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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

On the Development of an Efficient Parallel Hybrid Solver with Application to Acoustically Treated Aero-Engine Nacelles

A finite element solution to the convected Helmholtz equation in a nonuniform flow is used to model the noise field within 3-D acoustically treated aero-engine nacelles. Options to select linear or cubic Hermite polynomial basis functions and isoparametric elements are included. However, the key feature of the method is a domain decomposition procedure that is based upon the inter-mixing of an iterative and a direct solve strategy for solving the discrete finite element equations. This procedure is optimized to take full advantage of sparsity and exploit the increased memory and parallel processing capability of modern computer architectures. Example computations are presented for the Langley Flow Impedance Test facility and a rectangular mapping of a full scale, generic aero-engine nacelle. The accuracy and parallel performance of this new solver are tested on both model problems using a supercomputer that contains hundreds of central processing units. Results show that the method gives extremely accurate attenuation predictions, achieves super-linear speedup over hundreds of CPUs, and solves upward of 25 million complex equations in a quarter of an hour.

Watson, Willie R.↗
DOE OSTI2014

A semi-analytical solver for the Grad-Shafranov equation

In toroidally confined plasmas, the Grad-Shafranov equation, in general, a non-linear partial differential equation, describes the hydromagnetic equilibrium of the system. This equation becomes linear when the kinetic pressure is proportional to the poloidal magnetic flux and the squared poloidal current is a quadratic function of it. In this work, the eigenvalue of the associated homogeneous equation is related with the safety factor on the magnetic axis, the plasma beta, and the Shafranov shift; then, the adjustable parameters of the particular solution are bounded through physical constrains. The poloidal magnetic flux becomes a linear superposition of independent solutions and its parameters are adjusted with a non-linear fitting algorithm. This method is used to find hydromagnetic equilibria with normal and reversed magnetic shear and defined values of the elongation, triangularity, aspect-ratio, and X-point(s). The resultant toroidal and poloidal beta, the safety factor at the 95% flux surface, and the plasma current are in agreement with usual experimental values for high beta discharges and the model can be used locally to describe reversed magnetic shear equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

ButterflyPACK

ButterflyPACK is a mathematical software for rapidly solving large-scale dense linear systems that exhibit off-diagonal rank-deficiency properties. These targeted systems are either matrices arising from discretized boundary integral equations, or frontal matrices in multi-frontal solvers for differential equations. ButterflyPACK relies on low-rank and butterfly formats under Hierarchical matrix, HODLR or HSS frameworks to compress, factor/precondition and solve the linear system in quasi-linear time. ButterflyPACK is particularly useful for large-scale ill-conditioned matrices arising from high-frequency wave equations involving multiple right-hand-sides. ButterflyPACK is based on Fortran 2003, it also has interface written in C++. In addition, ButterflyPACK can be readily invoked from the software STRUMPACK. ButterflyPACK supports hybrid MPI/OpenMP programming models.

Liu, Yang↗
DOE OSTI2019

Paraniso 1.0: 3-D Full Waveform Seismic Simulation in General Anisotropic Media

Many geologic materials and minerals are seismically anisotropic, with the most general anisotropic material having up to 21 independent elastic coefficients. This report outlines the development of a 3-D, generally anisotropic, linear elastic full waveform finite-difference solver. First, a mathematical description of the solution equations will be described. The finite-difference implementation of these equations will then be shown. Finally, a comparison of results from this new solver to other solutions will be provided as verification that the new algorithm can accurately replicate these solutions.

