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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Nonlocal transport in bounded two-dimensional systems: An iterative method

Here, the concept of transport mediated through the dynamics of 'jumping' particles is used to develop an iterative method for obtaining steady-state solutions to the nonlocal transport equation in two dimensions (2D). The technique is self-adjoint and capable of correctly treating spatially non-uniform, asymmetric systems. An appropriate reduced version of the iteration method is used to compare with results obtained with a self-adjoint 1D transport matrix approach. The transport 'jump' probability distribution functions (pdfs) are based on Lévy α-stable distributions. The technique can handle the entire Lévy α-parameter range from one (Lorentz distributions) to two (Gaussian distributions). Cases with α = 2 (standard diffusion) are used to establish the validity of the iterative method. The capabilities of the iterative method are demonstrated by presenting examples from systems with various source configurations, boundary shapes, boundary conditions and spatial variations in parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Design Considerations to Ensure Robustness of the ITER Diagnostics Residual Gas Analyzer

Increasing robustness of the ITER diagnostic residual gas analyzer (DRGA) is critical for the potential control of plasma heating and fuel-cycle processing. Robustness is a requirement for a diagnostic to have a control function. The DRGA is a multisensor diagnostic system capable of resolving isotopic compositions of hydrogen and helium as well as other heavier elements and compounds. The divertor-specific DRGA system is intended to measure the composition of gases in the ITER subdivertor region and midplane. Its analysis station will be located in a port cell at the divertor level. From there, it will sample a slip stream of gas from the cryogenic pump duct. It will then exhaust into a shared roughing line where helium or other light gas impurities, some potentially from other diagnostic systems, are likely to be present. In order to provide reliable measurements, the DRGA must be robust in areas such as plasma optical emission source geometry for a compact design, mitigation of back-streaming from light gases and resilience to the ITER port cell environment, and radiation hardening of the DRGA electronics. By incorporating robustness into the design, areas of plasma heating and fuel-cycle control may be explored with the DRGA for ITER and next-generation fusion devices.

Quinlan, Brendan↗
DOE OSTI2023

PERKS: a Locality-Optimized Execution Model for Iterative Memory-bound GPU Applications

Iterative memory-bound solvers commonly occur in HPC codes. Typical GPU implementations have a loop on the host side that invokes the GPU kernel as much as time/algorithm steps there are. The termination of each kernel implicitly acts the barrier required after advancing the solution every time step. We propose an execution model for running memory-bound iterative GPU kernels: PERsistent KernelS (PERKS). In this model, the time loop is moved inside persistent kernel, and device-wide barriers are used for synchronization. We then reduce the traffic to device memory by caching subset of the output in each time step in the unused registers and shared memory. PERKS can be generalized to any iterative solver: they largely independent of the solver's implementation. We explain the design principle of PERKS and demonstrate effectiveness of PERKS for a wide range of iterative 2D/3D stencil benchmarks (geomean speedup of 2.12x for 2D stencils and 1.24x for 3D stencils over state-of-art libraries), and a Krylov subspace conjugate gradient solver (geomean speedup of 4.86x in smaller SpMV datasets from SuiteSparse and 1.43x in larger SpMV datasets over a state-of-art library). All PERKS-based implementations available at: https://github.com/neozhang307/PERKS.

Zhang, Lingqi↗
DOE OSTI2012

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

Bavier, Eric↗
DOE OSTI2015

Preliminary Neutronics Analysis of the ITER Toroidal Interferometer and Polarimeter Diagnostic Corner Cube Retroreflectors

ITER is an international project under construction in France that will demonstrate nuclear fusion at a power plant-relevant scale. The Toroidal Interferometer and Polarimeter (TIP) Diagnostic will be used to measure the plasma electron line density along 5 laser-beam chords. This line-averaged density measurement will be input to the ITER feedback-control system. The TIP is considered the primary diagnostic for these measurements, which are needed for basic ITER machine control. Therefore, system reliability & accuracy is a critical element in TIP’s design. There are two major challenges to the reliability of the TIP system. First is the survivability and performance of in-vessel optics and second is maintaining optical alignment over long optical paths and large vessel movements. Both of these issues greatly depend on minimizing the overall distortion due to neutron & gamma heating of the Corner Cube Retroreflectors (CCRs). These are small optical mirrors embedded in five first wall locations around the vacuum vessel, corresponding to certain plasma tangency radii. During the development of the design and location of these CCRs, several iterations of neutronics analyses were performed to determine and minimize the total distortion due to nuclear heating of the CCRs. The CCR corresponding to TIP Channel 2 was chosen for analysis as a good middle-road case, being an average distance from the plasma (of the five channels) and having moderate neutron shielding from its blanket shield housing. Results show that Channel 2 meets the requirements of the TIP Diagnostic, but barely. These results suggest other CCRs might be at risk of exceeding thermal deformation due to nuclear heating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Multiphysics Engineering Analysis for an Integrated Design of ITER Diagnostic First Wall and Diagnostic Shield Module Design

ITER diagnostic first walls (DFWs) and diagnostic shield modules (DSMs) inside the port plugs (PPs) are designed to protect diagnostic instrument and components from a harsh plasma environment and provide structural support while allowing for diagnostic access to the plasma. The design of DFWs and DSMs are driven by 1) plasma radiation and nuclear heating during normal operation 2) electromagnetic loads during plasma events and associate component structural responses. A multi-physics engineering analysis protocol for the design has been established at Princeton Plasma Physics Laboratory and it was used for the design of ITER DFWs and DSMs. The analyses were performed to address challenging design issues based on resultant stresses and deflections of the DFW-DSM-PP assembly for the main load cases. ITER Structural Design Criteria for In-Vessel Components (SDC-IC) required for design by analysis and three major issues driving the mechanical design of ITER DFWs are discussed. The general guidelines for the DSM design have been established as a result of design parametric studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Iterative HOMER with uncertainties

We present iHOMER, an iterative version of the HOMER method to extract Lund fragmentation functions from experimental data. Through iterations, we address the information gap between latent and observable phase spaces and systematically remove bias. To quantify uncertainties on the inferred weights, we use a combination of Bayesian neural networks and uncertainty-aware regression. We find that the combination of iterations and uncertainty quantification produces well-calibrated weights that accurately reproduce the data distribution. A parametric closure test shows that the iteratively learned fragmentation function is compatible with the true fragmentation function.

