A Non-smooth Newton Method for Multibody Dynamics
Erleben, K.; Ortiz, R.
2008-09-01
In this paper we deal with the simulation of rigid bodies. Rigid body dynamics have become very important for simulating rigid body motion in interactive applications, such as computer games or virtual reality. We present a novel way of computing contact forces using a Newton method. The contact problem is reformulated as a system of non-linear and non-smooth equations, and we solve this system using a non-smooth version of Newton's method. One of the main contribution of this paper is the reformulation of the complementarity problems, used to model impacts, as a system of equations that can be solved using traditional methods.
More, J. J.; Sorensen, D. C.
1982-02-01
Newton's method plays a central role in the development of numerical techniques for optimization. In fact, most of the current practical methods for optimization can be viewed as variations on Newton's method. It is therefore important to understand Newton's method as an algorithm in its own right and as a key introduction to the most recent ideas in this area. One of the aims of this expository paper is to present and analyze two main approaches to Newton's method for unconstrained minimization: the line search approach and the trust region approach. The other aim is to present some of the recent developments in the optimization field which are related to Newton's method. In particular, we explore several variations on Newton's method which are appropriate for large scale problems, and we also show how quasi-Newton methods can be derived quite naturally from Newton's method.
Sometimes "Newton's Method" Always "Cycles"
ERIC Educational Resources Information Center
Latulippe, Joe; Switkes, Jennifer
2012-01-01
Are there functions for which Newton's method cycles for all non-trivial initial guesses? We construct and solve a differential equation whose solution is a real-valued function that two-cycles under Newton iteration. Higher-order cycles of Newton's method iterates are explored in the complex plane using complex powers of "x." We find a class of…
Quasi-Newton and multigrid methods for semiconductor device simulation
Slamet, S.
1983-12-01
A finite difference approximation to the semiconductor device equations using the Bernoulli function approximation to the exponential function is described, and the robustness of this approximation is demonstrated. Sheikh's convergence analysis of Gummel's method and quasi-Newton methods is extended to a nonuniform mesh and the Bernoulli function discretization. It is proved that Gummel's method and the quasi-Newton methods for the scaled carrier densities and carrier densities converge locally for sufficiently smooth problems.
Fractal aspects and convergence of Newton`s method
Drexler, M.
1996-12-31
Newton`s Method is a widely established iterative algorithm for solving non-linear systems. Its appeal lies in its great simplicity, easy generalization to multiple dimensions and a quadratic local convergence rate. Despite these features, little is known about its global behavior. In this paper, we will explain a seemingly random global convergence pattern using fractal concepts and show that the behavior of the residual is entirely explicable. We will also establish quantitative results for the convergence rates. Knowing the mechanism of fractal generation, we present a stabilization to the orthodox Newton method that remedies the fractal behavior and improves convergence.
[Isaac Newton's Anguli Contactus method].
Wawrzycki, Jarosław
2014-01-01
In this paper we discuss the geometrical method for calculating the curvature of a class of curves from the third Book of Isaac Newton's Principia. The method involves any curve which is generated from an elementary curve (actually from any curve whose curvature we known of) by means of transformation increasing the polar angular coordinate in a constant ratio, but unchanging the polar radial angular coordinate. PMID:25033525
OPF by Newton`s method: A comparison between polar and rectangular formulations
Gutierrez, G.; Guzman, C.R.; Chavez, S.; Madrigal, M.; Tovar, J.H.
1998-12-31
The purpose of an Optimal Power Flow (OPF) is to schedule power system controls which optimizes an objective function while at the same time satisfying a set of nonlinear equality and inequality constraints. This problem has been solved by Newton`s approach using polar coordinates to represent power flow equations. In this paper Newton`s method is used to solve the optimal power flow problem, but using rectangular coordinates. Extensive comparison are made against the polar version. The results show superiority in computing time and robustness of the rectangular coordinates Newton`s OPF.
A combined modification of Newton`s method for systems of nonlinear equations
Monteiro, M.T.; Fernandes, E.M.G.P.
1996-12-31
To improve the performance of Newton`s method for the solution of systems of nonlinear equations a modification to the Newton iteration is implemented. The modified step is taken as a linear combination of Newton step and steepest descent directions. In the paper we describe how the coefficients of the combination can be generated to make effective use of the two component steps. Numerical results that show the usefulness of the combined modification are presented.
The Newton Modified Barrier Method for QP Problems
NASA Technical Reports Server (NTRS)
Melman, A.; Polyak, R.
1996-01-01
The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a "hot start". Starting at such a "hot start", at most Omicron(1n 1n epsilon(exp -1)) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, epsilon > 0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that only Omicron(1n epsilon(exp -1))omicron(ln 1n epsilon(exp-1)) Newton steps are required to reach an epsilon-approximation to the solution from any "hot start". In order to reach the "hot start", one has to perform Omicron(square root(m) 1n C) Newton steps, where m characterizes the size of the problem and C > 0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.
Newton-Krylov methods applied to nonequilibrium radiation diffusion
Knoll, D.A.; Rider, W.J.; Olsen, G.L.
1998-03-10
The authors present results of applying a matrix-free Newton-Krylov method to a nonequilibrium radiation diffusion problem. Here, there is no use of operator splitting, and Newton`s method is used to convert the nonlinearities within a time step. Since the nonlinear residual is formed, it is used to monitor convergence. It is demonstrated that a simple Picard-based linearization produces a sufficient preconditioning matrix for the Krylov method, thus elevating the need to form or store a Jacobian matrix for Newton`s method. They discuss the possibility that the Newton-Krylov approach may allow larger time steps, without loss of accuracy, as compared to an operator split approach where nonlinearities are not converged within a time step.
Newton iterative methods for large scale nonlinear systems
Walker, H.F.; Turner, K.
1993-01-01
Objective is to develop robust, efficient Newton iterative methods for general large scale problems well suited for discretizations of partial differential equations, integral equations, and other continuous problems. A concomitant objective is to develop improved iterative linear algebra methods. We first outline research on Newton iterative methods and then review work on iterative linear algebra methods. (DLC)
Newton-Krylov-Schwarz methods in unstructured grid Euler flow
Keyes, D.E.
1996-12-31
Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton`s method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on an aerodynamic application emphasizing comparisons with a standard defect-correction approach and subdomain preconditioner consistency.
Low-rank Quasi-Newton updates for Robust Jacobian lagging in Newton methods
Brown, J.; Brune, P.
2013-07-01
Newton-Krylov methods are standard tools for solving nonlinear problems. A common approach is to 'lag' the Jacobian when assembly or preconditioner setup is computationally expensive, in exchange for some degradation in the convergence rate and robustness. We show that this degradation may be partially mitigated by using the lagged Jacobian as an initial operator in a quasi-Newton method, which applies unassembled low-rank updates to the Jacobian until the next full reassembly. We demonstrate the effectiveness of this technique on problems in glaciology and elasticity. (authors)
Choosing the forcing terms in an inexact Newton method
Eisenstat, S.C.; Walker, H.F.
1994-12-31
An inexact Newton method is a generalization of Newton`s method for solving F(x) = 0, F: {Re}{sup n} {r_arrow} {Re}{sup n}, in which each step reduces the norm of the local linear model of F. At the kth iteration, the norm reduction is usefully expressed by the inexact Newton condition where x{sub k} is the current approximate solution and s{sub k} is the step. In many applications, an {eta}{sub k} is first specified, and then an S{sub k} is found for which the inexact Newton condition holds. Thus {eta}{sub k} is often called a {open_quotes}forcing term{close_quotes}. In practice, the choice of the forcing terms is usually critical to the efficiency of the method and can affect robustness as well. Here, the authors outline several promising choices, discuss theoretical support for them, and compare their performance in a Newton iterative (truncated Newton) method applied to several large-scale problems.
Convergence of Newton's method for a single real equation
NASA Technical Reports Server (NTRS)
Campbell, C. W.
1985-01-01
Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed.
An improved generalized Newton method for absolute value equations.
Feng, Jingmei; Liu, Sanyang
2016-01-01
In this paper, we suggest and analyze an improved generalized Newton method for solving the NP-hard absolute value equations [Formula: see text] when the singular values of A exceed 1. We show that the global and local quadratic convergence of the proposed method. Numerical experiments show the efficiency of the method and the high accuracy of calculation. PMID:27462490
On collinear scaling algorithms that extend quasi-Newton methods
Ariyawansa, K.A.
1994-12-31
Quasi-Newton methods for unconstrained minimization are based on local affine scalings of the domain, and local quadratic approximations to the objective function that interpolate the gradient. Quasi-Newton algorithms have finite termination on quadratic functions, and are invariant under affine scalings. In 1980, Davidon presented a new class of algorithms for unconstrained minimization based on local collinear scalings of the domain, and local conic approximations to the objective function that interpolate both the gradient and function value. We refer to these algorithms as Davidon`s collinear scaling algorithms. Collinear scalings and conic functions generalize affine scalings and quadratic functions respectively, and therefore collinear scaling algorithms extend quasi-Newton algorithms. Davidon`s collinear scaling algorithms have finite termination on conic functions, and are invariant under collinear scalings. In this talk, we present a new derivation of Davidon`s collinear scaling algorithms. It indicates that collinear scaling algorithms extending quasi-Newton methods studied to date are different from those of Davidon. It also explains why it has not been possible to demonstrate that these other collinear scaling algorithms have finite termination on conic functions, and are invariant under collinear scalings.
Global convergence of inexact Newton methods for transonic flow
NASA Technical Reports Server (NTRS)
Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.
1990-01-01
In computational fluid dynamics, nonlinear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these nonlinear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modeled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.
Puso, M A; Laursen, T A
2002-05-02
Smoothing of contact surfaces can be used to eliminate the chatter typically seen with node on facet contact and give a better representation of the actual contact surface. The latter affect is well demonstrated for problems with interference fits. In this work we present two methods for the smoothing of contact surfaces for 3D finite element contact. In the first method, we employ Gregory patches to smooth the faceted surface in a node on facet implementation. In the second method, we employ a Bezier interpolation of the faceted surface in a mortar method implementation of contact. As is well known, node on facet approaches can exhibit locking due to the failure of the Babuska-Brezzi condition and in some instances fail the patch test. The mortar method implementation is stable and provides optimal convergence in the energy of error. In the this work we demonstrate the superiority of the smoothed versus the non-smoothed node on facet implementations. We also show where the node on facet method fails and some results from the smoothed mortar method implementation.
Newton's method for large bound-constrained optimization problems.
Lin, C.-J.; More, J. J.; Mathematics and Computer Science
1999-01-01
We analyze a trust region version of Newton's method for bound-constrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active constraints. We also show that the convergence theory leads to an efficient implementation for large bound-constrained problems.
Smoothing Methods for Estimating Test Score Distributions.
ERIC Educational Resources Information Center
Kolen, Michael J.
1991-01-01
Estimation/smoothing methods that are flexible enough to fit a wide variety of test score distributions are reviewed: kernel method, strong true-score model-based method, and method that uses polynomial log-linear models. Applications of these methods include describing/comparing test score distributions, estimating norms, and estimating…
Newton's method with a model trust-region modification
Sorensen, D C
1980-09-01
A modified Newton method for unconstrained minimization is presented and analyzed. The modification is based upon the model trust region approach. This report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified Newton iteration. Several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis. Very strong convergence results are presented concerning the minimization algorithm. In particular, the explicit use of second-order information is justified by demonstrating that the iterates converge to a point that satisfies the second-order necessary conditions for minimization. With the exception of very pathological cases this convergence occurs whenever the algorithm is applied to problems with continuous second partial derivatives.
Newton like: Minimal residual methods applied to transonic flow calculations
NASA Technical Reports Server (NTRS)
Wong, Y. S.
1984-01-01
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.
Multiple predictor smoothing methods for sensitivity analysis.
Helton, Jon Craig; Storlie, Curtis B.
2006-08-01
The use of multiple predictor smoothing methods in sampling-based sensitivity analyses of complex models is investigated. Specifically, sensitivity analysis procedures based on smoothing methods employing the stepwise application of the following nonparametric regression techniques are described: (1) locally weighted regression (LOESS), (2) additive models, (3) projection pursuit regression, and (4) recursive partitioning regression. The indicated procedures are illustrated with both simple test problems and results from a performance assessment for a radioactive waste disposal facility (i.e., the Waste Isolation Pilot Plant). As shown by the example illustrations, the use of smoothing procedures based on nonparametric regression techniques can yield more informative sensitivity analysis results than can be obtained with more traditional sensitivity analysis procedures based on linear regression, rank regression or quadratic regression when nonlinear relationships between model inputs and model predictions are present.
Gauss-Newton method for DEM co-registration
NASA Astrophysics Data System (ADS)
Wang, Kunlun; Zhang, Tonggang
2015-12-01
Digital elevation model (DEM) co-registration is one of the hottest research problems, and it is the critical technology for multi-temporal DEM analysis, which has wide potential application in many fields, such as geological hazards. Currently, the least-squares principle is used in most DEM co-registration methods, in which the matching parameters are obtained by iteration; the surface co-registration is then accomplished. To improve the iterative convergence rate, a Gauss-Newton method for DEM co-registration (G-N) is proposed in this paper. A gradient formula based on a gridded discrete surface is derived in theory, and then the difficulty of applying the Gauss-Newton method to DEM matching is solved. With the G-N algorithm, the surfaces approach each other along the maximal gradient direction, and therefore the iterative convergence and the performance efficiency of the new method can be enhanced greatly. According to experimental results based on the simulated datasets, the average convergence rates of rotation and translation parameters of the G-N algorithm are increased by 40 and 15% compared to those of the ICP algorithm, respectively. The performance efficiency of the G-N algorithm is 74.9% better.
Method for producing smooth inner surfaces
Cooper, Charles A.
2016-05-17
The invention provides a method for preparing superconducting cavities, the method comprising causing polishing media to tumble by centrifugal barrel polishing within the cavities for a time sufficient to attain a surface smoothness of less than 15 nm root mean square roughness over approximately a 1 mm.sup.2 scan area. The method also provides for a method for preparing superconducting cavities, the method comprising causing polishing media bound to a carrier to tumble within the cavities. The method also provides for a method for preparing superconducting cavities, the method comprising causing polishing media in a slurry to tumble within the cavities.
Newton iterative methods for large scale nonlinear systems. Progress report, 1992--1993
Walker, H.F.; Turner, K.
1993-06-01
Objective is to develop robust, efficient Newton iterative methods for general large scale problems well suited for discretizations of partial differential equations, integral equations, and other continuous problems. A concomitant objective is to develop improved iterative linear algebra methods. We first outline research on Newton iterative methods and then review work on iterative linear algebra methods. (DLC)
Smooth electrode and method of fabricating same
Weaver, Stanton Earl; Kennerly, Stacey Joy; Aimi, Marco Francesco
2012-08-14
A smooth electrode is provided. The smooth electrode includes at least one metal layer having thickness greater than about 1 micron; wherein an average surface roughness of the smooth electrode is less than about 10 nm.
Recent developments in quasi-Newton methods for structural analysis and synthesis
NASA Technical Reports Server (NTRS)
Kamat, M. P.; Hayduk, R. J.
1981-01-01
Unlike the Newton-Raphson method, quasi-Newton methods by virture of the updates and step length control procedures are globally convergent and hence better suited for the solution of nonlinear problems of structural analysis and synthesis. Extension of quasi-Newton algorithms to large scale problems has led to the development of sparse update algorithms and to economical strategies for evaluating sparse Hessians. Ill-conditioning problems have led to the development of self-scaled variable metric and conjugate gradient algorithms, as well as the use of the singular perturbation theory. This paper emphasizes the effectiveness of such quasi-Newton algorithms for nonlinear structural analysis and synthesis.
Parallel full-waveform inversion in the frequency domain by the Gauss-Newton method
NASA Astrophysics Data System (ADS)
Zhang, Wensheng; Zhuang, Yuan
2016-06-01
In this paper, we investigate the full-waveform inversion in the frequency domain. We first test the inversion ability of three numerical optimization methods, i.e., the steepest-descent method, the Newton-CG method and the Gauss- Newton method, for a simple model. The results show that the Gauss-Newton method performs well and efficiently. Then numerical computations for a benchmark model named Marmousi model by the Gauss-Newton method are implemented. Parallel algorithm based on message passing interface (MPI) is applied as the inversion is a typical large-scale computational problem. Numerical computations show that the Gauss-Newton method has good ability to reconstruct the complex model.
Solving Cocoa Pod Sigmoid Growth Model with Newton Raphson Method
NASA Astrophysics Data System (ADS)
Chang, Albert Ling Sheng; Maisin, Navies
Cocoa pod growth modelling are useful in crop management, pest and disease management and yield forecasting. Recently, the Beta Growth Function has been used to determine the pod growth model due to its unique for the plant organ growth which is zero growth rate at both the start and end of a precisely defined growth period. Specific pod size (7cm to 10cm in length) is useful in cocoa pod borer (CPB) management for pod sleeving or pesticide spraying. The Beta Growth Function is well-fitted to the pods growth data of four different cocoa clones under non-linear function with time (t) as its independent variable which measured pod length and diameter weekly started at 8 weeks after fertilization occur until pods ripen. However, the same pod length among the clones did not indicate the same pod age since the morphological characteristics for cocoa pods vary among the clones. Depending on pod size for all the clones as guideline in CPB management did not give information on pod age, therefore it is important to study the pod age at specific pod sizes on different clones. Hence, Newton Raphson method is used to solve the non-linear equation of the Beta Growth Function of four different group of cocoa pod at specific pod size.
On the semilocal convergence of inexact Newton methods in Banach spaces
NASA Astrophysics Data System (ADS)
Argyros, Ioannis K.
2009-06-01
We provide two types of semilocal convergence theorems for approximating a solution of an equation in a Banach space setting using an inexact Newton method [I.K. Argyros, Relation between forcing sequences and inexact Newton iterates in Banach spaces, Computing 63 (2) (1999) 134-144; I.K. Argyros, A new convergence theorem for the inexact Newton method based on assumptions involving the second Fréchet-derivative, Comput. Appl. Math. 37 (7) (1999) 109-115; I.K. Argyros, Forcing sequences and inexact Newton iterates in Banach space, Appl. Math. Lett. 13 (1) (2000) 77-80; I.K. Argyros, Local convergence of inexact Newton-like iterative methods and applications, Comput. Math. Appl. 39 (2000) 69-75; I.K. Argyros, Computational Theory of Iterative Methods, in: C.K. Chui, L. Wuytack (Eds.), in: Studies in Computational Mathematics, vol. 15, Elsevier Publ. Co., New York, USA, 2007; X. Guo, On semilocal convergence of inexact Newton methods, J. Comput. Math. 25 (2) (2007) 231-242]. By using more precise majorizing sequences than before [X. Guo, On semilocal convergence of inexact Newton methods, J. Comput. Math. 25 (2) (2007) 231-242; Z.D. Huang, On the convergence of inexact Newton method, J. Zheijiang University, Nat. Sci. Ed. 30 (4) (2003) 393-396; L.V. Kantorovich, G.P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982; X.H. Wang, Convergence on the iteration of Halley family in weak condition, Chinese Sci. Bull. 42 (7) (1997) 552-555; T.J. Ypma, Local convergence of inexact Newton methods, SIAM J. Numer. Anal. 21 (3) (1984) 583-590], we provide (under the same computational cost) under the same or weaker hypotheses: finer error bounds on the distances involved; an at least as precise information on the location of the solution. Moreover if the splitting method is used, we show that a smaller number of inner/outer iterations can be obtained.
Newton's method: A link between continuous and discrete solutions of nonlinear problems
NASA Technical Reports Server (NTRS)
Thurston, G. A.
1980-01-01
Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.
Solving Nonlinear Solid Mechanics Problems with the Jacobian-Free Newton Krylov Method
J. D. Hales; S. R. Novascone; R. L. Williamson; D. R. Gaston; M. R. Tonks
2012-06-01
The solution of the equations governing solid mechanics is often obtained via Newton's method. This approach can be problematic if the determination, storage, or solution cost associated with the Jacobian is high. These challenges are magnified for multiphysics applications with many coupled variables. Jacobian-free Newton-Krylov (JFNK) methods avoid many of the difficulties associated with the Jacobian by using a finite difference approximation. BISON is a parallel, object-oriented, nonlinear solid mechanics and multiphysics application that leverages JFNK methods. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and solid mechanics coupled to other PDEs using a series of demonstration problems.
Flux vector splitting and approximate Newton methods. [for solution of steady Euler equations
NASA Technical Reports Server (NTRS)
Jespersen, D. C.; Pulliam, T. H.
1983-01-01
In the present investigation, the basic approach is employed to view an iterative scheme as Newton's method or as a modified Newton's method. Attention is given to various modified Newton methods which can arise from differencing schemes for the Euler equations. Flux vector splitting is considered as the basic spatial differencing technique. This technique is based on the partition of a flux vector into groups which have certain properties. The Euler equations fluxes can be split into two groups, the first group having a flux Jacobian with all positive eigenvalues, and the second group having a flux Jacobian with all negative eigenvalues. Flux vector splitting based on a velocity-sound speed split is considered along with the use of numerical techniques to analyze nonlinear systems, and the steady Euler equations for quasi-one-dimensional flow in a nozzle. Results are given for steady flows with shocks.
Application of Newton's method to the postbuckling of rings under pressure loadings
NASA Technical Reports Server (NTRS)
Thurston, Gaylen A.
1989-01-01
The postbuckling response of circular rings (or long cylinders) is examined. The rings are subjected to four types of external pressure loadings; each type of pressure is defined by its magnitude and direction at points on the buckled ring. Newton's method is applied to the nonlinear differential equations of the exact inextensional theory for the ring problem. A zeroth approximation for the solution of the nonlinear equations, based on the mode shape corresponding to the first buckling pressure, is derived in closed form for each of the four types of pressure. The zeroth approximation is used to start the iteration cycle in Newton's method to compute numerical solutions of the nonlinear equations. The zeroth approximations for the postbuckling pressure-deflection curves are compared with the converged solutions from Newton's method and with similar results reported in the literature.
A high-order fast method for computing convolution integral with smooth kernel
Qiang, Ji
2009-09-28
In this paper we report on a high-order fast method to numerically calculate convolution integral with smooth non-periodic kernel. This method is based on the Newton-Cotes quadrature rule for the integral approximation and an FFT method for discrete summation. The method can have an arbitrarily high-order accuracy in principle depending on the number of points used in the integral approximation and a computational cost of O(Nlog(N)), where N is the number of grid points. For a three-point Simpson rule approximation, the method has an accuracy of O(h{sup 4}), where h is the size of the computational grid. Applications of the Simpson rule based algorithm to the calculation of a one-dimensional continuous Gauss transform and to the calculation of a two-dimensional electric field from a charged beam are also presented.
On a class of Newton-like methods for solving nonlinear equations
NASA Astrophysics Data System (ADS)
Argyros, Ioannis K.