58 GEOSCIENCES↗
DOE OSTI2014

Robust parallel iterative solvers for linear and least-squares problems (Final Technical Report)

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners for solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Meade, Andrew J., Jr.↗
NASA NTRS1991

Parallel variable-band Choleski solvers for computational structural analysis applications on vector multiprocessor supercomputers

A Choleski method used to solve linear systems of equations that arise in large scale structural analyses is described. The method uses a novel variable-band storage scheme and is structured to exploit fast local memory caches while minimizing data access delays between main memory and vector registers. Several parallel implementations of this method are described for the CRAY-2 and CRAY Y-MP computers demonstrating the use of microtasking and autotasking directives. A portable parallel language, FORCE, is also used for two different parallel implementations, demonstrating the use of CRAY macrotasking. Results are presented comparing the matrix factorization times for three representative structural analysis problems from runs made in both dedicated and multi-user modes on both the CRAY-2 and CRAY Y-MP computers. CPU and wall clock timings are given for the various parallel methods and are compared to single processor timings of the same algorithm. Computation rates over 1 GIGAFLOP (1 billion floating point operations per second) on a four processor CRAY-2 and over 2 GIGAFLOPS on an eight processor CRAY Y-MP are demonstrated as measured by wall clock time in a dedicated environment. Reduced wall clock times for the parallel methods relative to the single processor implementation of the same Choleski algorithm are also demonstrated for runs made in multi-user mode.

Poole, E. L.↗
DOE OSTI2018

Kinetic-j : A computational kernel for solving the linearized Vlasov equation applied to calculations of the kinetic, configuration space plasma current for time harmonic wave electric fields

We present the Kinetic-j code, a computational kernel for evaluating the linearized Vlasov equation withapplication to calculating the kinetic plasma response (current) to an applied time harmonic wave electricfield. This code addresses the need for a configuration space evaluation of the plasma current to enablekinetic full-wave solvers for waves in hot plasmas to move beyond the limitations of the traditional Fourierspectral methods. We benchmark the kernel via comparison with the standard k-space forms of the hotplasma conductivity tensor.

Green, David L.↗
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 OSTI2014

A semi-local spectral/hp element solver for linear elasticity problems:

We develop an efficient semi-local method for speeding up the solution of linear systems arising in spectral/hp element discretization of the linear elasticity equations. The main idea is to approximate the element-wise residual distribution with a localization operator we introduce in this paper, and subsequently solve the local linear system. Additionally, we decouple the three directions of displacement in the localization operator, hence enabling the use of an efficient low energy preconditioner for the conjugate gradient solver. This approach is effective for both nodal and modal bases in the spectral/hp element method, but here, we focus on the modal hierarchical basis. In numerical tests, we verify that there is no loss of accuracy in the semi-local method, and we obtain good parallel scalability and substantial speed-up compared to the original formulation. In particular, our tests include both structure-only and fluid-structure interaction problems, with the latter modeling a 3D patient-specific brain aneurysm. Copyright © 2014 John Wiley & Sons, Ltd.

Engineering↗
DOE OSTI2021

A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients

Abstract Domain decomposition methods have been proved to be an effective strategy to reduce the dimension of parametric partial differential equations (PDEs). However, existing domain decomposition methods for parametric PDEs are usually intrusive, which means domain decomposition based solvers need to be implemented from scratch for each target parametric PDE. To address this issue, we develop a new non‐intrusive domain‐decomposition model reduction method for linear steady‐state PDEs with random‐field coefficients. As a variant of our previous work by Mu and Zhang, the new method only needs access to the final linear system, that is, the global stiffness matrix and the right hand side, of a deterministic PDE solver, in order to build a domain‐decomposition‐based reduced model without intrusive implementation from scratch. The key idea is to remove the interface condition between sub‐domains and rely on the correlation between columns of the linear system to couple the sub‐domains. The non‐intrusive feature enables the applicability of the proposed method to a broader class of uncertainty quantification problems, where many legacy codes/solvers can be fully reused by our method. Two numerical examples including diffusion equations with random diffusivity and convection‐dominated transport with random velocity, are provided to demonstrate the effectiveness and efficiency of our method.

