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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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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A fast implicit solver for semiconductor models in one space dimension

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Agglomeration-based geometric multigrid solvers for compact discontinuous Galerkin discretizations on unstructured meshes

Here, we present a geometric multigrid solver for the Compact Discontinuous Galerkin method through building a hierarchy of coarser meshes using a simple agglomeration method which handles arbitrary element shapes and dimensions. The method is easily extendable to other discontinuous Galerkin discretizations, including the Local DG method and the Interior Penalty method. We demonstrate excellent solver performance for Poisson's equation, provided a flux formulation is used for the operator coarsening and a suitable switch function chosen for the numerical fluxes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Scalable Implicit Solvers with Dynamic Mesh Adaptation for a Relativistic Drift-Kinetic Fokker–Planck–Boltzmann Model

In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. Here, we develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management framework in the PETSc library based on the p4est library is developed to enable simulations with dynamic adaptive mesh refinement (AMR), distributed memory parallelization, and dynamic load balancing of computational work. This framework and the runaway electron solver building on the framework are able to dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the AMR algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. This strategy is complemented by the introduction of computationally cheap feature-based AMR indicators that are analyzed theoretically. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies; and we demonstrate trade-offs regarding computational costs. The robustness with respect to model parameters, algorithmic scalability, and parallel scalability are demonstrated through several benchmark problems including manufactured solutions and solutions of different physics models. We focus on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

On fast simulation of dynamical system with neural vector enhanced numerical solver

The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a trade-off between accuracy and computational efficiency. To address this challenge, we introduce a deep learning-based corrector called Neural Vector (NeurVec), which can compensate for integration errors and enable larger time step sizes in simulations. Our extensive experiments on a variety of complex dynamical system benchmarks demonstrate that NeurVec exhibits remarkable generalization capability on a continuous phase space, even when trained using limited and discrete data. NeurVec significantly accelerates traditional solvers, achieving speeds tens to hundreds of times faster while maintaining high levels of accuracy and stability. Moreover, NeurVec’s simple-yet-effective design, combined with its ease of implementation, has the potential to establish a new paradigm for fast-solving differential equations based on deep learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A fluid-structure interaction solver for investigating torsional galloping in solar-tracking photovoltaic panel arrays

Solar-tracking photovoltaic arrays are susceptible to aeroelastic fluttering during high-wind events. This dynamic fluttering behavior can grow in amplitude until the panels enter an unstable mode known as torsional galloping which can lead to panel failure or total array destruction. To better understand the physics of the torsional galloping phenomenon and to inform the discussion around panel design and recommended panel stow positions during high wind events, a fluid-structure interaction solver composed of a simulated atmospheric boundary layer with simplified panel structural responses was designed. The simulation choices and features of this solver were informed by the geometry and physical properties of an experimental panel array known to exhibit torsional galloping behavior during hind-wind events. Furthermore, these simulations revealed that the torsional galloping instability is driven by a combination of cyclic vortex shedding from the sun-facing side of the panel and the elastic properties of the torque tube linking the panel assemblies. Testing different stow angles across a range of wind speeds indicates that panels are generally more stable when stowed at negative angles where the leading edge is closer to the ground, hypothesized to be due to ground-blocking effects. These results are supplemented by a discussion of stability trends noted during testing and possible implications when considering multi-row array interactions.

14 SOLAR ENERGY↗
DOE OSTI2025

FreeMHD: Validation and verification of the open-source, multi-domain, multi-phase solver for electrically conductive flows