2009-06-01
We provide a semilocal convergence analysis for a certain class of Newton-like methods considered also in [I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004) 374-397; I.K. Argyros, Computational theory of iterative methods, in: C.K. Chui, L. Wuytack (Eds.), Series: Studies in Computational Mathematics, vol. 15, Elsevier Publ. Co, New York, USA, 2007; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971], in order to approximate a locally unique solution of an equation in a Banach space. Using a combination of Lipschitz and center-Lipschitz conditions, instead of only Lipschitz conditions [F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84], we provide an analysis with the following advantages over the work in [F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84] which improved the works in [W.E. Bosarge, P.L. Falb, A multipoint method of third order, J. Optimiz. Theory Appl. 4 (1969) 156-166; W.E. Bosarge, P.L. Falb, Infinite dimensional multipoint methods and the solution of two point boundary value problems, Numer. Math. 14 (1970) 264-286; J.E. Dennis, On the Kantorovich hypothesis for Newton's method, SIAM J. Numer. Anal. 6 (3) (1969) 493-507; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971; H.J. Kornstaedt, Ein allgemeiner Konvergenzstaz fü r verschä rfte Newton-Verfahrem, in: ISNM, vol. 28, Birkhaü ser Verlag, Basel and Stuttgart, 1975, pp. 53-69; P. Laasonen, Ein überquadratisch konvergenter iterativer algorithmus, Ann. Acad. Sci. Fenn. Ser I 450 (1969) 1-10; F.A. Potra, On a modified secant method, L'analyse num
NASA Astrophysics Data System (ADS)
Antipin, A. S.; Vasil'Ev, F. P.; Stukalov, A. S.
2007-01-01
Unstable equilibrium problems are examined in which the objective function and the set where the equilibrium point is sought are specified inexactly. A regularized Newton method, combined with penalty functions, is proposed for solving such problems, and its convergence is analyzed. A regularizing operator is constructed.
A multigrid Newton-Krylov method for flux-limited radiation diffusion
Rider, W.J.; Knoll, D.A.; Olson, G.L.
1998-09-01
The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques.
Markov chain Mote Carlo solution of BK equation through Newton-Kantorovich method
NASA Astrophysics Data System (ADS)
BoŻek, Krzysztof; Kutak, Krzysztof; Placzek, Wieslaw
2013-07-01
We propose a new method for Monte Carlo solution of non-linear integral equations by combining the Newton-Kantorovich method for solving non-linear equations with the Markov Chain Monte Carlo (MCMC) method for solving linear equations. The Newton-Kantorovich method allows to express the non-linear equation as a system of the linear equations which then can be treated by the MCMC (random walk) algorithm. We apply this method to the Balitsky-Kovchegov (BK) equation describing evolution of gluon density at low x. Results of numerical computations show that the MCMC method is both precise and efficient. The presented algorithm may be particularly suited for solving more complicated and higher-dimensional non-linear integral equation, for which traditional methods become unfeasible.
3D CSEM data inversion using Newton and Halley class methods
NASA Astrophysics Data System (ADS)
Amaya, M.; Hansen, K. R.; Morten, J. P.
2016-05-01
For the first time in 3D controlled source electromagnetic data inversion, we explore the use of the Newton and the Halley optimization methods, which may show their potential when the cost function has a complex topology. The inversion is formulated as a constrained nonlinear least-squares problem which is solved by iterative optimization. These methods require the derivatives up to second order of the residuals with respect to model parameters. We show how Green's functions determine the high-order derivatives, and develop a diagrammatical representation of the residual derivatives. The Green's functions are efficiently calculated on-the-fly, making use of a finite-difference frequency-domain forward modelling code based on a multi-frontal sparse direct solver. This allow us to build the second-order derivatives of the residuals keeping the memory cost in the same order as in a Gauss-Newton (GN) scheme. Model updates are computed with a trust-region based conjugate-gradient solver which does not require the computation of a stabilizer. We present inversion results for a synthetic survey and compare the GN, Newton, and super-Halley optimization schemes, and consider two different approaches to set the initial trust-region radius. Our analysis shows that the Newton and super-Halley schemes, using the same regularization configuration, add significant information to the inversion so that the convergence is reached by different paths. In our simple resistivity model examples, the convergence speed of the Newton and the super-Halley schemes are either similar or slightly superior with respect to the convergence speed of the GN scheme, close to the minimum of the cost function. Due to the current noise levels and other measurement inaccuracies in geophysical investigations, this advantageous behaviour is at present of low consequence, but may, with the further improvement of geophysical data acquisition, be an argument for more accurate higher-order methods like those
Mohamad, Mohd Saberi; Abdullah, Afnizanfaizal
2015-01-01
This paper presents an in silico optimization method of metabolic pathway production. The metabolic pathway can be represented by a mathematical model known as the generalized mass action model, which leads to a complex nonlinear equations system. The optimization process becomes difficult when steady state and the constraints of the components in the metabolic pathway are involved. To deal with this situation, this paper presents an in silico optimization method, namely the Newton Cooperative Genetic Algorithm (NCGA). The NCGA used Newton method in dealing with the metabolic pathway, and then integrated genetic algorithm and cooperative co-evolutionary algorithm. The proposed method was experimentally applied on the benchmark metabolic pathways, and the results showed that the NCGA achieved better results compared to the existing methods. PMID:25961295
A compressible Navier-Stokes flow solver using the Newton-Krylov method on unstructured grids
NASA Astrophysics Data System (ADS)
Wong, Peterson
A Newton-Krylov algorithm is presented for the compressible Navier-Stokes equations on hybrid unstructured grids. The Spalart-Allmaras turbulence model is used for turbulent flows. The spatial discretization is based on a finite-volume matrix dissipation scheme. A preconditioned matrix-free generalized minimal residual method is used to solve the linear system that arises in the Newton iterations. The incomplete lower-upper factorization based on an approximate Jacobian is used as the preconditioner after applying the reverse Cuthill-McKee reordering. Various aspects of the Newton-Krylov algorithm are studied to improve efficiency and reliability. The inexact Newton method is studied to avoid over-solving of the linear system to reduce computational cost. The ILU(1) approach is selected in three dimensions, based on a comparison among various preconditioners. Approximate viscous formulations involving only the nearest neighboring terms are studied to reduce the cost of preconditioning. The resulting preconditioners are found to be effective and provide Newton-type convergence. Scaling of the linear system is studied to improve convergence of the inexact matrix-free approach. Numerical studies are performed for two-dimensional cases as well as flows over the ONERA M6 wing and the DLR-F6 wing-body configuration. A ten-order-of-magnitude residual reduction can be obtained with a computing cost equivalent to 4,000 residual function evaluations for two-dimensional cases, while the same convergence can be obtained in 5,500 and 8,000 function evaluations for the wing and wing-body configuration, respectively, on grids with a half million nodes.
NASA Technical Reports Server (NTRS)
Chapman, G.; Kirk, D.
1974-01-01
The parameter identification scheme being used is a differential correction least squares procedure (Gauss-Newton method). The position, orientation, and derivatives of these quantities with respect to the parameters of interest (i.e., sensitivity coefficients) are determined by digital integration of the equations of motion and the parametric differential equations. The application of this technique to three vastly different sets of data is used to illustrate the versatility of the method and to indicate some of the problems that still remain.
Kim, T; Pasciak, J E; Vassilevski, P S
2004-09-20
In this paper, we consider an inexact Newton method applied to a second order nonlinear problem with higher order nonlinearities. We provide conditions under which the method has a mesh-independent rate of convergence. To do this, we are required to first, set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced with one iterative step provided that the initial nonlinear iterate is accurate enough. The closeness criteria can be taken independent of the mesh size. Finally, the results of numerical experiments are given to support the theory.
Postprocessing Fourier spectral methods: The case of smooth solutions
Garcia-Archilla, B.; Novo, J.; Titi, E.S.
1998-11-01
A postprocessing technique to improve the accuracy of Galerkin methods, when applied to dissipative partial differential equations, is examined in the particular case of smooth solutions. Pseudospectral methods are shown to perform poorly. This performance is analyzed and a refined postprocessing technique is proposed.
Application of smoothed particle hydrodynamics method in aerodynamics
NASA Astrophysics Data System (ADS)
Cortina, Miguel
2014-11-01
Smoothed Particle Hydrodynamics (SPH) is a meshless Lagrangian method in which the domain is represented by particles. Each particle is assigned properties such as mass, pressure, density, temperature, and velocity. These properties are then evaluated at the particle positions using a smoothing kernel that integrates over the values of the surrounding particles. In the present study the SPH method is first used to obtain numerical solutions for fluid flows over a cylinder and then we are going to apply the same principle over an airfoil obstacle.
Modeling of hydrogen-assisted cracking in iron crystal using a quasi-Newton method.
Telitchev, Igor Ye; Vinogradov, Oleg
2008-07-01
A Quasi-Newton method was applied in the context of a molecular statics approach to simulate the phenomenon of hydrogen embrittlement of an iron lattice. The atomic system is treated as a truss-type structure. The interatomic forces between the hydrogen-iron and the iron-iron atoms are defined by Morse and modified Morse potential functions, respectively. Two-dimensional hexagonal and 3D bcc crystal structures were subjected to tensile numerical tests. It was shown that the Inverse Broyden's Algorithm-a quasi-Newton method-provides a computationally efficient technique for modeling of the hydrogen-assisted cracking in iron crystal. Simulation results demonstrate that atoms of hydrogen placed near the crack tip produce a strong deformation and crack propagation effect in iron lattice, leading to a decrease in the residual strength of numerically tested samples. PMID:18481119
A method of smoothed particle hydrodynamics using spheroidal kernels
NASA Technical Reports Server (NTRS)
Fulbright, Michael S.; Benz, Willy; Davies, Melvyn B.
1995-01-01
We present a new method of three-dimensional smoothed particle hydrodynamics (SPH) designed to model systems dominated by deformation along a preferential axis. These systems cause severe problems for SPH codes using spherical kernels, which are best suited for modeling systems which retain rough spherical symmetry. Our method allows the smoothing length in the direction of the deformation to evolve independently of the smoothing length in the perpendicular plane, resulting in a kernel with a spheroidal shape. As a result the spatial resolution in the direction of deformation is significantly improved. As a test case we present the one-dimensional homologous collapse of a zero-temperature, uniform-density cloud, which serves to demonstrate the advantages of spheroidal kernels. We also present new results on the problem of the tidal disruption of a star by a massive black hole.
NASA Technical Reports Server (NTRS)
Achar, N. S.; Gaonkar, G. H.
1993-01-01
Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.
Fattebert, J
2008-07-29
We describe an iterative algorithm to solve electronic structure problems in Density Functional Theory. The approach is presented as a Subspace Accelerated Inexact Newton (SAIN) solver for the non-linear Kohn-Sham equations. It is related to a class of iterative algorithms known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of real applications using a finite difference discretization and multigrid preconditioning.
Hyperbolic Divergence Cleaning Method for Godunov Smoothed Particle Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Iwasaki, K.; Inutsuka, S.-I.
2013-04-01
In this paper, we implement a divergence cleaning method into Godunov smoothed particle magnetohydrodynamics (GSPM). In the GSPM, to describe MHD shocks accurately, a Riemann solver is applied to the SPH method instead of artificial viscosity and resistivity that have been used in previous works. We confirmed that the divergence cleaning method reduces divergence errors significantly. The performance of the method is demonstrated in the numerical simulations of a strongly magnetized gas and bipolar outflow from the first core.
Solving nonlinear heat conduction problems with multigrid preconditioned Newton-Krylov methods
Rider, W.J.; Knoll, D.A.
1997-09-01
Our objective is to investigate the utility of employing multigrid preconditioned Newton-Krylov methods for solving initial value problems. Multigrid based method promise better performance from the linear scaling associated with them. Our model problem is nonlinear heat conduction which can model idealized Marshak waves. Here we will investigate the efficiency of using a linear multigrid method to precondition a Krylov subspace method. In effect we will show that a fixed point nonlinear iterative method provides an effective preconditioner for the nonlinear problem.
Modified Newton-Raphson GRAPE methods for optimal control of spin systems
NASA Astrophysics Data System (ADS)
Goodwin, D. L.; Kuprov, Ilya
2016-05-01
Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy.
Modified Newton-Raphson GRAPE methods for optimal control of spin systems.
Goodwin, D L; Kuprov, Ilya
2016-05-28
Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy. PMID:27250279
Likelihood Methods for Adaptive Filtering and Smoothing. Technical Report #455.
ERIC Educational Resources Information Center
Butler, Ronald W.
The dynamic linear model or Kalman filtering model provides a useful methodology for predicting the past, present, and future states of a dynamic system, such as an object in motion or an economic or social indicator that is changing systematically with time. Recursive likelihood methods for adaptive Kalman filtering and smoothing are developed.…
Smoothness Evaluation of Cotton Nonwovens Using Quality Energy Method
Technology Transfer Automated Retrieval System (TEKTRAN)
Nonwovens are finding enhanced use in next-to-skin application such as wipes. The global wipe industry is estimated somewhere between $6-8 billion. One important attributes of the wipes is its smoothness as it determines it end use applications. Although there are a number of methods and techniques ...
Cooley, R.L.; Hill, M.C.
1992-01-01
Three methods of solving nonlinear least-squares problems were compared for robustness and efficiency using a series of hypothetical and field problems. A modified Gauss-Newton/full Newton hybrid method (MGN/FN) and an analogous method for which part of the Hessian matrix was replaced by a quasi-Newton approximation (MGN/QN) solved some of the problems with appreciably fewer iterations than required using only a modified Gauss-Newton (MGN) method. In these problems, model nonlinearity and a large variance for the observed data apparently caused MGN to converge more slowly than MGN/FN or MGN/QN after the sum of squared errors had almost stabilized. Other problems were solved as efficiently with MGN as with MGN/FN or MGN/QN. Because MGN/FN can require significantly more computer time per iteration and more computer storage for transient problems, it is less attractive for a general purpose algorithm than MGN/QN.
Acceleration of k-Eigenvalue / Criticality Calculations using the Jacobian-Free Newton-Krylov Method
Dana Knoll; HyeongKae Park; Chris Newman
2011-02-01
We present a new approach for the $k$--eigenvalue problem using a combination of classical power iteration and the Jacobian--free Newton--Krylov method (JFNK). The method poses the $k$--eigenvalue problem as a fully coupled nonlinear system, which is solved by JFNK with an effective block preconditioning consisting of the power iteration and algebraic multigrid. We demonstrate effectiveness and algorithmic scalability of the method on a 1-D, one group problem and two 2-D two group problems and provide comparison to other efforts using silmilar algorithmic approaches.
NASA Astrophysics Data System (ADS)
Stein, David B.; Guy, Robert D.; Thomases, Becca
2016-01-01
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit-explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems.
Moschetti, Morgan P.; Mueller, Charles S.; Boyd, Oliver S.; Petersen, Mark D.
2014-01-01
In anticipation of the update of the Alaska seismic hazard maps (ASHMs) by the U. S. Geological Survey, we report progress on the comparison of smoothed seismicity models developed using fixed and adaptive smoothing algorithms, and investigate the sensitivity of seismic hazard to the models. While fault-based sources, such as those for great earthquakes in the Alaska-Aleutian subduction zone and for the ~10 shallow crustal faults within Alaska, dominate the seismic hazard estimates for locations near to the sources, smoothed seismicity rates make important contributions to seismic hazard away from fault-based sources and where knowledge of recurrence and magnitude is not sufficient for use in hazard studies. Recent developments in adaptive smoothing methods and statistical tests for evaluating and comparing rate models prompt us to investigate the appropriateness of adaptive smoothing for the ASHMs. We develop smoothed seismicity models for Alaska using fixed and adaptive smoothing methods and compare the resulting models by calculating and evaluating the joint likelihood test. We use the earthquake catalog, and associated completeness levels, developed for the 2007 ASHM to produce fixed-bandwidth-smoothed models with smoothing distances varying from 10 to 100 km and adaptively smoothed models. Adaptive smoothing follows the method of Helmstetter et al. and defines a unique smoothing distance for each earthquake epicenter from the distance to the nth nearest neighbor. The consequence of the adaptive smoothing methods is to reduce smoothing distances, causing locally increased seismicity rates, where seismicity rates are high and to increase smoothing distances where seismicity is sparse. We follow guidance from previous studies to optimize the neighbor number (n-value) by comparing model likelihood values, which estimate the likelihood that the observed earthquake epicenters from the recent catalog are derived from the smoothed rate models. We compare likelihood
A speciation solver for cement paste modeling and the semismooth Newton method
Georget, Fabien; Prévost, Jean H.; Vanderbei, Robert J.
2015-02-15
The mineral assemblage of a cement paste may vary considerably with its environment. In addition, the water content of a cement paste is relatively low and the ionic strength of the interstitial solution is often high. These conditions are extreme conditions with respect to the common assumptions made in speciation problem. Furthermore the common trial and error algorithm to find the phase assemblage does not provide any guarantee of convergence. We propose a speciation solver based on a semismooth Newton method adapted to the thermodynamic modeling of cement paste. The strong theoretical properties associated with these methods offer practical advantages. Results of numerical experiments indicate that the algorithm is reliable, robust, and efficient.
Chemical method for producing smooth surfaces on silicon wafers
Yu, Conrad
2003-01-01
An improved method for producing optically smooth surfaces in silicon wafers during wet chemical etching involves a pre-treatment rinse of the wafers before etching and a post-etching rinse. The pre-treatment with an organic solvent provides a well-wetted surface that ensures uniform mass transfer during etching, which results in optically smooth surfaces. The post-etching treatment with an acetic acid solution stops the etching instantly, preventing any uneven etching that leads to surface roughness. This method can be used to etch silicon surfaces to a depth of 200 .mu.m or more, while the finished surfaces have a surface roughness of only 15-50 .ANG. (RMS).
NASA Astrophysics Data System (ADS)
Bendinelli, O.; Parmeggiani, G.; Piccioni, A.; Zavatti, F.
1987-10-01
Modification of the Newton-Gauss linearization method in the Tikhonov regularization sense is described. Its ability to give reliable estimates of a large number of parameters is shown by application to the PSF determination from CCD frames. Extension of the Van Altena and Auer star-image model using a weighted sum of two Gaussians, and explicitly taking its integration on the pixel into account, enables the authors to determine the PSF up to about 10 mag below the central value with an error fit in the range 0.01 - 0.03 mag arcsec-2.
Method for smoothing the surface of a protective coating
Sangeeta, D.; Johnson, Curtis Alan; Nelson, Warren Arthur
2001-01-01
A method for smoothing the surface of a ceramic-based protective coating which exhibits roughness is disclosed. The method includes the steps of applying a ceramic-based slurry or gel coating to the protective coating surface; heating the slurry/gel coating to remove volatile material; and then further heating the slurry/gel coating to cure the coating and bond it to the underlying protective coating. The slurry/gel coating is often based on yttria-stabilized zirconia, and precursors of an oxide matrix. Related articles of manufacture are also described.
NASA Technical Reports Server (NTRS)
Bailey, Harry E.; Beam, Richard M.
1991-01-01
Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.
Modeling Electrokinetic Flows by the Smoothed Profile Method
Luo, Xian; Beskok, Ali; Karniadakis, George Em
2010-01-01
We propose an efficient modeling method for electrokinetic flows based on the Smoothed Profile Method (SPM) [1–4] and spectral element discretizations. The new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the the surrounding electrolyte solution. The electrokinetic forces are included into the flow equations so that the Poisson-Boltzmann and electric charge continuity equations are cast into forms suitable for SPM. The method is validated by benchmark problems of electroosmotic flow in straight channels and electrophoresis of charged cylinders. We also present simulation results of electrophoresis of charged microtubules, and show that the simulated electrophoretic mobility and anisotropy agree with the experimental values. PMID:20352076
Arima model and exponential smoothing method: A comparison
NASA Astrophysics Data System (ADS)
Wan Ahmad, Wan Kamarul Ariffin; Ahmad, Sabri
2013-04-01
This study shows the comparison between Autoregressive Moving Average (ARIMA) model and Exponential Smoothing Method in making a prediction. The comparison is focused on the ability of both methods in making the forecasts with the different number of data sources and the different length of forecasting period. For this purpose, the data from The Price of Crude Palm Oil (RM/tonne), Exchange Rates of Ringgit Malaysia (RM) in comparison to Great Britain Pound (GBP) and also The Price of SMR 20 Rubber Type (cents/kg) with three different time series are used in the comparison process. Then, forecasting accuracy of each model is measured by examinethe prediction error that producedby using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute deviation (MAD). The study shows that the ARIMA model can produce a better prediction for the long-term forecasting with limited data sources, butcannot produce a better prediction for time series with a narrow range of one point to another as in the time series for Exchange Rates. On the contrary, Exponential Smoothing Method can produce a better forecasting for Exchange Rates that has a narrow range of one point to another for its time series, while itcannot produce a better prediction for a longer forecasting period.
NASA Astrophysics Data System (ADS)
Hoppe, R. H. W.; Linsenmann, C.
2012-05-01
The immersed boundary method (IB) is known as a powerful technique for the numerical solution of fluid-structure interaction problems as, for instance, the motion and deformation of viscoelastic bodies immersed in an external flow. It is based on the treatment of the flow equations within an Eulerian framework and of the equations of motion of the immersed bodies with respect to a Lagrangian coordinate system including interaction equations providing the transfer between both frames. The classical IB uses finite differences, but the IBM can be set up within a finite element approach in the spatial variables as well (FE-IB). The discretization in time usually relies on the Backward Euler (BE) method for the semidiscretized flow equations and the Forward Euler (FE) method for the equations of motion of the immersed bodies. The BE/FE FE-IB is subject to a CFL-type condition, whereas the fully implicit BE/BE FE-IB is unconditionally stable. The latter one can be solved numerically by Newton-type methods whose convergence properties are dictated by an appropriate choice of the time step size, in particular, if one is faced with sudden changes in the total energy of the system. In this paper, taking advantage of the well developed affine covariant convergence theory for Newton-type methods, we study a predictor-corrector continuation strategy in time with an adaptive choice of the continuation steplength. The feasibility of the approach and its superiority to BE/FE FE-IB is illustrated by two representative numerical examples.
Multi-scale crystal growth computations via an approximate block Newton method
NASA Astrophysics Data System (ADS)
Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.
2010-04-01
Multi-scale and multi-physics simulations, such as the computational modeling of crystal growth processes, will benefit from the modular coupling of existing codes rather than the development of monolithic, single-application software. An effective coupling approach, the approximate block Newton approach (ABN), is developed and applied to the steady-state computation of crystal growth in an electrodynamic gradient freeze system. Specifically, the code CrysMAS is employed for furnace-scale heat transfer computations and is coupled with the code Cats2D to calculate melt fluid dynamics and phase-change phenomena. The ABN coupling strategy proves to be vastly more reliable and cost efficient than simpler coupling methods for this problem and is a promising approach for future crystal growth models.
Systems identification using a modified Newton-Raphson method: A FORTRAN program
NASA Technical Reports Server (NTRS)
Taylor, L. W., Jr.; Iliff, K. W.
1972-01-01
A FORTRAN program is offered which computes a maximum likelihood estimate of the parameters of any linear, constant coefficient, state space model. For the case considered, the maximum likelihood estimate can be identical to that which minimizes simultaneously the weighted mean square difference between the computed and measured response of a system and the weighted square of the difference between the estimated and a priori parameter values. A modified Newton-Raphson or quasilinearization method is used to perform the minimization which typically requires several iterations. A starting technique is used which insures convergence for any initial values of the unknown parameters. The program and its operation are described in sufficient detail to enable the user to apply the program to his particular problem with a minimum of difficulty.
NASA Astrophysics Data System (ADS)
Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.
2009-12-01
A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss-Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.
