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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Parallel implicit unstructured grid Euler solvers

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a multiple-instruction/multiple-data stream parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed: one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All of the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the Intel iPSC/860.

TRT-THEORETICAL↗
DOE OSTI2020

A High-Throughput Solver for Marginalized Graph Kernels on GPU

Here, we present the design and optimization of a solver for efficient and high-throughput computation of the marginalized graph kernel on General Purpose GPUs. The graph kernel is computed using the conjugate gradient method to solve a generalized Laplacian of the tensor product between a pair of graphs. To cope with the large gap between the instruction throughput and the memory bandwidth of the GPUs, our solver forms the graph tensor product on-the-fly without storing it in memory. This is achieved by using threads in a warp cooperatively to stream the adjacency and edge label matrices of individual graphs by small square matrix blocks called tiles, which are then staged in registers and the shared memory for later reuse. Warps across a thread block can further share tiles via the shared memory to increase data reuse. We exploit the sparsity of the graphs hierarchically by storing only non-empty tiles using a coordinate format and nonzero elements within each tile using bitmaps. We propose a new partition-based reordering algorithm for aggregating nonzero elements of the graphs into fewer but denser tiles to further exploit sparsity. We carry out extensive theoretical analyses on the graph tensor product primitives for tiles of various density and evaluate their performance on synthetic and real-world datasets. Our solver delivers three to four orders of magnitude speedup over existing CPU-based solvers such as GraKeL and GraphKernels. The capability of the solver enables kernel-based learning tasks at unprecedented scales.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Sparse Linear Algebra Toolkit for Computational Aerodynamics

Finding solutions to sparse linear systems of equations is an essential step in Computational Engineering applications of interest to NASA. Linear systems of equations are composed and solved in almost every computational engineering application. The characteristics of linear systems vary greatly from one application to another. Accordingly, there are a wide variety of methods for the solution of linear systems of equations. The operations and methods prepared by the authors are focused on linear systems of interest to NASA, primarily those associated with Computational Fluid Dynamics (CFD), Aeroelasticity, and Aeroacoustics. The Sparse Linear Algebra Toolkit (SLAT) is a coordinated collection of software featuring operations, methods, and data structures that are useful when solving sparse linear systems of equations on modern computer architectures. The implemented operations and methods are designed and tuned for parallelism in shared memory, in distributed memory, and across the hybrid combination of distributed-shared memory. The toolkit includes novel methods and implementations for modern architectures and facilitates development of new approaches for meeting NASA’s evolving computational engineering challenges using evolving computer architectures that are not available in vendor libraries. In this paper, significant features and interfaces within SLAT are presented and verified for simulations performed with NASA’s CFD solver, FUN3D. The runtime and scaling performance of the Generalized Minimum Residual (GMRES) method implemented in SLAT is analyzed for the linear subproblems within the solution of turbulent Navier-Stokes equations employed in the simulation of high-lift configurations. Prior to this work, the SPARSKIT GMRES implementation was the only Krylov subspace method available within FUN3D. A strong scaling study shows the SLAT GMRES implementation facilitates accurate Reynolds-averaged Navier-Stokes CFD solutions between 15% and 56% faster than the SPARSKIT GMRES implementation.

Stephen L Wood↗
DOE OSTI2020

A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media

Simulation of multiphase poromechanics involves solving a multiphysics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also known as monolithic approaches, are usually preferred. The main bottleneck of a monolithic approach is that it requires solution of large linear systems that result from the discretization and linearization of the governing balance equations. Because such systems are nonsymmetric, indefinite, and highly ill-conditioned, preconditioning is critical for fast convergence. Recently, most efforts in designing efficient preconditioners for multiphase poromechanics have been dominated by physics-based strategies. Current state-of-the-art “black-box” solvers such as algebraic multigrid (AMG) are ineffective because they cannot effectively capture the strong coupling between the mechanics and the flow subproblems, as well as the coupling inherent in the multiphase flow and transport process. In this work, we develop an algebraic framework based on multigrid reduction (MGR) that is suited for tightly coupled systems of PDEs. Using this framework, the decoupling between the equations is done algebraically through defining appropriate interpolation and restriction operators. One can then employ existing solvers for each of the decoupled blocks or design a new solver based on knowledge of the physics. We demonstrate the applicability of our framework when used as a “black-box” solver for multiphase poromechanics. Here, we show that the framework is flexible to accommodate a wide range of scenarios, as well as efficient and scalable for large problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Sensor enabled data-driven predictive analytics for modeling and control with high penetration of DERs in distribution systems

