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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Stability and convergence analysis of the quasi-dynamics method for the initial pebble packing

The simulation for the pebble flow recirculation within Pebble Bed Reactors (PBRs) requires an efficient algorithm to generate an initial overlap-free pebble configuration within the reactor core. In the previous work, a dynamics-based approach, the Quasi-Dynamics Method (QDM), has been proposed to generate densely distributed pebbles in PBRs with cylindrical and annular core geometries. However, the stability and the efficiency of the QDM were not fully addressed. In this work, the algorithm is reformulated with two control parameters and the impact of these parameters on the algorithm performance is investigated. Firstly, the theoretical analysis for a 1-D packing system is conducted and the range of the parameter in which the algorithm is convergent is estimated. Then, this estimation is verified numerically for a 3-D packing system. Finally, the algorithm is applied to modeling the PBR fuel loading configuration and the convergence performance at different packing fractions is presented. Results show that the QDM is efficient in packing pebbles within the realistic range of the packing fraction in PBRs, and it is capable in handling cylindrical geometry with packing fractions up to 63.5%. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2014

A convergence analysis of stochastic collocation method for Navier-Stokes equations with random input data

Stochastic collocation method has proved to be an efficient method and been widely applied to solve various partial differential equations with random input data, including Navier- Stokes equations. However, up to now, rigorous convergence analyses are limited to linear elliptic and parabolic equations; its performance for Navier-Stokes equations was demonstrated mostly by numerical experiments. In this paper, we provide an error analysis of stochastic collocation method for a semi-implicit Backward Euler discretization for NSE and prove the exponential decay of the interpolation error in the probability space. Our analysis indicates that due to the nonlinearity, as final time T increases and NSE solvers pile up, the accuracy may be reduced significantly. Subsequently, the theoretical results are illustrated by the numerical test of time dependent fluid flow around a bluff body.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Convergence analysis of Anderson-type acceleration of Richardson's iteration

We consider here Anderson extrapolation to accelerate the (stationary) Richardson iterative method for sparse linear systems. Using an Anderson mixing at periodic intervals, we assess how this benefits convergence to a prescribed accuracy. The method, named alternating Anderson–Richardson, has appealing properties for high-performance computing, such as the potential to reduce communication and storage in comparison to more conventional linear solvers. We establish sufficient conditions for convergence, and we evaluate the performance of this technique in combination with various preconditioners through numerical examples. Furthermore, we propose an augmented version of this technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Convergence Analysis of Fixed Point Chance Constrained Optimal Power Flow Problems

For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach is not necessarily guaranteed. Here this article analyses the convergence conditions for this fixed point approach, and reports numerical experiments including for large IEEE networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Model-Free Control of Indoor Temperatures in Residential Buildings: Convergence Analysis

Model-free control (MFC) has recently been applied in multiple fields, including indoor air temperature regulation in buildings. It is a data-enabled feedback tracking control strategy for complex systems using a simplified representation of the ultra-local approximation model through the unique information of input-output behavior. MFC is a prevailing control strategy for systems with unknown or poorly known system dynamic models. Thus, it is a relatively simple, but efficient, trajectory tracking controller. In this paper, we investigate the convergence rate of MFC when applied to controlling indoor temperatures in residential buildings subject to outdoor weather disturbances. Numerical results show that MFC is quite robust to external disturbances, and its rate of convergence is almost one, i.e., it converges Q-sublinearly (slower than linearly).

Wu, Tumin↗
DOE OSTI2018

Reconstructing the membrane detection of a 1D electrostatic-driven MEMS device by the shooting method: convergence analysis and ghost solutions identification

In this paper, in the domain of 1D-membrane micro-electro-mechanical systems in which the electrostatic field is expressed in terms of geometric curvature of the membrane, we present a numerical approach based on shooting techniques to reconstruct the membrane profile in the device in steady-state case. In particular, starting from known results in literature about existence achieved by Schauder–Tychonoff’s fixed point approach and uniqueness, and focusing on two physical–mathematical parameters appropriately indicative of the applied voltage and electromechanical properties of the membrane, respectively, we will discuss what operation parameters (applied voltage, amplitude of electrostatic field) and for which electromechanical membrane characteristic of the device is permitted or not a convergence of the method with respect to analytical results. Finally, we will discuss in detail the detected ghost solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media

