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Results for “numerical algorithm computing”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Open-source MFIX-DEM software for gas-solids flows: Part II — Validation studies

With rapid advancements in computer hardware and numerical algorithms, computational fluid dynamics (CFD) has been increasingly employed as a useful tool for investigating the complex hydrodynamics inherent in multiphase flows. An important step during the development of a CFD model and prior to its application is conducting careful and comprehensive verification and validation studies. Accordingly, efforts to verify and validate the open-source MFIX-DEM software, which can be used for simulating the gas–solids flow using an Eulerian reference frame for the continuum fluid and a Lagrangian discrete framework (Discrete Element Method) for the particles, have been made at the National Energy Technology Laboratory (NETL). In part I of this paper, extensive verification studies were presented and in this part, detailed validation studies of MFIX-DEM are presented. A series of test cases covering a range of gas–solids flow applications were conducted. In particular the numerical results for the random packing of a binary particle mixture, the repose angle of a sandpile formed during a side charge process, velocity, granular temperature, and voidage profiles from a bounded granular shear flow, lateral voidage and velocity profiles from a monodisperse bubbling fluidized bed, lateral velocity profiles from a spouted bed, and the dynamics of segregation of a binary mixture in a bubbling bed were compared with available experimental data, and in some instances with empirical correlations. In addition, sensitivity studies were conducted for various parameters to quantify the error in the numerical simulation.

42 ENGINEERING↗
DOE OSTI2026

Local reduced-order modeling for electrostatic plasmas by physics-informed solution manifold decomposition

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.

Electrostatic plasmas↗
NASA NTRS1989

Numerical algorithms for computations of feedback laws arising in control of flexible systems

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Lasiecka, Irena↗
DOE OSTI2011

NSLS-II HIGH LEVEL APPLICATION INFRASTRUCTURE AND CLIENT API DESIGN

The beam commissioning software framework of NSLS-II project adopts a client/server based architecture to replace the more traditional monolithic high level application approach. It is an open structure platform, and we try to provide a narrow API set for client application. With this narrow API, existing applications developed in different language under different architecture could be ported to our platform with small modification. This paper describes system infrastructure design, client API and system integration, and latest progress. As a new 3rd generation synchrotron light source with ultra low emittance, there are new requirements and challenges to control and manipulate the beam. A use case study and a theoretical analysis have been performed to clarify requirements and challenges to the high level applications (HLA) software environment. To satisfy those requirements and challenges, adequate system architecture of the software framework is critical for beam commissioning, study and operation. The existing traditional approaches are self-consistent, and monolithic. Some of them have adopted a concept of middle layer to separate low level hardware processing from numerical algorithm computing, physics modelling, data manipulating, plotting, and error handling. However, none of the existing approaches can satisfy the requirement. A new design has been proposed by introducing service oriented architecture technology. The HLA is combination of tools for accelerator physicists and operators, which is same as traditional approach. In NSLS-II, they include monitoring applications and control routines. Scripting environment is very important for the later part of HLA and both parts are designed based on a common set of APIs. Physicists and operators are users of these APIs, while control system engineers and a few accelerator physicists are the developers of these APIs. With our Client/Server mode based approach, we leave how to retrieve information to the developers of APIs and how to use them to form a physics application to the users. For example, how the channels are related to magnet and what the current real-time setting of a magnet is in physics unit are the internals of APIs. Measuring chromaticities are the users of APIs. All the users of APIs are working with magnet and instrument names in a physics unit. The low level communications in current or voltage unit are minimized. In this paper, we discussed our recent progress of our infrastructure development, and client API.

43 PARTICLE ACCELERATORS↗
NASA NTRS1990

The development and evaluation of numerical algorithms for MIMD computers

Two activities were pursued under this grant. The first was a visitor program to conduct research on numerical algorithms for MIMD computers. The program is summarized in the following attachments. Attachment A - List of Researchers Supported; Attachment B - List of Reports Completed; and Attachment C - Reports. The second activity was a workshop on the Control of fluid Dynamic Systems held on March 28 to 29, 1989. The workshop is summarized in attachments. Attachment D - Workshop Summary; and Attachment E - List of Workshop Participants.