The extreme heat fluxes in the divertor region of tokamaks may require an alternative to solid plasma-facing components, for the extraction of heat and the protection of the surrounding walls. Flowing liquid metals are proposed as an alternative, but raise additional challenges that require investigation and numerical simulations. Free surface designs are desirable for plasma-facing components, but steady flow profiles and surface stability must be ensured to limit undesirable interactions with the plasma. Previous studies have mainly used steady-state, 2D, or simplified models for internal flows and have not been able to adequately model free-surface liquid metal (LM) experiments. Therefore, FreeMHD has been recently developed as an open-source magnetohydrodynamics (MHD) solver for free-surface electrically conductive flows subject to a strong external magnetic field. The FreeMHD solver computes incompressible free-surface flows with multi-region coupling for the investigation of MHD phenomena involving fluid and solid domains. The model utilizes the finite-volume OpenFOAM framework under the low magnetic Reynolds number approximation. FreeMHD is validated using analytical solutions for the velocity profiles of closed channel flows with various Hartmann numbers and wall conductance ratios. Next, experimental measurements are then used to verify FreeMHD, through a series of cases involving dam breaking, 3D magnetic fields, and free-surface LM flows. These results demonstrate that FreeMHD is a reliable tool for the design of LM systems under free surface conditions at the reactor scale. Furthermore, it is flexible, computationally inexpensive, and can be used to solve fully 3D transient MHD flows.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Phase field dislocation dynamics formulation coupled with Fourier based micromechanics solver and its application to grain boundary–dislocation interactions

A new phase field dislocation dynamics (PFDD) formulation for homogeneous and heterogeneous materials is presented, which couples micromechanical solvers and the time-dependent Ginzburg–Landau equation. The strain fields are obtained from the micromechanical solver by solving the Lippmann–Schwinger equation and then used to define energy terms to model the evolution of the dislocations. Grain boundary (GB)–dislocation interactions are studied using the coupled PFDD formulation and by describing GBs as inclusions. GB energy and stiffness tensors are computed from molecular statics simulations, and a newly proposed lattice energy term that is dependent on the GB energy is considered in the calculations. Interaction of a screw dislocation with minimum energy and metastable states of low and high angle ⟨110⟩ symmetric tilt grain boundaries are studied. We show good agreement between predictions from our PFDD formulation and molecular dynamics simulations of grain boundary–dislocation interactions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. Here, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10 –9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low amplitude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices

The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or non-trivial high-dimensional classical optimization. In this work, we introduce a quantum solver of contracted eigenvalue equations, the quantum analogue of classical methods for the energies and reduced density matrices of ground and excited states. The solver does not require deep circuits or difficult classical optimization and achieves an exponential speed-up over its classical counterpart. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An Interior-Point Solver for Optimal Power Flow Problem Considering Distributed FACTS Devices

In this paper, we propose an AC optimal power flow (ACOPF) model considering distributed flexible AC transmission system (D-FACTS) devices, in which the reactance of D-FACTS equipped lines are introduced as decision variables. This is motivated by increasing interests in using D-FACTS devices to address system operational and cyber-security concerns. First, D-FACTS devices can be incorporated in real-time operations for economic benefits such as managing power congestions and reducing system losses. Second, D-FACTS devices can be utilized by moving target defense (MTD), an emerging concept against cyber-attacks, to prevent attackers from knowing true system configurations. Therefore, system operators can use the proposed ACOPF model to achieve economic benefits and provide the setpoints of D-FACTS devices for MTD at the same time. In addition, we rigorously derive the gradient and Hessian matrices of the objective function and constraints, which are further used to build an interior-point solver of the proposed ACOPF. Numerical results on the IEEE 118-bus transmission system show the validity of the proposed ACOPF model as well as the efficacy of the interior-point solver in minimizing system losses and generation costs.

Liu, Bo↗
DOE OSTI2024

Early Exploration of a Flexible Framework for Efficient Quantum Linear Solvers in Power Systems

The rapid integration of renewable energy resources presents formidable challenges in managing power grids. While advanced computing and machine learning techniques offer some solutions for accelerating grid modeling and simulation, there remain complex problems that classical computers cannot effectively address. Quantum computing, a promising technology, has the potential to fundamentally transform how we manage power systems, especially in scenarios with a higher proportion of renewable energy sources. One critical aspect is solving linear systems of equations, crucial for power system applications like power flow analysis, for which the Harrow-Hassidim-Lloyd (HHL) algorithm is a well-known quantum solution. However, HHL quantum circuits often exhibit excessive depth, making them impractical for current Noisy-Intermediate-Scale-Quantum (NISQ) devices. In this paper, we introduce a versatile framework, powered by NWQSim, that bridges the gap between power system applications and quantum linear solvers available in Qiskit. This framework empowers researchers to efficiently explore power system applications using quantum linear solvers. Through innovative gate fusion strategies, reduced circuit depth, and GPU acceleration, our simulator significantly enhances resource efficiency. Power flow case studies have demonstrated up to a eight-fold speedup compared to Qiskit Aer, all while maintaining comparable levels of accuracy.