The electric power grid is undergoing a tremendous transformation due to the increasing penetration of renewable energy resources beginning with wind and more recently with the distributed energy resources (DERs) such as solar and battery storage. DERs have dramatically changed the role of the distribution systems in the overall power grid, and they are expected to contribute a significant portion of power generation in the future. If current trends for DERs continue, system operation and control will need to change dramatically for improved grid reliability and resiliency. As renewable resources increase in penetration, new and challenging operational, planning, and design problems are expected to emerge. Some of the key challenges that arise in the planning and operation of the future grid are: 1) Quantifying the impact of high DER penetration in distribution systems on bulk grid behavior over multiple time scales. 2) Identifying whether a particular DER configuration/settings have a large impact on the overall grid behavior. These challenges can be addressed in an offline manner using detailed T&D grid models and they can also be addressed in an online manner using sensor measurements. In particular, the advancement and planned growth in sensor technology in power grid over various voltage levels provide us with a unique opportunity to tackle these challenges from a data analytic perspective without needing detailed T&D grid models. A few questions that naturally arise when addressing the challenges from DERs using sensor data are: 1) How can we use limited sensor measurements to monitor & control voltage stability and small signal stability of the bulk system? 2) How can we ensure that the developed data analytic methods are robust to data availability and quality issues? 3) How can we compute the developed analytics in a scalable manner using streaming measurements? In this project, we addressed the aforementioned challenges arising from DERs and answered the questions raised above on how to effectively use the sensor measurements to enhance the reliability and performance of the electric grid. Thus, the overarching goal of this project is to develop effective reduced/representative system models from data that make the computational complexity sufficiently manageable so as to be useful to simulate, analyze, and even control complex non-linear power systems dynamics with large penetrations of DERs. In order to achieve the objective, the project team established a four-fold technical approach 1) Formulated a combined transmission-distribution co-simulation framework for data generation and validation, 2) Derived reduced/representative models of power systems based on data-driven methods for efficient computation and appropriate representation of system behavior, 3) Developed data driven characterization of power system behavior based on transfer operator theory, machine learning and optimization for model estimation, 4) Incorporated a scalable data management and processing architecture using distributed Kafka streaming applications that coordinate input data streams to the developed data analytics. The key accomplishments of the project are: 1) Development of a scalable multi-timescale T&D co-simulation framework (both for steady state and for dynamic co-simulation) using commercial solvers (PSSE and GridLAB-D). The steady-state T&D co-simulation interface is shared with our industry partner (PJM). 2) A structured reduced order dynamic model of distribution systems that can represent partial motor stalling along with a systematic procedure to derive the model parameters. 3) A PMU based online method to monitor, localize and mitigate fault-induced delayed voltage recovery using DER reactive support and load control in distribution systems. 4) Development of linear operator based robust methodologies for dynamic state estimation, uncertainty quantification, system identification and trajectory prediction for power system dynamics. 5) An adaptive damping control for utilizing wind energy resources to provide oscillation damping and system stability. 6) Implementation of Kafka-based framework for efficient processing of streaming data using Linux-based local virtual environment.

