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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 901 records · Page 50
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Binary tree eigen solver in finite element analysis

This paper presents a transputer-based binary tree eigensolver for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on the method of recursive doubling, which parallel implementation of a number of associative operations on an arbitrary set having N elements is of the order of o(log2N), compared to (N-1) steps if implemented sequentially. The hardware used in the implementation of the binary tree consists of 32 transputers. The algorithm is written in OCCAM which is a high-level language developed with the transputers to address parallel programming constructs and to provide the communications between processors. The algorithm can be replicated to match the size of the binary tree transputer network. Parallel and sequential finite element analysis programs have been developed to solve for the set of the least-order eigenpairs using the modified subspace method. The speed-up obtained for a typical analysis problem indicates close agreement with the theoretical prediction given by the method of recursive doubling.

Akl, F. A.↗
DOE OSTI2018

Generalized Multiscale Finite Element Methods with energy minimizing oversampling

In this work, we propose a general concept for constructing multiscale basis functions within Generalized Multiscale Finite Element Method, which uses oversampling and stable decomposition. The oversampling refers to using larger regions in constructing multiscale basis functions and stable decomposition allows estimating the local errors. The analysis of multiscale methods involves decomposing the error by coarse regions, where each error contribution is estimated. In this estimate, we often use oversampling techniques to achieve a fast convergence. We demonstrate our concepts in the mixed, the Interior Penalty Discontinuous Galerkin, and Hybridized Discontinuous Galerkin discretizations. One of the important features of the proposed basis functions is that they can be used in online Generalized Multiscale Finite Element Method, where one constructs multiscale basis functions using residuals. In these problems, it is important to achieve a fast convergence, which can be guaranteed if we have a stable decomposition. In our numerical results, we present examples for both offline and online multiscale basis functions. Our numerical results show that one can achieve a fast convergence when using online basis functions. Moreover, we observe that coupling using Hybridized Discontinuous Galerkin provides a better accuracy compared with Interior Penalty Discontinuous Galerkin, which is due to using multiscale glueing functions.

42 ENGINEERING↗
DOE OSTI2020

Efficient solvers for hybridized three-field mixed finite element coupled poromechanics

We consider a mixed hybrid finite element formulation for coupled poromechanics. A stabilization strategy based on a macro-element approach is advanced to eliminate the spurious pressure modes appearing in undrained/incompressible conditions. The efficient solution of the stabilized mixed hybrid block system is addressed by developing a class of block triangular preconditioners based on a Schur-complement approximation strategy. Robustness, computational efficiency and scalability of the proposed approach are theoretically discussed and tested using challenging benchmark problems on massively parallel architectures.

42 ENGINEERING↗
DOE OSTI2021

A priori error analysis of high-order LL* (FOSLL*) finite element methods

A number of non-standard finite element methods have been proposed in recent years, each of which derives from a specific class of PDE-constrained norm minimization problems. The most notable examples are LL* methods. In this work, we argue that all high-order methods in this class should be expected to deliver substandard uniform h-refinement convergence rates. In fact, one may not even see rates proportional to the polynomial order p > 1 when the exact solution is a constant function. Here, we show that the convergence rate is limited by the regularity of an extraneous Lagrange multiplier variable which naturally appears via a saddle-point analysis. In turn, limited convergence rates appear because the regularity of this Lagrange multiplier is determined, in part, by the geometry of the domain. Numerical experiments support our conclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Finite Element Method for Electrochemical Transport

This code provides Finite Element solvers for Electrochemical Transport. A few examples from the literature are reproduced, with a focus on CO2 electrolysis. The Discontinuous Galerkin scheme for the electroneutral Nernst-Planck equations is from Roy, T., Andrej, J. and Beck, V.A., 2021. A scalable DG solver for the electroneutral Nernst-Planck equations. arXiv preprint arXiv:2112.09271. This work also includes a scalable preconditioner.

Beck, VictorA↗
NASA NTRS1972

Experiences in interfacing NASTRAN with another finite element program

The coupling of NASTRAN to another finite element program developed for the static analysis of automotive structures is discussed. The two programs were coupled together to use the substructuring capability of the in-house program and the normal mode analysis capability of NASTRAN. Modifications were made to the NASTRAN program in order to make the coupling feasible.

Schwerzler, D. D.↗
NASA NTRS1981

On the utility of finite element theory for computational fluid dynamics

An implicit finite element numerical solution algorithm is derived for the compressible Navier-Stokes equations expressed in generalized coordinates. The theoretical basis utilizes a Galerkin-Weighted Residuals formulation, and extremization of approximation error within the context of a multipole expansion. A von Neumann analysis for a simplified form indicates the algorithm fourth- to sixth-order phase accurate, with third-order dissipation for the elementary linear element construction. Performance is improved for the algorithm constructed using quadratic interpolation. Numerical experiments for shocked duct flows are employed to optimize the several algorithm parameters. Additional numerical solutions validate algorithm accuracy and utility for aerodynamics applications.

Baker, A. J.↗
NASA NTRS1982

Finite element analysis of nonisothermal polymer processing operations

A finite element formulation for the analysis of polymer processing is presented and its use in some typical situation including entry flow, transient Couette flow, and the Graetz (forced convection) problem is illustrated. The element formulations are constructed on the premise that momentum convection can be neglected (polymer melt flows typically have very low Reynolds' numbers), but that convective heat transfer may be significant (high Peclet numbers). Nonisothermal effects are considered important in polymer processing, due in part to the significant heating which may occur due to viscous dissipation, and also to the very strong influence of temperature on fluid viscosity. The flow is treated as Newtonian with the flow field being coupled to the heat transfer equation only through the viscous heat generation.

Douglas, C.↗
NASA NTRS1982

The finite element machine: An experiment in parallel processing

The finite element machine is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described.

Storaasli, O. O.↗
NASA NTRS1982

the finite element machine: An experiment in parallel processing

The Finite Element Machine at the NASA Langley Research Center is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described. Directions for future work are presented.

Storaasli, O. O.↗
NASA NTRS1982

On the rates of convergence of the finite element method

The rate of convergence of the finite element method is a function of the strategy by which the number of degrees-of-freedom are increased. Alternative strategies are examined in the light of recent theoretical results and computational experience.

Babuska, I.↗
NASA NTRS1984

Interactive Finite Elements for General Engine Dynamics Analysis

General nonlinear finite element codes were adapted for the purpose of analyzing the dynamics of gas turbine engines. In particular, this adaptation required the development of a squeeze-film damper element software package and its implantation into a representative current generation code. The ADINA code was selected because of prior use of it and familiarity with its internal structure and logic. This objective was met and the results indicate that such use of general purpose codes is viable alternative to specialized codes for general dynamics analysis of engines.

Adams, M. L.↗
NASA NTRS1983

A finite element model for sound transmission through panels

A finite element method (FEM) is applied to predicting coupled frequencies and pressures within an acoustic cavity in order to characterize sound transmission through a panel. Structural equations of motion are defined and the FEM model is configured with four-noded plate elements, the lateral displacement and two slopes being the unknowns at every node. Each element then has 12 degrees of freedom (DOF) and the displacement variation is expressed by a 12-term nonconforming polynomial. A consistent mass matrix is used to represent the panel mass matrix and a wave equation governs the acoustic volume. Analysis of pressure and displacement over the panel yields a square coupling matrix, and an eigenanalysis leads to a solution of the forced vibration problem.

Ramakrishnan, J. V.↗