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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 sources NASA NTRS DOE OSTI

DOE OSTI2023

The Simons Observatory: A fully remote controlled calibration system with a sparse wire grid for cosmic microwave background telescopes

For cosmic microwave background (CMB) polarization observations, calibration of detector polarization angles is essential. We have developed a fully remote controlled calibration system with a sparse wire grid that reflects linearly polarized light along the wire direction. The new feature is a remote-controlled system for regular calibration, which has not been possible in sparse wire grid calibrators in past experiments. The remote control can be achieved by two electric linear actuators that load or unload the sparse wire grid into a position centered on the optical axis of a telescope between the calibration time and CMB observation. Furthermore, the sparse wire grid can be rotated by using a motor. A rotary encoder and a gravity sensor are installed on the sparse wire grid to monitor the wire direction. They allow us to achieve detector polarization angle calibration with an expected systematic error of 0.08°. The calibration system will be installed in small-aperture telescopes at Simons Observatory.

47 OTHER INSTRUMENTATION↗

NASA NTRS1977

Timing formulas for dissection algorithms on vector computers

The use of the finite element and finite difference methods often leads to the problem of solving large, sparse, positive definite systems of linear equations. MACSYMA plays a major role in the generation of formulas representing the time required for execution of the dissection algorithms. The use of MACSYMA in the generation of those formulas is described.

Poole, W. G., Jr.↗

NASA NTRS1991

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. An implementation is presented of a look-ahead version of the Lanczos algorithm that, except for the very special situation of an incurable breakdown, overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead.

Freund, Roland W.↗

NASA NTRS1990

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 1

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. We present an implementation of a look-ahead version of the Lanczos algorithm which overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and is not restricted to steps of length 2, as earlier implementations are. Also, our implementation has the feature that it requires roughly the same number of inner products as the standard Lanczos process without look-ahead.

Freund, Roland W.↗

NASA NTRS1990

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included.

Freund, Roland W.↗

NASA NTRS2016

An Optimized Multicolor Point-Implicit Solver for Unstructured Grid Applications on Graphics Processing Units

In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.

Zubair, Mohammad↗

DOE OSTI2023

Batched Sparse Linear Algebra (Final Report for Subcontract B648960)

This report finalizes design specifications for developing batched kernels for small tensor operations for unassembled matrix-free iterative solvers, batched solvers for partially assembled operators, and batched solvers with support for various sparse formats. The outcome of the project milestones is a set of interfaces to Batched Sparse LA solvers running on hardware accelerators for use in ECP Libraries and Applications. It is part of the development of sparse batched kernels, solvers/preconditioners as well as creating interoperability in xSDK libraries with sparse and dense batched functions to benefit ECP applications. The participants included representatives from ECP libraries (not limited to the xSDK project), applications, and vendors (AMD, Intel, and NVIDIA). Batched sparse linear algebra solvers form the new frontier for algorithmic development and performance engineering. Many applications (ECP and non-ECP alike) require simultaneous solutions of small linear systems of equations that are structurally sparse. To move towards high hardware utilization, it is important to provide these applications with appropriate interfaces to efficient batched sparse solvers running on modern hardware accelerators. We present interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the software portable between the major hardware accelerators from AMD, Intel, and NVIDIA. The presented interface specifications includes batched band, sparse iterative, and sparse direct solvers. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, SUNDIALS, and SuperLU_dist.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Linear solvers for power grid optimization problems: A review of GPU-accelerated linear solvers

The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite, and they become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDL T decompositions. Here, we benchmark five well known direct linear solver packages on CPU- and GPU-based hardware, using matrices extracted from power grid optimization problems. The achieved solution accuracy varies greatly among the packages. None of the tested packages delivers significant GPU acceleration for our test cases. For completeness of the comparison we include results for MA57, which is one of the most efficient and reliable CPU solvers for this class of problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Advanced Computing is at the Forefront of a New “Moonshot” Revolutionizing the North American Power Grid

In the 50+ years since the first humans landed on the moon, computing has grown at breakneck speed. We are faced with another challenge that is just as daunting, and just as important to overcome-modernizing the North American electric power grid-and high-performance computing (HPC) systems with specialized software will be an important element in rising to this challenge. We describe at a high level how software developed in the ExaSGD project addresses this "moonshot" goal by utilizing exascale computing and a novel high performance solver software stack to support the mission of decarbonizing power grid operations in an environment of uncertain weather and climate. To reach the exascale benchmark the team has made a number of first-of-their-kind innovations, including novel method for stochastic optimization, fine grained parallel methods for modeling power systems, and GPU resident sparse numerical linear solvers.

