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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 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↗
DOE OSTI2025

Variational quantum and neural quantum states algorithms for the linear complementarity problem

Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems—and whether quantum-inspired classical algorithms can match their performance—remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid-body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modelling certain physical systems.

neural quantum states↗
DOE OSTI2023

PETSc/TAO Users Manual (Rev. 3.19)

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication. PETSc/TAO includes a large suite of parallel linear solvers, nonlinear solvers, time integrators, and opti mization that may be used in application codes written in Fortran, C, C++, and Python (via petsc4py; see Getting Started). PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than packages such as MATLAB or a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++, python, or Fortran and experience using a debugger such as gdb or lldb, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than “rolling them” yourself. For many tasks a package such as MATLAB is often the best tool; PETSc is not intended for the classes of problems for which effective MATLAB code can be written. There are several packages, built on PETSc, that may satisfy your needs without requiring directly using PETSc. We recommend reviewing these packages functionality before starting to code directly with PETSc. PETSc can be used to provide a “MPI parallel linear solver” in an otherwise sequential, or OpenMP parallel code. This approach cannot provide extremely large improvements in the application time by utilizing large numbers of MPI processes but can still improve the performance. Certainly all parts of a previously sequential code need not be parallelized but the matrix generation portion must be parallelized to expect true scalability to large numbers of MPI processes. See PCMPI for details on how to utilize the PETSc MPI linear solver server. Since PETSc is under continued development, small changes in usage and calling sequences of routines will occur. PETSc has been supported for twenty-five years; see mailing list information on our website for information on contacting support.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Performance and Energy Study of GPU-Resident Preconditioners for Conjugate Gradient Solvers: In the Context of Existing and Novel Approaches

Optimizing a particular subprogram out of the set of Basic (sparse) Linear Algebra Subprograms (BLAS) for a given architecture is a common topic of research. In applications, however, these BLAS functions rarely appear in isolation; usually, many of them are used together, in various combinations and with varying inputs. As the need to solve a large, sparse linear system is ubiquitous throughout HPC applications, linear solvers constitute a realistic, sufficiently complex and well-defined representative use case for composite BLAS routines. To this end, based on a representative set of matrices drawn from a diverse set of fields, we present a framework to study, from the performance and energy perspective, the efficacy of GPU- resident parallel Conjugate Gradient (CG) linear solver with different preconditioner options, including Gauss-Seidel, Jacobi, and incomplete Cholesky. We also propose a novel GPU-based preconditioner, in which the triangular solves are approximated by an iterative process. The development of this preconditioner was motivated by solving large graph Laplacian linear systems, for which the existing preconditioners either perform slow on GPU-based platforms or are not applicable. We compare the performance of these preconditioners on different hardware accelerator architectures, i.e., AMD MI250X, MI100, Nvidia A100, V100, and Jetson. Our experiments reveal performance trade-offs and provide information on how to select the best strategy for the given linear system, dictated by its properties, and the platform of interest. We demonstrate the application of our novel preconditioner for solving CG and graph Laplacian systems. Overall, the framework can be utilized as a benchmark to guide informed decisions in choosing a specific preconditioner, i.e., whether it is better to rely on the performance of a triangular solver or on the performance of sparse matrix-vector product. Finally, by considering power consumption to solve the linear systems, we report the energy footprint for the solvers.

Preconditioned Conjugate Gradient, GPUs, iterative↗
DOE OSTI2026

Quantum Solver Using Singular Value Decomposition for Computational Fluid Dynamics

Numerical solutions for fluid flow problems are challenging and have been focus of Computational Fluid Dynamics (CFD) research for past several decades. The advent of quantum computing promises exponential speedup in comparison to existing classical methods and alleviate computational constraints posed by CFD problems. Although solutions for most problems of interest in fluid dynamics using quantum computing are distant, recent advances in algorithms, software and hardware provide a path towards realizing this goal. Quantum linear solver algorithms (QLSA) such as Harrow–Hassidim–Lloyd (HHL) and Variational Quantum Linear Solver (VQLS) have been successfully implemented to solve for canonical problems such as Hele-Shaw flow. However, these algorithms still suffer to scale and address problems with ill-conditioned Jacobians. In the current paper, we alleviate these restrictions with a new quantum solver based on Singular Value Decomposition (SVD) and simulate flow past a 2D cylinder. The fidelity of the SVD based quantum solver in predicting the flow past 2D cylinder is computed along with an assessment of errors. Classical and quantum solutions for the flow are compared for different resolutions. Finally, we discuss variation in the solutions based on number of shots used.