quantum computing, Harrow-Hassidim-Lloyd, high-per↗
DOE OSTI2024

ACOPF Transmission Switching Using Open-Source MINLP Solvers

The optimal transmission switching (OTS) problem with AC physics represents a mixed integer non-linear non-convex optimization problem which can provide benefits to transmission level power system operations. In this paper we benchmark a set of open-source mixed integer non-linear programming (MINLP) solvers on the OTS problem with AC physics using the pglib set of power system test cases. Results characterizing the performance of the different solvers are reported and discussed.

ACOPF↗
DOE OSTI2021

A Fast Solver for the Fractional Helmholtz Equation

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in Geophysical Electromagnetics. In this work, we establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales aswell as the best possible solver for the classical integer-order Helmholtz equation. We conclude withseveral illustrative examples that confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Ipopt Interface to Re::Solve Linear Solver

The software provides Ipopt optimization package an interface to the Re::Solve linear solver library. Re::Solve features GPU-resident direct and iterative linear solvers that could be used to accelerate optimization computations.

Alam, Maksudul [Oak Ridge National Laboratory (ORN↗
DOE OSTI2026

SPUS-Small-PDE-U-net-Solver

Small PDE U-Net Solver (SPUS) is a compact and efficient foundation model (FM) designed as a unified neural operator for solving a wide range of partial differentialequations (PDEs). SPUS leverages a lightweight residual U-Net-based architecture as a foundation model architecture. To enable effective learning in this minimalist framework, SPUS utilizes a simple yet powerful auto-regressive pretraining strategy which closely replicates the behavior of numerical solvers to learn the underlying physics. SPUS is designed to be pretrained on a diverse set of fluid dynamics PDEs from public benchmark datasets.

Siddik, Abu↗
DOE OSTI2022

Sampling electronic structure quadratic unconstrained binary optimization problems (QUBOs) with Ocean and Mukai solvers

The most advanced D-Wave Advantage quantum annealer has 5000+ qubits, however, every qubit is connected to a small number of neighbors. As such, implementation of a fully-connected graph results in an order of magnitude reduction in qubit count. To compensate for the reduced number of qubits, one has to rely on special heuristic software such as qbsolv, the purpose of which is to decompose a large quadratic unconstrained binary optimization (QUBO) problem into smaller pieces that fit onto a quantum annealer. In this work, we compare the performance of the open-source qbsolv which is a part of the D-Wave Ocean tools and a new Mukai QUBO solver from Quantum Computing Inc. (QCI). The comparison is done for solving the electronic structure problem and is implemented in a classical mode (Tabu search techniques). The Quantum Annealer Eigensolver is used to map the electronic structure eigenvalue-eigenvector equation to a QUBO problem, solvable on a D-Wave annealer. We find that the Mukai QUBO solver outperforms the Ocean qbsolv with one to two orders of magnitude more accurate energies for all calculations done in the present work, both the ground and excited state calculations. This work stimulates the further development of software to assist in the utilization of modern quantum annealers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Extending PETSc's Composable Hierarchical Solvers (Final Technical Report)

This report documents research activities conducted at CU Boulder as part of Extending PETSc’s Composable Hierarchical Solvers, which has been part of a collaboration with Argonne National Laboratory (separate award). Our work has focused on performance-portable end-to-end GPU solvers demonstrated via exemplary applications in nonlinear fluid and structural mechanics. We describe advances in algorithmic composition and analysis in the context of these applications, but the implementations are fully documented and decoupled, and in use by other projects. We believe the vertical integration achieved through collaboration with ECP’s CEED and the PSAAP center at CU was necessary to take risks with data structures and algorithms.

42 ENGINEERING↗