DER integration↗
DOE OSTI2023

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling

Abstract In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled 60 Co (Type M) and 131 I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method ( expm ). The differences generally observed between the implicit solvers and expm are attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

61 RADIATION PROTECTION AND DOSIMETRY↗
NASA NTRS2001

Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation With No Radial Axis Inputs

Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame, propulsion system simplifications and weight reduction may be accomplished. This work focuses on the validation of this control system on its own merits, and in comparison to a related system which does provide thrust along the radial axis of the relative frame. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. Control algorithm performance is evaluated based on measures such as the fuel required to complete a maneuver and the maximum acceleration required by the controller. Based on this evaluation, the exclusion of the radial axis of control still allows enough control authority to use Linear Quadratic Regulator (LQR) techniques to design a gain matrix of adequate performance over finite maneuvers. Additional simulations are conducted including perturbations and using no radial control inputs. A major conclusion presented is that control inputs along the three axes have significantly different relationships to the governing orbital dynamics that may be exploited using LQR.

Starin, Scott R.↗
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↗
NASA NTRS2016

Validation of High-Fidelity CFD/CAA Framework for Launch Vehicle Acoustic Environment Simulation against Scale Model Test Data

A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed for launch vehicle liftoff acoustic environment predictions. The framework couples the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate discontinuous Galerkin solver developed in the same production framework, Loci/THRUST, to accurately resolve and propagate acoustic physics across the entire launch environment. Time-accurate, Hybrid RANS/LES CFD modeling is applied for predicting the acoustic generation physics at the plume source, and a high-order accurate unstructured discontinuous Galerkin (DG) method is employed to propagate acoustic waves away from the source across large distances using high-order accurate schemes. The DG solver is capable of solving 2nd, 3rd, and 4th order Euler solutions for non-linear, conservative acoustic field propagation. Initial application testing and validation has been carried out against high resolution acoustic data from the Ares Scale Model Acoustic Test (ASMAT) series to evaluate the capabilities and production readiness of the CFD/CAA system to resolve the observed spectrum of acoustic frequency content. This paper presents results from this validation and outlines efforts to mature and improve the computational simulation framework.

Liever, Peter A.↗
NASA NTRS2016

Validation of High-Fidelity CFD/CAA Framework for Launch Vehicle Acoustic Environment Simulation against Scale Model Test Data

A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed for launch vehicle liftoff acoustic environment predictions. The framework couples the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate Discontinuous Galerkin solver developed in the same production framework, Loci/THRUST, to accurately resolve and propagate acoustic physics across the entire launch environment. Time-accurate, Hybrid RANS/LES CFD modeling is applied for predicting the acoustic generation physics at the plume source, and a high-order accurate unstructured mesh Discontinuous Galerkin (DG) method is employed to propagate acoustic waves away from the source across large distances using high-order accurate schemes. The DG solver is capable of solving 2nd, 3rd, and 4th order Euler solutions for non-linear, conservative acoustic field propagation. Initial application testing and validation has been carried out against high resolution acoustic data from the Ares Scale Model Acoustic Test (ASMAT) series to evaluate the capabilities and production readiness of the CFD/CAA system to resolve the observed spectrum of acoustic frequency content. This paper presents results from this validation and outlines efforts to mature and improve the computational simulation framework.

