Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Implicit functions”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17

Sierra/SolidMechanics 4.54 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

42 ENGINEERING↗

Sierra/SolidMechanics 4.56.2 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes . This document describes the functionality and input syntax for Sierra/SM.

97 MATHEMATICS AND COMPUTING↗

Sierra/SolidMechanics 5.0 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

97 MATHEMATICS AND COMPUTING↗

Sierra/SolidMechanics 5.2 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

97 MATHEMATICS AND COMPUTING↗

Sierra/SolidMechanics 5.4 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

74 ATOMIC AND MOLECULAR PHYSICS↗

Sierra/SolidMechanics 5.8 User's Manual

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

42 ENGINEERING↗

Sierra/SolidMechanics 5.10 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

42 ENGINEERING↗

Sierra/Solid Mechanics 5.16 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

36 MATERIALS SCIENCE↗

Digital computer program for generating dynamic turbofan engine models (DIGTEM)

This report describes DIGTEM, a digital computer program that simulates two spool, two-stream turbofan engines. The turbofan engine model in DIGTEM contains steady-state performance maps for all of the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. Altogether there are 16 state variables and state equations. DIGTEM features a backward-differnce integration scheme for integrating stiff systems. It trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off-design points and iterates to a balanced engine condition. Transients can also be run. They are generated by defining controls as a function of time (open-loop control) in a user-written subroutine (TMRSP). DIGTEM has run on the IBM 370/3033 computer using implicit integration with time steps ranging from 1.0 msec to 1.0 sec. DIGTEM is generalized in the aerothermodynamic treatment of components.

Daniele, C. J.↗

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Meade, Andrew James, Jr.↗

A Route to Design Novel Functional Peptides by Applying a Denoising Diffusional Model to mRNA Display Libraries

In vitro directed evolution techniques, such as mRNA display, enable peptide ligand discovery and optimization. However, physical libraries that rely on a genetic code can only search a small fraction of sequence space due to inherent biases in the genetic code and experimental limitations. To address this challenge, denoising diffusion implicit models (DDIMs) are applied to generate novel peptide ligands against B‐cell lymphoma extra‐large (Bcl‐x L ), a key cancer target. Starting with high‐throughput sequencing data from previous selections, a DDIM is trained to produce novel sequences with high affinity binding. Experimental validation confirms that most generated sequences are functionally equivalent to the original library members for Bcl‐x L binding and demonstrated comparable binding kinetics and affinity relative to the wildtype and nearest original neighbors. Importantly, this approach generated rare sequences not easily accessible via mutation and directed evolution. These results indicate that DDIMs can complement and expand directed evolution data, efficiently exploring underrepresented regions of sequence space. This approach provides a broadly applicable framework for accelerating ligand discovery and optimizing molecular properties across diverse targets.

Qi, Pearl [Mork Family Department of Chemical Engi↗

Explicate '78: Uncovering the Implicit Assurance Case in DO-178C

For about two decades, compliance with Software Considerations in Airborne Systems and Equipment Certification (DO-178B/ED-12B) has been the primary means for receiving regulatory approval for using software on commercial airplanes. A new edition of the standard, DO-178C/ED-12C, was published in December 2011, and recognized by regulatory bodies in 2013. The purpose remains unchanged: to provide guidance 'for the production of software for airborne systems and equipment that performs its intended function with a level of confidence in safety that complies with airworthiness requirements.' The text of the guidance does not directly explain how its collection of objectives contributes to achieving this purpose; thus, the assurance case for the document is implicit. This paper presents an explicit assurance case developed as part of research jointly sponsored by the Federal Aviation Administration and the National Aeronautics and Space Administration.

Holloway, C. Michael↗

Ab initio calculation of the deprotonation constants of an atomistically defined nanometer-sized, aluminium hydroxide oligomer

Aluminium possesses significant and diverse chemistry. Numerous compounds have been defined, and the elucidation of their chemistry is of significant geochemical interest. In this paper, a brucite-like, eight-aluminium aqueous cluster is modelled with density functional theory to identify its primary site of deprotonation and the associated pK(a) constant using both explicit (a full first solvent shell) and implicit solvent. Two methods for calculating the pK(a) are compared. We found that a bond density approach is better than a direct energy calculation for ions with large charge and high symmetry. The terminal aluminium atoms have equatorial ligated waters that in solvent have one long O-H bond. This site is more reactive than any of the other protons on the particle. Insights into the experimental crystal structure and Bader's Atoms in Molecules density analysis are presented as routes to reduce the computational time required for the identification of protonation sites.