Voigt, Robert G.↗
NASA NTRS2008

A Comparison of Three PML Treatments for CAA (and CFD)

In this paper we compare three Perfectly Matched Layer (PML) treatments by means of a series of numerical experiments, using common numerical algorithms, computational grids, and code implementations. These comparisons are with the Linearized Euler Equations, for base uniform base flow. We see that there are two very good PML candidates, and that can both control the introduced error. Furthermore, we also show that corners can be handled with essentially no increase in the introduced error, and that with a good PML, the outer boundary is the most significant source of err

Goodrich, John W.↗
DOE OSTI2011

SERVER DEVELOPMENT FOR NSLS-II PHYSICS APPLICATIONS AND PERFORMANCE ANALYSIS

The beam commissioning software framework of NSLS-II project adopts a client/server based architecture to replace the more traditional monolithic high level application approach. The server software under development is available via an open source sourceforge project named epics-pvdata, which consists of modules pvData, pvAccess, pvIOC, and pvService. Examples of two services that already exist in the pvService module are itemFinder, and gather. Each service uses pvData to store in-memory transient data, pvService to transfer data over the network, and pvIOC as the service engine. The performance benchmarking for pvAccess and both gather service and item finder service are presented in this paper. The performance comparison between pvAccess and Channel Access are presented also. For an ultra low emittance synchrotron radiation light source like NSLS II, the control system requirements, especially for beam control are tight. To control and manipulate the beam effectively, a use case study has been performed to satisfy the requirement and theoretical evaluation has been performed. The analysis shows that model based control is indispensable for beam commissioning and routine operation. However, there are many challenges such as how to re-use a design model for on-line model based control, and how to combine the numerical methods for modeling of a realistic lattice with the analytical techniques for analysis of its properties. To satisfy the requirements and challenges, adequate system architecture for the software framework for beam commissioning and operation is critical. The existing traditional approaches are self-consistent, and monolithic. Some of them have adopted a concept of middle layer to separate low level hardware processing from numerical algorithm computing, physics modelling, data manipulating and plotting, and error handling. However, none of the existing approaches can satisfy the requirement. A new design has been proposed by introducing service oriented architecture technology, and client interface is undergoing. The design and implementation adopted a new EPICS implementation, namely epics-pvdata [9], which is under active development. The implementation of this project under Java is close to stable, and binding to other language such as C++ and/or Python is undergoing. In this paper, we focus on the performance benchmarking and comparison for pvAccess and Channel Access, the performance evaluation for 2 services, gather and item finder respectively.

43 PARTICLE ACCELERATORS↗
DOE OSTI2017

Algorithms for Computing the Magnetic Field, Vector Potential, and Field Derivatives for a Thin Solenoid with Uniform Current Density

A numerical algorithm for computing the field components B r and B z and their r and z derivatives with open boundaries in cylindrical coordinates for radially thin solenoids with uniform current density is described in this note. An algorithm for computing the vector potential A θ is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. The (apparently) new feature of the algorithms described in this note applies to cases where the field point is outside of the bore of the solenoid and the field-point radius approaches the solenoid radius. Since the elliptic integrals of the third kind normally used in computing B z and A θ become infinite in this region of parameter space, fields for points with the axial coordinate z outside of the ends of the solenoid and near the solenoid radius are treated by use of elliptic integrals of the third kind of modified argument, derived by use of an addition theorem. Also, the algorithms also avoid the numerical difficulties the textbook solutions have for points near the axis arising from explicit factors of 1/r or 1/r 2 in the some of the expressions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

