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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
DOE OSTI2022

HyKKT: a hybrid direct-iterative method for solving KKT linear systems

Here, we propose a solution strategy for the large indefinite linear systems arising in interior methods for nonlinear optimization. The method is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for sparse indefinite systems is the LBLT factorization where L is a lower triangular matrix and B is 1×1 or 2×2 block diagonal. However, this requires pivoting, which substantially increases communication cost and degrades performance on GPUs. Our approach solves a large indefinite system by solving multiple smaller positive definite systems, using an iterative solver on the Schur complement and an inner direct solve (via Cholesky factorization) within each iteration. Cholesky is stable without pivoting, thereby reducing communication and allowing reuse of the symbolic factorization. We demonstrate the practicality of our approach on large optimal power flow problems and show that it can efficiently utilize GPUs and outperform LBL T factorization of the full system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Airfoil Computational Fluid Dynamics - 2k shapes, 25 AoA's, 3 Re numbers

This dataset contains aerodynamic quantities - including flow field values (momentum, energy, and vorticity) and summary values (coefficients of lift, drag, and momentum) - for 1,830 airfoil shapes computed using the HAM2D CFD (computational fluid dynamics) model. The airfoil shapes were designed using the separable shape tensor parameterization that encodes two-dimensional shapes as elements of the Grassmann manifold. This data-driven approach learns two independent spaces of parameter from a collection of sample airfoils. The first captures large-scale, linear perturbations, and the second defines small-scale, higher-order perturbations. For this dataset, we used the G2Aero database of over 19,000 airfoil shapes to learn a parameter space that captured a wide array of shape characteristics. We sampled airfoil designs over both parameter spaces to explore the full range of possible shape variations. The aerodynamic quantities for the generated airfoil were obtained using the HAM2D code, which is a finite-volume Reynolds-averaged Navier-Stokes (RANS) flow solver. We employ a fifth-order WENO scheme for spatial reconstruction with Roe's flux difference scheme for inviscid flux and second-order central differencing for viscous flux. A preconditioned GMRES method is applied for implicit integration. The Spalart-Allmaras 1-eq turbulence model is used for the turbulence closure, and the Medida-Baeder 2-eq transition model is applied to account for the effects of laminar turbulent transition. The airfoil grid is generated with a total of 400 points on the airfoil surface, the initial wall-normal spacing of y+ = 1, and an outer boundary located at 300 chord lengths away from the wall. The CFD simulations are performed at a freestream Mach number of 0.1, for or three different Reynolds' numbers (3M, 6M, and 9M), and for 25 angles of attack from -4 deg. to 20 deg. with 1 degree increments. Across all these various parameters, this dataset includes the results from over 250,000 CFD simulations. The simulations were performed using the Bridges-2 system at the Pittsburgh Supercomputing Center in February 2023 as part of the INTEGRATE project funded by the Advanced Research Projects Agency - Energy, in the U.S. Department of Energy. The data was collected, reformatted, and preprocessed for this OEDI submission in July 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub Repository resource under explore_airfoil_2k_data.ipynb.

2k↗
DOE OSTI2023

Simulation of Reverse Osmosis Membrane Compaction Using Material Point Method (MPM)

Access to fresh drinking water in the future requires effective management of industrial wastewater and water purification from available resources. In this study, we present the simulation methodology and the analysis of a Reverse Osmosis (RO) membrane under various pressure conditions using the Material Point Method (MPM). In contrast to other numerical methods, MPM solves the continuum governing equations on material points in a Lagrangian framework. The method does not require a grid connecting the material points hence making it suitable to simulate large deformations during membrane compaction. The time integration is carried out using the explicit Euler method, while the spatial discretization is performed using linear or cubic-spline shape functions. A series of planar images containing detailed pore structures obtained from X-ray tomography experiments is converted to a three-dimensional collection of material points to simulate the membrane. Compressive loads are applied to the top layer of the membrane to simulate the experiments. The membrane deformation and pore size distribution before and after load application are reported and compared with the experimental measurements. The presentation discusses the numerical methods used, the performance of the solver on high-performance computing machines, and the results of membrane compaction in detail.

