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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Domain decomposition preconditioners for the spectral collocation method

Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.

Quarteroni, Alfio↗
DOE OSTI2022

Performance enhancement of planar MOC calculation in hexagonal geometries by assembly-wise domain decomposition

The parallelization of planar Method of Characteristics (MOC) calculation with the higher order scattering in the hexagonal version of the nTRACER direct whole core calculation code is enhanced by adopting assembly-wise domain decomposition and other techniques. In order to augment the hexagonal domain decomposition, the three-color scheme, the angular decomposition, and the angular flux storage scheme are examined. The parallel performance assessed for the VVER benchmark problems demonstrates that the hexagonal assembly-wise domain decomposition significantly reduces the computing time in ray tracing by up to 64 %. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1993

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Farhat, Charbel↗
NASA NTRS2009

Preliminary Axial Flow Turbine Design and Off-Design Performance Analysis Methods for Rotary Wing Aircraft Engines: Validation - Part 1

For the preliminary design and the off-design performance analysis of axial flow turbines, a pair of intermediate level-of-fidelity computer codes, TD2-2 (design; reference 1) and AXOD (off-design; reference 2), are being evaluated for use in turbine design and performance prediction of the modern high performance aircraft engines. TD2-2 employs a streamline curvature method for design, while AXOD approaches the flow analysis with an equal radius-height domain decomposition strategy. Both methods resolve only the flows in the annulus region while modeling the impact introduced by the blade rows. The mathematical formulations and derivations involved in both methods are documented in references 3, 4 for TD2-2) and in reference 5 (for AXOD). The focus of this paper is to discuss the fundamental issues of applicability and compatibility of the two codes as a pair of companion pieces, to perform preliminary design and off-design analysis for modern aircraft engine turbines. Two validation cases for the design and the off-design prediction using TD2-2 and AXOD conducted on two existing high efficiency turbines, developed and tested in the NASA/GE Energy Efficient Engine (GE-E3) Program, the High Pressure Turbine (HPT; two stages, air cooled) and the Low Pressure Turbine (LPT; five stages, un-cooled), are provided in support of the analysis and discussion presented in this paper.

Chen, Shu-cheng, S.↗
DOE OSTI2016

Spectral Schur complement techniques for symmetric eigenvalue problems

This paper presents a domain decomposition-type method for solving real symmetric (Hermitian) eigenvalue problems in which we seek all eigenpairs in an interval [α; β] or a few eigenpairs next to a given real shift. Here, a Newton-based scheme is described whereby the problem is converted to one that deals with the interface nodes of the computational domain. This approach relies on the fact that the inner solves related to each local subdomain are relatively inexpensive. This Newton scheme exploits spectral Schur complements, and these lead to so-called eigenbranches, which are rational functions whose roots are eigenvalues of the original matrix. Theoretical and practical aspects of domain decomposition techniques for computing eigenvalues and eigenvectors are discussed. A parallel implementation is presented and its performance on distributed computing environments is illustrated by means of a few numerical examples.

parallel computing↗
DOE OSTI2015

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained from the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

Here, we explore the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparing with explicit time stepping of the same order accuracy in time, the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By dividing the original problem into many subdomain problems of smaller sizes and solving them locally, the proposed approach could speed up the calculation of matrix exponential vector products. Several standard test cases for shallow water equations of one or multiple layers are considered. The results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.

58 GEOSCIENCES↗
NASA NTRS1989

Compressible flow calculations employing the Galerkin/least-squares method

A multielement group, domain decomposition algorithm is presented for solving linear nonsymmetric systems arising in the finite-element analysis of compressible flows employing the Galerkin/least-squares method. The iterative strategy employed is based on the generalized minimum residual (GMRES) procedure originally proposed by Saad and Shultz. Two levels of preconditioning are investigated. Applications to problems of high-speed compressible flow illustrate the effectiveness of the scheme.

