditioned using different preconditioners. We demonstrate the framework on simulated examples reflecting basic characteristics of the forthcoming data sets issued by ground-based and satellite-borne instruments, executing it on as many as 16,384 compute cores. The software is developed as an open source project freely available to the community at: https://github.com/B3Dcmb/midapack.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The linearized LLGE is obtained by assuming a small deviation around the equilibrium state of the magnetic system. Inserting such expansion into LLGE and keeping only first order terms gives the linearized LLGE, which gives a frequency domain solution for the complex magnetization amplitudes under an external time-harmonic applied field of a given frequency. We solve the linear system with an iterative solver using generalized minimal residual method. We construct a preconditioner matrix to effectively solve the linear system. The validity, effectiveness, speed, and scalability of the linear solver are demonstrated via numerical examples.

36 MATERIALS SCIENCE↗