ERIC Educational Resources Information Center
Geiger, H. Bruce
Compared were inductive programed, deductive programed, and conventional lecture-question methods of instruction related to Newton's Second Law of Motion on outcome gains including recall of factual information, ability to solve mathematical problems, and retention. Some 266 students in three schools participated and were compared for…
A Particle-Particle Collision Model for Smoothed Profile Method
NASA Astrophysics Data System (ADS)
Mohaghegh, Fazlolah; Mousel, John; Udaykumar, H. S.
2014-11-01
Smoothed Profile Method (SPM) is a type of continuous forcing approach that adds the particles to the fluid using a forcing. The fluid-structure interaction is through a diffuse interface which avoids sudden transition from solid to fluid. The SPM simulation as a monolithic approach uses an indicator function field in the whole domain based on the distance from each particle's boundary where the possible particle-particle interaction can occur. A soft sphere potential based on the indicator function field has been defined to add an artificial pressure to the flow pressure in the potential overlapping regions. Thus, a repulsion force is obtained to avoid overlapping. Study of two particles which impulsively start moving in an initially uniform flow shows that the particle in the wake of the other one will have less acceleration leading to frequent collisions. Various Reynolds numbers and initial distances have been chosen to test the robustness of the method. Study of Drafting-Kissing Tumbling of two cylindrical particles shows a deviation from the benchmarks due to lack of rotation modeling. The method is shown to be accurate enough for simulating particle-particle collision and can easily be extended for particle-wall modeling and for non-spherical particles.
General purpose nonlinear system solver based on Newton-Krylov method.
Energy Science and Technology Software Center (ESTSC)
2013-12-01
KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].
NASA Astrophysics Data System (ADS)
Salucci, Marco; Oliveri, Giacomo; Massa, Andrea; Randazzo, Andrea; Pastorino, Matteo
2014-05-01
Ground penetrating radars (GPRs) are key instruments for subsurface monitoring and imaging. They can be used in different applicative fields, e.g., for the assessment of the structural stability of concrete structures and for the detection of targets buried inside inaccessible materials. In this framework, imaging systems based on the solution of the underlying inverse electromagnetic scattering problem have been acquiring an ever growing interest in the scientific community. In fact, they are able - at least in principle - to provide a quantitative reconstruction of the distributions of the dielectric properties (e.g., the dielectric permittivity and the electric conductivity) of the investigated scenario. Although good results have been obtained in recent years, there is still the need of further research, especially concerning the development of inversion procedure able to deal with the limitations arising from the non-linearity and ill-posedness of the underlying electromagnetic imaging formulation. In this work, a novel electromagnetic inverse scattering method is proposed for the reconstruction of shallow buried objects. The inversion procedure is based on the combination of different imaging modalities. In particular, an iterative multi-scaling approach [1] is adopted for focusing the reconstruction only on limited subdomains of the original investigation region. The data inversion is performed by applying an inexact-Newton method (which exhibits very good regularization properties) within the second-order Born approximation [2]. The use of this approximation allows a reduction of the problem unknowns and a mitigation of the nonlinear effects. The proposed approach has been validated by means of several numerical simulations. In particular, the reconstruction performances have been evaluated in terms of accuracy, robustness, noise levels, and computational efficiency, with particular emphasis on the comparisons with the results obtained by using the standard
Recovery Discontinuous Galerkin Jacobian-free Newton-Krylov Method for all-speed flows
HyeongKae Park; Robert Nourgaliev; Vincent Mousseau; Dana Knoll
2008-07-01
There is an increasing interest to develop the next generation simulation tools for the advanced nuclear energy systems. These tools will utilize the state-of-art numerical algorithms and computer science technology in order to maximize the predictive capability, support advanced reactor designs, reduce uncertainty and increase safety margins. In analyzing nuclear energy systems, we are interested in compressible low-Mach number, high heat flux flows with a wide range of Re, Ra, and Pr numbers. Under these conditions, the focus is placed on turbulent heat transfer, in contrast to other industries whose main interest is in capturing turbulent mixing. Our objective is to develop singlepoint turbulence closure models for large-scale engineering CFD code, using Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) tools, requireing very accurate and efficient numerical algorithms. The focus of this work is placed on fully-implicit, high-order spatiotemporal discretization based on the discontinuous Galerkin method solving the conservative form of the compressible Navier-Stokes equations. The method utilizes a local reconstruction procedure derived from weak formulation of the problem, which is inspired by the recovery diffusion flux algorithm of van Leer and Nomura [?] and by the piecewise parabolic reconstruction [?] in the finite volume method. The developed methodology is integrated into the Jacobianfree Newton-Krylov framework [?] to allow a fully-implicit solution of the problem.
NASA Astrophysics Data System (ADS)
Danaila, Ionut; Moglan, Raluca; Hecht, Frédéric; Le Masson, Stéphane
2014-10-01
We present a new numerical system using finite elements with mesh adaptivity for the simulation of solid-liquid phase change systems. In the liquid phase, the natural convection flow is simulated by solving the incompressible Navier-Stokes equations with Boussinesq approximation. A variable viscosity model allows the velocity to progressively vanish in the solid phase, through an intermediate mushy region. The phase change is modeled by introducing an implicit enthalpy source term in the heat equation. The final system of equations describing the liquid-solid system by a single domain approach is solved using a Newton iterative algorithm. The space discretization is based on a P2-P1 Taylor-Hood finite elements and mesh adaptivity by metric control is used to accurately track the solid-liquid interface or the density inversion interface for water flows. The numerical method is validated against classical benchmarks that progressively add strong non-linearities in the system of equations: natural convection of air, natural convection of water, melting of a phase-change material and water freezing. Very good agreement with experimental data is obtained for each test case, proving the capability of the method to deal with both melting and solidification problems with convection. The presented numerical method is easy to implement using FreeFem++ software using a syntax close to the mathematical formulation.
A convergence rates result for an iteratively regularized Gauss-Newton-Halley method in Banach space
NASA Astrophysics Data System (ADS)
Kaltenbacher, B.
2015-01-01
The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification problems for differential equation models. On the other hand the use of general (non-Hilbert) Banach spaces has recently found much interest due to its usefulness in many applications. This motivates us to extend the second order method from Kaltenbacher (2014 Numer. Math. at press), (see also Hettlich and Rundell 2000 SIAM J. Numer. Anal. 37 587620) to a Banach space setting and analyze its convergence. We here show rates results for a particular source condition and different exponents in the formulation of Tikhonov regularization in each step. This includes a complementary result on the (first order) iteratively regularized Gauss-Newton method in case of a one-homogeneous data misfit term, which corresponds to exact penalization. The results clearly show the possible advantages of using second order information, which get most pronounced in this exact penalization case. Numerical simulations for an inverse source problem for a nonlinear elliptic PDE illustrate the theoretical findings.
Weighted Wilcoxon-type Smoothly Clipped Absolute Deviation Method
Wang, Lan; Li, Runze
2009-01-01
Summary Shrinkage-type variable selection procedures have recently seen increasing applications in biomedical research. However, their performance can be adversely influenced by outliers in either the response or the covariate space. This paper proposes a weighted Wilcoxon-type smoothly clipped absolute deviation (WW-SCAD) method, which deals with robust variable selection and robust estimation simultaneously. The new procedure can be conveniently implemented with the statistical software R. We establish that the WW-SCAD correctly identifies the set of zero coefficients with probability approaching one and estimates the nonzero coefficients with the rate n−1/2. Moreover, with appropriately chosen weights the WW-SCAD is robust with respect to outliers in both the x and y directions. The important special case with constant weights yields an oracle-type estimator with high efficiency at the presence of heavier-tailed random errors. The robustness of the WW-SCAD is partly justified by its asymptotic performance under local shrinking contamination. We propose a BIC-type tuning parameter selector for the WW-SCAD. The performance of the WW-SCAD is demonstrated via simulations and by an application to a study that investigates the effects of personal characteristics and dietary factors on plasma beta-carotene level. PMID:18647294
Impact of beam smoothing method on direct drive target performance for the NIF
Rothenberg, J.E.; Weber, S.V.
1996-11-01
The impact of smoothing method on the performance of a direct drive target is modeled and examined in terms of its l-mode spectrum. In particular, two classes of smoothing methods are compared, smoothing by spectral dispersion (SSD) and the induced spatial incoherence (ISI) method. It is found that SSD using sinusoidal phase modulation (FM) results in poor smoothing at low l-modes and therefore inferior target performance at both peak velocity and ignition. Modeling of the hydrodynamic nonlinearity shows that saturation tends to reduce the difference between target performance for the smoothing methods considered. However, using SSD with more generalized phase modulation results in a smoothed spatial spectrum, and therefore target performance, which is identical to that obtained with the ISI or similar method where random phase plates are present in both methods and identical beam divergence is assumed.
NASA Astrophysics Data System (ADS)
Muthuvalu, Mohana Sundaram; Aruchunan, Elayaraja; Akhir, Mohd Kamalrulzaman Md; Sulaiman, Jumat; Karim, Samsul Ariffin Abdul
2014-10-01
In this paper, application of the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is extended by solving second order composite closed Newton-Cotes quadrature (2-CCNC) system. The performance of HSSOR method in solving 2-CCNC system is comparatively studied by their application on linear Fredholm integral equations of the second kind. The derivation and implementation of the method are discussed. In addition, numerical results by solving two test problems are included and compared with the standard Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) methods. Numerical results demonstrate that HSSOR method is an efficient method among the tested methods.
Rapid springback compensation for age forming based on quasi Newton method
NASA Astrophysics Data System (ADS)
Xiong, Wei; Gan, Zhong; Xiong, Shipeng; Xia, Yushan
2014-05-01
Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mm ×750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment (DA) method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method (0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively). In following experimental verification, mold contour for another integrated panel with 400 mm×380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel's design contour is less than 1 mm. Finally, the iterations with different mesh sizes (40 mm, 35 mm, 30 mm, 25 mm, 20 mm) in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear functions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel
NASA Astrophysics Data System (ADS)
Hendry, Archibald W.
2007-05-01
Isaac Newton may have seen an apple fall, but it was Robert Hooke who had a better idea of where it would land. No one really knows whether or not Isaac Newton actually saw an apple fall in his garden. Supposedly it took place in 1666, but it was a tale he told in his old age more than 60 years later, a time when his memory was failing and his recollections of events did not always match known facts. However, one thing is certain-falling objects were to play a key part in Newton's eventual understanding of how objects move.
Methods and electrolytes for electrodeposition of smooth films
Zhang, Jiguang; Xu, Wu; Graff, Gordon L; Chen, Xilin; Ding, Fei; Shao, Yuyan
2015-03-17
Electrodeposition involving an electrolyte having a surface-smoothing additive can result in self-healing, instead of self-amplification, of initial protuberant tips that give rise to roughness and/or dendrite formation on the substrate and/or film surface. For electrodeposition of a first conductive material (C1) on a substrate from one or more reactants in an electrolyte solution, the electrolyte solution is characterized by a surface-smoothing additive containing cations of a second conductive material (C2), wherein cations of C2 have an effective electrochemical reduction potential in the solution lower than that of the reactants.
NASA Technical Reports Server (NTRS)
Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.
2007-01-01
The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.
Impact of beam smoothing method on direct drive target performance for the NIF
Rothenberg, J.E.; Weber, S.V.
1997-01-01
The impact of smoothing method on the performance of a direct drive target is modeled and examined in terms of its 1-mode spectrum. In particular, two classes of smoothing methods are compared, smoothing by spectral dispersion (SSD) and the induced spatial incoherence (ISI) method. It is found that SSD using sinusoidal phase modulation (FM) results in poor smoothing at low 1-modes and therefore inferior target performance at both peak velocity and ignition. This disparity is most notable if the effective imprinting integration time of the target is small. However, using SSD with more generalized phase modulation can result in smoothing at low l-modes which is identical to that obtained with ISI. For either smoothing method, the calculations indicate that at peak velocity the surface perturbations are about 100 times larger than that which leads to nonlinear hydrodynamics. Modeling of the hydrodynamic nonlinearity shows that saturation can reduce the amplified nonuniformities to the level required to achieve ignition for either smoothing method. The low l- mode behavior at ignition is found to be strongly dependent on the induced divergence of the smoothing method. For the NIF parameters the target performance asymptotes for smoothing divergence larger than {approximately}100 {mu}rad.
ERIC Educational Resources Information Center
Hendry, Archibald W.
2007-01-01
Isaac Newton may have seen an apple fall, but it was Robert Hooke who had a better idea of where it would land. No one really knows whether or not Isaac Newton actually saw an apple fall in his garden. Supposedly it took place in 1666, but it was a tale he told in his old age more than 60 years later, a time when his memory was failing and his…
Methods for Smoothing Expectancy Tables Applied to the Prediction of Success in College
ERIC Educational Resources Information Center
Perrin, David W.; Whitney, Douglas R.
1976-01-01
The gains in accuracy resulting from applying any of the smoothing methods appear sufficient to justify the suggestion that all expectancy tables used by colleges for admission, guidance, or planning purposes should be smoothed. These methods on the average, reduce the criterion measure (an index of inaccuracy) by 30 percent. (Author/MV)
Suppression of stochastic pulsation in laser-plasma interaction by smoothing methods
NASA Astrophysics Data System (ADS)
Hora, Heinrich; Aydin, Meral
1992-04-01
The control of the very complex behavior of a plasma with laser interaction by smoothing with induced spatial incoherence or other methods was related to improving the lateral uniformity of the irradiation. While this is important, it is shown from numerical hydrodynamic studies that the very strong temporal pulsation (stuttering) will mostly be suppressed by these smoothing methods too.
Suppression of stochastic pulsation in laser-plasma interaction by smoothing methods
Hora, H. ); Aydin, M. )
1992-04-15
The control of the very complex behavior of a plasma with laser interaction by smoothing with induced spatial incoherence or other methods was related to improving the lateral uniformity of the irradiation. While this is important, it is shown from numerical hydrodynamic studies that the very strong temporal pulsation (stuttering) will mostly be suppressed by these smoothing methods too.
Quasi-Newton methods for parameter estimation in functional differential equations
NASA Technical Reports Server (NTRS)
Brewer, Dennis W.
1988-01-01
A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.
Stochastic quasi-Newton method: Application to minimal model for proteins
NASA Astrophysics Data System (ADS)
Chau, C. D.; Sevink, G. J. A.; Fraaije, J. G. E. M.
2011-01-01
Knowledge of protein folding pathways and inherent structures is of utmost importance for our understanding of biological function, including the rational design of drugs and future treatments against protein misfolds. Computational approaches have now reached the stage where they can assess folding properties and provide data that is complementary to or even inaccessible by experimental imaging techniques. Minimal models of proteins, which make possible the simulation of protein folding dynamics by (systematic) coarse graining, have provided understanding in terms of descriptors for folding, folding kinetics, and folded states. Here we focus on the efficiency of equilibration on the coarse-grained level. In particular, we applied a new regularized stochastic quasi-Newton (S-QN) method, developed for accelerated configurational space sampling while maintaining thermodynamic consistency, to analyze the folding pathway and inherent structures of a selected protein, where regularization was introduced to improve stability. The adaptive compound mobility matrix B in S-QN, determined by a factorized secant update, gives rise to an automated scaling of all modes in the protein, in particular an acceleration of protein domain dynamics or principal modes and a slowing down of fast modes or “soft” bond constraints, similar to lincs/shake algorithms, when compared to conventional Langevin dynamics. We used and analyzed a two-step strategy. Owing to the enhanced sampling properties of S-QN and increased barrier crossing at high temperatures (in reduced units), a hierarchy of inherent protein structures is first efficiently determined by applying S-QN for a single initial structure and T=1>Tθ, where Tθ is the collapse temperature. Second, S-QN simulations for several initial structures at very low temperature (T=0.01
Alternative methods to smooth the Earth's gravity field
NASA Technical Reports Server (NTRS)
Jekeli, C.
1981-01-01
Convolutions on the sphere with corresponding convolution theorems are developed for one and two dimensional functions. Some of these results are used in a study of isotropic smoothing operators or filters. Well known filters in Fourier spectral analysis, such as the rectangular, Gaussian, and Hanning filters, are adapted for data on a sphere. The low-pass filter most often used on gravity data is the rectangular (or Pellinen) filter. However, its spectrum has relatively large sidelobes; and therefore, this filter passes a considerable part of the upper end of the gravity spectrum. The spherical adaptations of the Gaussian and Hanning filters are more efficient in suppressing the high-frequency components of the gravity field since their frequency response functions are strongly field since their frequency response functions are strongly tapered at the high frequencies with no, or small, sidelobes. Formulas are given for practical implementation of these new filters.
A numerical study of the Regge calculus and smooth lattice methods on a Kasner cosmology
NASA Astrophysics Data System (ADS)
Brewin, Leo
2015-10-01
Two lattice based methods for numerical relativity, the Regge calculus and the smooth lattice relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge calculus is of the order of 110 times slower than the smooth lattice method.
Smoothing methods comparison for CMB E- and B-mode separation
NASA Astrophysics Data System (ADS)
Wang, Yi-Fan; Wang, Kai; Zhao, Wen
2016-04-01
The anisotropies of the B-mode polarization in the cosmic microwave background radiation play a crucial role in the study of the very early Universe. However, in real observations, a mixture of the E-mode and B-mode can be caused by partial sky surveys, which must be separated before being applied to a cosmological explanation. The separation method developed by Smith (2006) has been widely adopted, where the edge of the top-hat mask should be smoothed to avoid numerical errors. In this paper, we compare three different smoothing methods and investigate leakage residuals of the E-B mixture. We find that, if less information loss is needed and a smaller region is smoothed in the analysis, the sin- and cos-smoothing methods are better. However, if we need a cleanly constructed B-mode map, the larger region around the mask edge should be smoothed. In this case, the Gaussian-smoothing method becomes much better. In addition, we find that the leakage caused by numerical errors in the Gaussian-smoothing method is mostly concentrated in two bands, which is quite easy to reduce for further E-B separations.
A solution to the Navier-Stokes equations based upon the Newton Kantorovich method
NASA Technical Reports Server (NTRS)
Davis, J. E.; Gabrielsen, R. E.; Mehta, U. B.
1977-01-01
An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.
Rotating vector methods for smooth torque control of a switched reluctance motor drive
Nagel, N.J.; Lorenz, R.D.
2000-04-01
This paper has two primary contributions to switched reluctance motor (SRM) control: a systematic approach to smooth torque production and a high-performance technique for sensorless motion control. The systematic approach to smooth torque production is based on development of novel rotating spatial vectors methods that can be used to predict the torque produced in an arbitrary SRM. This analysis directly leads to explicit, insightful methods to provide smooth torque control of SRM's. The high-performance technique for sensorless motion control is based on a rotating vector method for high bandwidth, high resolution, position, and velocity estimation suitable for both precise torque and motion control. The sensorless control and smooth torque control methods are both verified experimentally.
The two-level Newton method and its application to electronic simulation.
Hoekstra, Robert John; Waters, Lon J.; Rankin, Eric Lamont; Hutchinson, Scott Alan; Keiter, Eric Richard; Russo, Thomas V.
2004-06-01
Coupling between transient simulation codes of different fidelity can often be performed at the nonlinear solver level, if the time scales of the two codes are similar. A good example is electrical mixed-mode simulation, in which an analog circuit simulator is coupled to a PDE-based semiconductor device simulator. Semiconductor simulation problems, such as single-event upset (SEU), often require the fidelity of a mesh-based device simulator but are only meaningful when dynamically coupled with an external circuit. For such problems a mixed-level simulator is desirable, but the two types of simulation generally have different (somewhat conflicting) numerical requirements. To address these considerations, we have investigated variations of the two-level Newton algorithm, which preserves tight coupling between the circuit and the PDE device, while optimizing the numerics for both. The research was done within Xyce, a massively parallel electronic simulator under development at Sandia National Laboratories.
SKRYN: A fast semismooth-Krylov-Newton method for controlling Ising spin systems
NASA Astrophysics Data System (ADS)
Ciaramella, G.; Borzì, A.
2015-05-01
The modeling and control of Ising spin systems is of fundamental importance in NMR spectroscopy applications. In this paper, two computer packages, ReHaG and SKRYN, are presented. Their purpose is to set-up and solve quantum optimal control problems governed by the Liouville master equation modeling Ising spin-1/2 systems with pointwise control constraints. In particular, the MATLAB package ReHaG allows to compute a real matrix representation of the master equation. The MATLAB package SKRYN implements a new strategy resulting in a globalized semismooth matrix-free Krylov-Newton scheme. To discretize the real representation of the Liouville master equation, a norm-preserving modified Crank-Nicolson scheme is used. Results of numerical experiments demonstrate that the SKRYN code is able to provide fast and accurate solutions to the Ising spin quantum optimization problem.
A new adaptive exponential smoothing method for non-stationary time series with level shifts
NASA Astrophysics Data System (ADS)
Monfared, Mohammad Ali Saniee; Ghandali, Razieh; Esmaeili, Maryam
2014-07-01
Simple exponential smoothing (SES) methods are the most commonly used methods in forecasting and time series analysis. However, they are generally insensitive to non-stationary structural events such as level shifts, ramp shifts, and spikes or impulses. Similar to that of outliers in stationary time series, these non-stationary events will lead to increased level of errors in the forecasting process. This paper generalizes the SES method into a new adaptive method called revised simple exponential smoothing (RSES), as an alternative method to recognize non-stationary level shifts in the time series. We show that the new method improves the accuracy of the forecasting process. This is done by controlling the number of observations and the smoothing parameter in an adaptive approach, and in accordance with the laws of statistical control limits and the Bayes rule of conditioning. We use a numerical example to show how the new RSES method outperforms its traditional counterpart, SES.
Shadid, J.N.; Tuminaro, R.S.; Walker, H.F.
1997-02-01
The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.
Bladder Smooth Muscle Strip Contractility as a Method to Evaluate Lower Urinary Tract Pharmacology
Kullmann, F. Aura; Daugherty, Stephanie L.; de Groat, William C.; Birder, Lori A.
2015-01-01
We describe an in vitro method to measure bladder smooth muscle contractility, and its use for investigating physiological and pharmacological properties of the smooth muscle as well as changes induced by pathology. This method provides critical information for understanding bladder function while overcoming major methodological difficulties encountered in in vivo experiments, such as surgical and pharmacological manipulations that affect stability and survival of the preparations, the use of human tissue, and/or the use of expensive chemicals. It also provides a way to investigate the properties of each bladder component (i.e. smooth muscle, mucosa, nerves) in healthy and pathological conditions. The urinary bladder is removed from an anesthetized animal, placed in Krebs solution and cut into strips. Strips are placed into a chamber filled with warm Krebs solution. One end is attached to an isometric tension transducer to measure contraction force, the other end is attached to a fixed rod. Tissue is stimulated by directly adding compounds to the bath or by electric field stimulation electrodes that activate nerves, similar to triggering bladder contractions in vivo. We demonstrate the use of this method to evaluate spontaneous smooth muscle contractility during development and after an experimental spinal cord injury, the nature of neurotransmission (transmitters and receptors involved), factors involved in modulation of smooth muscle activity, the role of individual bladder components, and species and organ differences in response to pharmacological agents. Additionally, it could be used for investigating intracellular pathways involved in contraction and/or relaxation of the smooth muscle, drug structure-activity relationships and evaluation of transmitter release. The in vitro smooth muscle contractility method has been used extensively for over 50 years, and has provided data that significantly contributed to our understanding of bladder function as well as to
NASA Astrophysics Data System (ADS)
Asgharzadeh, Hafez; Borazjani, Iman
2014-11-01
Time step-size restrictions and low convergence rates are major bottle necks for implicit solution of the Navier-Stokes in simulations involving complex geometries with moving boundaries. Newton-Krylov method (NKM) is a combination of a Newton-type method for super-linearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations, which can theoretically address both bottle necks. The efficiency of this method vastly depends on the Jacobian forming scheme e.g. automatic differentiation is very expensive and Jacobian-free methods slow down as the mesh is refined. A novel, computationally efficient analytical Jacobian for NKM was developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered curvilinear grids with immersed boundaries. The NKM was validated and verified against Taylor-Green vortex and pulsatile flow in a 90 degree bend and efficiently handles complex geometries such as an intracranial aneurysm with multiple overset grids, pulsatile inlet flow and immersed boundaries. The NKM method is shown to be more efficient than the semi-implicit Runge-Kutta methods and Jabobian-free Newton-Krylov methods. We believe NKM can be applied to many CFD techniques to decrease the computational cost. This work was supported partly by the NIH Grant R03EB014860, and the computational resources were partly provided by Center for Computational Research (CCR) at University at Buffalo.