ENGINEERING,MATHEMATICS AND COMPUTING↗
DOE OSTI2020

thornado-transport: Anderson- and GPU-accelerated nonlinear solvers for neutrino-matter coupling

Algorithms for neutrino-matter coupling in core-collapse supernovae (CCSNe) are investigated in the context of a spectral two-moment model, which is discretized in space with the discontinuous Galerkin method, integrated in time with implicit-explicit (IMEX) methods, and implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado). The model considers electron neutrinos and antineutrinos and tabulated opacities from Bruenn (1985), which includes neutrino-electron scattering and pair processes. The nonlinear system arising from implicit time discretization of the equations governing neutrino-matter coupling is iterated to convergence using Anderson-accelerated fixed-point methods, which avoid formation of Jacobians and inversion of dense linear systems. Numerical experiments show that, for a given tolerance, a nested iteration scheme which aims to reduce opacity evaluations can lower the computational cost. Our initial port to GPUs, using both OpenMP and OpenACC, shows an overall speedup of up to ~ 100× when compared to results using a single CPU core. These results indicate that the algorithms implemented in thornado are well-suited to GPU acceleration.

Laiu, Paul↗
DOE OSTI2020

A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid

This paper investigates matrix-free algorithms for problems in quasi-static finite-strain hyperelasticity. Iterative solvers with matrix-free operator evaluation have emerged as an attractive alternative to sparse matrices in the fluid dynamics and wave propagation communities because they significantly reduce the memory traffic, the limiting factor in classical finite element solvers. Specifically, we study different matrix-free realizations of the finite element tangent operator and determine whether generalized methods of incorporating complex constitutive behavior might be feasible. Furthermore, in order to improve the convergence behavior of iterative solvers, we also propose a method by which to construct level tangent operators and employ them to define a geometric multigrid preconditioner. Additionally, the performance of the matrix-free operator and the geometric multigrid preconditioner is compared to the matrix-based implementation with an algebraic multigrid (AMG) preconditioner on a single node for a representative numerical example of a heterogeneous hyperelastic material in two and three dimensions. We find that matrix-free methods for finite-strain solid mechanics are very promising, outperforming linear matrix-based schemes by two to five times, and that it is possible to develop numerically efficient implementations that are independent of the hyperelastic constitutive law.

42 ENGINEERING↗
DOE OSTI2026

Block encoding of the three-dimensional heterogeneous Poisson equation with application to fracture flow

Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as state preparation, data loading, and efficient information extraction. In this work, we study the feasibility of applying QLS algorithms to solve discretized three-dimensional (3D) heterogeneous Poisson equations, with specific examples relating to groundwater flow through geologic fracture networks. We explicitly construct a block encoding for the 3D heterogeneous Poisson matrix by leveraging the sparse local structure of the discretized operator. While classical solvers benefit from preconditioning, we show that block encoding the system matrix and preconditioner separately does not improve the effective condition number that dominates the QLS run-time. This differs from classical approaches where the preconditioner and the system matrix can often be implemented independently. Nevertheless, due to the structure of the problem in three dimensions, the quantum algorithm achieves a run-time of 𝑂⁡(𝑁 2/3 polylog 𝑁 ⋅log (1/𝜖)), outperforming the best classical methods (with run times of 𝑂⁡(𝑁⁢log 𝑁 ⋅log (1/𝜖))) and offering exponential memory savings. These results highlight both the promise and limitations of QLS algorithms for practical scientific computing, and point to effective condition-number reduction as a key barrier in achieving quantum advantages.

