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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
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 OSTI2018

The General Atomics Center for Magnetohydrodynamic Modeling (CEMM) Final Report

The Center for Extended Magnetohydrodynamic Modeling (CEMM) is built around the further development, verification, validation, and other application of two major extended magnetohydrodynamics (MHD) codes NIMROD and M3D-C1. The General Atomics (GA) CEMM Program focuses on three main research areas: extension of the M3D-C1 MHD code plasma response calculations to new regimes, coupling of the DK4D drift kinetic equation solver to a temperature evolution equation, and simulations of disruption mitigation for unstable plasmas with pre-existing magnetic islands using massive gas injection (MGI) with the NIMROD MHD code. A systematic scan of the zero-crossing of the rotation profile in a DIII-D ITER-similar shape equilibrium using linear, time-independent modeling with M3D-C1 was performed. A new Python utility, autoC1, has been developed to automate the running of M3D-C1 for linear simulations. A number of ELM suppression experiments were analyzed including a validation and cross-code verification with the MARS-F MHD code of magnetic signal phase shifts across ELM-suppression bifurcations. A linearized, time-dependent temperature equation was tightly coupled to the electron and ion drift-kinetic equations (DKEs) in the DK4D drift-kinetic equation solver. Various explicit and implicit implementations were attempted, but all methods proved numerically unstable, even with the addition of numerical dissipation. Several simulations were completed investigating the effects of pre-existing islands on disruption mitigation by MGI in DIII-D using NIMROD.

3D MHD Simulation↗
DOE OSTI2021

ANTS

The ANTS code (Alternate Non-Linear Two-phase Solver) is based on a novel non-linear solution algorithm for the solution of the two-phase, subchannel fluid equations. It achieves its performance through decoupling of the two-phase momentum equations (axial and transverse) from the axial phasic mass and energy equations which allows for a nested non-linear iteration scheme. This enables a plane-by-plane solution which the inner iteration focuses on a reduced non-linear equation set for the primitives in phasic mass flow rate, enthalpy and void for each node edge. Single node edges are coupled as part of the outer iteration via surface mass fluxes which appear as source terms in the inner iteration scheme. The outer iteration readily accommodates two-phase flow phenomena closure relationships for subchannel mixing and void drift. A primary feature is the use of a non-staggered mesh computational mesh and steady-state iterative solver in contrast to all existing subchannel codes.

Kropaczek, David J↗
DOE OSTI2018

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used to compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A Low-Rank Solver for the Navier--Stokes Equations with Uncertain Viscosity

In this work, we study an iterative low-rank approximation method for the solution of the steady-state stochastic Navier--Stokes equations with uncertain viscosity. The method is based on linearization schemes using Picard and Newton iterations and stochastic finite element discretizations of the linearized problems. For computing the low-rank approximate solution, we adapt the nonlinear iterations to an inexact and low-rank variant, where the solution of the linear system at each nonlinear step is approximated by a quantity of low rank. This is achieved by using a tensor variant of the GMRES method as a solver for the linear systems. We explore the inexact low-rank nonlinear iteration with a set of benchmark problems, using a model of flow over an obstacle, under various configurations characterizing the statistical features of the uncertain viscosity, and we demonstrate its effectiveness by extensive numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Compare linear-system solver and preconditioner stacks with emphasis on GPU performance and propose phase-2 NGP solver development pathway