Nonequilibrium flows with smooth particle applied mechanics
Kum, O.
1995-07-01
Smooth particle methods are relatively new methods for simulating solid and fluid flows through they have a 20-year history of solving complex hydrodynamic problems in astrophysics, such as colliding planets and stars, for which correct answers are unknown. The results presented in this thesis evaluate the adaptability or fitness of the method for typical hydrocode production problems. For finite hydrodynamic systems, boundary conditions are important. A reflective boundary condition with image particles is a good way to prevent a density anomaly at the boundary and to keep the fluxes continuous there. Boundary values of temperature and velocity can be separately controlled. The gradient algorithm, based on differentiating the smooth particle expression for (u{rho}) and (T{rho}), does not show numerical instabilities for the stress tensor and heat flux vector quantities which require second derivatives in space when Fourier`s heat-flow law and Newton`s viscous force law are used. Smooth particle methods show an interesting parallel linking to them to molecular dynamics. For the inviscid Euler equation, with an isentropic ideal gas equation of state, the smooth particle algorithm generates trajectories isomorphic to those generated by molecular dynamics. The shear moduli were evaluated based on molecular dynamics calculations for the three weighting functions, B spline, Lucy, and Cusp functions. The accuracy and applicability of the methods were estimated by comparing a set of smooth particle Rayleigh-Benard problems, all in the laminar regime, to corresponding highly-accurate grid-based numerical solutions of continuum equations. Both transient and stationary smooth particle solutions reproduce the grid-based data with velocity errors on the order of 5%. The smooth particle method still provides robust solutions at high Rayleigh number where grid-based methods fails.
NASA Astrophysics Data System (ADS)
Lala, P.; Thao, Bui Van
1986-11-01
The first step in the treatment of satellite laser ranging data is its smoothing and rejection of incorrect points. The proposed method uses the comparison of observations with ephemerides and iterative matching of corresponding parameters. The method of solution and a program for a minicomputer are described. Examples of results for satellite Starlette are given.
Yang, Zhongming; Wang, Kailiang; Cheng, Jinlong; Gao, Zhishan; Yuan, Qun
2016-06-10
We have proposed a virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer to measure the large radius of curvature for a spherical surface. In a quadratic polar coordinate system, linear carrier testing Newton rings interferogram and virtual Newton rings interferogram form the moiré fringes. It is possible to retrieve the wavefront difference data between the testing and standard spherical surface from the moiré fringes after low-pass filtering. Based on the wavefront difference data, we deduced a precise formula to calculate the radius of curvature in the quadratic polar coordinate system. We calculated the retrace error in the nonnull interferometer using the multi-configuration model of the nonnull interferometric system in ZEMAX. Our experimental results indicate that the measurement accuracy is better than 0.18% for a spherical mirror with a radius of curvature of 41,400 mm. PMID:27409038
ERIC Educational Resources Information Center
Nunan, E.
1973-01-01
Presents a brief biography of Sir Isaac Newton, lists contemporary scientists and scientific developments and discusses Newton's optical research and conceptual position concerning the nature of light. (JR)
A Meshfree Cell-based Smoothed Point Interpolation Method for Solid Mechanics Problems
NASA Astrophysics Data System (ADS)
Zhang, Guiyong; Liu, Gui-Rong
2010-05-01
In the framework of a weakened weak (W2) formulation using a generalized gradient smoothing operation, this paper introduces a novel meshfree cell-based smoothed point interpolation method (CS-PIM) for solid mechanics problems. The W2 formulation seeks solutions from a normed G space which includes both continuous and discontinuous functions and allows the use of much more types of methods to create shape functions for numerical methods [1]. When PIM shape functions are used, the functions constructed are in general not continuous over the entire problem domain and hence are not compatible. Such an interpolation is not in a traditional H1 space, but in a G1 space. By introducing the generalized gradient smoothing operation properly, the requirement on function is now further weakened upon the already weakened requirement for functions in a H1 space and G1 space can be viewed as a space of functions with weakened weak (W2) requirement on continuity [1-3]. The cell-based smoothed point interpolation method (CS-PIM) is formulated based on the W2 formulation, in which displacement field is approximated using the PIM shape functions, which possess the Kronecker delta property facilitating the enforcement of essential boundary conditions [3]. The gradient (strain) field is constructed by the generalized gradient smoothing operation within the cell-based smoothing domains, which are exactly the triangular background cells. A W2 formulation of generalized smoothed Galerkin (GS-Galerkin) weak form is used to derive the discretized system equations [2]. It was found that the CS-PIM possesses the following attractive properties: (1) It is very easy to implement and works well with the simplest linear triangular mesh without introducing additional degrees of freedom; (2) it is at least linearly conforming; (3) this method is temporally stable and works well for dynamic analysis; (4) it possesses a close-to-exact stiffness, which is much softer than the overly-stiff FEM model
A Meshfree Cell-based Smoothed Point Interpolation Method for Solid Mechanics Problems
Zhang Guiyong; Liu Guirong
2010-05-21
In the framework of a weakened weak (W{sup 2}) formulation using a generalized gradient smoothing operation, this paper introduces a novel meshfree cell-based smoothed point interpolation method (CS-PIM) for solid mechanics problems. The W{sup 2} formulation seeks solutions from a normed G space which includes both continuous and discontinuous functions and allows the use of much more types of methods to create shape functions for numerical methods. When PIM shape functions are used, the functions constructed are in general not continuous over the entire problem domain and hence are not compatible. Such an interpolation is not in a traditional H{sup 1} space, but in a G{sup 1} space. By introducing the generalized gradient smoothing operation properly, the requirement on function is now further weakened upon the already weakened requirement for functions in a H{sup 1} space and G{sup 1} space can be viewed as a space of functions with weakened weak (W{sup 2}) requirement on continuity. The cell-based smoothed point interpolation method (CS-PIM) is formulated based on the W{sup 2} formulation, in which displacement field is approximated using the PIM shape functions, which possess the Kronecker delta property facilitating the enforcement of essential boundary conditions [3]. The gradient (strain) field is constructed by the generalized gradient smoothing operation within the cell-based smoothing domains, which are exactly the triangular background cells. A W{sup 2} formulation of generalized smoothed Galerkin (GS-Galerkin) weak form is used to derive the discretized system equations. It was found that the CS-PIM possesses the following attractive properties: (1) It is very easy to implement and works well with the simplest linear triangular mesh without introducing additional degrees of freedom; (2) it is at least linearly conforming; (3) this method is temporally stable and works well for dynamic analysis; (4) it possesses a close-to-exact stiffness, which is much
Tests of smoothing methods for topological study of galaxy redshift surveys
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Dominik, Kurt G.
1993-01-01
Studying the topology of large-scale structure as a way to better understand initial conditions has become more widespread in recent years. Studying topology of simulations (which have periodic boundary conditions) in redshift space produces results compatible with the real topological characteristics of the simulation. Thus we expect we can extract useful information from redshift surveys. However, with nonperiodic boundary conditions, the use of smoothing must result in the loss of information at survey boundaries. In this paper, we test different methods of smoothing samples with nonperiodic boundary conditions to see which most efficiently preserves the topological features of the real distribution. We find that a smoothing method which (unlike most previous published analysis) sums only over cells inside the survey volume produces the best results among the schemes tested.
Code of Federal Regulations, 2013 CFR
2013-07-01
... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43... accordance with the quality assurance requirements of section 5.1.1 of 40 CFR part 60, appendix F. Each...
Code of Federal Regulations, 2014 CFR
2014-07-01
... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43... of 40 CFR part 60, appendix F. Each SO2 and diluent CEMs shall be subject to cylinder gas audits...
Code of Federal Regulations, 2012 CFR
2012-07-01
... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43... accordance with the quality assurance requirements of section 5.1.1 of 40 CFR part 60, appendix F. Each...
Code of Federal Regulations, 2011 CFR
2011-07-01
... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43... accordance with the quality assurance requirements of section 5.1.1 of 40 CFR part 60, appendix F. Each...
Code of Federal Regulations, 2010 CFR
2010-07-01
... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43... accordance with the quality assurance requirements of section 5.1.1 of 40 CFR part 60, appendix F. Each...
NASA Astrophysics Data System (ADS)
Abrashkevich, Alexander; Puzynin, I. V.
2004-01-01
A FORTRAN program is presented which solves a system of nonlinear simultaneous equations using the continuous analog of Newton's method (CANM). The user has the option of either to provide a subroutine which calculates the Jacobian matrix or allow the program to calculate it by a forward-difference approximation. Five iterative schemes using different algorithms of determining adaptive step size of the CANM process are implemented in the program. Program summaryTitle of program: CANM Catalogue number: ADSN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSN Program available from: CPC Program Library, Queen's University of Belfast, Northern Ireland Licensing provisions: none Computer for which the program is designed and others on which it has been tested: Computers: IBM RS/6000 Model 320H, SGI Origin2000, SGI Octane, HP 9000/755, Intel Pentium IV PC Installation: Department of Chemistry, University of Toronto, Toronto, Canada Operating systems under which the program has been tested: IRIX64 6.1, 6.4 and 6.5, AIX 3.4, HP-UX 9.01, Linux 2.4.7 Programming language used: FORTRAN 90 Memory required to execute with typical data: depends on the number of nonlinear equations in a system. Test run requires 80 KB No. of bits in distributed program including test data, etc.: 15283 Distribution format: tar gz format No. of lines in distributed program, including test data, etc.: 1794 Peripherals used: line printer, scratch disc store External subprograms used: DGECO and DGESL [1] Keywords: nonlinear equations, Newton's method, continuous analog of Newton's method, continuous parameter, evolutionary differential equation, Euler's method Nature of physical problem: System of nonlinear simultaneous equations F i(x 1,x 2,…,x n)=0,1⩽i⩽n, is numerically solved. It can be written in vector form as F( X)= 0, X∈ Rn, where F : Rn→ Rn is a twice continuously differentiable function with domain and range in n-dimensional Euclidean space. The solutions of such systems of
NASA Astrophysics Data System (ADS)
Abrashkevich, Alexander; Puzynin, I. V.
2004-01-01
A FORTRAN program is presented which solves a system of nonlinear simultaneous equations using the continuous analog of Newton's method (CANM). The user has the option of either to provide a subroutine which calculates the Jacobian matrix or allow the program to calculate it by a forward-difference approximation. Five iterative schemes using different algorithms of determining adaptive step size of the CANM process are implemented in the program. Program summaryTitle of program: CANM Catalogue number: ADSN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSN Program available from: CPC Program Library, Queen's University of Belfast, Northern Ireland Licensing provisions: none Computer for which the program is designed and others on which it has been tested: Computers: IBM RS/6000 Model 320H, SGI Origin2000, SGI Octane, HP 9000/755, Intel Pentium IV PC Installation: Department of Chemistry, University of Toronto, Toronto, Canada Operating systems under which the program has been tested: IRIX64 6.1, 6.4 and 6.5, AIX 3.4, HP-UX 9.01, Linux 2.4.7 Programming language used: FORTRAN 90 Memory required to execute with typical data: depends on the number of nonlinear equations in a system. Test run requires 80 KB No. of bits in distributed program including test data, etc.: 15283 Distribution format: tar gz format No. of lines in distributed program, including test data, etc.: 1794 Peripherals used: line printer, scratch disc store External subprograms used: DGECO and DGESL [1] Keywords: nonlinear equations, Newton's method, continuous analog of Newton's method, continuous parameter, evolutionary differential equation, Euler's method Nature of physical problem: System of nonlinear simultaneous equations F i(x 1,x 2,…,x n)=0,1⩽i⩽n, is numerically solved. It can be written in vector form as F( X)= 0, X∈ Rn, where F : Rn→ Rn is a twice continuously differentiable function with domain and range in n-dimensional Euclidean space. The solutions of such systems of
NASA Astrophysics Data System (ADS)
Virieux, J.; Bretaudeau, F.; Metivier, L.; Brossier, R.
2013-12-01
Simultaneous inversion of seismic velocities and source parameters have been a long standing challenge in seismology since the first attempts to mitigate trade-off between very different parameters influencing travel-times (Spencer and Gubbins 1980, Pavlis and Booker 1980) since the early development in the 1970s (Aki et al 1976, Aki and Lee 1976, Crosson 1976). There is a strong trade-off between earthquake source positions, initial times and velocities during the tomographic inversion: mitigating these trade-offs is usually carried empirically (Lemeur et al 1997). This procedure is not optimal and may lead to errors in the velocity reconstruction as well as in the source localization. For a better simultaneous estimation of such multi-parametric reconstruction problem, one may take benefit of improved local optimization such as full Newton method where the Hessian influence helps balancing between different physical parameter quantities and improving the coverage at the point of reconstruction. Unfortunately, the computation of the full Hessian operator is not easily computed in large models and with large datasets. Truncated Newton (TCN) is an alternative optimization approach (Métivier et al. 2012) that allows resolution of the normal equation H Δm = - g using a matrix-free conjugate gradient algorithm. It only requires to be able to compute the gradient of the misfit function and Hessian-vector products. Traveltime maps can be computed in the whole domain by numerical modeling (Vidale 1998, Zhao 2004). The gradient and the Hessian-vector products for velocities can be computed without ray-tracing using 1st and 2nd order adjoint-state methods for the cost of 1 and 2 additional modeling step (Plessix 2006, Métivier et al. 2012). Reciprocity allows to compute accurately the gradient and the full Hessian for each coordinates of the sources and for their initial times. Then the resolution of the problem is done through two nested loops. The model update Δm is
An Imbricate Finite Element Method (I-FEM) using full, reduced, and smoothed integration
NASA Astrophysics Data System (ADS)
Cazes, Fabien; Meschke, Günther
2013-11-01
A method to design finite elements that imbricate with each other while being assembled, denoted as imbricate finite element method, is proposed to improve the smoothness and the accuracy of the approximation based upon low order elements. Although these imbricate elements rely on triangular meshes, the approximation stems from the shape functions of bilinear quadrilateral elements. These elements satisfy the standard requirements of the finite element method: continuity, delta function property, and partition of unity. The convergence of the proposed approximation is investigated by means of two numerical benchmark problems comparing three different schemes for the numerical integration including a cell-based smoothed FEM based on a quadratic shape of the elements edges. The method is compared to related existing methods.
A relativistic smoothed particle hydrodynamics method tested with the shock tube
NASA Astrophysics Data System (ADS)
Mann, Patrick J.
1991-12-01
The smoothed particle hydrodynamics method is applied to an ADM 3 + 1 formulation of the equations for relativistic fluid flow. In particular the one-dimensional shock tube is addressed. Three codes are described. The first is a straightforward extension of classic SPH, while the other two are modifications which allow for time-dependent smoothing lengths. The first of these modifications approximates the internal energy density, while the second approximates the total energy density. Two smoothing forms are tested: an artificial viscosity and the direct method of A.J. Baker [Finite Element Computation Fluid Mechanics (Hemisphere, New York, 1983)]. The results indicate that the classic SPH code with particle-particle based artificial viscosity is reasonably accurate and very consistent. It gives quite sharp edges and flat plateaus, but the velocity plateau is significantly overestimated, and an oscillation can appear in the rarefaction wave. The modified versions with Baker smoothing procedure better results for moderate initial conditions, but begin to show spikes when the initial density jump is large. Generally the results are comparable to simple finite element and finite difference methods.
NASA Astrophysics Data System (ADS)
Danilewicz, Andrzej; Sikora, Zbigniew
2015-02-01
A theoretical base of SPH method, including the governing equations, discussion of importance of the smoothing function length, contact formulation, boundary treatment and finally utilization in hydrocode simulations are presented. An application of SPH to a real case of large penetrations (crater creating) into the soil caused by falling mass in Dynamic Replacement Method is discussed. An influence of particles spacing on method accuracy is presented. An example calculated by LS-DYNA software is discussed. Chronological development of Smooth Particle Hydrodynamics is presented. Theoretical basics of SPH method stability and consistency in SPH formulation, artificial viscosity and boundary treatment are discussed. Time integration techniques with stability conditions, SPH+FEM coupling, constitutive equation and equation of state (EOS) are presented as well.
A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Scott, James R.; Chang, Sin-Chung
1993-01-01
A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel
Khandogin, Jana; Gregersen, Brent A; Thiel, Walter; York, Darrin M
2005-05-19
The present paper describes the extension of a recently developed smooth conductor-like screening model for solvation to a d-orbital semiempirical framework (MNDO/d-SCOSMO) with analytic gradients that can be used for geometry optimizations, transition state searches, and molecular dynamics simulations. The methodology is tested on the potential energy surfaces for separating ions and the dissociative phosphoryl transfer mechanism of methyl phosphate. The convergence behavior of the smooth COSMO method with respect to discretization level is examined and the numerical stability of the energy and gradient are compared to that from conventional COSMO calculations. The present method is further tested in applications to energy minimum and transition state geometry optimizations of neutral and charged metaphosphates, phosphates, and phosphoranes that are models for stationary points in transphosphorylation reaction pathways of enzymes and ribozymes. The results indicate that the smooth COSMO method greatly enhances the stability of quantum mechanical geometry optimization and transition state search calculations that would routinely fail with conventional solvation methods. The present MNDO/d-SCOSMO method has considerable computational advantages over hybrid quantum mechanical/molecular mechanical methods with explicit solvation, and represents a potentially useful tool in the arsenal of multi-scale quantum models used to study biochemical reactions. PMID:16852180
A method for smoothing segmented lung boundary in chest CT images
NASA Astrophysics Data System (ADS)
Yim, Yeny; Hong, Helen
2007-03-01
To segment low density lung regions in chest CT images, most of methods use the difference in gray-level value of pixels. However, radiodense pulmonary vessels and pleural nodules that contact with the surrounding anatomy are often excluded from the segmentation result. To smooth lung boundary segmented by gray-level processing in chest CT images, we propose a new method using scan line search. Our method consists of three main steps. First, lung boundary is extracted by our automatic segmentation method. Second, segmented lung contour is smoothed in each axial CT slice. We propose a scan line search to track the points on lung contour and find rapidly changing curvature efficiently. Finally, to provide consistent appearance between lung contours in adjacent axial slices, 2D closing in coronal plane is applied within pre-defined subvolume. Our method has been applied for performance evaluation with the aspects of visual inspection, accuracy and processing time. The results of our method show that the smoothness of lung contour was considerably increased by compensating for pulmonary vessels and pleural nodules.
Testing local anisotropy using the method of smoothed residuals I — methodology
Appleby, Stephen; Shafieloo, Arman E-mail: arman@apctp.org
2014-03-01
We discuss some details regarding the method of smoothed residuals, which has recently been used to search for anisotropic signals in low-redshift distance measurements (Supernovae). In this short note we focus on some details regarding the implementation of the method, particularly the issue of effectively detecting signals in data that are inhomogeneously distributed on the sky. Using simulated data, we argue that the original method proposed in Colin et al. [1] will not detect spurious signals due to incomplete sky coverage, and that introducing additional Gaussian weighting to the statistic as in [2] can hinder its ability to detect a signal. Issues related to the width of the Gaussian smoothing are also discussed.
A new enzymic method for the isolation and culture of human bladder body smooth muscle cells.
Ma, F -H; Higashira, H; Ukai, Y; Hanai, T; Kiwamoto, H; Park, Y C; Kurita, T
2002-01-01
Cultured cells of the human urinary bladder smooth muscle are useful for investigating bladder function, but methods for culturing them are not well developed. We have now established a novel enzymic technique. The smooth muscle layer was separated out and incubated with 0.2% trypsin for 30 min at 37 degrees C. The samples were then minced and incubated with 0.1% collagenase for 30 min and centrifuged at 900 g. The pellets were resuspended in RPMI-1640 medium containing 10% fetal calf serum (FCS) and centrifuged at 250 g. The smooth muscle cells from the supernatant were cultured in RPMI-1640 containing 10% FCS. The cells grew to confluence after 7-10 days, forming the "hills and valleys" growth pattern characteristic of smooth muscle cells. Immunostaining with anti-alpha-actin, anti-myosin, and anti-caldesmon antibodies demonstrated that 99% of the cells were smooth muscle cells. To investigate the pharmacological properties of the cultured cells, we determined the inhibitory effect of muscarinic receptor antagonists on the binding of [3H]N-methylscopolamine to membranes from cultured cells. The pKi values obtained for six antagonists agreed with the corresponding values for transfected cells expressing the human muscarinic M2 subtype. Furthermore, carbachol produced an increase in the concentration of cytoplasmic free Ca2+ an action that was blocked by 4-diphenylacetoxy-N-methylpiperidine methiodide, an M3 selective antagonist. This result suggests that these cells express functional M3 muscarinic receptors, in addition to M2 receptors. The subcultured cells therefore appear to be unaffected by our new isolation method. PMID:11835427
McHugh, P.R.; Knoll, D.A.
1992-01-01
A fully implicit solution algorithm based on Newton's method is used to solve the steady, incompressible Navier-Stokes and energy equations. An efficiently evaluated numerical Jacobian is used to simplify implementation, and mesh sequencing is used to increase the radius of convergence of the algorithm. We employ finite volume discretization using the power law scheme of Patankar to solve the benchmark backward facing step problem defined by the ASME K-12 Aerospace Heat Transfer Committee. LINPACK banded Gaussian elimination and the preconditioned transpose-free quasi-minimal residual (TFQMR) algorithm of Freund are studied as possible linear equation solvers. Implementation of the preconditioned TFQMR algorithm requires use of the switched evolution relaxation algorithm of Mulder and Van Leer to ensure convergence. The preconditioned TFQMR algorithm is more memory efficient than the direct solver, but our implementation is not as CPU efficient. Results show that for the level of grid refinement used, power law differencing was not adequate to yield the desired accuracy for this problem.
Methods for Least Squares Data Smoothing by Adjustment of Divided Differences
NASA Astrophysics Data System (ADS)
Demetriou, I. C.
