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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Multigrid techniques for the numerical solution of the diffusion equation

An accurate numerical solution of diffusion problems containing large local gradients can be obtained with a significant reduction in computational time by using a multigrid computational scheme. The spatial domain is covered with sets of uniform square grids of different sizes. The finer grid patterns overlap the coarse grid patterns. The finite-difference expressions for each grid pattern are solved independently by iterative techniques. Two interpolation methods were used to establish the values of the potential function on the fine grid boundaries with information obtained from the coarse grid solution. The accuracy and computational requirements for solving a test problem by a simple multigrid and a multilevel-multigrid method were compared. The multilevel-multigrid method combined with a Taylor series interpolation scheme was found to be best.

Phillips, R. E.↗
DOE OSTI2016

Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations

The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle–mesh Ewald method falls short.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

Multilevel algorithms for nonlinear optimization

Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.

Alexandrov, Natalia↗
DOE OSTI2020

Multigrid Algorithms with Projection and Prolongation over Elements of the Phase Space for K-Eigenvalue Transport Problems

This paper describes new multilevel acceleration methods for solving the multigroup neu- tron transport eigenvalue problems. These multilevel algorithms use different projection and prolongation operators in the phase space. The Nonlinear Diffusion Acceleration (NDA) method with multiple grids in energy is formulated with the prolongation oper- ator based on multiplication iterative correction and linear-in-energy mapping. Another multilevel NDA method uses the projection operator with coarsening in energy between the high-order transport and low-order NDA equations. The third algorithm is formu- lated with the partial-current based CMFD low-order equations and applies projection operators in space and energy. The numerical results are presented.

Cornejo, Luke↗
NASA NTRS1990

Integrated control/structure optimization by multilevel decomposition

A method for integrated control/structure optimization by multilevel decomposition is presented. It is shown that several previously reported methods were actually partial decompositions wherein only the control was decomposed into a subsystem design. One of these partially decomposed problems was selected as a benchmark example for comparison. The system is fully decomposed into structural and control subsystem designs and an improved design is produced. Theory, implementation, and results for the method are presented and compared with the benchmark example.

Zeiler, Thomas A.↗
NASA NTRS1990

Integrated control/structure optimization by multilevel decomposition

A method for integrated control/structure optimization by multilevel decomposition is presented. It is shown that several previously reported methods were actually partial decompositions wherein only the control was decomposed into a subsystem design. One of these partially decomposed problems was selected as a benchmark example for comparison. The present paper fully decomposes the system into structural and control subsystem designs and produces an improved design. Theory, implementation, and results for the method are presented and compared with the benchmark example.

Zeiler, Thomas A.↗
NASA NTRS1985

Theoretical and software considerations for general dynamic analysis using multilevel substructured models

The dynamic analysis of complex structural systems using the finite element method and multilevel substructured models is presented. The fixed-interface method is selected for substructure reduction because of its efficiency, accuracy, and adaptability to restart and reanalysis. This method is extended to reduction of substructures which are themselves composed of reduced substructures. The implementation and performance of the method in a general purpose software system is emphasized. Solution algorithms consistent with the chosen data structures are presented. It is demonstrated that successful finite element software requires the use of software executives to supplement the algorithmic language. The complexity of the implementation of restart and reanalysis porcedures illustrates the need for executive systems to support the noncomputational aspects of the software. It is shown that significant computational efficiencies can be achieved through proper use of substructuring and reduction technbiques without sacrificing solution accuracy. The restart and reanalysis capabilities and the flexible procedures for multilevel substructured modeling gives economical yet accurate analyses of complex structural systems.

Schmidt, R. J.↗
NASA NTRS1983

Structural optimization by multilevel decomposition

A method is described for decomposing an optimization problem into a set of subproblems and a coordination problem which preserves coupling between the subproblems. The method is introduced as a special case of multilevel, multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type. Numerical results are given for an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition. It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers, using different computers to work concurrently on the same large problem.

Sobieszczanski-Sobieski, J.↗
DOE OSTI2017

Numerical Multilevel Upscaling for Incompressible Flow in Reservoir Simulation: An Element-Based Algebraic Multigrid (AMGe) Approach

Here, we study the application of a finite element numerical upscaling technique to the incompressible two-phase porous media total velocity formulation. Specifically, an element-agglomeration-based algebraic multigrid (AMGe) technique with improved approximation properties is used, for the first time, to generate upscaled and accurate coarse systems for the reservoir simulation equations. The upscaling technique is applied to both the mixed system for velocity and pressure and to the hyperbolic transport equations, providing fully upscaled systems. By introducing additional degrees of freedom associated with nonplanar interfaces between agglomerates, the coarse velocity space has guaranteed approximation properties. The employed AMGe technique provides coarse spaces with desirable local mass conservation and stability properties analogous to the original pair of Raviart--Thomas and piecewise discontinuous polynomial spaces, resulting in strong mass conservation for the upscaled systems. Due to the guaranteed approximation properties and the generic nature of the AMGe method, recursive multilevel upscaling is automatically obtained. Furthermore, this technique works for both structured and unstructured meshes. Multiscale mixed finite elements exhibit accuracy for general unstructured meshes but do not in general lead to nested hierarchy of spaces. Multiscale multilevel mimetic finite differences generate nested spaces but lack the adaptivity of the flux representation on coarser levels that the proposed AMGe approach offers. Thus, the proposed approach can be seen as a rigorous bridge that merges the best properties of these two existing methods. The accuracy and stability of the studied multilevel AMGe upscaling technique is demonstrated on two challenging test cases.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

Space construction base control system

Several approaches for an attitude control system are studied and developed for a large space construction base that is structurally flexible. Digital simulations were obtained using the following techniques: (1) the multivariable Nyquist array method combined with closed loop pole allocation, (2) the linear quadratic regulator method. Equations for the three-axis simulation using the multilevel control method were generated and are presented. Several alternate control approaches are also described. A technique is demonstrated for obtaining the dynamic structural properties of a vehicle which is constructed of two or more submodules of known dynamic characteristics.