17 WIND ENERGY↗

DOE OSTI2024

Milestone 49 Report: Batched Sparse LA Phase 5 Implementation

Batched sparse linear algebra operations in general, and solvers in particular, have become the major algorithmic development activity and foremost performance engineering effort in the numerical software libraries work on modern hardware with accelerators such as GPUs. Many applications, ECP and non-ECP alike, require simultaneous solutions of many small linear systems of equations that are structurally sparse in one form or another. In order to move towards high hardware utilization levels, it is important to provide these applications with appropriate interface designs to be both functionally efficient and performance portable and give full access to the appropriate batched sparse solvers running on modern hardware accelerators prevalent across DOE supercomputing sites since the inception of ECP. To this end, we present here a summary of recent advances on the interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the corresponding software portable between the major hardware accelerators from AMD, Intel, and NVIDIA, while maintaining the appropriate disclosure levels conforming to the active NDA agreements. The presented interface specifications include a mix of batched band, sparse iterative, and sparse direct solvers with their accompanying functionality that is already required by the application codes or we anticipated to be needed in the near future. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, PETSc, and SuperLU.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Xyce(™) Parallel Electronic Simulator v.7.5

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.! ! Xyce is primarily used to simulate the voltage and current behavior of a circuit network (a network of electronic devices connected via a conductive network). As a tool, it is mainly used for the design and analysis of electronic circuits.! ! Kirchoff's conservation laws are enforced over a network using modified nodal analysis. This results in a set of differential algebraic equations (DAEs). The resulting nonlinear problem is solved iteratively using a fully coupled Newton method, which in turn results in a linear system that is solved by either a standard sparse-direct solver or iteratively using Trilinos linear solver packages, also developed at Sandia National Laboratories.

Source record↗

NASA NTRS1983

M-step preconditioned conjugate gradient methods

Preconditioned conjugate gradient methods for solving sparse symmetric and positive finite systems of linear equations are described. Necessary and sufficient conditions are given for when these preconditioners can be used and an analysis of their effectiveness is given. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.

Adams, L.↗

NASA NTRS1983

An M-step preconditioned conjugate gradient method for parallel computation

This paper describes a preconditioned conjugate gradient method that can be effectively implemented on both vector machines and parallel arrays to solve sparse symmetric and positive definite systems of linear equations. The implementation on the CYBER 203/205 and on the Finite Element Machine is discussed and results obtained using the method on these machines are given.

Adams, L.↗

NASA NTRS1973

Sparse matrix methods based on orthogonality and conjugacy

A matrix having a high percentage of zero elements is called spares. In the solution of systems of linear equations or linear least squares problems involving large sparse matrices, significant saving of computer cost can be achieved by taking advantage of the sparsity. The conjugate gradient algorithm and a set of related algorithms are described.

Lawson, C. L.↗

NASA NTRS1976

An iterative decoupling solution method for large scale Lyapunov equations

A great deal of attention has been given to the numerical solution of the Lyapunov equation. A useful classification of the variety of solution techniques are the groupings of direct, transformation, and iterative methods. The paper summarizes those methods that are at least partly favorable numerically, giving special attention to two criteria: exploitation of a general sparse system matrix structure and efficiency in resolving the governing linear matrix equation for different matrices. An iterative decoupling solution method is proposed as a promising approach for solving large-scale Lyapunov equation when the system matrix exhibits a general sparse structure. A Fortran computer program that realizes the iterative decoupling algorithm is also discussed.

Athay, T. M.↗

NASA NTRSDate not supplied

Component-Based Development of CFD Software FUN3D

FUN3D, a suite of Computational Fluid Dynamics simulation and design tools developed at the NASA Langley Research Center, has undergone continuous development since the late1980s. It contains a large portion of legacy code. Extending it with new capabilities becomes increasingly difficult. To improve the extensibility and reusability, FUN3D is moving toward component-based development. New features, such as Stabilized Finite Elements, Yoga, and Sparse Linear Algebra Toolkit, are integrated into the system as components. Some existing features such as the Node-Centered Finite Volume Solver, are also being refactored to components. The integration of these components poses new requirements on the development workflow. In this paper, we describe the Continuous Integration of FUN3D to support component-based development, and discuss the tools used, the practices followed, and lessons learned during the transition from the traditional approach.

computational fluid dynamics software↗

DOE OSTI2023

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs.

24 POWER TRANSMISSION AND DISTRIBUTION↗