Liever, Peter A.↗
DOE OSTI2024

Towards a NEAMS-based high-fidelity model of the MARVEL reactor

This report outlines the progress of Idaho National Laboratory in developing a high-fidelity and high-resolution model of the Microreactor Applications Research Validation and Evaluation reactor. The model was developed under the Nuclear Energy Advanced Modeling and Simulation microreactor application driver at Idaho National Laboratory. The overarching objective of this activity is the development of a high-fidelity multiphysics MARVEL model using NEAMS tools, and to verify and validate NEAMS tools against MARVEL reference simulation and experimental data, respectively. This is a unique opportunity to conduct multiphysics analysis on a soon-to-be-deployed microreactor. This multiphysics model developed under the NEAMS-funded INL microreactor application driver leverages three single-physics models coupled via the MOOSE’s MultiApp and Transfer systems. The latter systems enable in-memory data transfer between MOOSE-based and MOOSE-wrapped applications. The first single-physics model, that functions as main application, leverages Griffin to model the neutron transport in the core through the discontinuous finite element (DFEM) discrete ordinates solver (SN). Several optimization flags that were developed by the Griffin developer team were beta-tested to enhance the solver’s performance. These include the combined use of using_average_xs and update_averaged_xs_on that enable to avoid expensive on-the-fly cross sections evaluations at each linear iterations in favor of evaluations of the macroscopic cross sections at each Picard iteration. The second single-physics model uses BISON to handle solid heat transfer and asymptotic hydrogen redistribution analysis in the fuel. While the model returns consistent results for the temperature and hydrogen distribution in the fuel, a mismatch was noticed in the calculated temperature in the reflector due to the value of the gap conductance used in our model. Ongoing investigations are being performed to assess the origin of this discrepancy. Finally, the System Analysis Module (SAM) was used to model the flow of the sodium-potassium eutectic in the primary loop. A first verification was also performed showing good agreement in terms of mass flow rate and inlet temperature. All mesh files were generated using the MOOSE Reactor module, removing the need for external meshing tools. Notably, this workscope represents one of the initial applications of the MOOSE Reactor module for modeling highly irregular geometries. The use of the reactor module significantly streamlined the mesh generation process. The full multiphysics mode, that combines all the single physics models, was leveraged to conduct initial steady-state multiphysics simulations to compute power, and temperature distribution in the reactor. Initial testing was performed for transient simulations as well. In this case, the new checkpoint restart capability for eigenvalue calculations was tested showing the capability for streamlined restart of transient calculations. Future work will focus on improving the fidelity of the model by performing comprehensive code-to-code comparisons. For instance, the full-core Griffin neutronics model will be benchmarked against MCNP reference results, that were provided by the MARVEL design team. Additionally, the SAM T/H model will be verified against reference RELAP-5 results for selected accident scenarios. Besides code-to-code verification exercises, the model fidelity will be improved by replacing the single-channel SAM model with a more complex SAM-Pronghorn coupled model, in which the sub-channel capability is deployed to obtain radial temperature resolution in the coolant. This model will be developed in synergy with the NEAMS thermal hydraulics team.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Advanced Quantum Poisson Solver in the NISQ era

The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental results, and discuss the sources of errors. Finally, we conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.

Robson, Walter↗
DOE OSTI2020

SAM Plug-in Development (Phase I Final Report)

The DOE Office of Nuclear Energy (NE) has created an extensive set of advanced modeling and simulation tools for nuclear engineering analysis. The advanced capabilities of these newer analysis codes require more in-depth training, skills, and knowledge in order to effectively utilize them for the design, analysis, and licensing of advanced nuclear systems and experiments. A high learning curve for inexperienced users may deter organizations from incorporating these tools into their internal processes. This project involved development of a plug-in to the Symbolic Nuclear Analysis Package (SNAP) for the System Analysis Module (SAM) tool. SAM is an advanced system analysis tool for reactor transient analyses being developed at Argonne National Laboratory under the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SAM utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage modern advanced software environments and numerical methods. SNAP provides a highly flexible framework for creating, modifying and documenting input for engineering analysis codes such as SAM as well as extensive functionality for submitting, monitoring, and interacting with the codes through an intuitive graphical user interface (GUI). The common user interface provided by SNAP minimizes the learning curve for engineers starting with a new analysis code and provides an intuitive framework for transitioning between different analysis codes. SNAP provides a powerful but intuitive interface to facilitate access to advanced modeling and simulation tools for inexperienced users. Unlike many “form based” GUI’s, SNAP maps each engineering code’s component input to an internal database which manages all component input parameters along with component interconnections. This level of abstraction permits SNAP to support several advanced capabilities such as renodalization, model validation and consistency checks, embedded documentation, model notebook generation, data ownership and reviewer tracking, and variable assignment for inputs to name a few. SNAP includes a built-in Python interpreter and is interfaced to several commercial and open source packages including CPython, MATLAB/OCTAVE, Microsoft Office, Open Office, and SANDIA’s DAKOTA package which provides Uncertainty Quantification analysis through the SNAP plug-ins. Phase I of this project involved development a fully functional basic SAM plug-in to SNAP. This plug-in provides the ability to import existing models, graphically construct, edit and submit models using SNAP’s extensive functionality.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