58 GEOSCIENCES↗
DOE OSTI2023

Scalable DPG multigrid solver for Helmholtz problems: A study on convergence

This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov–Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12–26) and extends the convergence results from $\mathscr{O}$(10 7 ) degrees of freedom (DOFs) to $\mathscr{O}$(10 9 ) DOFs using a new scalable parallel MPI/OpenMP implementation. Novel contributions of this paper include an alternative definition of coarse-grid systems based on restriction of fine-grid operators, yielding superior convergence results. In the uniform refinement setting, a detailed convergence study is provided, demonstrating h and p robust convergence and linear scaling with respect to the wave frequency. Finally, the paper concludes with numerical results on hp -adaptive simulations including a large-scale seismic modeling benchmark problem with high material contrast.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

CMLM (Co-Optimized Machine-Learned Manifolds) [SWR-23-41]

Co-optimized Machine-Learned Manifolds (CMLM) is a data-driven approach for developing reduced-order manifold models for high-dimensional chemically reacting systems. It involves a specially designed neural network, the training of which simultaneously optimizes linear combinations of species that define the manifold, nonlinear mapping to outputs of interest such as reaction rates, and (optionally) subfilter closure for large eddy simulation. This software package provides an implementation of the CMLM approach in Python using the PyTorch machine learning library. A few example cases are included, showing how the tool can be applied to different types of data from 0D and 1D reacting simulations performed using Cantera. The neural networks can be saved in a format that is readable by the Pele suite of combustion solvers for use in reacting computational fluid dynamics simulations. This software repository contains several python scripts to perform various tasks associated with the Co-optimized Machine Learned Manifolds (CMLM) model, which is described in Perry, Henry de Frahan, and Yellapantula, CNF, 2022 (https://doi.org/10.1016/j.combustflame.2022.112286). This includes not only the code that defines the CMLM model, but also scripts to generate suitable training data, scripts to pre-process the data, scripts to train the CMLM model, and scripts to plot the output, as well as various other helper files. The scripts depend on several commonly used python libraries for data analysis and chemical reaction computations. The trained models that result from this tool are designed to work with the an interface being implemented in the Pele suite of reacting flow solvers (https://github.com/AMReX-Combustion).

Perry, Bruce↗
DOE OSTI2023

A Fast Butterfly-Compressed Hadamard–Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources

Here we present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. For a computational domain discretized with Nv discretization cells, the proposed algorithm first solves and tabulates the phase and HB coefficients via eikonal and transport equations with observation points and point sources located at the Chebyshev nodes using a set of much coarser computation grids, and then butterfly compresses the resulting HB interactions from all Nv cell centers to each other. The overall CPU time and memory requirement scale as O(Nv log2 Nv) for any bounded two-dimensional (2D) domains with arbitrary excitation sources. A direct extension of this scheme to bounded 3D domains yields an O(Nv4/3) CPU complexity, which can be further reduced to quasi-linear complexities with proposed remedies. The scheme can also efficiently handle scattering problems involving inclusions in inhomogeneous media. Although the current construction of our HB integrator does not accommodate caustics, the resulting HB integrator itself can be applied to certain sources, such as concave-shaped sources, to produce caustic effects. Compared to finite-difference frequency domain methods, the proposed HB integrator is free of numerical dispersion and requires fewer discretization points per wavelength. As a result, it can solve wave propagation problems well beyond the capability of existing solvers. Remarkably, the proposed scheme can accurately model wave propagation in 2D domains with 640 wavelengths per direction and in 3D domains with 54 wavelengths per direction on a state-of-the-art supercomputer at Lawrence Berkeley National Laboratory.

Hadamard--Babich ansatz↗
DOE OSTI2022

Design-Space Exploration for Inverse-Design of Wind Turbine Blades Using Data-Driven Methods

The state-of-the-practice aerodynamic design methods for wind turbine blades is typically based on Blade-Element Momentum (BEM) theory using a pre-designed frozen family of airfoils. The airfoils are themselves typically designed using panel methods. The design of the next-generation of large flexible rotors will need to capture the non-linear aerodynamics and three-dimensional flow to reduce the levelized cost of wind energy. Data-driven methods for aerodynamic design using data generated by computational fluid dynamics offer an attractive alternative to BEM-based methods that captures the non-linear aerodynamics of the component airfoils as well as the root and tip sections. In this work, we develop and demonstrate a framework to "smartly" explore the relevant design space in combination with an appropriate automated CFD pipeline to evaluate the aerodynamics of each design. The design-space exploration framework uses appropriate perturbations to the airfoil shape and induction profile from a baseline shape in combination with the inverse-design using BEM. The resulting designs are evaluated using an automated CFD pipeline using the in-house CFD solver framework "Mercury". We perform verification and validation to establish the capability of the Mercury framework to predict the aerodynamic performance of wind turbines. The CFD simulation of the perturbed blade shapes are optimized to restart from the converged baseline simulation to reduce the computational time. Finally, we demonstrate the design-space exploration technique for the design of the outboard section and the full rotor using perturbations to the shape and operating conditions of the NREL 5-MW turbine.

