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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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15 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Nonoverlapping block smoothers for the Stokes equations

Overlapping block smoothers efficiently damp the error contributions from highly oscillatory components within multigrid methods for the Stokes equations but they are computationally expensive. This paper is concentrated on the development and analysis of new block smoothers for the Stokes equations that are discretized on staggered grids. These smoothers are nonoverlapping and therefore desirable due to reduced computational costs. Traditional geometric multigrid methods are based on simple pointwise smoothers. However, using multigrid methods to efficiently solve more difficult problems such as the Stokes equations leads to computationally more expensive smoothers, for example, overlapping block smoothers. Nonoverlapping smoothers are less expensive, but have been considered less efficient in the literature. In this paper, we develop new nonoverlapping smoothers, the so-called triad-wise smoothers, and show their efficiency within multigrid methods to solve the Stokes equations. In addition, we compare overlapping and nonoverlapping smoothers by measuring their computational costs and analyzing their behavior by the use of local Fourier analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Block smoothers and generalized ideal interpolation in AMG (Final Report)

The Pennsylvania State University (“Subcontractor”) worked on developing new parallel algebraic multilevel methods suitable for solving PDEs. Specifically, work on the design of multigrid solvers for coupled systems of partial differential equations arising in numerical modeling of various applications was completed. A main emphasis was on the design of new ideal algebraic multigrid interpolation for problems such as Maxwell’s equations where block smoothers are needed and the standard form of ideal interpolation is not an effective choice.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2020

Multigrid Preconditioning for a Space-Time Spectral-Element Discontinuous-Galerkin Solver

In this work we examine a multigrid preconditioning approach in the context of a high- order tensor-product discontinuous-Galerkin spectral-element solver. We couple multigrid ideas together with memory lean and efficient tensor-product preconditioned matrix-free smoothers. Block ILU(0)-preconditioned GMRES smoothers are employed on the coarsest spaces. The performance is evaluated on nonlinear problems arising from unsteady scale- resolving solutions of the Navier-Stokes equations: separated low-Mach unsteady ow over an airfoil from laminar to turbulent ow. A reduction in the number of ne space iterations is observed, which proves the efficiency of the approach in terms of preconditioning the linear systems, however this gain was not reflected in the CPU time. Finally, the preconditioner is successfully applied to problems characterized by stiff source terms such as the set of RANS equations, where the simple tensor product preconditioner fails. Theoretical justification about the findings is reported and future work is outlined.

Franciolini, Matteo↗
DOE OSTI2021

Algebraic Multigrid with Optimal Interpolation and Adaptive Smoothers (Final Report)

The project team continued with work on developing new bootstrap AMG techniques for solving symmetric and non-symmetric PDE systems. The focus of this work is to derive more reliable measures of the quality of the coarse space set than the convergence rate of the standard F-relaxation form of CR and a more robust form of interpolation than the so-called ideal form. We have successfully derived a sharp variant of CR that gives the precise convergence rate of the two-grid method using this optimal interpolation and, in addition, we derived a new Generalized Bootstrap AMG setup algorithm that uses as its main tool a multilevel eigensolver for the generalized eigenvalue problem involving the system matrix and the symmetrized smoother. In addition, the approach allows for general block smoothers with overlap. We have applied the method to scalar diffusion problems, linear elasticity, and Maxwell’s and the method shows marked improvements over existing AMG methods for these problems. In addition, the team worked with CASC members on new forms of ideal AMG interpolation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Overlapping Schwarz Methods Are Not Anisotropy‐Robust Multigrid Smoothers

We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, it is well known that the smoothing properties of point-wise smoothers, such as Gauss Seidel, rapidly deteriorate as the strength of anisotropy increases. On the other hand, global smoothers based on line smoothing are known to generally provide good smoothing for diffusion problems, independent of the anisotropy strength. Here, a natural question is whether global methods are really necessary to achieve good smoothing in such problems, or whether it can be obtained with locally overlapping block smoothers using sufficiently large blocks and overlap. Through local Fourier analysis and careful numerical experimentation, we show that global methods are indeed necessary to achieve anisotropy-robust smoothing. Specifically, for any fixed block size bounded sufficiently far away from the global domain size, we find that the smoothing properties of overlapping multiplicative Schwarz rapidly deteriorate with increasing anisotropy, irrespective of the amount of overlap between blocks. Moreover, our results indicate that anisotropy-robust smoothing requires blocks of diameter 𝒪⁡(𝜖 −1/2 ) for anisotropy ratio 𝜖 ∈(0,1] .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla$ x $\nabla$ x operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1999

