Newton Trust Region Methods for Nuclear Waste Repository Porous Media Simulations.
Abstract not provided.
Park, Heeho↗
SEARCH · Engineering Papers
Results for “Newton’s method”
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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Demonstration of the Dynamic Flowgraph Methodology using the Titan 2 Space Launch Vehicle Digital Flight Control System
Dynamic Flowgraph Methodology (DFM) is a new approach developed to integrate the modeling and analysis of the hardware and software components of an embedded system. The objective is to complement the traditional approaches which generally follow the philosophy of separating out the hardware and software portions of the assurance analysis. In this paper, the DFM approach is demonstrated using the Titan 2 Space Launch Vehicle Digital Flight Control System. The hardware and software portions of this embedded system are modeled in an integrated framework. In addition, the time dependent behavior and the switching logic can be captured by this DFM model. In the modeling process, it is found that constructing decision tables for software subroutines is very time consuming. A possible solution is suggested. This approach makes use of a well-known numerical method, the Newton-Raphson method, to solve the equations implemented in the subroutines in reverse. Convergence can be achieved in a few steps.
Yau, M.↗
Newton Trust Region methods for Nuclear Waste Repository Porous Media Flow Simulations.
Abstract not provided.
Park, Heeho↗
Newton like: Minimal residual methods applied to transonic flow calculations
A computational technique for the solution of the full potential equation is presented. The method consists of outer and inner iterations. The outer iterate is based on a Newton like algorithm, and a preconditioned Minimal Residual method is used to seek an approximate solution of the system of linear equations arising at each inner iterate. The present iterative scheme is formulated so that the uncertainties and difficulties associated with many iterative techniques, namely the requirements of acceleration parameters and the treatment of additional boundary conditions for the intermediate variables, are eliminated. Numerical experiments based on the new method for transonic potential flows around the NACA 0012 airfoil at different Mach numbers and different angles of attack are presented, and these results are compared with those obtained by the Approximate Factorization technique. Extention to three dimensional flow calculations and application in finite element methods for fluid dynamics problems by the present method are also discussed. The Inexact Newton like method produces a smoother reduction in the residual norm, and the number of supersonic points and circulations are rapidly established as the number of iterations is increased.
Wong, Y. S.↗
Newton-like minimal residual methods applied to transonic flow calculations
A computational technique for the solution of the full potential equation is presented. The method consists of outer and inner iterations. The outer iterate is based on a Newton like algorithm, and a preconditioned Minimal Residual method is used to seek an approximate solution of the system of linear equations arising at each inner iterate. The present iterative scheme is formulated so that the uncertainties and difficulties associated with many iterative techniques, namely the requirements of acceleration parameters and the treatment of additional boundary conditions for the intermediate variables, are eliminated. Numerical experiments based on the new method for transonic potential flows around the NACA 0012 airfoil at different Mach numbers and different angles of attack are presented, and these results are compared with those obtained by the Approximate Factorization technique. Extention to three dimensional flow calculations and application in finite element methods for fluid dynamics problems by the present method are also discussed. The Inexact Newton like method produces a smoother reduction in the residual norm, and the number of supersonic points and circulations are rapidly established as the number of iterations is increased.
Wong, Y. S.↗
Several trajectory optimization techniques. i - discussion.
Numerical techniques for trajectory optimization discussing steepest descent, second variation and generalized newton-raphson methods
TRAJECTORY CONTROL↗
Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem
Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.
Chang, C. J.↗
A comparison of Newton-Raphson and other methods for determining stability derivatives from flight data.
Newton-Raphson technique development for determining stability derivatives from flight data, noting use of a priori wind tunnel information
Iliff, K. W.↗
A quasi-Newton versus a homotopy method for nonlinear structural analysis
The globally convergent quasi-Newton minimization algorithm and the homotopy algorithms are discussed in detail and their effectiveness in solving certain classes of highly nonlinear problems of structural analysis is demonstrated. The application of the double dogleg strategy controls the directions and step-lengths of the quasi-Newtonian algorithm and overcomes the problem of nonpositive definite Hessians being produced during the iteration process. The algorithms are applied to a centrally loaded clamped beam, the snap-through of a shallow arch, and a shallow reticulated dome.