2008-09-01
A brief survey is presented for the main methods that are used in least squares data smoothing by adjusting the signs of divided differences of the smoothed values. The most distinctive feature of the smoothing approach is that it provides automatically a piecewise monotonic or a piecewise convex/concave fit to the data. The data are measured values of a function of one variable that contain random errors. As a consequence of the errors, the number of sign alterations in the sequence of mth divided differences is usually unacceptably large, where m is a prescribed positive integer. Therefore, we make the least sum of squares change to the measurements by requiring the sequence of the divided differences of order m to have at most k-1 sign changes, for some positive integer k. Although, it is a combinatorial problem, whose solution can require about O(nk) quadratic programming calculations in n variables and n-m constraints, where n is the number of data, very efficient algorithms have been developed for the cases when m = 1 or m = 2 and k is arbitrary, as well as when m>2 for small values of k. Attention is paid to the purpose of each method instead of to its details. Some software packages make the methods publicly accessible through library systems.
Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong
2016-01-01
In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student’s t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods. PMID:27187405
Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong
2016-01-01
In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student's t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods. PMID:27187405
NASA Astrophysics Data System (ADS)
Kang, S.; Suh, Y. K.
2011-02-01
The so-called smoothed profile method, originally suggested by Nakayama and Yamamoto and further improved by Luo et al. in 2005 and 2009, respectively, is an efficient numerical solver for fluid-structure interaction problems, which represents the particles by a certain smoothed profile on a fixed grid and constructs some form of body force added into the momentum (Navier-Stokes) equation by ensuring the rigidity of particles. For numerical simulations, the method first advances the flow and pressure fields by integrating the momentum equation except the body-force (momentum impulse) term in time and next updates them by separately taking temporal integration of the body-force term, thus requiring one more Poisson-equation solver for the extra pressure field due to the rigidity of particles to ensure the divergence-free constraint of the total velocity field. In the present study, we propose a simplified version of the smoothed profile method or the one-stage method, which combines the two stages of velocity update (temporal integration) into one to eliminate the necessity for the additional solver and, thus, significantly save the computational cost. To validate the proposed one-stage method, we perform the so-called direct numerical simulations on the two-dimensional motion of multiple inertialess paramagnetic particles in a nonmagnetic fluid subjected to an external uniform magnetic field and compare their results with the existing benchmark solutions. For the validation, we develop the finite-volume version of the direct simulation method by employing the proposed one-stage method. Comparison shows that the proposed one-stage method is very accurate and efficient in direct simulations of such magnetic particulate flows.
A Newton-Raphson Method Approach to Adjusting Multi-Source Solar Simulators
NASA Technical Reports Server (NTRS)
Snyder, David B.; Wolford, David S.
2012-01-01
NASA Glenn Research Center has been using an in house designed X25 based multi-source solar simulator since 2003. The simulator is set up for triple junction solar cells prior to measurements b y adjusting the three sources to produce the correct short circuit current, lsc, in each of three AM0 calibrated sub-cells. The past practice has been to adjust one source on one sub-cell at a time, iterating until all the sub-cells have the calibrated Isc. The new approach is to create a matrix of measured lsc for small source changes on each sub-cell. A matrix, A, is produced. This is normalized to unit changes in the sources so that Ax(delta)s = (delta)isc. This matrix can now be inverted and used with the known Isc differences from the AM0 calibrated values to indicate changes in the source settings, (delta)s = A ·'x.(delta)isc This approach is still an iterative one, but all sources are changed during each iteration step. It typically takes four to six steps to converge on the calibrated lsc values. Even though the source lamps may degrade over time, the initial matrix evaluation i s not performed each time, since measurement matrix needs to be only approximate. Because an iterative approach is used the method will still continue to be valid. This method may become more important as state-of-the-art solar cell junction responses overlap the sources of the simulator. Also, as the number of cell junctions and sources increase, this method should remain applicable.
NASA Astrophysics Data System (ADS)
Li, Jiang-Tao; Decourchelle, Anne; Miceli, Marco; Vink, Jacco; Bocchino, Fabrizio
2015-11-01
Based on our newly developed methods and the XMM-Newton large program of SN1006, we extract and analyse the spectra from 3596 tessellated regions of this supernova remnant (SNR) each with 0.3-8 keV counts >104. For the first time, we map out multiple physical parameters, such as the temperature (kT), electron density (ne), ionization parameter (net), ionization age (tion), metal abundances, as well as the radio-to-X-ray slope (α) and cutoff frequency (νcutoff) of the synchrotron emission. We construct probability distribution functions of kT and net, and model them with several Gaussians, in order to characterize the average thermal and ionization states of such an extended source. We construct equivalent width (EW) maps based on continuum interpolation with the spectral model of each region. We then compare the EW maps of O VII, O VIII, O VII Kδ - ζ, Ne, Mg, Si XIII, Si XIV, and S lines constructed with this method to those constructed with linear interpolation. We further extract spectra from larger regions to confirm the features revealed by parameter and EW maps, which are often not directly detectable on X-ray intensity images. For example, O abundance is consistent with solar across the SNR, except for a low-abundance hole in the centre. This `O hole' has enhanced O VII Kδ - ζ and Fe emissions, indicating recently reverse shocked ejecta, but also has the highest net, indicating forward shocked interstellar medium (ISM). Therefore, a multitemperature model is needed to decompose these components. The asymmetric metal distributions suggest there is either an asymmetric explosion of the supernova or an asymmetric distribution of the ISM.
Shot noise limit of the optical 3D measurement methods for smooth surfaces
NASA Astrophysics Data System (ADS)
Pavliček, Pavel; Pech, Miroslav
2016-03-01
The measurement uncertainty of optical 3D measurement methods for smooth surfaces caused by shot noise is investigated. The shot noise is a fundamental property of the quantum nature of light. If all noise sources are eliminated, the shot noise represents the ultimate limit of the measurement uncertainty. The measurement uncertainty is calculated for several simple model methods. The analysis shows that the measurement uncertainty depends on the wavelength of used light, the number of photons used for the measurement, and on a factor that is connected with the geometric arrangement of the measurement setup.
Bramble, J. H.; Pasciak, J. E.; Sammon, P. H.; Thomee, V.
1989-04-01
Backward difference methods for the discretization of parabolic boundary value problems are considered in this paper. In particular, we analyze the case when the backward difference equations are only solved 'approximately' by a preconditioned iteration. We provide an analysis which shows that these methods remain stable and accurate if a suitable number of iterations (often independent of the spatial discretization and time step size) are used. Results are provided for the smooth as well as nonsmooth initial data cases. Finally, the results of numerical experiments illustrating the algorithms' performance on model problems are given.
NASA Astrophysics Data System (ADS)
Preza, Chrysanthe; Miller, Michael I.; Conchello, Jose-Angel
1993-07-01
We have shown that the linear least-squares (LLS) estimate of the intensities of a 3-D object obtained from a set of optical sections is unstable due to the inversion of small and zero-valued eigenvalues of the point-spread function (PSF) operator. The LLS solution was regularized by constraining it to lie in a subspace spanned by the eigenvectors corresponding to a selected number of the largest eigenvalues. In this paper we extend the regularized LLS solution to a maximum a posteriori (MAP) solution induced by a prior formed from a 'Good's like' smoothness penalty. This approach also yields a regularized linear estimator which reduces noise as well as edge artifacts in the reconstruction. The advantage of the linear MAP (LMAP) estimate over the current regularized LLS (RLLS) is its ability to regularize the inverse problem by smoothly penalizing components in the image associated with small eigenvalues. Computer simulations were performed using a theoretical PSF and a simple phantom to compare the two regularization techniques. It is shown that the reconstructions using the smoothness prior, give superior variance and bias results compared to the RLLS reconstructions. Encouraging reconstructions obtained with the LMAP method from real microscopical images of a 10 micrometers fluorescent bead, and a four-cell Volvox embryo are shown.
A Fast Variational Method for the Construction of Resolution Adaptive C-Smooth Molecular Surfaces.
Bajaj, Chandrajit L; Xu, Guoliang; Zhang, Qin
2009-05-01
We present a variational approach to smooth molecular (proteins, nucleic acids) surface constructions, starting from atomic coordinates, as available from the protein and nucleic-acid data banks. Molecular dynamics (MD) simulations traditionally used in understanding protein and nucleic-acid folding processes, are based on molecular force fields, and require smooth models of these molecular surfaces. To accelerate MD simulations, a popular methodology is to employ coarse grained molecular models, which represent clusters of atoms with similar physical properties by psuedo- atoms, resulting in coarser resolution molecular surfaces. We consider generation of these mixed-resolution or adaptive molecular surfaces. Our approach starts from deriving a general form second order geometric partial differential equation in the level-set formulation, by minimizing a first order energy functional which additionally includes a regularization term to minimize the occurrence of chemically infeasible molecular surface pockets or tunnel-like artifacts. To achieve even higher computational efficiency, a fast cubic B-spline C(2) interpolation algorithm is also utilized. A narrow band, tri-cubic B-spline level-set method is then used to provide C(2) smooth and resolution adaptive molecular surfaces. PMID:19802355
Cen, Guanjun; Zeng, Xianru; Long, Xiuzhen; Wei, Dewei; Gao, Xuyuan; Zeng, Tao
2015-01-01
In insects, the frequency distribution of the measurements of sclerotized body parts is generally used to classify larval instars and is characterized by a multimodal overlap between instar stages. Nonparametric methods with fixed bandwidths, such as histograms, have significant limitations when used to fit this type of distribution, making it difficult to identify divisions between instars. Fixed bandwidths have also been chosen somewhat subjectively in the past, which is another problem. In this study, we describe an adaptive kernel smoothing method to differentiate instars based on discontinuities in the growth rates of sclerotized insect body parts. From Brooks’ rule, we derived a new standard for assessing the quality of instar classification and a bandwidth selector that more accurately reflects the distributed character of specific variables. We used this method to classify the larvae of Austrosimulium tillyardianum (Diptera: Simuliidae) based on five different measurements. Based on head capsule width and head capsule length, the larvae were separated into nine instars. Based on head capsule postoccipital width and mandible length, the larvae were separated into 8 instars and 10 instars, respectively. No reasonable solution was found for antennal segment 3 length. Separation of the larvae into nine instars using head capsule width or head capsule length was most robust and agreed with Crosby’s growth rule. By strengthening the distributed character of the separation variable through the use of variable bandwidths, the adaptive kernel smoothing method could identify divisions between instars more effectively and accurately than previous methods. PMID:26546689
The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB)
NASA Astrophysics Data System (ADS)
Shah, Swej; Møyner, Olav; Tene, Matei; Lie, Knut-Andreas; Hajibeygi, Hadi
2016-08-01
A novel multiscale method for multiphase flow in heterogeneous fractured porous media is devised. The discrete fine-scale system is described using an embedded fracture modeling approach, in which the heterogeneous rock (matrix) and highly-conductive fractures are represented on independent grids. Given this fine-scale discrete system, the method first partitions the fine-scale volumetric grid representing the matrix and the lower-dimensional grids representing fractures into independent coarse grids. Then, basis functions for matrix and fractures are constructed by restricted smoothing, which gives a flexible and robust treatment of complex geometrical features and heterogeneous coefficients. From the basis functions one constructs a prolongation operator that maps between the coarse- and fine-scale systems. The resulting method allows for general coupling of matrix and fracture basis functions, giving efficient treatment of a large variety of fracture conductivities. In addition, basis functions can be adaptively updated using efficient global smoothing strategies to account for multiphase flow effects. The method is conservative and because it is described and implemented in algebraic form, it is straightforward to employ it to both rectilinear and unstructured grids. Through a series of challenging test cases for single and multiphase flow, in which synthetic and realistic fracture maps are combined with heterogeneous petrophysical matrix properties, we validate the method and conclude that it is an efficient and accurate approach for simulating flow in complex, large-scale, fractured media.
NASA Astrophysics Data System (ADS)
Zhao, Yuanyuan; Jiang, Guoliang; Hu, Jiandong; Hu, Fengjiang; Wei, Jianguang; Shi, Liang
2010-10-01
of biomolecular interaction by using Newton Iteration Method and Least Squares Method. First, the pseudo first order kinetic model of biomolecular interaction was established. Then the data of molecular interaction of HBsAg and HBsAb was obtained by bioanalyzer. Finally, we used the optical SPR bioanalyzer software which was written by ourselves to make nonlinear fit about the association and dissociation curves. The correlation coefficient R-squared is 0.99229 and 0.99593, respectively. Furthermore, the kinetic parameters and affinity constants were evaluated using the obtained data from the fitting results.
Is Newton's second law really Newton's?
NASA Astrophysics Data System (ADS)
Pourciau, Bruce
2011-10-01
When we call the equation f = ma "Newton's second law," how much historical truth lies behind us? Many textbooks on introductory physics and classical mechanics claim that the Principia's second law becomes f = ma, once Newton's vocabulary has been translated into more familiar terms. But there is nothing in the Principia's second law about acceleration and nothing about a rate of change. If the Principia's second law does not assert f = ma, what does it assert, and is there some other axiom or some proposition in the Principia that does assert f = ma? Is there any historical truth behind us when we call f = ma "Newton's second law"? This article answers these questions.
NASA Technical Reports Server (NTRS)
Verger, Aleixandre; Baret, F.; Weiss, M.; Kandasamy, S.; Vermote, E.
2013-01-01
Consistent, continuous, and long time series of global biophysical variables derived from satellite data are required for global change research. A novel climatology fitting approach called CACAO (Consistent Adjustment of the Climatology to Actual Observations) is proposed to reduce noise and fill gaps in time series by scaling and shifting the seasonal climatological patterns to the actual observations. The shift and scale CACAO parameters adjusted for each season allow quantifying shifts in the timing of seasonal phenology and inter-annual variations in magnitude as compared to the average climatology. CACAO was assessed first over simulated daily Leaf Area Index (LAI) time series with varying fractions of missing data and noise. Then, performances were analyzed over actual satellite LAI products derived from AVHRR Long-Term Data Record for the 1981-2000 period over the BELMANIP2 globally representative sample of sites. Comparison with two widely used temporal filtering methods-the asymmetric Gaussian (AG) model and the Savitzky-Golay (SG) filter as implemented in TIMESAT-revealed that CACAO achieved better performances for smoothing AVHRR time series characterized by high level of noise and frequent missing observations. The resulting smoothed time series captures well the vegetation dynamics and shows no gaps as compared to the 50-60% of still missing data after AG or SG reconstructions. Results of simulation experiments as well as confrontation with actual AVHRR time series indicate that the proposed CACAO method is more robust to noise and missing data than AG and SG methods for phenology extraction.
Smoothed Particle Inference: A Kilo-Parametric Method for X-ray Galaxy Cluster Modeling
Peterson, John R.; Marshall, P.J.; Andersson, K.; /Stockholm U. /SLAC
2005-08-05
We propose an ambitious new method that models the intracluster medium in clusters of galaxies as a set of X-ray emitting smoothed particles of plasma. Each smoothed particle is described by a handful of parameters including temperature, location, size, and elemental abundances. Hundreds to thousands of these particles are used to construct a model cluster of galaxies, with the appropriate complexity estimated from the data quality. This model is then compared iteratively with X-ray data in the form of adaptively binned photon lists via a two-sample likelihood statistic and iterated via Markov Chain Monte Carlo. The complex cluster model is propagated through the X-ray instrument response using direct sampling Monte Carlo methods. Using this approach the method can reproduce many of the features observed in the X-ray emission in a less assumption-dependent way that traditional analyses, and it allows for a more detailed characterization of the density, temperature, and metal abundance structure of clusters. Multi-instrument X-ray analyses and simultaneous X-ray, Sunyaev-Zeldovich (SZ), and lensing analyses are a straight-forward extension of this methodology. Significant challenges still exist in understanding the degeneracy in these models and the statistical noise induced by the complexity of the models.
Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures
Sevastianov, L. A.; Egorov, A. A.; Sevastyanov, A. L.
2013-02-15
Basic steps in developing an original method of adiabatic modes that makes it possible to solve the direct and inverse problems of simulating and designing three-dimensional multilayered smoothly irregular open waveguide structures are described. A new element in the method is that an approximate solution of Maxwell's equations is made to obey 'inclined' boundary conditions at the interfaces between themedia being considered. These boundary conditions take into account the obliqueness of planes tangent to nonplanar boundaries between the media and lead to new equations for coupled vector quasiwaveguide hybrid adiabatic modes. Solutions of these equations describe the phenomenon of 'entanglement' of two linear polarizations of an irregular multilayered waveguide, the appearance of a new mode in an entangled state, and the effect of rotation of the polarization plane of quasiwaveguide modes. The efficiency of the method is demonstrated by considering the example of numerically simulating a thin-film generalized waveguide Lueneburg lens.
NASA Astrophysics Data System (ADS)
Rezaee, Mousa; Shaterian-Alghalandis, Vahid; Banan-Nojavani, Ali
2013-04-01
In this paper, the smooth orthogonal decomposition (SOD) method is developed to the light damped systems in which the inputs are time shifted functions of one or more random processes. An example of such practical cases is the vehicle suspension system in which the random inputs due to the road roughness applied to the rear wheels are the shifted functions of the same random inputs on the front wheels with a time lag depending on the vehicle wheelbase as well as its velocity. The developed SOD method is applied to determine the natural frequencies and mode shapes of a certain vehicle suspension system and the results are compared with the true values obtained by the structural eigenvalue problem. The consistency of the results indicates that the SOD method can be applied with a high degree of accuracy to calculate the modal parameters of vibrating systems in which the system inputs are shifted functions of one or more random processes.
Immersed smoothed finite element method for fluid-structure interaction simulation of aortic valves
NASA Astrophysics Data System (ADS)
Yao, Jianyao; Liu, G. R.; Narmoneva, Daria A.; Hinton, Robert B.; Zhang, Zhi-Qian
2012-12-01
This paper presents a novel numerical method for simulating the fluid-structure interaction (FSI) problems when blood flows over aortic valves. The method uses the immersed boundary/element method and the smoothed finite element method and hence it is termed as IS-FEM. The IS-FEM is a partitioned approach and does not need a body-fitted mesh for FSI simulations. It consists of three main modules: the fluid solver, the solid solver and the FSI force solver. In this work, the blood is modeled as incompressible viscous flow and solved using the characteristic-based-split scheme with FEM for spacial discretization. The leaflets of the aortic valve are modeled as Mooney-Rivlin hyperelastic materials and solved using smoothed finite element method (or S-FEM). The FSI force is calculated on the Lagrangian fictitious fluid mesh that is identical to the moving solid mesh. The octree search and neighbor-to-neighbor schemes are used to detect efficiently the FSI pairs of fluid and solid cells. As an example, a 3D idealized model of aortic valve is modeled, and the opening process of the valve is simulated using the proposed IS-FEM. Numerical results indicate that the IS-FEM can serve as an efficient tool in the study of aortic valve dynamics to reveal the details of stresses in the aortic valves, the flow velocities in the blood, and the shear forces on the interfaces. This tool can also be applied to animal models studying disease processes and may ultimately translate to a new adaptive methods working with magnetic resonance images, leading to improvements on diagnostic and prognostic paradigms, as well as surgical planning, in the care of patients.
A method for the accurate and smooth approximation of standard thermodynamic functions
NASA Astrophysics Data System (ADS)
Coufal, O.
2013-01-01
A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program summaryProgram title:SmoothSTF Catalogue identifier: AENH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 131965 Distribution format: tar.gz Programming language: C++. Computer: Any computer with gcc version 4.3.2 compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed, see http://gcc.gnu.org/install/specific.html. RAM: 256 MB are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are
NASA Technical Reports Server (NTRS)
Zeng, S.; Wesseling, P.
1993-01-01
The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.
NASA Astrophysics Data System (ADS)
Sugio, Tetsuya; Yamamoto, Masayoshi; Funabiki, Shigeyuki
The use of an SMES (Superconducting Magnetic Energy Storage) for smoothing power fluctuations in a railway substation has been discussed. This paper proposes a smoothing control method based on fuzzy reasoning for reducing the SMES capacity at substations along high-speed railways. The proposed smoothing control method comprises three countermeasures for reduction of the SMES capacity. The first countermeasure involves modification of rule 1 for smoothing out the fluctuating electric power to its average value. The other countermeasures involve the modification of the central value of the stored energy control in the SMES and revision of the membership function in rule 2 for reduction of the SMES capacity. The SMES capacity in the proposed smoothing control method is reduced by 49.5% when compared to that in the nonrevised control method. It is confirmed by computer simulations that the proposed control method is suitable for smoothing out power fluctuations in substations along high-speed railways and for reducing the SMES capacity.
An incompressible smoothed particle hydrodynamics method for the motion of rigid bodies in fluids
NASA Astrophysics Data System (ADS)
Tofighi, N.; Ozbulut, M.; Rahmat, A.; Feng, J. J.; Yildiz, M.
2015-09-01
A two-dimensional incompressible smoothed particle hydrodynamics scheme is presented for simulation of rigid bodies moving through Newtonian fluids. The scheme relies on combined usage of the rigidity constraints and the viscous penalty method to simulate rigid body motion. Different viscosity ratios and interpolation schemes are tested by simulating a rigid disc descending in quiescent medium. A viscosity ratio of 100 coupled with weighted harmonic averaging scheme has been found to provide satisfactory results. The performance of the resulting scheme is systematically tested for cases with linear motion, rotational motion and their combination. The test cases include sedimentation of a single and a pair of circular discs, sedimentation of an elliptic disc and migration and rotation of a circular disc in linear shear flow. Comparison with previous results at various Reynolds numbers indicates that the proposed method captures the motion of rigid bodies driven by flow or external body forces accurately.
NASA Astrophysics Data System (ADS)
Yang, G.; Han, X.; Hu, D. A.
2015-11-01
Modified cylindrical smoothed particle hydrodynamics (MCSPH) approximation equations are derived for hydrodynamics with material strength in axisymmetric cylindrical coordinates. The momentum equation and internal energy equation are represented to be in the axisymmetric form. The MCSPH approximation equations are applied to simulate the process of explosively driven metallic tubes, which includes strong shock waves, large deformations and large inhomogeneities, etc. The meshless and Lagrangian character of the MCSPH method offers the advantages in treating the difficulties embodied in these physical phenomena. Two test cases, the cylinder test and the metallic tube driven by two head-on colliding detonation waves, are presented. Numerical simulation results show that the new form of the MCSPH method can predict the detonation process of high explosives and the expansion process of metallic tubes accurately and robustly.
NASA Astrophysics Data System (ADS)
Mozdgir, A.; Mahdavi, Iraj; Seyyedi, I.; Shiraqei, M. E.
2011-06-01
An assembly line is a flow-oriented production system where the productive units performing the operations, referred to as stations, are aligned in a serial manner. The assembly line balancing problem arises and has to be solved when an assembly line has to be configured or redesigned. The so-called simple assembly line balancing problem (SALBP), a basic version of the general problem, has attracted attention of researchers and practitioners of operations research for almost half a century. There are four types of objective functions which are considered to this kind of problem. The versions of SALBP may be complemented by a secondary objective which consists of smoothing station loads. Many heuristics have been proposed for the assembly line balancing problem due to its computational complexity and difficulty in identifying an optimal solution and so many heuristic solutions are supposed to solve this problem. In this paper a differential evolution algorithm is developed to minimize workload smoothness index in SALBP-2 and the algorithm parameters are optimized using Taguchi method.
Kerfriden, P.; Gosselet, P.; Adhikari, S.; Bordas, S.