Shakib, F.↗
DOE OSTI2016

Improved scaling of temperature-accelerated dynamics using localization

While temperature-accelerated dynamics (TAD) is a powerful method for carrying out non-equilibrium simulations of systems over extended time scales, the computational cost of serial TAD increases approximately as N{sup 3} where N is the number of atoms. In addition, although a parallel TAD method based on domain decomposition [Y. Shim et al., Phys. Rev. B 76, 205439 (2007)] has been shown to provide significantly improved scaling, the dynamics in such an approach is only approximate while the size of activated events is limited by the spatial decomposition size. Accordingly, it is of interest to develop methods to improve the scaling of serial TAD. As a first step in understanding the factors which determine the scaling behavior, we first present results for the overall scaling of serial TAD and its components, which were obtained from simulations of Ag/Ag(100) growth and Ag/Ag(100) annealing, and compare with theoretical predictions. We then discuss two methods based on localization which may be used to address two of the primary “bottlenecks” to the scaling of serial TAD with system size. By implementing both of these methods, we find that for intermediate system-sizes, the scaling is improved by almost a factor of N{sup 1/2}. Some additional possible methods to improve the scaling of TAD are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Scharz Preconditioners for Krylov Methods: Theory and Practice

Several numerical methods were produced and analyzed. The main thrust of the work relates to inexact Krylov subspace methods for the solution of linear systems of equations arising from the discretization of partial differential equations. These are iterative methods, i.e., where an approximation is obtained and at each step. Usually, a matrix-vector product is needed at each iteration. In the inexact methods, this product (or the application of a preconditioner) can be done inexactly. Schwarz methods, based on domain decompositions, are excellent preconditioners for these systems. We contributed towards their understanding from an algebraic point of view, developed new ones, and studied their performance in the inexact setting. We also worked on combinatorial problems to help define the algebraic partition of the domains, with the needed overlap, as well as PDE-constraint optimization using the above-mentioned inexact Krylov subspace methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

Domain Decomposition Algorithms for First-Order System Least Squares Methods

Least squares methods based on first-order systems have been recently proposed and analyzed for second-order elliptic equations and systems. They produce symmetric and positive definite discrete systems by using standard finite element spaces, which are not required to satisfy the inf-sup condition. In this paper, several domain decomposition algorithms for these first-order least squares methods are studied. Some representative overlapping and substructuring algorithms are considered in their additive and multiplicative variants. The theoretical and numerical results obtained show that the classical convergence bounds (on the iteration operator) for standard Galerkin discretizations are also valid for least squares methods.

Pavarino, Luca F.↗
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 OSTI2012

Robust volume calculations for Constructive Solid Geometry (CSG) components in Monte Carlo transport calculations

In this paper we consider a new generalized algorithm for the efficient calculation of component object volumes given their equivalent constructive solid geometry (CSG) definition. The new method relies on domain decomposition to recursively subdivide the original component into smaller pieces with volumes that can be computed analytically or stochastically, if needed. Unlike simpler brute-force approaches, the proposed decomposition scheme is guaranteed to be robust and accurate to within a user-defined tolerance. The new algorithm is also fully general and can handle any valid CSG component definition, without the need for additional input from the user. The new technique has been specifically optimized to calculate volumes of component definitions commonly found in models used for Monte Carlo particle transport simulations for criticality safety and reactor analysis applications. However, the algorithm can be easily extended to any application which uses CSG representations for component objects. The paper provides a complete description of the novel volume calculation algorithm, along with a discussion of the conjectured error bounds on volumes calculated within the method. In addition, numerical results comparing the new algorithm with a standard stochastic volume calculation algorithm are presented for a series of problems spanning a range of representative component sizes and complexities. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy

A novel and efficient algorithm is presented in this paper to deal with DNS of turbulent reacting flows under the low-Mach-number assumption, with detailed chemistry and a quasi-spectral accuracy. The temporal integration of the equations relies on an operating-split strategy, where chemical reactions are solved implicitly with a stiff solver and the convection-diffusion operators are solved with a Runge-Kutta-Chebyshev method. The spatial discretisation is performed with high-order compact schemes, and a FFT based constant-coefficient spectral solver is employed to solve a variable-coefficient Poisson equation. The numerical implementation takes advantage of the 2DECOMP&FFT libraries developed by, which are based on a pencil decomposition method of the domain and are proven to be computationally very efficient. An enhanced pressure-correction method is proposed to speed up the achievement of machine precision accuracy. It is demonstrated that a second-order accuracy is reached in time, while the spatial accuracy ranges from fourth-order to sixth-order depending on the set of imposed boundary conditions. In conclusion, the software developed to implement the present algorithm is called HOLOMAC, and its numerical efficiency opens the way to deal with DNS of reacting flows to understand complex turbulent and chemical phenomena in flames.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