Kamat, M. P.↗
Simulating sticky particles: A Monte Carlo method to sample a stratification
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample probability distributions subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. More generally, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher-dimensional manifolds. We show several applications of the method in polymer physics, self-assembly of colloids, and volume calculation in high dimensions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications
In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton–Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms’ scalability and efficiency in domain applications.
hybrid software for QC-HPC↗
Similar solutions for viscous hypersonic flow over a slender three-fourths-power body of revolution
For hypersonic flow with a shock wave, there is a similar solution consistent throughout the viscous and inviscid layers along a very slender three-fourths-power body of revolution The strong pressure interaction problem can then be treated by the method of similarity. Numerical calculations are performed in the viscous region with the edge pressure distribution known from the inviscid similar solutions. The compressible laminar boundary-layer equations are transformed into a system of ordinary differential equations. The resulting two-point boundary value problem is then solved by the Runge-Kutta method with a modified Newton's method for the corresponding boundary conditions. The effects of wall temperature, mass bleeding, and body transverse curvature are investigated. The induced pressure, displacement thickness, skin friction, and heat transfer due to the previously mentioned parameters are estimated and analyzed.
Lin, Chin-Shun↗
RESOLVING THE ELECTROCHEMICAL EQUATIONS OF A SOLID OXIDE FUEL CELL FOR USE IN TRANSIENT SIMULATION AND INTEGRATION INTO CYBER-PHYSICAL SYSTEMS
A major challenge with complex cyber-physical systems stems from long model computational time that creates a mismatch between the model system and the physical system. The numerical modeling of solid oxide fuel cells (SOFCs) presents particular challenges due to the highly coupled nature of the underlying equations and the multiphysics needed to fully resolve their behavior during a transient event. To this end current approaches revolve around splitting the computational efforts into resolving temperature effects and resolving electrochemical effects. Current methods employed for the transient simulation of an SOFC for implementation in the Hybrid Performance (HyPer) facility cyberphysical plant at the National Energy Technology Laboratory reveal a distinct need for accelerated results with a high degree of stability. To this aim, an investigation into the computational time for the code reveals that the underlying electrochemical algorithm takes an order of magnitude more time than its thermal counterpart and has a tendency to vary in terms of iteration time and as such a rework of the underlying system is proposed. The primary method for accelerated electrochemical algorithm solutions is to employ higher order root finding recipes for the resolution of the highly coupled electrochemical equations. This is done with the intention to reduce the overall number of subiterations necessary for resolving voltage, current density, and species concentration, properties of the fuel cell that are all directly coupled and require nested iterative approaches. The overall objective of this approach is an order of magnitude reduction in calculation time without sacrificing stability and increasing accuracy. Specific approaches involve using both bounded and unbounded techniques, such as the False Position method and the Secant method (or if applicable Newton-Raphson) respectively, the drawbacks being slower convergence for False Position and instability for the Secant or Newton-Raphson methods. Current preliminary results on simplified versions of the parent functions involved for electrochemical calculations indicate a reduction in computational steps by a factor of two for the secant method and a factor of three for Newton-Raphson. When implemented into new modified electrochemical algorithms, the results indicate a possible order of magnitude reduction in calculation time.
Arias, Jesus↗
SIERRA Multimechanics Module: Aria User Manual (V.5.4)
Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.
97 MATHEMATICS AND COMPUTING↗
SIERRA Multimechanics Module: Aria User Manual (Version.5.2)
Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.
97 MATHEMATICS AND COMPUTING↗
SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.2)
Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.
97 MATHEMATICS AND COMPUTING↗
SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.4)
Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton’s method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic ℎ-adaptivity and dynamic load balancing are some of Aria’s more advanced capabilities.
97 MATHEMATICS AND COMPUTING↗
SIERRA Multimechanics Module: Aria User Manual (V.5.6)
Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( $Re$ < 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic $h$-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities.
97 MATHEMATICS AND COMPUTING↗