Plane Smoothers for Multiblock Grids: Computational Aspects

Standard multigrid methods are not well suited for problems with anisotropic discrete operators, which can occur, for example, on grids that are stretched in order to resolve a boundary layer. One of the most efficient approaches to yield robust methods is the combination of standard coarsening with alternating-direction plane relaxation in the three dimensions. However, this approach may be difficult to implement in codes with multiblock structured grids because there may be no natural definition of global lines or planes. This inherent obstacle limits the range of an implicit smoother to only the portion of the computational domain in the current block. This report studies in detail, both numerically and analytically, the behavior of blockwise plane smoothers in order to provide guidance to engineers who use block-structured grids. The results obtained so far show alternating-direction plane smoothers to be very robust, even on multiblock grids. In common computational fluid dynamics multiblock simulations, where the number of subdomains crossed by the line of a strong anisotropy is low (up to four), textbook multigrid convergence rates can be obtained with a small overlap of cells between neighboring blocks.

Llorente, Ignacio M.↗
DOE OSTI2024

From roads to roofs: How urban and rural mobility influence building energy consumption

In this article, understanding the relationship between travel behavior and building energy use at an urban scale is crucial for developing effective energy management strategies. Mobility patterns significantly impact building occupancy, which in turn affects energy consumption. However, existing methods often focus on individual buildings, whereas geographical influences on energy usage are not adequately examined. This study addresses this gap by using transportation origin-destination (OD) data to estimate building occupancy and energy. The proposed method assigns OD trips from census block groups to the building level, incorporating building, travel survey, and census data to derive building occupancy profiles. This method was applied to urban and rural areas with 4062 buildings in 70 census block groups. We found that the OD-informed occupancy profile exhibits smoother energy consumption patterns compared with that of Department of Energy reference occupancy profiles. Our analysis reveals distinct building energy consumption patterns among groups with long and short commutes, emphasizing the effect of commute times and work schedules on residential energy usage. This framework is useful for practitioners in transportation agencies and utility companies, enabling the estimation of building energy based on mobility patterns. Overall, this study shows the potential of integrating transportation and building energy data to inform cross-sector energy management strategies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2015

Geology of Pluto and Charon Overview

Pluto's surface was found to be remarkably diverse in terms of its range of landforms, terrain ages, and inferred geological processes. There is a latitudinal zonation of albedo. The conspicuous bright albedo heart-shaped feature informally named Tombaugh Regio is comprised of several terrain types. Most striking is Texas-sized Sputnik Planum, which is apparently level, has no observable craters, and is divided by polygons and ovoids bounded by shallow troughs. Small smooth hills are seen in some of the polygon-bounding troughs. These hills could either be extruded or exposed by erosion. Sputnik Planum polygon/ovoid formation hypotheses range from convection to contraction, but convection is currently favored. There is evidence of flow of plains material around obstacles. Mountains, especially those seen south of Sputnik Planum, exhibit too much relief to be made of CH4, CO, or N2, and thus are probably composed of H2O-ice basement material. The north contact of Sputnik Planum abuts a scarp, above which is heavily modified cratered terrain. Pluto's large moon Charon is generally heavily to moderately cratered. There is a mysterious structure in the arctic. Charon's surface is crossed by an extensive system of rift faults and graben. Some regions are smoother and less cratered, reminiscent of lunar maria. On such a plain are large isolated block mountains surrounded by moats. At this conference we will present highlights of the latest observations and analysis. This work was supported by NASA's New Horizons project

Sputnik Planum↗
DOE OSTI2023

Scaled ILU Smoothers for Navier-Stokes Pressure Projection

Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) V-cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has demonstrated the advantages of Jacobi iteration as an alternative to direct solution of these systems. Depending on the threshold and fill-level parameters chosen, the factors can be highly nonnormal and Jacobi is unlikely to converge in a low number of iterations. We demonstrate that row scaling can reduce the departure from normality, allowing us to replace the inherently sequential solve with a rapidly converging Richardson iteration. There are several advantages beyond the lower compute time. Scaling is performed locally for a diagonal block of the global matrix because it is applied directly to the factor. Further, an ILUT Schur complement smoother maintains a constant GMRES iteration count as the number of MPI ranks increases, and thus parallel strong-scaling is improved. Our algorithms have been incorporated into hypre, and we demonstrate improved time to solution for linear systems arising in the Nalu-Wind and PeleLM pressure solvers. For large problem sizes, GMRES+AMG executes at least five times faster when using iterative triangular solves compared with direct solves on massively parallel GPUs.