Zhang, Guannan↗
DOE OSTI2014

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations

A recent proof-of-principle study proposes an energy- and charge-conserving, nonlinearly implicit electrostatic particle-in-cell (PIC) algorithm in one dimension [9]. The algorithm in the reference employs an unpreconditioned Jacobian-free Newton–Krylov method, which ensures nonlinear convergence at every timestep (resolving the dynamical timescale of interest). Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC as a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation. This study proposes such a preconditioner, in which the linearized moment equations are closed with moments computed from particles. Effective acceleration of the linear GMRES solve is demonstrated, on both uniform and non-uniform meshes. The algorithm performance is largely insensitive to the electron–ion mass ratio. Numerical experiments are performed on a 1D multi-scale ion acoustic wave test problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm is shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A neural approach for the numerical modeling of two-dimensional magnetic hysteresis

This paper deals with a neural network approach to model magnetic hysteresis at macro-magnetic scale. Such approach to the problem seems promising in order to couple the numerical treatment of magnetic hysteresis to FEM numerical solvers of the Maxwell's equations in time domain, as in case of the non-linear dynamic analysis of electrical machines, and other similar devices, making possible a full computer simulation in a reasonable time. The neural system proposed consists of four inputs representing the magnetic field and the magnetic inductions components at each time step and it is trained by 2-d measurements performed on the magnetic material to be modeled. The magnetic induction B is assumed as entry point and the output of the neural system returns the predicted value of the field H at the same time step. A suitable partitioning of the neural system, described in the paper, makes the computing process rather fast. Validations with experimental tests and simulations for non-symmetric and minor loops are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Preliminary Development of a Drift-Flux Model Based Pin-Resolved Core Thermal-Hydraulic Code for Dedicated Use in Efficient High-Fidelity Neutronics Coupled Calculations

As the high-fidelity multiphysics coupled core calculation becomes more practical with the advent of high-performance computing technology, efficient coupling of a neutronics code with a thermal-hydraulic (T/H) code at the pin level poses a new challenge. The COBRA-TF (CTF) code which is one of the well-known subchannel analysis codes based on the two-fluid, three-field model was coupled with many neutron transport codes such as MPACT, TORTTD, and nTRACER due to the easiness of coupling by its well-established coupling interface. Nevertheless, the calculation efficiency of such coupled codes is not satisfactory because of the heavy computational burden of CTF. The MATRA subchannel analysis code of KAERI which is based on the homogeneous equilibrium model (HEM) was coupled with neutronics codes as well. The choice of the HEM and the marching scheme in MATRA reduces the computational burden significantly. However, the applicability of the HEM for the two-phase flow conditions is limited to normal operating conditions of pressurized water reactors (PWRs) and therefore a better model which would allow wider applicability than HEM is necessary in order to deal with the core states involving nontrivial voiding. The drift-flux model (DFM) which uses 5 equations for two-fluid analyses by adopting the mixture velocity instead of two phasic velocities can be a good compromise between the two-fluid model and the HEM. With the DFM, the computational cost can be reduced and moreover the modeling of the interfacial area constitutive relations can be avoided. The phase separation for the mixture velocity can be incorporated by using the drift-flux parameters, C0 and Vgj, which can be obtained by using empirical formulas. Several subchannel codes such as WOSUB and ASSERT were developed based on the DFM. It was also adopted in some system analysis codes such as RETRAN3D. In the work here, the development of a DFM based pin-resolved T/H analysis code, ESCOT (Efficient Simulator of Core Thermal-hydraulics), is introduced for the use in efficient coupled calculations with a high-fidelity neutronics code. The field equations and the numerical methods are briefly described. Then the efficiency tests of various linear system solvers including the Krylov subspace methods (KSMs) are presented. A test problem is solved by ESCOT, MATRA and CTF for performance comparison and validation. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2012