Recently, the accurate modeling of flow–structure interactions has gained more attention and importance for both petroleum and environmental engineering applications. Of particular interest is the coupling between subsurface flow and reservoir geomechanics. Different single rate and multirate iterative and explicit coupling schemes have been proposed and analyzed in the past. In addition, Banach fixed point contraction results were obtained for iterative coupling schemes, and conditionally stable results were obtained for explicit coupling schemes. In this work, we will consider the mathematical analysis of the single rate and multirate fixed stress split iterative coupling schemes for spatially heterogeneous poroelastic media. We will re–establish the contractivity for both schemes in the localized case, and we will show that heterogeneities come at the expense of imposing more restricted conditions on the number of fine flow time steps that can be taken within one coarse mechanics time step in the multirate case. Our mathematical analysis is supplemented by numerical simulations validating our derived upper bounds. Finally, to the best of our knowledge, this is the first rigorous mathematical analysis of the multirate fixed–stress split iterative coupling scheme in heterogeneous poroelastic media.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Design and convergence analysis of the conforming virtual element method for polyharmonic problems

In the recent years, there has been a tremendous interest to numerical methods that approximate partial differential equations (PDEs) on computational meshes with arbitrarily-shaped polygonal/polyhedral (polytopal, for short) elements. A nonexhaustive list of such methods include the Mimetic Finite Difference method [4, 9, 21, 24, 28, 33, 35, 62, 64–67], the Polygonal Finite Element Method [68, 73, 74], the polygonal Discontinuous Galerkin Finite Element Methods [5, 7, 8, 10, 13–15, 18, 36, 38, 39, 41, 50], the Hybridizable Discontinuous Galerkin and Hybrid High-Order Methods [46–48, 51], the Gradient Discretization method [49, 53, 54], the Finite Volume Method [52], and the BEM-based FEM [71]. An alternative approach that also proved to be very successful is provided by the Virtual Element method (VEM), which was originally proposed in [19] for the numerical treatment of second-order elliptic problems [43, 44], and readily extended to linear and nonlinear elasticity [22, 25, 56], plate bending problems [37], Cahn-Hilliard equation [3], Stokes equations [2], Laplace-Beltrami equation [55], Darcy-Brinkam equation [76], discrete topology optimization problems [6], fracture networks problems [29], eigenvalue problems [59, 75]. The mixed virtual element formulation was proposed in [20, 34]; the nonconforming Virtual element formulations was proposed for second-order elliptic problems in [16], and later extended to general advection-reaction-diffusion problems, Stokes equation, the biharmonic problems, the iegenvalue problem, and the Schrodinger equation in [11, 30, 42, 45, 58, 80]. The p- and hp-version of the VEM were developed in [26, 27] and efficient multigrid methods for the resulting linear system of equations in [12]. A posteriori error estimates can be found in [40].

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Simulation and Analysis of Converging Shock Wave Test Problems

Results and analysis pertaining to the simulation of the Guderley converging shock wave test problem (and associated code verification hydrodynamics test problems involving converging shock waves) in the LANL ASC radiation-hydrodynamics code xRAGE are presented. One-dimensional (1D) spherical and two-dimensional (2D) axi-symmetric geometric setups are utilized and evaluated in this study, as is an instantiation of the xRAGE adaptive mesh refinement capability. For the 2D simulations, a 'Surrogate Guderley' test problem is developed and used to obviate subtleties inherent to the true Guderley solution's initialization on a square grid, while still maintaining a high degree of fidelity to the original problem, and minimally straining the general credibility of associated analysis and conclusions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

On the integration of image sources in exact image method of field analysis

Convergence conditions of image integration in the exact image method of field calculation have been investigated, and the method is extended to include more general media than previously considered. It is demonstrated that the integral is well behaved and the method works best when the field is calculated in a medium with less loss. If the medium has more loss, it is shown that the image line may enter the improper half-space and still produce valid results. Means of correctly selecting the integration path branch for the case of crossing branch cuts of the Green function in complex integration planes are proposed.

Lindell, I. V.↗