Gottiparthi, Kalyan [ORNL] (ORCID:0000000213540255↗
DOE OSTI2024

A Fast Algebraic Multigrid Solver and Accurate Discretization for Highly Anisotropic Heat Flux I: Open Field Lines

We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii) efficient implicit linear solvers. We simultaneously address each of these challenges by constructing a new finite element discretization with excellent accuracy properties, tailored to a novel solver approach based on algebraic multigrid (AMG) methods designed for advective operators. We pose the problem in a mixed formulation, introducing the directional temperature gradient as an auxiliary variable. The temperature and auxiliary fields are discretized in a scalar discontinuous Galerkin space with upwinding principles used for discretizations of advection. We demonstrate the proposed discretization’s superior accuracy over other discretizations of anisotropic heat flux, achieving error 1000x smaller for anisotropy ratio of 10 9 , for closed field lines. The block matrix system is reordered and solved in an approach where the two advection operators are inverted using AMG solvers based on approximate ideal restriction, which is particularly efficient for upwind discontinuous Galerkin discretizations of advection. To ensure that the advection operators are nonsingular, in this paper we restrict ourselves to considering open (acyclic) magnetic field lines for the linear solvers. We demonstrate fast convergence of the proposed iterative solver in highly anisotropic regimes where other diffusion-based AMG methods fail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Assessing VQLS for Fluid Dynamics on a Hybrid Quantum-HPC Stack

Recent advances in quantum linear solvers offer a promising direction for accelerating extreme scientific computations such as fluid dynamics. However, the deep and complex circuits required by many quantum algorithms limit their practical use on current quantum hardware. The Variational Quantum Linear Solver (VQLS) presents a viable alternative for near-term quantum devices (NISQ), and initial efforts have explored its application to select fluid dynamics problems. In this work, we evaluate the use of VQLS for canonical fluid dynamics problems, aiming to identify pathways for generalizing its implementation across a broader class of systems. We analyze the impact of various circuit ansatz and classical optimizers on solution quality and convergence behavior. Furthermore, we assess the algorithm's feasibility within a hybrid quantum–high-performance computing (HPC) framework by porting it to QFw, a state-of-the-art quantum-HPC software stack. 11This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the US DOE under Contract No. DE-AC05-00OR22725.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗
DOE OSTI2023

Towards Efficient Alternating Current Optimal Power Flow Analysis on Graphical Processing Units

We present a solution of sparse ACOPF analysis on GPU. In particular, we discuss the performance bottlenecks and detail our efforts to accelerate the linear solver, a core component of ACOPF that dominates the computational time. ACOPF solutions of two large-scale systems, synthetic Northeast (25,000 buses) and Eastern (70,000 buses) \cite{birchfield2017tamu-cases} on GPU show promising speed-up compared to CPU based solution using a state-of-the-art solver. To our knowledge, this is the first result demonstrating acceleration of sparse ACOPF on GPUs.

Power grid analysis, GPU↗
DOE OSTI2023

AMG2023

The AMG2023 benchmark solves two diffusion problems with a linear solver preconditioned with algebraic multigrid. The code only contains a driver, a Makefile, and a documentation file. It requires an installation of the open source software library hypre that needs to be downloaded elsewhere and is not included here. Its purpose is to benchmark linear solver performance on high performance computers.

Li, Ruipeng↗
DOE OSTI2025

Towards Seamless Interoperability of MPI-OpenMP Applications

A chasm exists between mathematical software libraries written for MPI-based applications and those written for OpenMP applications. Recently, however, PETSc enables the simple use of its MPI-based linear solvers from OpenMP applications. Separately, the MPICH MPI development team has started a new project to allow almost seamless MPI use in OpenMP applications. Both proposed approaches would result in a similar user experience. Here, we discuss the reasons for these projects and their potential for providing more numerical library choices for OpenMP applications, including the unlimited assortment of linear solvers available in PETSc. In addition, we present the performance of an application using the first approach, demonstrating its efficacy.