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind project are Nalu-Wind, which is an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, and OpenFAST, which is a whole-turbine simulation code. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. In this report we evaluated GPU-performance baselines for the linear solvers in the Trilinos and hypre solver stacks using two representative Nalu-Wind simulations: an atmospheric boundary layer precursor simulation on a structured mesh, and a fixed-wing simulation using unstructured overset meshes. Both strong-scaling and weak-scaling experiments were conducted on the OLCF supercomputer Summit and similar proxy clusters. We focused on the performance of multi-threaded Gauss-Seidel and two-stage Gauss-Seidel that are extensions of classical Gauss-Seidel; of one-reduce GMRES, a communication-reducing variant of the Krylov GMRES; and algebraic multigrid methods that incorporate the afore-mentioned methods. The team has established that AMG methods are capable of solving linear systems arising from the fixed-wing overset meshes on CPU, a critical intermediate result for ExaWind FY20 Q3 and Q4 milestones. For the fixed-wing strong-scaling study (model with 3M grid-points), the team identified that Nalu-Wind simulations with the new Trilinos and hypre solvers scale to modest GPU counts, maintaining above 70% efficiency up to 6 GPUs. However, there still remain significant bottlenecks to performance: matrix assembly (hypre), AMG setup (hypre and Trilinos) In the weak-scaling experiments (going from 0.4M to 211M gridpoints), it's shown that the solver apply phases are faster on GPUs, but that Nalu-Wind simulation times grow, primarily due to the multigrid-setup process. Finally, based on the report outcomes, we propose a linear solver path-forward for the remainder of the ExaWind project. Near term, the NREL team will continue their work on GPU-based linear-system assembly. They will also investigate how the use of alternatives to the NVIDIA UVM (unified virtual memory) paradigm affects performance. Longer term, the NREL team will evaluate algorithmic performance on other types of accelerators and merge their improvements back to the main hypre repository branch. Near term, the Trilinos team will address performance bottlenecks identified in this milestone, such as implementing a GPU-based segregated momentum solve and reusing matrix graphs across linear-system assembly phases. Longer term, the Trilinos team will do detailed analysis and optimization of multigrid setup.

17 WIND ENERGY↗
DOE OSTI2025

Consistent Second Moment Methods with Scalable Linear Solvers for Radiation Transport

Second moment methods (SMMs) are developed that are consistent with the discontinuous Galerkin spatial discretization of the discrete ordinates (or S\(_N\)) transport equations. The low-order (LO) diffusion system of equations is discretized with fully consistent P\(_1\), local discontinuous Galerkin (LDG), and interior penalty (IP) methods. A discrete residual approach is used to derive SMM correction terms that make each of the LO systems consistent with the high-order discretization. We show that the consistent methods are more accurate and have better solution quality than independently discretized LO systems, that they preserve the diffusion limit, and that the LDG and IP consistent SMMs can be scalably solved in parallel on a challenging, multimaterial benchmark problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multi-time case. In this paper, we establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we develop the relation between the regularized linear regression problem and the Linear Quadratic Regulator (LQR). We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ordinary differential equations) to design new training approaches for machine learning. Lastly, we provide some numerical examples that demonstrate the versatility and possible computational advantages of our Riccati-based approach in the context of continual learning, post-training calibration, transfer learning, and sparse dynamics identification.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A flexible gyro-fluid system of equations

Gyro-fluid equations are velocity space moments of the gyrokinetic equations. Special gyro-Landau-fluid closures have been developed that include the damping due to kinetic resonances by fitting to the collisionless local plasma response functions. This damping allows for accurate linear eigenmodes to be computed with a relatively low number of velocity space moments compared to the number of velocity quadrature points in gyrokinetic codes. However, none of the published gyro-Landau-fluid closure schemes considers the Onsager symmetries of the resulting quasi-linear fluxes as a constraint. Onsager symmetry guarantees that the matrix of diffusivities is positive definite, an important property for the numerical stability of a transport solver. A two-parameter real closure for improving the accuracy of low-resolution gyro-fluid equations, which preserves the Onsager symmetry and allows higher velocity space moments, is presented in this paper. The new linear gyro-fluid system (GFS) is used to extend the TGLF quasi-linear transport model so that it can compute the energy and momentum fluxes due to parallel magnetic fluctuations, completing the transport matrix. The GFS equations do not use a bounce average approximation. The GFS equations are fully electromagnetic with general flux surface magnetic geometry, pitch angle scattering for electron collisions, and subsonic equilibrium toroidal rotation. Using GFS eigenmodes in the quasi-linear TGLF model will be shown to yield a more accurate match to fluxes computed by CGYRO turbulence simulations. In conclusion, prospects for future applications of a quasi-linear theory to new plasma transport regimes and magnetic confinement devices in addition to tokamaks are opened by the flexibility of the GFS eigensolver.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

A vector unsymmetric eigenequation solver for nonlinear flutter analysis on high-performance computers

A finite element approach is presented for determining the nonlinear flutter characteristics of composite panels using unsteady, third-order piston theory aerodynamics. Both nonlinear structural (large-amplitude) and nonlinear aerodynamics terms are considered in the finite element formulation. Solution procedures are presented to solve the nonlinear panel flutter and the large-amplitude free vibration finite element equations. Nonlinear aerodynamic and linear structural finite element flutter results for composite panels are also presented. An efficient, vector-version generalized unsymmetric eigenequation solver is developed for large-amplitude vibration and nonlinear panel flutter analyses on high-performance computers.