aerodynamic design methods↗
DOE OSTI2026

Integrated Transmission-Distribution Multi-Period Switching for Wildfire Risk Mitigation: Improving Speed and Scalability with Distributed Optimization: Preprint

With increasingly severe wildfire conditions driven by climate change, utilities must manage the risk of wildfire ignitions from electric power lines. During "public safety power shutoff'" events, utilities de-energize power lines to reduce wildfire ignition risk, which may result in load shedding. Distributed energy resources provide flexibility that can help support the system to reduce load shedding when lines are de-energized. We investigate a coordinated transmission-distribution optimization problem that balances wildfire risk mitigation and load shedding. We model distribution systems that include battery energy storage systems which may support loads when transmission lines are de-energized. This multi-period integrated transmission-distribution optimal switching problem jointly optimizes line switching decisions, the generators' setpoints, load shedding, and the batteries' states of charge, resulting in significant computational challenges. To improve scalability, we decompose the problem over both space and time and apply a distributed optimization algorithm. Using a large-scale synthetic California test case with realistic distribution models and real wildfire risk data, we show that distributed optimization can solve large-scale multi-period switching problems that are otherwise intractable for centralized solvers. We also discuss challenges and future directions for improving the distributed algorithm's convergence performance as the number of time periods increases.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Multistage mixed precision iterative refinement

Abstract Low precision arithmetic, in particular half precision (16‐bit) floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings in energy. Motivated by this, there has been a renewed interest in mixed precision iterative refinement schemes for solving linear systems , and new variants of GMRES‐based iterative refinement have been developed. Each particular variant with a given combination of precisions leads to different condition number‐based constraints for convergence of the backward and forward errors, and each has different performance costs. The constraints for convergence given in the literature are, as an artifact of the analyses, often overly strict in practice, and thus could lead a user to select a more expensive variant when a less expensive one would have sufficed. In this work, we develop a multistage mixed precision iterative refinement solver which aims to combine existing mixed precision approaches to balance performance and accuracy and improve usability. For a user‐specified initial combination of precisions, the algorithm begins with the least expensive approach and convergence is monitored via inexpensive computations with quantities produced during the iteration. If slow convergence or divergence is detected using particular stopping criteria, the algorithm switches to use a more expensive, but more reliable variant. A novel aspect of our approach is that, unlike existing implementations, our algorithm first attempts to use “stronger” GMRES‐based solvers for the solution update before resorting to increasing the precision(s). In some scenarios, this can avoid the need to refactorize the matrix in higher precision. We perform extensive numerical experiments on a variety of random dense problems and problems from real applications which confirm the benefits of the multistage approach.

Oktay, Eda↗
DOE OSTI2025

A self-consistent electrostatic electrified shallow water model for charged liquid surface dynamics

The dynamics of an electrified liquid surface are investigated using a shallow water model that is self-consistently coupled with an electrostatic solver. To account for the spatiotemporal variation of a curved liquid surface, the electric field on curved surfaces is calculated by solving a two-dimensional electrostatic equation using the weighted least squares (WLSQ) interpolation method. First, the WLSQ implementation is verified with analytical theory obtained from a Laplace solution assuming a half-cylinder liquid surface profile. Then, the coupled electrified shallow water model is used to study the instability of liquid surface perturbation as a function of the potential drop between an electrode and conducting liquid, surface tension, and gravity. We present a linear dispersion theory of liquid surface instability for long-wavelength perturbations, including the effects of liquid viscosity. Furthermore, the effects of multiple sinusoidal surface perturbations on the electrified liquid surface instability are investigated.