Butter, Anja [Heidelberg Univ. (Germany); Sorbonne↗
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↗
DOE OSTI2014

Simple Construction of High Order Rational Iterative Equation Solvers

This article proposes a general technique to construct arbitrarily high order rational one-point iterative equation solvers based on truncated Taylor expansion from lower order schemes. With adding one more function call, an iterative equation solver of convergence order n can be accelerated to order (2n-1). Many existing (some recently published) one-point and two-point iterative equation solvers are special cases of the proposed construction. The proposed approach may be used to obtain new iterative equation solvers.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

A geometric theory for the QR, LU and power iterations.

Consideration of the task of computing the invariant subspaces of a given matrix. For this purpose the LU, QR, treppen and bi-iterations have been presented, used, and studied more or less independently of the old-fashioned power method. Each of these methods generates implicitly a sequence of subspaces which determines the convergence properties of the method. The iterations differ in the way in which a basis is constructed to represent each subspace. This aspect largely determines the usefulness of the method. It is shown that the first four iterations produce exactly the same sequence of subspaces as do direct and inverse iteration started from appropriate subspaces. Their convergence properties are therefore the same, and a complete geometric convergence theory is presented in terms of the power method. It is shown that Hessenberg matrices are associated with ideal starting spaces.

Parlett, B. N.↗
NASA NTRS1977

Comparison of linear inversion methods by examination of the duality between iterative and inverse matrix methods

Linear numerical inversion methods applied to atmospheric remote sounding generally can be categorized in two ways: (1) iterative, and (2) inverse matrix methods. However, these two categories are not unrelated; a duality exists between them. In other words, given an iterative scheme, a corresponding inverse matrix method exists, and conversely. This duality concept is developed for the more familiar linear methods. The iterative duals are compared with the classical linear iterative approaches and their differences analyzed. The importance of the initial profile in all methods is stressed. Calculations using simulated data are made to compare accuracies and to examine the dependence of the solution on the initial profile.

Fleming, H. E.↗
NASA NTRS1985

On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

Brand, J. C.↗
NASA NTRS1988

Leapfrog variants of iterative methods for linear algebra equations

Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial approximation, a variant of the iteration called the grand-leap method. In the case of the grand-leap variant, a set of parameters is required. An algorithm is presented to compute these parameters that is related to algorithms to compute the weights and abscissas for Gaussian quadrature. General algorithms to implement the leapfrog and grand-leap methods are presented. Algorithms for the important special case of the Chebyshev method are also given.

Saylor, Paul E.↗
NASA NTRS1991

Distributed Minimal Residual (DMR) method for acceleration of iterative algorithms

A new method for enhancing the convergence rate of iterative algorithms for the numerical integration of systems of partial differential equations was developed. It is termed the Distributed Minimal Residual (DMR) method and it is based on general Krylov subspace methods. The DMR method differs from the Krylov subspace methods by the fact that the iterative acceleration factors are different from equation to equation in the system. At the same time, the DMR method can be viewed as an incomplete Newton iteration method. The DMR method was applied to Euler equations of gas dynamics and incompressible Navier-Stokes equations. All numerical test cases were obtained using either explicit four stage Runge-Kutta or Euler implicit time integration. The formulation for the DMR method is general in nature and can be applied to explicit and implicit iterative algorithms for arbitrary systems of partial differential equations.

Lee, Seungsoo↗
NASA NTRS1990

A two-step iterative method for evolving nonlinear acoustic systems to a steady-state

A new approach for evolving two-dimensional nonlinear acoustic systems with flow to a steady state is presented. The approach is a two-step iterative method which is tested on a benchmark acoustic problem for which an exact analytical solution is available. Results are also calculated for a nonlinear acoustic problem for which an exact analytical solution is not known. Results indicate that the two-step method represents a powerful, efficient, and stable method for evolving two-dimensional acoustic systems to a steady state, and that the method is applicable to any number of spatial dimensions and to other hyperbolic systems. It is noted that for the benchmark problem only a single iteration on the method is required when the transient and steady-state field are of the same order of magnitude; however, four iterations are required when the steady-state field is several orders of magnitude smaller than the transient field. This method requires six iterations before achieving a steady state for the nonlinear test problem.

Watson, Willie R.↗
NASA NTRS1991

Comparing direct and iterative equation solvers in a large structural analysis software system

Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.

Poole, E. L.↗
NASA NTRS1992

Upwind relaxation methods for the Navier-Stokes equations using inner iterations

A subsonic and a supersonic problem are respectively treated by an upwind line-relaxation algorithm for the Navier-Stokes equations using inner iterations to accelerate steady-state solution convergence and thereby minimize CPU time. While the ability of the inner iterative procedure to mimic the quadratic convergence of the direct solver method is attested to in both test problems, some of the nonquadratic inner iterative results are noted to have been more efficient than the quadratic. In the more successful, supersonic test case, inner iteration required only about 65 percent of the line-relaxation method-entailed CPU time.

Taylor, Arthur C., III↗
NASA NTRS1993

Helicopter trim analysis by shooting and finite element methods with optimally damped Newton iterations

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Achar, N. S.↗