An Accelerated Recursive Doubling Algorithm for Block Tridiagonal Systems

Block tridiagonal systems of linear equations arise in a wide variety of scientific and engineering applications. Recursive doubling algorithm is a well-known prefix computation-based numerical algorithm that requires O(M^3(N/P + log P)) work to compute the solution of a block tridiagonal system with N block rows and block size M on P processors. In real-world applications, solutions of tridiagonal systems are most often sought with multiple, often hundreds and thousands, of different right hand sides but with the same tridiagonal matrix. Here, we show that a recursive doubling algorithm is sub-optimal when computing solutions of block tridiagonal systems with multiple right hand sides and present a novel algorithm, called the accelerated recursive doubling algorithm, that delivers O(R) improvement when solving block tridiagonal systems with R distinct right hand sides. Since R is typically about 100 1000, this improvement translates to very significant speedups in practice. Detailed complexity analyses of the new algorithm with empirical confirmation of runtime improvements are presented. To the best of our knowledge, this algorithm has not been reported before in the literature.

Seal, Sudip K↗
DOE OSTI2017

Algorithms for Computing the Magnetic Field, Vector Potential, and Field Derivatives for Circular Current Loops in Cylindrical Coordinates

A numerical algorithm for computing the field components B r and B z and their r and z derivatives with open boundaries in cylindrical coordinates for circular current loops is described. An algorithm for computing the vector potential is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations (especially for the field derivatives) are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. Since cel can evaluate complete elliptic integrals of a fairly general type, in some cases the elliptic integrals can be evaluated without first reducing them to forms containing standard Legendre forms. The algorithms avoid the numerical difficulties that many of the textbook solutions have for points near the axis because of explicit factors of 1=r or 1=r 2 in the some of the expressions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Development and application of unified algorithms for problems in computational science

A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting.

Shankar, Vijaya↗
NASA NTRS1990

Matrix-based, finite-difference algorithms for computational acoustics

A compact numerical algorithm is introduced for simulating multidimensional acoustic waves. The algorithm is expressed in terms of a set of matrix coefficients on a three-point spatial grid that approximates the acoustic wave equation with a discretization error of O(h exp 5). The method is based on tracking a local phase variable and its implementation suggests a convenient coordinate splitting along with natural intermediate boundary conditions. Results are presented for oblique plane waves and compared with other procedures. Preliminary computations of acoustic diffraction are also considered.

Davis, Sanford↗
NASA NTRS1981

Numerical algorithms for finite element computations on arrays of microprocessors

The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.

Ortega, J. M.↗
NASA NTRS1986

Numerical algorithms for finite element computations on concurrent processors

The work of several graduate students which relate to the NASA grant is briefly summarized. One student has worked on a detailed analysis of the so-called ijk forms of Gaussian elemination and Cholesky factorization on concurrent processors. Another student has worked on the vectorization of the incomplete Cholesky conjugate method on the CYBER 205. Two more students implemented various versions of Gaussian elimination and Cholesky factorization on the FLEX/32.

Ortega, J. M.↗
NASA NTRS1989

New computing systems and their impact on structural analysis and design

A review is given of the recent advances in computer technology that are likely to impact structural analysis and design. The computational needs for future structures technology are described. The characteristics of new and projected computing systems are summarized. Advances in programming environments, numerical algorithms, and computational strategies for new computing systems are reviewed, and a novel partitioning strategy is outlined for maximizing the degree of parallelism. The strategy is designed for computers with a shared memory and a small number of powerful processors (or a small number of clusters of medium-range processors). It is based on approximating the response of the structure by a combination of symmetric and antisymmetric response vectors, each obtained using a fraction of the degrees of freedom of the original finite element model. The strategy was implemented on the CRAY X-MP/4 and the Alliant FX/8 computers. For nonlinear dynamic problems on the CRAY X-MP with four CPUs, it resulted in an order of magnitude reduction in total analysis time, compared with the direct analysis on a single-CPU CRAY X-MP machine.

Noor, Ahmed K.↗
NASA NTRS1985

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Saltz, J. H.↗