Efficient Topology Design Algorithms for Power Grid Stability

The dynamic response of power grids to small disturbances influences their overall stability. This letter examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework utilizes H 2 -norm based stability metrics to study the optimal placement of lines on existing networks as well as the topology design of new networks. The design task is first posed as an NP-hard mixed-integer nonlinear program (MINLP) that is exactly reformulated as a mixed-integer linear program (MILP) using McCormick linearization. To improve computation time, graph-theoretic properties are exploited to derive valid inequalities (cuts) and tighten bounds on the continuous optimization variables. Moreover, a cutting plane generation procedure is put forth that is able to interject the MILP solver and augment additional constraints to the problem on-the-fly. Finally, the efficacy of our approach in designing optimal grid topologies is demonstrated through numerical tests on the IEEE 39-bus network.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2001

Development of Unsteady Aerodynamic State-Space Models from CFD-Based Pulse Responses

A method for computing discrete-time state-space models of linearized unsteady aerodynamic behavior directly from aeroelastic CFD codes is presented. The method involves the treatment of CFD-based pulse responses as Markov parameters for use in a system identification /realization algorithm. Results are presented for the AGARD 445.6 Aeroelastic Wing with four aeroelastic modes at a Mach number of 0.96 using the EZNSS Euler/Navier-Stokes flow solver with aeroelastic capability. The System/Observer/Controller Identification Toolbox (SOCIT) algorithm, based on the Ho-Kalman realization algorithm, is used to generate 15th- and 32nd-order discrete-time state-space models of the unsteady aerodynamic response of the wing over the entire frequency range of interest.

Silva, Walter A.↗
DOE OSTI2025

Parallel-in-Time Solution of Hyperbolic PDE Systems via Characteristic-Variable Block Preconditioning

We consider the parallel-in-time solution of both linear and nonlinear hyperbolic partial differential equation (PDE) systems in one spatial dimension. In the nonlinear setting, the discretized equations are solved with a preconditioned residual iteration based on a global linearization. The linear(ized) equation systems are approximately solved parallel-in-time using a block preconditioner applied in the characteristic variables of the underlying linear(ized) hyperbolic PDE. This change of variables is motivated by the observation that intervariable coupling between characteristic variables is weak, at least locally where spatio-temporal variations in the eigenvectors of the associated flux Jacobian are sufficiently small, while that between the original variables is not. For an ℓ-dimensional system of PDEs, applying the preconditioner consists of solving a sequence of ℓ scalar linear(ized)-advection-like problems, each associated with a different characteristic wave-speed in the underlying linear(ized) PDE. Furthermore, we approximately solve these linear advection problems using multigrid reduction-in-time (MGRIT); however, any other suitable parallel-in-time method could be used. Numerical examples are shown for the (linear) acoustics equations in heterogeneous media and for the (nonlinear) shallow water equations and Euler equations of gas dynamics with shocks and rarefactions. For many test problems, the solver converges in just a handful of iterations and with mesh-independent convergence rates.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Preconditioned conjugate gradient methods for the Navier-Stokes equations

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Ajmani, Kumud↗
DOE OSTI2020

Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems

Security-constrained unit commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via mixed-integer linear programming (MIP), sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine learning techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions, and affine subspaces where the optimal solution is likely to lie, leading to a significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that using the proposed techniques, SCUC can be solved on average 4.3 times faster with optimality guarantees and 10.2 times faster without optimality guarantees, with no observed reduction in solution quality. Out-of-distribution experiments provide evidence that the method is somewhat robust against data-set shift. Summary of Contribution. The paper describes a novel computational method, based on a combination of mixed-integer linear programming (MILP) and machine learning (ML), to solve a challenging and fundamental optimization problem in the energy sector. The method advances the state-of-the-art, not only for this particular problem, but also, more generally, in solving discrete optimization problems via ML. We expect that the techniques presented can be readily used by practitioners in the energy sector and adapted, by researchers in other fields, to other challenging operations research problems that are solved routinely.

Machine Learning↗