algebraic multigrid↗
DOE OSTI2023

Data-Driven Smoothers for Extreme-Scale Computing

Patch-based relaxation refers to a family of methods for solving linear systems which partitions the matrix into smaller pieces often corresponding to groups of adjacent degrees of freedom residing within patches of the computational domain. The two most common families of patch-based methods are block-Jacobi and Schwarz methods, where the former typically corresponds to non-overlapping domains and the later implies some overlap. We focus on cases where each patch consists of the degrees of freedom on a finite element method mesh cell. Patch methods often capture complex local physics much more effectively than simpler point-smoothers such as Jacobi; however, forming, inverting, and applying each patch can be prohibitively expensive in terms of both storage and computation time. To this end, we propose several approaches for performing analysis on these patches and constructing a reduced representation. The compression techniques rely on either matrix norm comparisons or unsupervised learning via a clustering approach. We illustrate how it is frequently possible to retain/factor less than 5% of all patches and still develop a method that converges only a little slower than when all patches are stored/factored.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2003

Production of Near-Mirror Surface Quality by Precision Grinding

Mechanical components such as gears and bearings operate with the working surfaces in intimate contact with a mating part. The performance of such components will be influenced by the quality of the working surface. In general, a smoother surface will perform better than a rougher surface since the lubrication conditions are improved. For example, surfaces with a special near-mirror quality finish of low roughness performed better than ground surfaces when tested using a block-on-ring arrangement. Bearings with near-mirror quality have been tested and analyzed; lower running torques were measured and improved fatigue life was anticipated. Experiments have been done to evaluate the performance of gears with improved, low roughness surface finishing. The measured performance improvements include an increased scuffing (scoring) load capacity by a factor of 1.6, a 30-percent reduction of gear tooth running friction, and longer fatigue lives by a factor of about four. One can also anticipate that near-mirror quality surface finishing could improve the performance of other mechanical components such as mechanical seals and heavily loaded journal bearings. Given these demonstrated benefits, capable and economical methods for the production of mechanical components with near-mirror quality surfaces are desired. One could propose the production of near-mirror quality surfaces by several methods such as abrasive polishing, chemical assisted polishing, or grinding. Production of the surfaces by grinding offers the possibility to control the macro-geometry (form), waviness, and surface texture with one process. The present study was carried out to investigate the possibility of producing near-mirror quality surfaces by grinding. The present study makes use of a specially designed grinding machine spindle to improve the surface quality relative to the quality produced when using a spindle of conventional design.

Dimofte, Florin↗
NASA NTRS1997

Multi-Scale Fractal Analysis of Image Texture and Pattern

Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely scale-independent. Self-similarity is a property of curves or surfaces where each part is indistinguishable from the whole. The fractal dimension D of remote sensing data yields quantitative insight on the spatial complexity and information content contained within these data. Analyses of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed(l0 to 80 meters). The forested scene behaves as one would expect-larger pixel sizes decrease the complexity of the image as individual clumps of trees are averaged into larger blocks. The increased complexity of the agricultural image with increasing pixel size results from the loss of homogeneous groups of pixels in the large fields to mixed pixels composed of varying combinations of NDVI values that correspond to roads and vegetation. The same process occur's in the urban image to some extent, but the lack of large, homogeneous areas in the high resolution NDVI image means the initially high D value is maintained as pixel size increases. The slope of the fractal dimension-resolution relationship provides indications of how image classification or feature identification will be affected by changes in sensor resolution.

Emerson, Charles W.↗
DOE OSTI2024

Impacts of Superalloys on the Surface Quality of Additively Manufactured Channels

Abstract Gas turbines feature many components that require superalloys capable of handling extreme thermal environments. Increasing the selection of materials available for these components is important to their use in these extremely high-temperature environments. This study investigated two recently developed materials intended to be used for additive manufacturing (AM), with one superalloy based on cobalt and the other on nickel. Sets of four test coupons were built using the materials, in addition to the commonly used Inconel-718, on multiple laser powder bed fusion machines. Several build conditions were varied between coupon sets, including coupon orientation, contour settings, and upskin and downskin treatment. Each set of test coupons featured four unique cooling designs to explore how different cooling technologies would be impacted by the variations in build conditions. After being built, coupons were computed tomography (CT) scanned to determine accuracy to design intent and quantify the surface roughness. The CT scans indicated that horizontally built test coupons had a significantly higher deviation from design intent and higher surface roughness than those built vertically. Results also indicated that the cobalt-based alloy consistently had a smoother surface quality with lower surface roughness compared to the nickel-based alloy. After geometric characterization, the cooling performance of the test coupons was measured experimentally. Pressure losses were found to correlate with increases in surface roughness; however, in some cases, the convective heat transfer did not increase proportionally to the pressure loss as a result of surface features significantly blocking the flow without proportionally increasing convective heat transfer.

Engineering↗
DOE OSTI2025

A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems

This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices.

97 MATHEMATICS AND COMPUTING↗