Kaczynski, R. F.↗
NASA NTRS1975

A multilevel control system for the large space telescope

A multilevel scheme was proposed for control of Large Space Telescope (LST) modeled by a three-axis-six-order nonlinear equation. Local controllers were used on the subsystem level to stabilize motions corresponding to the three axes. Global controllers were applied to reduce (and sometimes nullify) the interactions among the subsystems. A multilevel optimization method was developed whereby local quadratic optimizations were performed on the subsystem level, and global control was again used to reduce (nullify) the effect of interactions. The multilevel stabilization and optimization methods are presented as general tools for design and then used in the design of the LST Control System. The methods are entirely computerized, so that they can accommodate higher order LST models with both conceptual and numerical advantages over standard straightforward design techniques.

D D Siljak↗
NASA NTRS1993

Multigrid methods for flow transition in three-dimensional boundary layers with surface roughness

The efficient multilevel adaptive method has been successfully applied to perform direct numerical simulations (DNS) of flow transition in 3-D channels and 3-D boundary layers with 2-D and 3-D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semi-coarsening multigrid method associated with line distributive relaxation scheme, and an improved outflow boundary-condition treatment, which needs only a very short buffer domain to damp all order-one wave reflections, are developed. These approaches make the multigrid DNS code very accurate and efficient. This allows us not only to be able to do spatial DNS for the 3-D channel and flat plate at low computational costs, but also to do spatial DNS for transition in the 3-D boundary layer with 3-D single and multiple roughness elements, which would have extremely high computational costs with conventional methods. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments. The contribution of isolated and distributed roughness to transition is analyzed.

Liu, Chaoqun↗
DOE OSTI2022

High-order accurate solutions of the point kinetics equations with the spectral deferred correction method

Solving initial value problems with higher-order methods can improve the accuracy of the simulation results or the efficiency of the calculation. In this paper, we apply the spectral deferred correction (SDC) method to solve the initial value problem of the point kinetics equations (PKE). SDC is a stable, robust, and efficient high-order time-integration method capable of an arbitrary order of accuracy. For our implementation we show that it is A-stable for orders up to 8 and the order of accuracy is verified for PKE problems with a range of different reactivities. A 5.-order SDC method was then implemented to solve the exact PKE (EPKE) in the Transient Multilevel (TML) method of MPACT. The error from solutions of the EPKE is shown to be negligible. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1985

Multigrid techniques for the solution of the passive scalar advection-diffusion equation

The solution of elliptic passive scalar advection-diffusion equations is required in the analysis of many turbulent flow and convective heat transfer problems. The accuracy of the solution may be affected by the presence of regions containing large gradients of the dependent variables. The multigrid concept of local grid refinement is a method for improving the accuracy of the calculations in these problems. In combination with the multilevel acceleration techniques, an accurate and efficient computational procedure is developed. In addition, a robust implementation of the QUICK finite-difference scheme is described. Calculations of a test problem are presented to quantitatively demonstrate the advantages of the multilevel-multigrid method.

Phillips, R. E.↗
DOE OSTI2020

Multilevel Monte Carlo Predictions of First Passage Times in Three-Dimensional Discrete Fracture Networks: A Graph-Based Approach

In this paper, we present a method combining multilevel Monte Carlo (MLMC) and a graph-based primary subnetwork identification algorithm to provide estimates of the mean and variance of the distribution of first passage times in fracture media at significantly lower computational cost than standard Monte Carlo (MC) methods. Simulations of solute transport are performed using a discrete fracture network (DFN), and instead of using various grid resolutions for levels in the MLMC, which is standard practice in MLMC, we identify a hierarchy of subnetworks in the DFN based on the shortest topological paths through the network using a graph-based method. While the mean of these ensembles is of critical importance, the variance is also essential in fractured media where uncertainty is an overarching theme, and understanding variability across an ensemble is a requirement for safety assessments. The method provides good estimates of the mean and variance at two orders of magnitude lower computational cost than MC.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1996

Preconditioning Operators on Unstructured Grids

We consider systems of mesh equations that approximate elliptic boundary value problems on arbitrary (unstructured) quasi-uniform triangulations and propose a method for constructing optimal preconditioning operators. The method is based upon two approaches: (1) the fictitious space method, i.e., the reduction of the original problem to a problem in an auxiliary (fictitious) space, and (2) the multilevel decomposition method, i.e., the construction of preconditioners by decomposing functions on hierarchical meshes. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh step. The preconditioner has an optimal computational cost: the number of arithmetic operations required for its implementation is proportional to the number of unknowns in the problem. The construction of the preconditioning operators for three dimensional problems can be done in the same way.

Nepomnyaschikh, S. V.↗
DOE OSTI2018

System and method for optimizing fundamental frequency modulation for a cascaded multilevel inverter

A system and a method for optimizing fundamental frequency modulation in a cascaded multilevel inverter (CMI) are provided. The CMI includes at least a first H-bridge module and a second H-bridge module connected in series with the first H-bridge module. The first H-bridge module is operated according to a first duty cycle and the second H-bridge module is operated according to a second duty cycle. The first duty cycle is greater than the second duty cycle. The first and second H-bridge modules are controlled utilizing fundamental frequency modulation. A portion of the first duty cycle is transferred to the second duty cycle thereby optimizing fundamental frequency modulation by at least improving power sharing between the first and second H-bridge modules and improving equalization of DC capacitor currents and voltage ripples while maintaining the same fundamental modulation to the output voltage waveform.

42 ENGINEERING↗