2013-01-01
This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, “on-the-fly”, the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved. PMID:27076688
NASA Astrophysics Data System (ADS)
Chew, J. V. L.; Sulaiman, J.
2016-06-01
This paper considers Newton-MSOR iterative method for solving 1D nonlinear porous medium equation (PME). The basic concept of proposed iterative method is derived from a combination of one step nonlinear iterative method which known as Newton method with Modified Successive Over Relaxation (MSOR) method. The reliability of Newton-MSOR to obtain approximate solution for several PME problems is compared with Newton-Gauss-Seidel (Newton-GS) and Newton-Successive Over Relaxation (Newton-SOR). In this paper, the formulation and implementation of these three iterative methods have also been presented. From four examples of PME problems, numerical results showed that Newton-MSOR method requires lesser number of iterations and computational time as compared with Newton-GS and Newton-SOR methods.
HyeongKae Park; Robert R. Nourgaliev; Richard C. Martineau; Dana A. Knoll
2008-09-01
We present high-order accurate spatiotemporal discretization of all-speed flow solvers using Jacobian-free Newton Krylov framework. One of the key developments in this work is the physics-based preconditioner for the all-speed flow, which makes use of traditional semi-implicit schemes. The physics-based preconditioner is developed in the primitive variable form, which allows a straightforward separation of physical phenomena. Numerical examples demonstrate that the developed preconditioner effectively reduces the number of the Krylov iterations, and the efficiency is independent of the Mach number and mesh sizes under a fixed CFL condition.
NASA Astrophysics Data System (ADS)
Møyner, Olav; Lie, Knut-Andreas
2016-01-01
A wide variety of multiscale methods have been proposed in the literature to reduce runtime and provide better scaling for the solution of Poisson-type equations modeling flow in porous media. We present a new multiscale restricted-smoothed basis (MsRSB) method that is designed to be applicable to both rectilinear grids and unstructured grids. Like many other multiscale methods, MsRSB relies on a coarse partition of the underlying fine grid and a set of local prolongation operators (multiscale basis functions) that map unknowns associated with the fine grid cells to unknowns associated with blocks in the coarse partition. These mappings are constructed by restricted smoothing: Starting from a constant, a localized iterative scheme is applied directly to the fine-scale discretization to compute prolongation operators that are consistent with the local properties of the differential operators. The resulting method has three main advantages: First of all, both the coarse and the fine grid can have general polyhedral geometry and unstructured topology. This means that partitions and good prolongation operators can easily be constructed for complex models involving high media contrasts and unstructured cell connections introduced by faults, pinch-outs, erosion, local grid refinement, etc. In particular, the coarse partition can be adapted to geological or flow-field properties represented on cells or faces to improve accuracy. Secondly, the method is accurate and robust when compared to existing multiscale methods and does not need expensive recomputation of local basis functions to account for transient behavior: Dynamic mobility changes are incorporated by continuing to iterate a few extra steps on existing basis functions. This way, the cost of updating the prolongation operators becomes proportional to the amount of change in fluid mobility and one reduces the need for expensive, tolerance-based updates. Finally, since the MsRSB method is formulated on top of a cell
Coupling of Smoothed Particle Hydrodynamics with Finite Volume method for free-surface flows
NASA Astrophysics Data System (ADS)
Marrone, S.; Di Mascio, A.; Le Touzé, D.
2016-04-01
A new algorithm for the solution of free surface flows with large front deformation and fragmentation is presented. The algorithm is obtained by coupling a classical Finite Volume (FV) approach, that discretizes the Navier-Stokes equations on a block structured Eulerian grid, with an approach based on the Smoothed Particle Hydrodynamics (SPH) method, implemented in a Lagrangian framework. The coupling procedure is formulated in such a way that each solver is applied in the region where its intrinsic characteristics can be exploited in the most efficient and accurate way: the FV solver is used to resolve the bulk flow and the wall regions, whereas the SPH solver is implemented in the free surface region to capture details of the front evolution. The reported results clearly prove that the combined use of the two solvers is convenient from the point of view of both accuracy and computing time.
Wu, Wei; Fan, Qinwei; Zurada, Jacek M; Wang, Jian; Yang, Dakun; Liu, Yan
2014-02-01
The aim of this paper is to develop a novel method to prune feedforward neural networks by introducing an L1/2 regularization term into the error function. This procedure forces weights to become smaller during the training and can eventually removed after the training. The usual L1/2 regularization term involves absolute values and is not differentiable at the origin, which typically causes oscillation of the gradient of the error function during the training. A key point of this paper is to modify the usual L1/2 regularization term by smoothing it at the origin. This approach offers the following three advantages: First, it removes the oscillation of the gradient value. Secondly, it gives better pruning, namely the final weights to be removed are smaller than those produced through the usual L1/2 regularization. Thirdly, it makes it possible to prove the convergence of the training. Supporting numerical examples are also provided. PMID:24291693
NASA Astrophysics Data System (ADS)
Wang, Liang; Chen, Dong; Cheng, Tinghai; He, Pu; Lu, Xiaohui; Zhao, Hongwei
2016-08-01
The smooth impact drive mechanism (SIDM) is a type of piezoelectric actuator that has been developed for several decades. As a kind of driving method for the SIDM, the traditional sawtooth (TS) wave is always employed. The kinetic friction force during the rapid contraction stage usually results in the generation of a backward motion. A friction regulation hybrid (FRH) driving method realized by a composite waveform for the backward motion restraint of the SIDM is proposed in this paper. The composite waveform is composed of a sawtooth driving (SD) wave and a sinusoidal friction regulation (SFR) wave which is applied to the rapid deformation stage of the SD wave. A prototype of the SIDM was fabricated and its output performance under the excitation of the FRH driving method and the TS wave driving method was tested. The results indicate that the backward motion can be restrained obviously using the FRH driving method. Compared with the driving effect of the TS wave, the backward rates of the prototype in forward and reverse motions are decreased by 83% and 85%, respectively.
ERIC Educational Resources Information Center
Ryder, L. H.
1987-01-01
Discusses the history of scientific thought in terms of the theories of inertia and absolute space, relativity and gravitation. Describes how Sir Isaac Newton used the work of earlier scholars in his theories and how Albert Einstein used Newton's theories in his. (CW)
Experiments with "Newton's Cradle."
ERIC Educational Resources Information Center
Ehrlich, Robert
1996-01-01
Outlines the use of the toy popularly known as Newton's Cradle or Newton's Balls in illustrating the laws of conservation of momentum and mechanical energy. Discusses in detail the joint effects of elasticity, friction, and ball alignment on the rate of damping of this apparatus. (JRH)
Luanjing Guo; Hai Huang; Derek Gaston; Cody Permann; David Andrs; George Redden; Chuan Lu; Don Fox; Yoshiko Fujita
2013-03-01
Modeling large multicomponent reactive transport systems in porous media is particularly challenging when the governing partial differential algebraic equations (PDAEs) are highly nonlinear and tightly coupled due to complex nonlinear reactions and strong solution-media interactions. Here we present a preconditioned Jacobian-Free Newton-Krylov (JFNK) solution approach to solve the governing PDAEs in a fully coupled and fully implicit manner. A well-known advantage of the JFNK method is that it does not require explicitly computing and storing the Jacobian matrix during Newton nonlinear iterations. Our approach further enhances the JFNK method by utilizing physics-based, block preconditioning and a multigrid algorithm for efficient inversion of the preconditioner. This preconditioning strategy accounts for self- and optionally, cross-coupling between primary variables using diagonal and off-diagonal blocks of an approximate Jacobian, respectively. Numerical results are presented demonstrating the efficiency and massive scalability of the solution strategy for reactive transport problems involving strong solution-mineral interactions and fast kinetics. We found that the physics-based, block preconditioner significantly decreases the number of linear iterations, directly reducing computational cost; and the strongly scalable algebraic multigrid algorithm for approximate inversion of the preconditioner leads to excellent parallel scaling performance.
Crespo, Alejandro C.; Dominguez, Jose M.; Barreiro, Anxo; Gómez-Gesteira, Moncho; Rogers, Benedict D.
2011-01-01
Smoothed Particle Hydrodynamics (SPH) is a numerical method commonly used in Computational Fluid Dynamics (CFD) to simulate complex free-surface flows. Simulations with this mesh-free particle method far exceed the capacity of a single processor. In this paper, as part of a dual-functioning code for either central processing units (CPUs) or Graphics Processor Units (GPUs), a parallelisation using GPUs is presented. The GPU parallelisation technique uses the Compute Unified Device Architecture (CUDA) of nVidia devices. Simulations with more than one million particles on a single GPU card exhibit speedups of up to two orders of magnitude over using a single-core CPU. It is demonstrated that the code achieves different speedups with different CUDA-enabled GPUs. The numerical behaviour of the SPH code is validated with a standard benchmark test case of dam break flow impacting on an obstacle where good agreement with the experimental results is observed. Both the achieved speed-ups and the quantitative agreement with experiments suggest that CUDA-based GPU programming can be used in SPH methods with efficiency and reliability. PMID:21695185
Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method
NASA Astrophysics Data System (ADS)
Zhang, Mingyu
2010-09-01
The methods for simulating surface tension with smoothed particle hydrodynamics (SPH) method in two dimensions and three dimensions are developed. In 2D surface tension model, the SPH particle on the boundary in 2D is detected dynamically according to the algorithm developed by Dilts [G.A. Dilts, Moving least-squares particle hydrodynamics II: conservation and boundaries, International Journal for Numerical Methods in Engineering 48 (2000) 1503-1524]. The boundary curve in 2D is reconstructed locally with Lagrangian interpolation polynomial. In 3D surface tension model, the SPH particle on the boundary in 3D is detected dynamically according to the algorithm developed by Haque and Dilts [A. Haque, G.A. Dilts, Three-dimensional boundary detection for particle methods, Journal of Computational Physics 226 (2007) 1710-1730]. The boundary surface in 3D is reconstructed locally with moving least squares (MLS) method. By transforming the coordinate system, it is guaranteed that the interface function is one-valued in the local coordinate system. The normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated. Surface tension force acts only on the boundary particle. Density correction is applied to the boundary particle in order to remove the boundary inconsistency. The surface tension models in 2D and 3D have been applied to benchmark tests for surface tension. The ability of the current method applying to the simulation of surface tension in 2D and 3D is proved.
NASA Technical Reports Server (NTRS)
Tsiveriotis, K.; Brown, R. A.
1993-01-01
A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.
NASA Astrophysics Data System (ADS)
Viallet, M.; Goffrey, T.; Baraffe, I.; Folini, D.; Geroux, C.; Popov, M. V.; Pratt, J.; Walder, R.
2016-02-01
This work is a continuation of our efforts to develop an efficient implicit solver for multidimensional hydrodynamics for the purpose of studying important physical processes in stellar interiors, such as turbulent convection and overshooting. We present an implicit solver that results from the combination of a Jacobian-free Newton-Krylov method and a preconditioning technique tailored to the inviscid, compressible equations of stellar hydrodynamics. We assess the accuracy and performance of the solver for both 2D and 3D problems for Mach numbers down to 10-6. Although our applications concern flows in stellar interiors, the method can be applied to general advection and/or diffusion-dominated flows. The method presented in this paper opens up new avenues in 3D modeling of realistic stellar interiors allowing the study of important problems in stellar structure and evolution.
ERIC Educational Resources Information Center
Gardner, Don E.
The merits of double exponential smoothing are discussed relative to other types of pattern-based enrollment forecasting methods. The difficulties associated with selecting an appropriate weight factor are discussed, and their potential effects on prediction results are illustrated. Two methods for objectively selecting the "best" weight factor…
NASA Astrophysics Data System (ADS)
Dyachkov, S. A.; Parshikov, A. N.; Zhakhovsky, V. V.
2015-11-01
Experimental methods of observation of early stage of shock-induced ejecta from metal surface with micrometer-sized perturbations are still limited in terms of following a complete sequence of processes having microscale dimensions and nanoscale times. Therefore, simulations by the smoothed particle hydrodynamics (SPH) and molecular dynamics (MD) methods can shed of light on details of micro-jet evolution. The size of simulated sample is too restricted in MD, but the simulations with large enough number of atoms can be scaled well to the sizes of realistic samples. To validate such scaling the comparative MD and SPH simulations of tin samples are performed. SPH simulation takes the realistic experimental sizes, while MD uses the proportionally scaled sizes of samples. It is shown that the velocity and mass distributions along the jets simulated by MD and SPH are in a good agreement. The observed difference in velocity of spikes between MD and experiments can be partially explained by a profound effect of surface tension on jets ejected from the small-scale samples.
NASA Astrophysics Data System (ADS)
Barnard, R.; Greening, L. Shaw; Kolb, U.
2008-08-01
NGC253 is a local, starbursting spiral galaxy with strong X-ray emission from hot gas, as well as many point sources. We have conducted a spectral survey of the X-ray population of NGC253 using a deep XMM-Newton observation. NGC253 only accounts for ~20 per cent of the XMM-Newton EPIC field of view, allowing us to identify ~100 X-ray sources that are unlikely to be associated with NGC253. Hence, we were able to make a direct estimate of contamination from, for example, foreground stars and background galaxies. X-ray luminosity functions (XLFs) of galaxy populations are often used to characterize their properties. There are several methods for estimating the luminosities of X-ray sources with few photons. We have obtained spectral fits for the brightest 140 sources in the 2003 XMM-Newton observation of NGC253, and compare the best-fitting luminosities of those 69 non-nuclear sources associated with NGC253 with luminosities derived using other methods. We find the luminosities obtained from these various methods to vary systematically by a factor of up to 3 for the same data; this is largely due to differences in absorption. We therefore conclude that assuming Galactic absorption is probably unwise; rather, one should measure the absorption for the population. A remarkable correlation has been reported between the XLFs of galaxies and their star formation rates. However, the XLFs used in that study were obtained using several different methods. If the sample galaxies were revisited and a single method were applied, then this correlation may become stronger still. In addition, we find that standard estimations of the background contribution to the X-ray sources in the field are insufficient. We find that the background active galactic nuclei (AGN) may be systematically more luminous than previously expected. However, the excess in our measured AGN XLF with respect to the expected XLF may be due to an as yet unrecognized population associated with NGC253.
Bernsen, Erik; Dijkstra, Henk A.; Thies, Jonas; Wubs, Fred W.
2010-10-20
In present-day forward time stepping ocean-climate models, capturing both the wind-driven and thermohaline components, a substantial amount of CPU time is needed in a so-called spin-up simulation to determine an equilibrium solution. In this paper, we present methodology based on Jacobian-Free Newton-Krylov methods to reduce the computational time for such a spin-up problem. We apply the method to an idealized configuration of a state-of-the-art ocean model, the Modular Ocean Model version 4 (MOM4). It is shown that a typical speed-up of a factor 10-25 with respect to the original MOM4 code can be achieved and that this speed-up increases with increasing horizontal resolution.
NASA Astrophysics Data System (ADS)
Bernsen, Erik; Dijkstra, Henk A.; Thies, Jonas; Wubs, Fred W.
2010-10-01
In present-day forward time stepping ocean-climate models, capturing both the wind-driven and thermohaline components, a substantial amount of CPU time is needed in a so-called spin-up simulation to determine an equilibrium solution. In this paper, we present methodology based on Jacobian-Free Newton-Krylov methods to reduce the computational time for such a spin-up problem. We apply the method to an idealized configuration of a state-of-the-art ocean model, the Modular Ocean Model version 4 (MOM4). It is shown that a typical speed-up of a factor 10-25 with respect to the original MOM4 code can be achieved and that this speed-up increases with increasing horizontal resolution.
Pérez, Isidro A; Sánchez, M Luisa; García, M Ángeles; Pardo, Nuria
2013-07-01
CO₂ concentrations recorded for two years using a Picarro G1301 analyser at a rural site were studied applying two procedures. Firstly, the smoothing kernel method, which to date has been used with one linear and another circular variable, was used with pairs of circular variables: wind direction, time of day, and time of year, providing that the daily cycle was the prevailing cyclical evolution and that the highest concentrations were justified by the influence of one nearby city source, which was only revealed by directional analysis. Secondly, histograms were obtained, and these revealed most observations to be located between 380 and 410 ppm, and that there was a sharp contrast during the year. Finally, histograms were fitted to 14 distributions, the best known using analytical procedures, and the remainder using numerical procedures. RMSE was used as the goodness of fit indicator to compare and select distributions. Most functions provided similar RMSE values. However, the best fits were obtained using numerical procedures due to their greater flexibility, the triangular distribution being the simplest function of this kind. This distribution allowed us to identify directions and months of noticeable CO₂ input (SSE and April-May, respectively) as well as the daily cycle of the distribution symmetry. Among the functions whose parameters were calculated using an analytical expression, Erlang distributions provided satisfactory fits for monthly analysis, and gamma for the rest. By contrast, the Rayleigh and Weibull distributions gave the worst RMSE values. PMID:23602977
NASA Technical Reports Server (NTRS)
Pinson, Robin M.; Schmitt, Terri L.; Hanson, John M.
2008-01-01
Six degree-of-freedom (DOF) launch vehicle trajectories are designed to follow an optimized 3-DOF reference trajectory. A vehicle has a finite amount of control power that it can allocate to performing maneuvers. Therefore, the 3-DOF trajectory must be designed to refrain from using 100% of the allowable control capability to perform maneuvers, saving control power for handling off-nominal conditions, wind gusts and other perturbations. During the Ares I trajectory analysis, two maneuvers were found to be hard for the control system to implement; a roll maneuver prior to the gravity turn and an angle of attack maneuver immediately after the J-2X engine start-up. It was decided to develop an approach for creating smooth maneuvers in the optimized reference trajectories that accounts for the thrust available from the engines. A feature of this method is that no additional angular velocity in the direction of the maneuver has been added to the vehicle after the maneuver completion. This paper discusses the equations behind these new maneuvers and their implementation into the Ares I trajectory design cycle. Also discussed is a possible extension to adjusting closed-loop guidance.
ERIC Educational Resources Information Center
Erlichson, Herman
1995-01-01
Discusses Newton's apparent oversight of the role of energy considerations in collisions between two spherical bodies related to the third corollary of his "Laws of Motion." Investigates several theories that provide solutions to the mysterious oversight. (LZ)
NASA Astrophysics Data System (ADS)
Zouch, Wassim; Slima, Mohamed Ben; Feki, Imed; Derambure, Philippe; Taleb-Ahmed, Abdelmalik; Hamida, Ahmed Ben
2010-12-01
A new nonparametric method, based on the smooth weighted-minimum-norm (WMN) focal underdetermined-system solver (FOCUSS), for electrical cerebral activity localization using electroencephalography measurements is proposed. This method iteratively adjusts the spatial sources by reducing the size of the lead-field and the weighting matrix. Thus, an enhancement of source localization is obtained, as well as a reduction of the computational complexity. The performance of the proposed method, in terms of localization errors, robustness, and computation time, is compared with the WMN-FOCUSS and nonshrinking smooth WMN-FOCUSS methods as well as with standard generalized inverse methods (unweighted minimum norm, WMN, and FOCUSS). Simulation results for single-source localization confirm the effectiveness and robustness of the proposed method with respect to the reconstruction accuracy of a simulated single dipole.
ERIC Educational Resources Information Center
Kolen, Michael J.; And Others
Six methods for smoothing double-entry expectancy tables (tables that relate two predictor variables to probability of attaining a selected level of success on a criterion) were compared using data for entering students at 85 colleges and universities. ACT composite scores and self-reported high school grade averages were used to construct…
ERIC Educational Resources Information Center
Perrin, David W.; Whitney, Douglas R.
Six methods for smoothing expectancy tables were compared using data for entering students at 86 colleges and universities. Linear regression analyses were applied to ACT scores and high school grades to obtain predicted first term grade point averages (FGPA's) for students entering each institution in 1969-70. Expectancy tables were constructed…
Newton and scholastic philosophy.
Levitin, Dmitri
2016-03-01
This article examines Isaac Newton's engagement with scholastic natural philosophy. In doing so, it makes two major historiographical interventions. First of all, the recent claim that Newton's use of the concepts of analysis and synthesis was derived from the Aristotelian regressus tradition is challenged on the basis of bibliographical, palaeographical and intellectual evidence. Consequently, a new, contextual explanation is offered for Newton's use of these concepts. Second, it will be shown that some of Newton's most famous pronouncements - from the General Scholium appended to the second edition of the Principia (1713) and from elsewhere - are simply incomprehensible without an understanding of specific scholastic terminology and its later reception, and that this impacts in quite significant ways on how we understand Newton's natural philosophy more generally. Contrary to the recent historiographical near-consensus, Newton did not hold an elaborate metaphysics, and his seemingly 'metaphysical' statements were in fact anti-scholastic polemical salvoes. The whole investigation will permit us a brief reconsideration of the relationship between the self-proclaimed 'new' natural philosophy and its scholastic predecessors. PMID:26593733
Mazza, G; Roßmanith, E; Lang-Olip, I; Pfeiffer, D
2016-08-01
Even though umbilical cord arteries are a common source of vascular smooth muscle cells, the lack of reliable marker profiles have not facilitated the isolation of human umbilical artery smooth muscle cells (HUASMC). For accurate characterization of HUASMC and cells in their environment, the expression of smooth muscle and mesenchymal markers was analyzed in umbilical cord tissue sections. The resulting marker profile was then used to evaluate the quality of HUASMC isolation and culture methods. HUASMC and perivascular-Wharton's jelly stromal cells (pv-WJSC) showed positive staining for α-smooth muscle actin (α-SMA), smooth muscle myosin heavy chain (SM-MHC), desmin, vimentin and CD90. Anti-CD10 stained only pv-WJSC. Consequently, HUASMC could be characterized as α-SMA+ , SM-MHC+ , CD10- cells, which are additionally negative for endothelial markers (CD31 and CD34). Enzymatic isolation provided primary HUASMC batches with 90-99 % purity, yet, under standard culture conditions, contaminant CD10+ cells rapidly constituted more than 80 % of the total cell population. Contamination was mainly due to the poor adhesion of HUASMC to cell culture plates, regardless of the different protein coatings (fibronectin, collagen I or gelatin). HUASMC showed strong attachment and long-term viability only in 3D matrices. The explant isolation method achieved cultures with only 13-40 % purity with considerable contamination by CD10+ cells. CD10+ cells showed spindle-like morphology and up-regulated expression of α-SMA and SM-MHC upon culture in smooth muscle differentiation medium. Considering the high contamination risk of HUASMC cultures by CD10+ neighboring cells and their phenotypic similarities, precise characterization is mandatory to avoid misleading results. PMID:25535117
NASA Astrophysics Data System (ADS)
Borazjani, Iman; Asgharzadeh, Hafez
2015-11-01
Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.