AQUEOUS SOLVATION↗

Modelling high data rate communication network access protocol

Modeling of high data rate communication systems is different from the low data rate systems. Three simulations were built during the development phase of Carrier Sensed Multiple Access/Ring Network (CSMA/RN) modeling. The first was a model using SIMCRIPT based upon the determination and processing of each event at each node. The second simulation was developed in C based upon isolating the distinct object that can be identified as the ring, the message, the node, and the set of critical events. The third model further identified the basic network functionality by creating a single object, the node which includes the set of critical events which occur at the node. The ring structure is implicit in the node structure. This model was also built in C. Each model is discussed and their features compared. It should be stated that the language used was mainly selected by the model developer because of his past familiarity. Further the models were not built with the intent to compare either structure or language but because the complexity of the problem and initial results contained obvious errors, so alternative models were built to isolate, determine, and correct programming and modeling errors. The CSMA/RN protocol is discussed in sufficient detail to understand modeling complexities. Each model is described along with its features and problems. The models are compared and concluding observations and remarks are presented.

Khanna, S.↗

Implications of the fractional charge of hydroxide at the electrochemical interface

Rational design of materials that efficiently convert electrical energy into chemical bonds will ultimately depend on a thorough understanding of the electrochemical interface at the atomic level. Towards this goal, the use of density functional theory (DFT) at the generalized gradient approximation (GGA) level has been applied widely in the past 15 years. In the calculation of electrochemical reaction energetics using GGA-DFT, it is frequently implicitly assumed that ions in the Helmholtz plane have unit charge. However, the ion charge is observed to be fractional near the interface through both a capacitor model and through Bader charge partitioning. In this work, we show that this spurious charge transfer can be effectively mitigated by continuum charging of the electrolyte. Finally, we show that, similar to hydronium, the observed fractional charge of hydroxide is not due to a GGA level self-interaction error, as the partial charge is observed even when using hybrid level exchange–correlation functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Ampère system

In this paper, we consider the solution of the fully kinetic (including electrons) Vlasov-Ampère system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian algorithm. The problem of velocity-space meshing for disparate thermal and bulk velocities is dealt with by an adaptive coordinate transformation of the Vlasov equation for each species, which is then discretized, including the resulting inertial terms. Mass, momentum, and energy are conserved, and Gauss's law is enforced to within the nonlinear convergence tolerance of the iterative solver through a set of nonlinear constraint functions while permitting significant flexibility in choosing discretizations in time, configuration, and velocity space. We mitigate the temporal stiffness introduced by, e.g., the plasma frequency through the use of high-order/low-order (HOLO) acceleration of the iterative implicit solver. We present several numerical results for canonical problems of varying degrees of complexity, including the multiscale ion-acoustic shock wave problem, which demonstrate the efficacy, accuracy, and efficiency of the scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Implicit application of polynomial filters in a k-step Arnoldi method

The Arnoldi process is a well known technique for approximating a few eigenvalues and corresponding eigenvectors of a general square matrix. Numerical difficulties such as loss of orthogonality and assessment of the numerical quality of the approximations as well as a potential for unbounded growth in storage have limited the applicability of the method. These issues are addressed by fixing the number of steps in the Arnoldi process at a prescribed value k and then treating the residual vector as a function of the initial Arnoldi vector. This starting vector is then updated through an iterative scheme that is designed to force convergence of the residual to zero. The iterative scheme is shown to be a truncation of the standard implicitly shifted QR-iteration for dense problems and it avoids the need to explicitly restart the Arnoldi sequence. The main emphasis of this paper is on the derivation and analysis of this scheme. However, there are obvious ways to exploit parallelism through the matrix-vector operations that comprise the majority of the work in the algorithm. Preliminary computational results are given for a few problems on some parallel and vector computers.

Sorensen, D. C.↗

Multigrid treatment of implicit continuum diffusion

Implicit treatment of diffusive terms of various differential orders common in continuum mechanics modeling, such as computational fluid dynamics, is investigated with spectral and multigrid algorithms in non-periodic 2D domains. In doubly periodic time dependent problems these terms are handled efficiently by spectral methods, but in non-periodic systems solved with distributed memory parallel computing and 2D domain decomposition, this efficiency is lost for a large number of processors. Here, we built and present here a multigrid algorithm for these types of problems that outperforms a spectral solution employing the highly optimized FFTW library. This solver is suitable for high performance computing and may be able to efficiently treat implicit diffusion of arbitrary order by introducing auxiliary equations of lower order. We test these solvers for fourth and sixth order diffusion with harmonic test functions as well as turbulent 2D magnetohydrodynamic simulations. It is also shown that an anisotropic operator without mixed-derivative terms improves model accuracy and speed, and we examine the impact that the various diffusion operators have on the energy, the enstrophy, and the qualitative aspect of a simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