High performance radiation transport simulations: Preparing for TITAN

In this paper we describe the Denovo code system. Denovo solves the six-dimensional, steady-state, linear Boltzmann transport equation, of central importance to nuclear technology applications such as reactor core analysis (neutronics), radiation shielding, nuclear forensics and radiation detection. The code features multiple spatial differencing schemes, state-of-the-art linear solvers, the Koch-Baker-Alcouffe (KBA) parallel-wavefront sweep algorithm for inverting the transport operator, a new multilevel energy decomposition method scaling to hundreds of thousands of processing cores, and a modern, novel code architecture that supports straightforward integration of new features. In this paper we discuss the performance of Denovo on the 20+ petaflop ORNL GPU-based system, Titan. We describe algorithms and techniques used to exploit the capabilities of Titan's heterogeneous compute node architecture and the challenges of obtaining good parallel performance for this sparse hyperbolic PDE solver containing inherently sequential computations. Numerical results demonstrating Denovo performance on early Titan hardware are presented.

Baker, C.↗
DOE OSTI2018

Deploy threading in Nalu solver stack

The goal of the ExaWind project is to enable predictive simulations of wind farms composed of many MW-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 code in the ExaWind project is Nalu, which is an unstructured-grid solver for the acousticallyincompressible Navier-Stokes equations, and mass continuity is maintained through pressure projection. The 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 re-initialization of matrices and re-computation of preconditioners is required at every time step In this Milestone, we examine the effect of threading on the solver stack performance against flat-MPI results obtained from previous milestones using Haswell performance data full-turbine simulations. Whereas the momentum equations are solved only with the Trilinos solvers, we investigate two algebraic-multigrid preconditioners for the continuity equations: Trilinos/Muelu and HYPRE/BoomerAMG. These two packages embody smoothed-aggregation and classical Ruge-Stiiben AMG methods, respectively. In our FY18 Q2 report, we described our efforts to improve setup and solve of the continuity equations under flat-MPI parallelism. While significant improvement was demonstrated in the solve phase, setup times remained larger than expected. Starting with the optimized settings described in the Q2 report, we explore here simulation performance where OpenMP threading is employed in the solver stack. For Trilinos, threading is acheived through the Kokkos abstraction where, whereas HYPRE/BoomerAMG employs straight OpenMP. We examined results for our mid-resolution baseline turbine simulation configuration (229M DOF). Simulations on 2048 Haswell cores explored the effect of decreasing the number of MPI ranks while increasing the number of threads. Both HYPRE and Trilinos exhibited similar overal solution times, and both showed dramatic increases in simulation time in the shift from MPI ranks to OpenMP threads. This increase is attributed to the large amount of work per MPI rank starting at the single-thread configuration. Decreasing MPI ranks, while increasing threads, may be increasing simulation time due to thread synchronization and start-up overhead contributing to the latency and serial time in the model. These result showed that an MPI+OpenMP parallel decomposition will be more effective as the amount per MPI rank computation per MPI rank decreases and the communication latency increases. This idea was demonstrated in a strong scaling study of our low-resolution baseline model (29M DOF) with the Trilinos-HYPRE configuration. While MPI-only results showed scaling improvement out to about 1536 cores, engaging threading carried scaling improvements out to 4128 cores — roughly 7000 DOF per core. This is an important result as improved strong scaling is needed for simulations to be executed over sufficiently long simulated durations (i.e., for many timesteps). In addition to threading work described above, the team examined solver-performance improvements by exploring communication-overhead in the HYPRE-GMRES implementation through a communicationoptimal- GMRE algorithm (CO-GMRES), and offloading compute-intensive solver actions to GPUs. To those ends, a HYPRE mini-app was allow us to easily test different solver approaches and HYPRE parameter settings without running the entire Nalu code. With GPU acceleration on the Summitdev supercomputer, a 20x speedup was achieved for the overall preconditioner and solver execution time for the mini-app. A study on Haswell processors showed that CO-GMRES provides benefits as one increases MPI ranks.

17 WIND ENERGY↗
DOE OSTI2015

A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers

We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