Qin, Jiangning↗
DOE OSTI2016

Eigenvalue Solver for Fluid and Kinetic Plasma Models in Arbitrary Magnetic Topology

ArbiTER (Arbitrary Topology Equation Reader) is a new code for solving linear eigenvalue problems arising from a broad range of physics and geometry models. The primary application area envisioned is boundary plasma physics in magnetic confinement devices; however ArbiTER should be applicable to other science and engineering fields as well. The code permits a variable numbers of dimensions, making possible application to both fluid and kinetic models. Additionally, the use of specialized equation and topology parsers permits a high degree of flexibility in specifying the physics and geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE

Performing accurate and efficient numerical simulation of global atmospheric climate models is challenging due to the disparate length and time scales over which physical processes interact. Implicit solvers enable the physical system to be integrated with a time step commensurate with processes being studied. The dominant cost of an implicit time step is the ancillary linear system solves, so we have developed a preconditioner aimed at improving the efficiency of these linear system solves. Our preconditioner is based on an approximate block factorization of the linearized shallow-water equations and has been implemented within the spectral element dynamical core within the Community Atmospheric Model (CAM-SE). Furthermore, in this paper we discuss the development and scalability of the preconditioner for a suite of test cases with the implicit shallow-water solver within CAM-SE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

symPACK: A GPU-Capable Fan-Out Sparse Cholesky Solver

Sparse symmetric positive definite systems of equations are ubiquitous in scientific workloads and applications. Parallel sparse Cholesky factorization is the method of choice for solving such linear systems. Therefore, the development of parallel sparse Cholesky codes that can efficiently run on today’s large-scale heterogeneous distributed-memory platforms is of vital importance. Modern supercomputers offer nodes that contain a mix of CPUs and GPUs. To fully utilize the computing power of these nodes, scientific codes must be adapted to offload expensive computations to GPUs. We present symPACK, a GPU-capable parallel sparse Cholesky solver that uses one-sided communication primitives and remote procedure calls provided by the UPC++ library. We also utilize the UPC++ "memory kinds" feature to enable efficient communication of GPU-resident data. We show that on a number of large problems, symPACK outperforms comparable state-of-the-art GPU-capable Cholesky factorization codes by up to 14x on the NERSC Perlmutter supercomputer.

Bellavita, Julian↗
DOE OSTI2018

Small Non-Linear Solver

SNLS (small non-linear solver) is a C++ library for solving non-linear systems. The emphasis is on small systems on equations for which direct factorization of the Jacobian is appropriate. The systems of equations may be numerically ill-conditioned. Implementation is amenable to GPU usage, with the idea that class instantiate would occur within device functions.

Wayne, BrettM.↗
DOE OSTI2015

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, large conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.

58 GEOSCIENCES↗
NASA NTRS1988

Newton solution of inviscid and viscous problems

The application of Newton iteration to inviscid and viscous airfoil calculations is examined. Spatial discretization is performed using upwind differences with split fluxes. The system of linear equations which arises as a result of linearization in time is solved directly using either a banded matrix solver or a sparse matrix solver. In the latter case, the solver is used in conjunction with the nested dissection strategy, whose implementation for airfoil calculations is discussed. The boundary conditions are also implemented in a fully implicit manner, thus yielding quadratic convergence. Complexities such as the ordering of cell nodes and the use of a far field vortex to correct freestream for a lifting airfoil are addressed. Various methods to accelerate convergence and improve computational efficiency while using Newton iteration are discussed. Results are presented for inviscid, transonic nonlifting and lifting airfoils and also for laminar viscous cases.

Venkatakrishnan, V.↗
NASA NTRS1990

Computation of the unsteady facilitated transport of oxygen in hemoglobin

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

Davis, Sanford↗
DOE OSTI2024

Exploiting Power Flow Manifold to Solve AC Optimal Power Flow

AC optimal power flow has proven difficult to solve with interior point methods on GPUs. This is largely due to challenging linear algebra problems that current state of the art massively parallel linear solvers struggle with. However, the advent of Riemannian optimization techniques and the fact that the power flow equations form a smooth manifold present an alternative approach. In this talk, we present the basics of Riemannian optimization techniques in which optimization is done directly on a manifold. Then we present computational results showing that Riemannian techniques are capable of producing solutions of comparable quality as interior point methods.

AC optimal power flow↗