Induced Pluripotent Stem Cell-derived Vascular Smooth Muscle Cells: Methods and Application
Dash, Biraja C.; Jiang, Zhengxin; Suh, Carol; Qyang, Yibing
2015-01-01
Vascular smooth muscle cells (VSMCs) play a major role in the pathophysiology of cardiovascular diseases. The advent of induced pluripotent stem cell (iPSC) technology and their capability to differentiation into virtually every cell type in the human body make this field a ray of hope for vascular regenerative therapy and for understanding disease mechanism. In this review, we first discuss the recent iPSC technology and vascular smooth muscle development from embryo and then examine different methodology to derive VSMCs from iPSCs and their applications in regenerative therapy and disease modeling. PMID:25559088
Methods and energy storage devices utilizing electrolytes having surface-smoothing additives
Xu, Wu; Zhang, Jiguang; Graff, Gordon L; Chen, Xilin; Ding, Fei
2015-11-12
Electrodeposition and energy storage devices utilizing an electrolyte having a surface-smoothing additive can result in self-healing, instead of self-amplification, of initial protuberant tips that give rise to roughness and/or dendrite formation on the substrate and anode surface. For electrodeposition of a first metal (M1) on a substrate or anode from one or more cations of M1 in an electrolyte solution, the electrolyte solution is characterized by a surface-smoothing additive containing cations of a second metal (M2), wherein cations of M2 have an effective electrochemical reduction potential in the solution lower than that of the cations of M1.
NITSOL: A Newton iterative solver for nonlinear systems
Pernice, M.; Walker, H.F.
1996-12-31
Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.
NASA Astrophysics Data System (ADS)
Voznyuk, I.; Litman, A.; Tortel, H.
2015-08-01
A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.
NASA Astrophysics Data System (ADS)
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre
2013-11-01
A Continuous Boundary Force (CBF) method was developed for implementing Robin (Navier) boundary condition (BC) that can describe no-slip or slip conditions (slip length from zero to infinity) at the fluid-solid interface. In the CBF method the Robin BC is replaced by a homogeneous Neumann BC and an additional volumetric source term in the governing momentum equation. The formulation is derived based on an approximation of the sharp boundary with a diffuse interface of finite thickness, across which the BC is reformulated by means of a smoothed characteristic function. The CBF method is easy to be implemented in Lagrangian particle-based methods. We first implemented it in smoothed particle hydrodynamics (SPH) to solve numerically the Navier-Stokes equations subject to spatial-independent or dependent Robin BC in two and three dimensions. The numerical accuracy and convergence is examined through comparisons with the corresponding finite difference or finite element solutions. The CBF method is further implemented in smoothed dissipative particle dynamics (SDPD), a mesoscale scheme, for modeling slip flows commonly existent in micro/nano channels and microfluidic devices. The authors acknowledge the funding support by the ASCR Program of the Office of Science, U.S. Department of Energy.
2013-01-01
Background To facilitate new drug development, physiologically-based pharmacokinetic (PBPK) modeling methods receive growing attention as a tool to fully understand and predict complex pharmacokinetic phenomena. As the number of parameters to reproduce physiological functions tend to be large in PBPK models, efficient parameter estimation methods are essential. We have successfully applied a recently developed algorithm to estimate a feasible solution space, called Cluster Newton Method (CNM), to reveal the cause of irinotecan pharmacokinetic alterations in two cancer patient groups. Results After improvements in the original CNM algorithm to maintain parameter diversities, a feasible solution space was successfully estimated for 55 or 56 parameters in the irinotecan PBPK model, within ten iterations, 3000 virtual samples, and in 15 minutes (Intel Xeon E5-1620 3.60GHz × 1 or Intel Core i7-870 2.93GHz × 1). Control parameters or parameter correlations were clarified after the parameter estimation processes. Possible causes in the irinotecan pharmacokinetic alterations were suggested, but they were not conclusive. Conclusions Application of CNM achieved a feasible solution space by solving inverse problems of a system containing ordinary differential equations (ODEs). This method may give us reliable insights into other complicated phenomena, which have a large number of parameters to estimate, under limited information. It is also helpful to design prospective studies for further investigation of phenomena of interest. PMID:24555857
NASA Astrophysics Data System (ADS)
Szczesna, Dorota H.; Kulas, Zbigniew; Kasprzak, Henryk T.; Stenevi, Ulf
2009-11-01
A lateral shearing interferometer was used to examine the smoothness of the tear film. The information about the distribution and stability of the precorneal tear film is carried out by the wavefront reflected from the surface of tears and coded in interference fringes. Smooth and regular fringes indicate a smooth tear film surface. On corneae after laser in situ keratomileusis (LASIK) or radial keratotomy (RK) surgery, the interference fringes are seldom regular. The fringes are bent on bright lines, which are interpreted as tear film breakups. The high-intensity pattern seems to appear in similar location on the corneal surface after refractive surgery. Our purpose was to extract information about the pattern existing under the interference fringes and calculate its shape reproducibility over time and following eye blinks. A low-pass filter was applied and correlation coefficient was calculated to compare a selected fragment of the template image to each of the following frames in the recorded sequence. High values of the correlation coefficient suggest that irregularities of the corneal epithelium might influence tear film instability and that tear film breakup may be associated with local irregularities of the corneal topography created after the LASIK and RK surgeries.
Turning around Newton's Second Law
ERIC Educational Resources Information Center
Goff, John Eric
2004-01-01
Conceptual and quantitative difficulties surrounding Newton's second law often arise among introductory physics students. Simply turning around how one expresses Newton's second law may assist students in their understanding of a deceptively simple-looking equation.
NASA Astrophysics Data System (ADS)
Maulina, Hervin; Santoso, Iman; Subama, Emmistasega; Nurwantoro, Pekik; Abraha, Kamsul; Rusydi, Andrivo
2016-04-01
The extraction of the dielectric constant of nanostructured graphene on SiC substrates from spectroscopy ellipsometry measurement using the Gauss-Newton inversion (GNI) method has been done. This study aims to calculate the dielectric constant and refractive index of graphene by extracting the value of ψ and Δ from the spectroscopy ellipsometry measurement using GNI method and comparing them with previous result which was extracted using Drude-Lorentz (DL) model. The results show that GNI method can be used to calculate the dielectric constant and refractive index of nanostructured graphene on SiC substratesmore faster as compared to DL model. Moreover, the imaginary part of the dielectric constant values and coefficient of extinction drastically increases at 4.5 eV similar to that of extracted using known DL fitting. The increase is known due to the process of interband transition and the interaction between the electrons and electron-hole at M-points in the Brillouin zone of graphene.
"To Improve upon Hints of Things": Illustrating Isaac Newton.
Schilt, Cornelis J
2016-01-01
When Isaac Newton died in 1727 he left a rich legacy in terms of draft manuscripts, encompassing a variety of topics: natural philosophy, mathematics, alchemy, theology, and chronology, as well as papers relating to his career at the Mint. One thing that immediately strikes us is the textuality of Newton's legacy: images are sparse. Regarding his scholarly endeavours we witness the same practice. Newton's extensive drafts on theology and chronology do not contain a single illustration or map. Today we have all of Newton's draft manuscripts as witnesses of his working methods, as well as access to a significant number of books from his own library. Drawing parallels between Newton's reading practices and his natural philosophical and scholarly work, this paper seeks to understand Newton's recondite writing and publishing politics. PMID:27071300
ERIC Educational Resources Information Center
Cox, Carol
2001-01-01
Presents the Isaac Newton Olympics in which students complete a hands-on activity at seven stations and evaluate what they have learned in the activity and how it is related to real life. Includes both student and teacher instructions for three of the activities. (YDS)
NASA Astrophysics Data System (ADS)
Élie-Dit-Cosaque, Xavier J.-G.; Gakwaya, Augustin; Naceur, Hakim
2015-01-01
A smoothed finite element method formulation for the resultant eight-node solid-shell element is presented in this paper for geometrical linear analysis. The smoothing process is successfully performed on the element mid-surface to deal with the membrane and bending effects of the stiffness matrix. The strain smoothing process allows replacing the Cartesian derivatives of shape functions by the product of shape functions with normal vectors to the element mid-surface boundaries. The present formulation remains competitive when compared to the classical finite element formulations since no inverse of the Jacobian matrix is calculated. The three dimensional resultant shell theory allows the element kinematics to be defined only with the displacement degrees of freedom. The assumed natural strain method is used not only to eliminate the transverse shear locking problem encountered in thin-walled structures, but also to reduce trapezoidal effects. The efficiency of the present element is presented and compared with that of standard solid-shell elements through various benchmark problems including some with highly distorted meshes.
Simulation of wave mitigation by coastal vegetation using smoothed particle hydrodynamics method
NASA Astrophysics Data System (ADS)
Iryanto; Gunawan, P. H.
2016-02-01
Vegetation in coastal area lead to wave mitigation has been studied by some researchers recently. The effect of vegetation forest in coastal area is minimizing the negative impact of wave propagation. In order to describe the effect of vegetation resistance into the water flow, the modified model of framework smoothed hydrodynamics particle has been constructed. In the Lagrangian framework, the Darcy, Manning, and laminar viscosity resistances are added. The effect of each resistances is given in some results of numerical simulations. Simulation of wave mitigation on sloping beach is also given.
A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries
NASA Astrophysics Data System (ADS)
Gatsonis, Nikolaos A.; Potami, Raffaele; Yang, Jun
2014-01-01
A smooth dissipative particle dynamics method with dynamic virtual particle allocation (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains is presented. The physical domain in SDPD-DV may contain external and internal solid boundaries of arbitrary geometries, periodic inlets and outlets, and the fluid region. The SDPD-DV method is realized with fluid particles, boundary particles, and dynamically allocated virtual particles. The internal or external solid boundaries of the domain can be of arbitrary geometry and are discretized with a surface grid. These boundaries are represented by boundary particles with assigned properties. The fluid domain is discretized with fluid particles of constant mass and variable volume. Conservative and dissipative force models due to virtual particles exerted on a fluid particle in the proximity of a solid boundary supplement the original SDPD formulation. The dynamic virtual particle allocation approach provides the density and the forces due to virtual particles. The integration of the SDPD equations is accomplished with a velocity-Verlet algorithm for the momentum and a Runge-Kutta for the entropy equation. The velocity integrator is supplemented by a bounce-forward algorithm in cases where the virtual particle force model is not able to prevent particle penetration. For the incompressible isothermal systems considered in this work, the pressure of a fluid particle is obtained by an artificial compressibility formulation for liquids and the ideal gas law for gases. The self-diffusion coefficient is obtained by an implementation of the generalized Einstein and the Green-Kubo relations. Field properties are obtained by sampling SDPD-DV outputs on a post-processing grid that allows harnessing the particle information on desired spatiotemporal scales. The SDPD-DV method is verified and validated with simulations in bounded and periodic domains that cover the hydrodynamic and mesoscopic regimes for
A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries
NASA Astrophysics Data System (ADS)
Gatsonis, Nikolaos A.; Potami, Raffaele; Yang, Jun
2014-01-01
A smooth dissipative particle dynamics method with dynamic virtual particle allocation (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains is presented. The physical domain in SDPD-DV may contain external and internal solid boundaries of arbitrary geometries, periodic inlets and outlets, and the fluid region. The SDPD-DV method is realized with fluid particles, boundary particles, and dynamically allocated virtual particles. The internal or external solid boundaries of the domain can be of arbitrary geometry and are discretized with a surface grid. These boundaries are represented by boundary particles with assigned properties. The fluid domain is discretized with fluid particles of constant mass and variable volume. Conservative and dissipative force models due to virtual particles exerted on a fluid particle in the proximity of a solid boundary supplement the original SDPD formulation. The dynamic virtual particle allocation approach provides the density and the forces due to virtual particles. The integration of the SDPD equations is accomplished with a velocity-Verlet algorithm for the momentum and a Runge-Kutta for the entropy equation. The velocity integrator is supplemented by a bounce-forward algorithm in cases where the virtual particle force model is not able to prevent particle penetration. For the incompressible isothermal systems considered in this work, the pressure of a fluid particle is obtained by an artificial compressibility formulation for liquids and the ideal gas law for gases. The self-diffusion coefficient is obtained by an implementation of the generalized Einstein and the Green-Kubo relations. Field properties are obtained by sampling SDPD-DV outputs on a post-processing grid that allows harnessing the particle information on desired spatiotemporal scales. The SDPD-DV method is verified and validated with simulations in bounded and periodic domains that cover the hydrodynamic and mesoscopic regimes for
Users manual for Opt-MS : local methods for simplicial mesh smoothing and untangling.
Freitag, L.
1999-07-20
Creating meshes containing good-quality elements is a challenging, yet critical, problem facing computational scientists today. Several researchers have shown that the size of the mesh, the shape of the elements within that mesh, and their relationship to the physical application of interest can profoundly affect the efficiency and accuracy of many numerical approximation techniques. If the application contains anisotropic physics, the mesh can be improved by considering both local characteristics of the approximate application solution and the geometry of the computational domain. If the application is isotropic, regularly shaped elements in the mesh reduce the discretization error, and the mesh can be improved a priori by considering geometric criteria only. The Opt-MS package provides several local node point smoothing techniques that improve elements in the mesh by adjusting grid point location using geometric, criteria. The package is easy to use; only three subroutine calls are required for the user to begin using the software. The package is also flexible; the user may change the technique, function, or dimension of the problem at any time during the mesh smoothing process. Opt-MS is designed to interface with C and C++ codes, ad examples for both two-and three-dimensional meshes are provided.
Ariyawansa, K.A.; Lau, D.T.M.
1988-01-01
A derivation of collinear scaling algorithms for unconstrained minimization was presented. The local conic approximants to the objective function underlying these algorithms are forced to interpolate the value and gradient of the objective function at the two most recent iterates. The class of algorithms derived therein has a free parameter sequence /l brace/b/sub k//r brace/ and for a fixed choice of /l brace/b/sub k//r brace/ it contains collinear scaling algorithms that may be treated as extensions of quasi-Newton methods with Broyden family of updates. In this paper, under standard assumptions, it is shown that if b/sub k/ is set equal to the gradient of the objective function for all k and if /l brace/chemically bond1 /minus/ theta/sub k/chemically bond/r brace/ (where theta/sub k/ is the parameter in the Broyden family) is uniformly bounded, then these collinear scaling algorithms related to the Broyden family are locally and q-superlinearly convergent. 13 refs.
An implicit Smooth Particle Hydrodynamic code
Charles E. Knapp
2000-04-01
An implicit version of the Smooth Particle Hydrodynamic (SPH) code SPHINX has been written and is working. In conjunction with the SPHINX code the new implicit code models fluids and solids under a wide range of conditions. SPH codes are Lagrangian, meshless and use particles to model the fluids and solids. The implicit code makes use of the Krylov iterative techniques for solving large linear-systems and a Newton-Raphson method for non-linear corrections. It uses numerical derivatives to construct the Jacobian matrix. It uses sparse techniques to save on memory storage and to reduce the amount of computation. It is believed that this is the first implicit SPH code to use Newton-Krylov techniques, and is also the first implicit SPH code to model solids. A description of SPH and the techniques used in the implicit code are presented. Then, the results of a number of tests cases are discussed, which include a shock tube problem, a Rayleigh-Taylor problem, a breaking dam problem, and a single jet of gas problem. The results are shown to be in very good agreement with analytic solutions, experimental results, and the explicit SPHINX code. In the case of the single jet of gas case it has been demonstrated that the implicit code can do a problem in much shorter time than the explicit code. The problem was, however, very unphysical, but it does demonstrate the potential of the implicit code. It is a first step toward a useful implicit SPH code.
Globally convergent techniques in nonlinear Newton-Krylov
NASA Technical Reports Server (NTRS)
Brown, Peter N.; Saad, Youcef
1989-01-01
Some convergence theory is presented for nonlinear Krylov subspace methods. The basic idea of these methods is to use variants of Newton's iteration in conjunction with a Krylov subspace method for solving the Jacobian linear systems. These methods are variants of inexact Newton methods where the approximate Newton direction is taken from a subspace of small dimensions. The main focus is to analyze these methods when they are combined with global strategies such as linesearch techniques and model trust region algorithms. Most of the convergence results are formulated for projection onto general subspaces rather than just Krylov subspaces.
Higgitt, Rebekah
2004-03-01
Francis Baily's publication of the manuscripts of John Flamsteed, the first Astronomer Royal, provoked a furious response. Flamsteed had quarrelled with Isaac Newton, and described him in terms unforgivable to those who claimed him as a paragon of all virtues, both moral and scientific. Baily was condemned for putting Flamsteed's complaints in the public sphere. However, his supporters saw his work as a critique of the excessive hero-worship accorded to Newton. Written when the word 'scientist' had been newly coined, this work and the debates it provoked gives us an insight into contemporary views of the role of the man of science and of the use of science to back political, religious and moral positions. PMID:15036924
Renormalization of Newton's constant
NASA Astrophysics Data System (ADS)
Falls, Kevin
2015-12-01
The problem of obtaining a gauge independent beta function for Newton's constant is addressed. By a specific parametrization of metric fluctuations a gauge independent functional integral is constructed for the semiclassical theory around an arbitrary Einstein space. The effective action then has the property that only physical polarizations of the graviton contribute, while all other modes cancel with the functional measure. We are then able to compute a gauge independent beta function for Newton's constant in d dimensions to one-loop order. No Landau pole is present provided Ng<18 , where Ng=d (d -3 )/2 is the number of polarizations of the graviton. While adding a large number of matter fields can change this picture, the absence of a pole persists for the particle content of the standard model in four spacetime dimensions.
NASA Technical Reports Server (NTRS)
Herbert, Dexter (Editor)
1992-01-01
In this 'Liftoff to Learning' series video, astronauts (Charles Veach, Gregory Harbaugh, Donald McMonagle, Michael Coats, L. Blaine Hammond, Guion Bluford, Richard Hieb) from the STS-39 Mission use physical experiments and computer animation to explain how weightlessness and gravity affects everything and everyone onboard the Space Shuttle. The physics behind the differences between weight and mass, and the concepts of 'free fall', are demonstrated along with explanations and experiments of Sir Issac Newton's three laws of motion.
Newton polyhedron and applications
Bruno, A.D.
1994-12-31
We give a simple presentation of an algorithm of selecting asymptotical first approximations of equations (algebraic and ordinary differential and partial differential). Here the first approximation of a solution of the initial equation is a solution of the corresponding first approximation of the equation. The algorithm is based on the geometry of power exponents including the Newton polyhedron. We give also a survey of applications of the algorithm in problems of Celestial Mechanics and Hydrodynamics.
NASA Astrophysics Data System (ADS)
Herbert, Dexter
1992-03-01
In this 'Liftoff to Learning' series video, astronauts (Charles Veach, Gregory Harbaugh, Donald McMonagle, Michael Coats, L. Blaine Hammond, Guion Bluford, Richard Hieb) from the STS-39 Mission use physical experiments and computer animation to explain how weightlessness and gravity affects everything and everyone onboard the Space Shuttle. The physics behind the differences between weight and mass, and the concepts of 'free fall', are demonstrated along with explanations and experiments of Sir Issac Newton's three laws of motion.
NASA Astrophysics Data System (ADS)
Zhao, Xujun; Bordas, Stéphane P. A.; Qu, Jianmin
2013-12-01
Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis. When designing nanodevices and to understand the behavior of materials at the nano-scale, this interfacial energy must therefore be taken into account. The present work develops an effective numerical approach by means of a hybrid smoothed extended finite element/level set method to model nanoscale inhomogeneities with interfacial energy effect, in which the finite element mesh can be completely independent of the interface geometry. The Gurtin-Murdoch surface elasticity model is used to account for the interface stress effect and the Wachspress interpolants are used for the first time to construct the shape functions in the smoothed extended finite element method. Selected numerical results are presented to study the accuracy and efficiency of the proposed method as well as the equilibrium shapes of misfit particles in elastic solids. The presented results compare very well with those obtained from theoretical solutions and experimental observations, and the computational efficiency of the method is shown to be superior to that of its most advanced competitor.
The Unknown Detective Career of Isaac Newton
Levenson, Thomas
2010-03-17
Isaac Newton's fame is such that it would seem that almost nothing remains to be discovered about his deeds or his methods. But very little attention has been paid to the three decades Newton spent in charge of the Royal Mint, and especially to the first of those years, in which he supervised the remaking of England's entire silver money supply, all the while investigating, prosecuting, and executing the nation's currency criminals. That story provides unique perspectives on both his own habits of mind and on how what has come to be called the scientific revolution played out, not just in the minds of the great, but on the mean streets of London.
HyeongKae Park; R. Nourgaliev; Richard C. Martineau; Dana A. Knoll
2008-09-01
Multidimensional, higher-order (2nd and higher) numerical methods have come to the forefront in recent years due to significant advances of computer technology and numerical algorithms, and have shown great potential as viable design tools for realistic applications. To achieve this goal, implicit high-order accurate coupling of the multiphysics simulations is a critical component. One of the issues that arise from multiphysics simulation is the necessity to resolve multiple time scales. For example, the dynamical time scales of neutron kinetics, fluid dynamics and heat conduction significantly differ (typically >1010 magnitude), with the dominant (fastest) physical mode also changing during the course of transient [Pope and Mousseau, 2007]. This leads to the severe time step restriction for stability in traditional multiphysics (i.e. operator split, semi-implicit discretization) simulations. The lower order methods suffer from an undesirable numerical dissipation. Thus implicit, higher order accurate scheme is necessary to perform seamlessly-coupled multiphysics simulations that can be used to analyze the “what-if” regulatory accident scenarios, or to design and optimize engineering systems.
NASA Astrophysics Data System (ADS)
Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong
2013-02-01
A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.
Barceló, M Antònia; Saez, Marc; Cano-Serral, Gemma; Martínez-Beneito, Miguel Angel; Martínez, José Miguel; Borrell, Carme; Ocaña-Riola, Ricardo; Montoya, Imanol; Calvo, Montse; López-Abente, Gonzalo; Rodríguez-Sanz, Maica; Toro, Silvia; Alcalá, José Tomás; Saurina, Carme; Sánchez-Villegas, Pablo; Figueiras, Adolfo
2008-01-01
Although there is some experience in the study of mortality inequalities in Spanish cities, there are large urban centers that have not yet been investigated using the census tract as the unit of territorial analysis. The coordinated project
NASA Astrophysics Data System (ADS)
Gatsis, John
An investigation of preconditioning techniques is presented for a Newton-Krylov algorithm that is used for the computation of steady, compressible, high Reynolds number flows about airfoils. A second-order centred-difference method is used to discretize the compressible Navier-Stokes (NS) equations that govern the fluid flow. The one-equation Spalart-Allmaras turbulence model is used. The discretized equations are solved using Newton's method and the generalized minimal residual (GMRES) Krylov subspace method is used to approximately solve the linear system. These preconditioning techniques are first applied to the solution of the discretized steady convection-diffusion equation. Various orderings, iterative block incomplete LU (BILU) preconditioning and multigrid preconditioning are explored. The baseline preconditioner is a BILU factorization of a lower-order discretization of the system matrix in the Newton linearization. An ordering based on the minimum discarded fill (MDF) ordering is developed and compared to the widely popular reverse Cuthill-McKee ordering. An evolutionary algorithm is used to investigate and enhance this ordering. For the convection-diffusion equation, the MDF-based ordering performs well and RCM is superior for the NS equations. Experiments for inviscid, laminar and turbulent cases are presented to show the effectiveness of iterative BILU preconditioning in terms of reducing the number of GMRES iterations, and hence the memory requirements of the Newton-Krylov algorithm. Multigrid preconditioning also reduces the number of GMRES iterations. The framework for the iterative BILU and BILU-smoothed multigrid preconditioning algorithms is presented in detail.