MPI↗
DOE OSTI2023

High Fidelity Computational Model for Fluidized Bed Experiments (Final Report)

MFiX was integrated with preconditioners and linear solver packages in Trilinos via MFIX, Fortran, C, and C++ wrappers. The MFIX wrapper interpreted the structure of the matrix and vector from MFiX while the Fortran wrapper transfers this information to a low-level language, C. C-wrapper transforms the memory semantic between Fortran and C++ language. C++ wrapper passes the matrix and vector to a Trilinos package and gets the solution. This solution was transferred to MFiX via C++, C, Fortran, MFIX wrapper. The framework is used to integrate first, second and third generation linear solvers in Trilinos with MFiX.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

LuGo: An enhanced quantum phase estimation implementation

Quantum Phase Estimation (QPE) is a cardinal algorithm in quantum computing that plays a crucial role in various applications, including cryptography, molecular simulation, and solving systems of linear equations. However, the standard implementation of QPE faces challenges related to time complexity and circuit depth, which limit its practicality for large-scale computations. We introduce LuGo, a novel framework designed to enhance the performance of QPE by reducing circuit duplication, as well as using parallelization techniques to achieve faster generation of the QPE circuit and gate reduction. We validate the effectiveness of our framework by generating quantum linear solver circuits, which require both QPE and inverse QPE, to solve linear systems of equations. LuGo achieves significant improvements in both computational efficiency and hardware requirements without compromising on accuracy. Compared to a standard QPE implementation, LuGo reduces time consumption to generate a circuit that solves a 2 6 × 2 6 system matrix by a factor of 50.68 and over 31× reduction of quantum gates and circuit depth, with no fidelity loss on an ideal quantum simulator. Furthermore, we demonstrated the versatility and scalability of LuGo enabled HHL algorithm by simulating a canonical Hele-Shaw fluid problem using a quantum simulator. With these advantages, LuGo paves the way for more efficient implementations of QPE, enabling broader applications across several quantum computing domains.

Quantum algorithm↗
DOE OSTI2025

GPU acceleration of hybrid functional calculations in the SPARC electronic structure code

We present a Graphics Processing Unit (GPU)-accelerated version of the real-space SPARC electronic structure code for performing hybrid functional calculations in generalized Kohn–Sham density functional theory. In particular, we develop a batch variant of the recently formulated Kronecker product-based linear solver for the simultaneous solution of multiple linear systems. We then develop a modular, math kernel based implementation for hybrid functionals on NVIDIA architectures, where computationally intensive operations are offloaded to the GPUs, while the remaining workload is handled by the central processing units (CPUs). Considering bulk and slab examples, we demonstrate that GPUs enable up to 8× speedup in node-hours and 80× in core-hours compared to CPU-only execution, reducing the time to solution on V100 GPUs to around 300 s for a metallic system with over 6000 electrons, and significantly reducing the computational resources required for a given wall time.

Kohn-Sham density functional theory↗
DOE OSTI2025

Half-closed discontinuous Galerkin discretisations

Here we introduce the concept of half-closed nodes for nodal discontinuous Galerkin (DG) discretisations. Unlike more commonly used closed nodes in DG, where on every element nodes are placed on all of its boundaries, half-closed nodes only require nodes to be placed on a subset of the element's boundaries. The effect of using different nodes on DG operator sparsity is studied and we find in particular for there to be no difference in the sparsity pattern of the Laplace operator whether closed or half-closed nodes are used. On quadrilateral/hexahedral elements we use the Gauss-Radau points as the half-closed nodes of choice, which we demonstrate is able to speed up DG operator assembly in addition to leverage previously known superconvergence results. We also discuss in this work some linear solver techniques commonly used for Finite Element or discontinuous Galerkin methods such as static condensation and block-based methods, and how they can be applied to half-closed DG discretisations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Noisy-Intermediate-Scale Quantum Electromagnetic Transients Program

Quantum-empowered electromagnetic transients program (QEMTP) is a promising paradigm for tackling EMTP's computational burdens. Nevertheless, no existing studies truly achieve a practical and scalable QEMTP operable on today's noisy-intermediate-scale quantum (NISQ) computers. The strong reliance on noise-free and fault-tolerant quantum devices--which appears to be decades away--hinder practical applications of current QEMTP methods. Here, we devise a NISQ-QEMTP methodology which for the first time transitions the QEMTP operations from ideal, noise-free quantum simulators to real, noisy quantum computers. The main contributions lie in: (1) a shallow-depth QEMTP quantum circuit for mitigating noises on NISQ quantum devices; (2) practical QEMTP linear solvers incorporating executable quantum state preparation and measurements for nodal voltage computations; (3) a noise-resilient QEMTP algorithm leveraging quantum resources logarithmically scaled with power system dimension; (4) a quantum shifted frequency analysis (QSFA) for accelerating QEMTP by exploiting dynamic phasor simulations with larger time steps; (5) a systematical analysis on QEMTPs performance under various noisy quantum environments. Extensive experiments systematically verify the accuracy, efficacy, universality and noise-resilience of QEMTP on both noise-free simulators and IBM real quantum computers.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