Capillary waves↗
DOE OSTI2021

Verification of Coupled Hydraulic Fracturing Simulators Using Laboratory-Scale Experiments

In this work, we aim to verify the predictions of the numerical simulators, which are used for designing field-scale hydraulic stimulation experiments. Although a strong theoretical understanding of this process has been gained over the past few decades, numerical predictions of fracture propagation in low-permeability rocks still remains a challenge. Against this background, we performed controlled laboratory-scale hydraulic fracturing experiments in granite samples, which not only provides high-quality experimental data but also a well-characterized experimental set-up. Using the experimental pressure responses and the final fracture sizes as benchmark, we compared the numerical predictions of two coupled hydraulic fracturing simulators—CSMP and GEOS. Both the simulators reproduced the experimental pressure behavior by implementing the physics of Linear Elastic Fracture Mechanics (LEFM) and lubrication theory within a reasonable degree of accuracy. The simulation results indicate that even in the very low-porosity (1–2 %) and low-permeability (10 -18 m 2 - 10 -19 m 2 ) crystalline rocks, which are usually the target of EGS, fluid-loss into the matrix and unsaturated flow impacts the formation breakdown pressure and the post-breakdown pressure trends. Therefore, underestimation of such parameters in numerical modeling can lead to significant underestimation of breakdown pressure. The simulation results also indicate the importance of implementing wellbore solvers for considering the effect of system compressibility and pressure drop due to friction in the injection line. The varying injection rate as a result of decompression at the instant of fracture initiation affects the fracture size, while the entry friction at the connection between the well and the initial notch may cause an increase in the measured breakdown pressure.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

Acausality-driven instabilities in relativistic viscous hydrodynamics

We investigate non-linear instabilities stemming from superluminal propagation of information in Israel-Stewart-like models of relativistic viscous fluid dynamics. In relativity, the characteristic speed of propagation of information, $w$, and the speed of the fluid, $v$, allow us to differentiate between regimes of the hydrodynamic equations that are acausal but stable ($w>1$), unstable ($v^{2} w^{2} \geq 1$), and covariantly ill-posed ($w^{2} \leq 0$). As an analytical benchmark, we present a new solution that illustrates these distinct regimes. We compare this analytical solution to the result of a numerical relativistic viscous fluid dynamics solver, and confirm that the analytical result can be recovered numerically in the stable regime, whether causal or acausal. The onset of numerical instabilities is further found to occur in the regime predicted by the analytical solution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations

Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. This study explores a quantum-inspired approach to solving DEs, combining quantum- inspired techniques with classical methods. It focuses on fixed- point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate DE solutions. We expand upon the techniques introduced by Zanger et al. [Quantum, 5, 502 (2021)] by offering a precise computation for a fixed-point signed multiplication scheme, while also presenting a quantum circuit capable of executing the fixed-point division algorithm. We demonstrate the feasibility of our approach through the simulation of a linear Ordinary Differential Equation (ODE), where initial conditions and parameters are encoded into quantum circuits using fixed- point representation. By executing sequences of quantum gates mimicking numerical integration steps, we obtain approximate solutions to the ODE with specified fixed-point precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

GPU-acceleration of the ELPA2 distributed eigensolver for dense symmetric and hermitian eigenproblems

The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems can easily exceed the capacity of a single compute node, thus must be solved on distributed-memory parallel computers. We here present GPU-oriented optimizations of the ELPA two-stage tridiagonalization eigensolver (ELPA2). On top of cuBLAS-based GPU offloading, we add a CUDA kernel to speed up the back-transformation of eigenvectors, which can be the computationally most expensive part of the two-stage tridiagonalization algorithm. Furthermore, we benchmark the performance of this GPU-accelerated eigensolver on two hybrid CPU–GPU architectures, namely a compute cluster based on Intel Xeon Gold CPUs and NVIDIA Volta GPUs, and the Summit supercomputer based on IBM POWER9 CPUs and NVIDIA Volta GPUs. Consistent with previous benchmarks on CPU-only architectures, the GPU-accelerated two-stage solver exhibits a parallel performance superior to the one-stage counterpart. Finally, we demonstrate the performance of the GPU-accelerated eigensolver developed in this work for routine semi-local KS-DFT calculations comprising thousands of atoms.

97 MATHEMATICS AND COMPUTING↗