ERIC Educational Resources Information Center
Develaki, Maria
2012-01-01
The availability of teaching units on the nature of science (NOS) can reinforce classroom instruction in the subject, taking into account the related deficiencies in textbook material and teacher training. We give a sequence of teaching units in which the teaching of Newton's gravitational theory is used as a basis for reflecting on the…
Kawato, M; Isobe, M; Maeda, Y; Suzuki, R
1988-01-01
In order to control visually-guided voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: (1) determination of a desired trajectory in the visual coordinates, (2) transformation of the coordinates of the desired trajectory to the body coordinates and (3) generation of motor command. In this paper, the second and the third problems are treated at computational, representational and hardware levels of Marr. We first study the problems at the computational level, and then propose an iterative learning scheme as a possible algorithm. This is a trial and error type learning such as repetitive training of golf swing. The amount of motor command needed to coordinate activities of many muscles is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Actually, the motor command in the (n + 1)-th iteration is a sum of the motor command in the n-th iteration plus two modification terms which are, respectively, proportional to acceleration and speed errors between the desired trajectory and the realized trajectory in the n-th iteration. We mathematically formulate this iterative learning control as a Newton-like method in functional spaces and prove its convergence under appropriate mathematical conditions with use of dynamical system theory and functional analysis. Computer simulations of this iterative learning control of a robotic manipulator in the body or visual coordinates are shown. Finally, we propose that areas 2, 5, and 7 of the sensory association cortex are possible sites of this learning control. Further we propose neural network model which acquires transformation matrices from acceleration or velocity to motor command, which are used in these schemes. PMID:3179342
2013-01-01
Background There is a rising public and political demand for prospective cancer cluster monitoring. But there is little empirical evidence on the performance of established cluster detection tests under conditions of small and heterogeneous sample sizes and varying spatial scales, such as are the case for most existing population-based cancer registries. Therefore this simulation study aims to evaluate different cluster detection methods, implemented in the open soure environment R, in their ability to identify clusters of lung cancer using real-life data from an epidemiological cancer registry in Germany. Methods Risk surfaces were constructed with two different spatial cluster types, representing a relative risk of RR = 2.0 or of RR = 4.0, in relation to the overall background incidence of lung cancer, separately for men and women. Lung cancer cases were sampled from this risk surface as geocodes using an inhomogeneous Poisson process. The realisations of the cancer cases were analysed within small spatial (census tracts, N = 1983) and within aggregated large spatial scales (communities, N = 78). Subsequently, they were submitted to the cluster detection methods. The test accuracy for cluster location was determined in terms of detection rates (DR), false-positive (FP) rates and positive predictive values. The Bayesian smoothing models were evaluated using ROC curves. Results With moderate risk increase (RR = 2.0), local cluster tests showed better DR (for both spatial aggregation scales > 0.90) and lower FP rates (both < 0.05) than the Bayesian smoothing methods. When the cluster RR was raised four-fold, the local cluster tests showed better DR with lower FPs only for the small spatial scale. At a large spatial scale, the Bayesian smoothing methods, especially those implementing a spatial neighbourhood, showed a substantially lower FP rate than the cluster tests. However, the risk increases at this scale were mostly diluted by data
NASA Astrophysics Data System (ADS)
Aghamousa, Amir; Shafieloo, Arman
2015-05-01
The observable time delays between multiple images of strong lensing systems with time variable sources can provide us with some valuable information for probing the expansion history of the universe. Estimating these time delays can be very challenging due to complexities in the observed data caused by seasonal gaps, various noises, and systematics such as unknown microlensing effects. In this paper, we introduce a novel approach for estimating the time delays for strong lensing systems, implementing various statistical methods of data analysis including the smoothing and cross-correlation methods. The method we introduce in this paper has recently been used in the TDC0 and TDC1 Strong Lens Time Delay Challenges and has shown its power in providing reliable and precise estimates of time delays dealing with data with different complexities.
NASA Astrophysics Data System (ADS)
Nassauer, Benjamin; Liedke, Thomas; Kuna, Meinhard
2016-03-01
In the present paper, the direct coupling of a discrete element method (DEM) with polyhedral particles and smoothed particle hydrodynamics (SPH) is presented. The two simulation techniques are fully coupled in both ways through interaction forces between the solid DEM particles and the fluid SPH particles. Thus this simulation method provides the possibility to simulate the individual movement of polyhedral, sharp-edged particles as well as the flow field around these particles in fluid-saturated granular matter which occurs in many technical processes e.g. wire sawing, grinding or lapping. The coupled method is exemplified and validated by the simulation of a particle in a shear flow, which shows good agreement with analytical solutions.
NASA Astrophysics Data System (ADS)
Wang, Li; Sun, Xiaogang; Xing, Jian
2012-12-01
An inversion technique which combines the pattern search algorithm with the Tikhonov smoothing functional for retrieval of particle size distribution (PSD) by light extinction method is proposed. In the unparameterized shape-independent model, we first transform the PSD inversion problem into an optimization problem, with the Tikhonov smoothing functional employed to model the objective function. The optimization problem is then solved by the pattern search algorithm. To ensure good convergence rate and accuracy of the whole retrieval, a competitive strategy for determining the initial point of the pattern search algorithm is also designed. The accuracy and limitations of the proposed technique are tested by the inversion results of synthetic and real standard polystyrene particles immersed in water. In addition, the issues about the objective function and computation time are further discussed. Both simulation and experimental results show that the technique can be successfully applied to retrieve the PSD with high reliability and stability in the presence of random noise. Compared with the Phillips-Twomey method and genetic algorithm, the proposed technique has certain advantages in terms of reaching a more accurate and steady optimal solution with less computational effort, thus making this technique more suitable for quick and accurate measurement of PSD.
NASA Astrophysics Data System (ADS)
Sohn, Dongwoo; Im, Seyoung
2013-06-01
In this paper, novel finite elements that include an arbitrary number of additional nodes on each edge of a quadrilateral element are proposed to achieve compatible connection of neighboring nonmatching meshes in plate and shell analyses. The elements, termed variable-node plate elements, are based on two-dimensional variable-node elements with point interpolation and on the Mindlin-Reissner plate theory. Subsequently the flat shell elements, termed variable-node shell elements, are formulated by further extending the plate elements. To eliminate a transverse shear locking phenomenon, the assumed natural strain method is used for plate and shell analyses. Since the variable-node plate and shell elements allow an arbitrary number of additional nodes and overcome locking problems, they make it possible to connect two nonmatching meshes and to provide accurate solutions in local mesh refinement. In addition, the curvature and strain smoothing methods through smoothed integration are adopted to improve the element performance. Several numerical examples are presented to demonstrate the effectiveness of the elements in terms of the accuracy and efficiency of the analyses.
Critical Parameters of the In Vitro Method of Vascular Smooth Muscle Cell Calcification
Hortells, Luis; Sosa, Cecilia; Millán, Ángel; Sorribas, Víctor
2015-01-01
Background Vascular calcification (VC) is primarily studied using cultures of vascular smooth muscle cells. However, the use of very different protocols and extreme conditions can provide findings unrelated to VC. In this work we aimed to determine the critical experimental parameters that affect calcification in vitro and to determine the relevance to calcification in vivo. Experimental Procedures and Results Rat VSMC calcification in vitro was studied using different concentrations of fetal calf serum, calcium, and phosphate, in different types of culture media, and using various volumes and rates of change. The bicarbonate content of the media critically affected pH and resulted in supersaturation, depending on the concentration of Ca2+ and Pi. Such supersaturation is a consequence of the high dependence of bicarbonate buffers on CO2 vapor pressure and bicarbonate concentration at pHs above 7.40. Such buffer systems cause considerable pH variations as a result of minor experimental changes. The variations are more critical for DMEM and are negligible when the bicarbonate concentration is reduced to ¼. Particle nucleation and growth were observed by dynamic light scattering and electron microscopy. Using 2mM Pi, particles of ~200nm were observed at 24 hours in MEM and at 1 hour in DMEM. These nuclei grew over time, were deposited in the cells, and caused osteogene expression or cell death, depending on the precipitation rate. TEM observations showed that the initial precipitate was amorphous calcium phosphate (ACP), which converts into hydroxyapatite over time. In blood, the scenario is different, because supersaturation is avoided by a tightly controlled pH of 7.4, which prevents the formation of PO43--containing ACP. Conclusions The precipitation of ACP in vitro is unrelated to VC in vivo. The model needs to be refined through controlled pH and the use of additional procalcifying agents other than Pi in order to reproduce calcium phosphate deposition in vivo
Wong Unhong; Wong Honcheng; Tang Zesheng
2010-05-21
The smoothed particle hydrodynamics (SPH), which is a class of meshfree particle methods (MPMs), has a wide range of applications from micro-scale to macro-scale as well as from discrete systems to continuum systems. Graphics hardware, originally designed for computer graphics, now provide unprecedented computational power for scientific computation. Particle system needs a huge amount of computations in physical simulation. In this paper, an efficient parallel implementation of a SPH method on graphics hardware using the Compute Unified Device Architecture is developed for fluid simulation. Comparing to the corresponding CPU implementation, our experimental results show that the new approach allows significant speedups of fluid simulation through handling huge amount of computations in parallel on graphics hardware.
Newton-Krylov-Schwarz: An implicit solver for CFD
NASA Technical Reports Server (NTRS)
Cai, Xiao-Chuan; Keyes, David E.; Venkatakrishnan, V.
1995-01-01
Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.
Egorov, A A; Sevast'yanov, L A; Sevast'yanov, A L
2014-02-28
We consider the application of the method of adiabatic waveguide modes for calculating the propagation of electromagnetic radiation in three-dimensional (3D) irregular integrated optical waveguides. The method of adiabatic modes takes into account a three-dimensional distribution of quasi-waveguide modes and explicit ('inclined') tangential boundary conditions. The possibilities of the method are demonstrated on the example of numerical research of two major elements of integrated optics: a waveguide of 'horn' type and a thin-film generalised waveguide Luneburg lens by the methods of adiabatic modes and comparative waveguides. (integral optical waveguides)
Isaac Newton: Man, Myth, and Mathematics.
ERIC Educational Resources Information Center
Rickey, V. Frederick
1987-01-01
This article was written in part to celebrate the anniversaries of landmark mathematical works by Newton and Descartes. It's other purpose is to dispel some myths about Sir Isaac Newton and to encourage readers to read Newton's works. (PK)
Telecommunications Handbook: Connecting to Newton.
ERIC Educational Resources Information Center
Baker, Christopher; And Others
This handbook was written by the Argonne National Laboratory for use with their electronic bulletin board system (BBS) called Newton. Newton is an educational BBS for use by teachers, students, and parents. Topics range from discussions of science fair topics to online question and answer sessions with scientists. Future capabilities will include…
Edme Mariotte and Newton's Cradle
ERIC Educational Resources Information Center
Cross, Rod
2012-01-01
The first recorded experiments describing the phenomena made popular by Newton's cradle appear to be those conducted by Edme Mariotte around 1670. He was quoted in Newton's "Principia," along with Wren, Wallis, and Huygens, as having conducted pioneering experiments on the collisions of pendulum balls. Each of these authors concluded that momentum…
MODFLOW-NWT, A Newton formulation for MODFLOW-2005
Niswonger, Richard G.; Panday, Sorab; Ibaraki, Motomu
2011-01-01
This report documents a Newton formulation of MODFLOW-2005, called MODFLOW-NWT. MODFLOW-NWT is a standalone program that is intended for solving problems involving drying and rewetting nonlinearities of the unconfined groundwater-flow equation. MODFLOW-NWT must be used with the Upstream-Weighting (UPW) Package for calculating intercell conductances in a different manner than is done in the Block-Centered Flow (BCF), Layer Property Flow (LPF), or Hydrogeologic-Unit Flow (HUF; Anderman and Hill, 2000) Packages. The UPW Package treats nonlinearities of cell drying and rewetting by use of a continuous function of groundwater head, rather than the discrete approach of drying and rewetting that is used by the BCF, LPF, and HUF Packages. This further enables application of the Newton formulation for unconfined groundwater-flow problems because conductance derivatives required by the Newton method are smooth over the full range of head for a model cell. The NWT linearization approach generates an asymmetric matrix, which is different from the standard MODFLOW formulation that generates a symmetric matrix. Because all linear solvers presently available for use with MODFLOW-2005 solve only symmetric matrices, MODFLOW-NWT includes two previously developed asymmetric matrix-solver options. The matrix-solver options include a generalized-minimum-residual (GMRES) Solver and an Orthomin / stabilized conjugate-gradient (CGSTAB) Solver. The GMRES Solver is documented in a previously published report, such that only a brief description and input instructions are provided in this report. However, the CGSTAB Solver (called XMD) is documented in this report. Flow-property input for the UPW Package is designed based on the LPF Package and material-property input is identical to that for the LPF Package except that the rewetting and vertical-conductance correction options of the LPF Package are not available with the UPW Package. Input files constructed for the LPF Package can be used
Fourth-order solutions of nonlinear two-point boundary value problems by Newton-HSSOR iteration
NASA Astrophysics Data System (ADS)
Sulaiman, Jumat; Hasan, Mohd. Khatim; Othman, Mohamed; Karim, Samsul Ariffin Abdul
2014-06-01
In this paper, the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method together with Newton scheme namely Newton-HSSOR is investigated in solving the nonlinear systems generated from the fourth-order half-sweep finite difference approximation equation for nonlinear two-point boundary value problems. The Newton scheme is proposed to linearize the nonlinear system into the form of linear system. On top of that, we also present the basic formulation and implementation of Newton-HSSOR iterative method. For comparison purpose, combinations between the Full-Sweep Gauss-Seidel (FSGS) and Full-Sweep Successive Over-Relaxation (FSSOR) iterative methods with Newton scheme, which are indicated as Newton-FSGS and Newton-FSSOR methods respectively have been implemented numerically. Numerical experiments of two problems are given to illustrate that the Newton-HSSOR method is more superior compared with the tested methods.
Computing modified Newton directions using a partial Cholesky factorization
Forsgren, A.; Gill, P.E.; Murray, W.
1993-03-01
The effectiveness of Newton`s method for finding an unconstrained minimizer of a strictly convex twice continuously differentiable function has prompted the proposal of various modified Newton inetliods for the nonconvex case. Linesearch modified Newton methods utilize a linear combination of a descent direction and a direction of negative curvature. If these directions are sufficient in a certain sense, and a suitable linesearch is used, the resulting method will generate limit points that satisfy the second-order necessary conditions for optimality. We propose an efficient method for computing a descent direction and a direction of negative curvature that is based on a partial Cholesky factorization of the Hessian. This factorization not only gives theoretically satisfactory directions, but also requires only a partial pivoting strategy, i.e., the equivalent of only two rows of the Schur complement need be examined at each step.
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.
2014-02-15
Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to various forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.
A limited-memory, quasi-Newton preconditioner for nonnegatively constrained image reconstruction.
Bardsley, Johnathan M
2004-05-01
Image reconstruction gives rise to some challenging large-scale constrained optimization problems. We consider a convex minimization problem with nonnegativity constraints that arises in astronomical imaging. To solve this problem, we use an efficient hybrid gradient projection-reduced Newton (active-set) method. By "reduced Newton," we mean that we take Newton steps only in the inactive variables. Owing to the large size of our problem, we compute approximate reduced Newton steps by using the conjugate gradient (CG) iteration. We introduce a limited-memory, quasi-Newton preconditioner that speeds up CG convergence. A numerical comparison is presented that demonstrates the effectiveness of this preconditioner. PMID:15139424
ERIC Educational Resources Information Center
Price, Beverley; Pincott, Maxine; Rebman, Ashley; Northcutt, Jen; Barsanti, Amy; Silkunas, Betty; Brighton, Susan K.; Reitz, David; Winkler, Maureen
1999-01-01
Presents discipline tips from several teachers to keep classrooms running smoothly all year. Some of the suggestions include the following: a bear-cave warning system, peer mediation, a motivational mystery, problem students acting as the teacher's assistant, a positive-behavior-reward chain, a hallway scavenger hunt (to ensure quiet passage…
Well-tempered metadynamics: a smoothly converging and tunable free-energy method.
Barducci, Alessandro; Bussi, Giovanni; Parrinello, Michele
2008-01-18
We present a method for determining the free-energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Convergence and errors can be rigorously and easily controlled. The parameters of the simulation can be tuned so as to focus the computational effort only on the physically relevant regions of the order parameter space. The algorithm is tested on the reconstruction of an alanine dipeptide free-energy landscape. PMID:18232845
Adaptive particle refinement and derefinement applied to the smoothed particle hydrodynamics method
NASA Astrophysics Data System (ADS)
Barcarolo, D. A.; Le Touzé, D.; Oger, G.; de Vuyst, F.
2014-09-01
SPH simulations are usually performed with a uniform particle distribution. New techniques have been recently proposed to enable the use of spatially varying particle distributions, which encouraged the development of automatic adaptivity and particle refinement/derefinement algorithms. All these efforts resulted in very interesting and promising procedures leading to more efficient and faster SPH simulations. In this article, a family of particle refinement techniques is reviewed and a new derefinement technique is proposed and validated through several test cases involving both free-surface and viscous flows. Besides, this new procedure allows higher resolutions in the regions requiring increased accuracy. Moreover, several levels of refinement can be used with this new technique, as often encountered in adaptive mesh refinement techniques in mesh-based methods.
A method of smooth bivariate interpolation for data given on a generalized curvilinear grid
NASA Technical Reports Server (NTRS)
Zingg, David W.; Yarrow, Maurice
1992-01-01
A method of locally bicubic interpolation is presented for data given at the nodes of a two-dimensional generalized curvilinear grid. The physical domain is transformed to a computational domain in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. The metrics of the transformation are obtained by finite differences in the computational domain. Metric derivatives are determined by repeated application of the chain rule for partial differentiation. Given the metrics and the metric derivatives, the partial derivatives required to determine a locally bicubic interpolant can be estimated at each data point using finite differences in the computational domain. A bilinear transformation is used to analytically transform the individual quadrilateral cells in the physical domain into unit squares, thus allowing the use of simple formulas for bicubic interpolation.
Modern methods for calculating ground-wave field strength over a smooth spherical Earth
NASA Astrophysics Data System (ADS)
Eckert, R. P.
1986-02-01
The report makes available the computer program that produces the proposed new FCC ground-wave propagation prediction curves for the new band of standard broadcast frequencies between 1605 and 1705 kHz. The curves are included in recommendations to the U.S. Department of State in preparation for an International Telecommunication Union Radio Conference. The history of the FCC curves is traced from the early 1930's, when the Federal Radio Commission and later the FFC faced an intensifying need for technical information concerning interference distances. A family of curves satisfactorily meeting this need was published in 1940. The FCC reexamined the matter recently in connection with the planned expansion of the AM broadcast band, and the resulting new curves are a precise representation of the mathematical theory. Mathematical background is furnished so that the computer program can be critically evaluated. This will be particularly valuable to persons implementing the program on other computers or adapting it for special applications. Technical references are identified for each of the formulas used by the program, and the history of the development of mathematical methods is outlined.
PEOPLE IN PHYSICS: Newton's apple
NASA Astrophysics Data System (ADS)
Sandford Smith, Daniel
1997-03-01
This essay has a long history. It was triggered at university by one of my tutors describing the dispute between Robert Hooke and Isaac Newton. He conjured up an image of Newton sitting at his desk doing calculations while Hooke went down mineshafts trying to detect a change in the strength of gravity. To someone who was finding the maths content of a physics degree somewhat challenging this was a symbolic image. I believe that the story of Newton and the apple illustrates the complex nature of scientific discovery.
NASA Astrophysics Data System (ADS)
Belenkiy, Ari
2007-08-01
Among the Newtonian manuscripts, owned by the Jewish National and University Library at Jerusalem and known as MS Yahuda 24, there is a proposal for the reform of the Julian and Ecclesiastical calendars, written in three drafts in early 1700. This was Newton's response to the challenge suggested by Continental mathematicians and astronomers, G.W. Leibniz in particular. This calendar, if implemented in England, would have become a formidable rival to the Gregorian calendar. Despite having a different algorithm, its solar part agrees with the latter until 2400 AD and is more precise in the long run, within a period of 5,000 years. Its lunar algorithm is simpler than the Gregorian, but remained incomplete. Though the calendar was buried under a pile of theological papers, were it now to be implemented it would have a glorious future, since it includes the most characteristic features of the Christian, Jewish, and Muslim calendars and can aspire to become the universal calendar. Looking for the best astronomical parameters Newton attempted to compute the length of the tropical year using the ancient equinox observations reported by Hipparchus of Rhodes. Though Newton had a very thin sample of data, he obtained a tropical year only a few seconds longer than the correct length. We show that the reason lies in Newton's application of a technique similar (though not identical) to the modern ordinary least squares method. Newton also had a clear understanding of qualitative variables. Open historic-astronomical problems related to inclination of the Earth's axis of rotation are discussed. In particular, ignorance about the long-range variation in inclination and nutation is likely responsible for the wide variety in the lengths of the tropical year assigned by different 17th century astronomers - the problem that led Newton to Hipparchus.
Newton and the Second Law of Motion
ERIC Educational Resources Information Center
Gauld, C. F.
1975-01-01
Deals generally with historical errors in science teaching and specifically with Newton's conception of his second law of motion. With reference to Newton's "Principia", the author concludes that Newton would not understand what we today refer to as "Newton's Second Law." (MLH)
Li, Bin; Sang, Jizhang; Zhang, Zhongping
2016-01-01
A critical requirement to achieve high efficiency of debris laser tracking is to have sufficiently accurate orbit predictions (OP) in both the pointing direction (better than 20 arc seconds) and distance from the tracking station to the debris objects, with the former more important than the latter because of the narrow laser beam. When the two line element (TLE) is used to provide the orbit predictions, the resultant pointing errors are usually on the order of tens to hundreds of arc seconds. In practice, therefore, angular observations of debris objects are first collected using an optical tracking sensor, and then used to guide the laser beam pointing to the objects. The manual guidance may cause interrupts to the laser tracking, and consequently loss of valuable laser tracking data. This paper presents a real-time orbit determination (OD) and prediction method to realize smooth and efficient debris laser tracking. The method uses TLE-computed positions and angles over a short-arc of less than 2 min as observations in an OD process where simplified force models are considered. After the OD convergence, the OP is performed from the last observation epoch to the end of the tracking pass. Simulation and real tracking data processing results show that the pointing prediction errors are usually less than 10″, and the distance errors less than 100 m, therefore, the prediction accuracy is sufficient for the blind laser tracking. PMID:27347958
NASA Astrophysics Data System (ADS)
Suwa, T.; Imamura, F.; Sugawara, D.; Ogasawara, K.; Watanabe, M.; Hirahara, T.
2014-12-01
A tsunami simulator integrating a 3-D fluid simulation technology that runs on large-scale parallel computers using smoothed-particle hydrodynamics (SPH) method has been developed together with a 2-D tsunami propagation simulation technique using a nonlinear shallow water wave model. We use the 2-D simulation to calculate tsunami propagation of scale of about 1000km from epicenter to near shore. The 3-D SPH method can be used to calculate the water surface and hydraulic force that a tsunami can exert on a building, and to simulate flooding patterns at urban area of at most km scale. With our simulator we can also see three dimensional fluid feature such as complex changes a tsunami undergoes as it interacts with coastal topography or structures. As a result it is hoped that, e.g. , effect of the structures to dissipate waves energy passing over it can be elucidated. The authors utilize the simulator in the third of five fields of the Strategic Programs for Innovative Research, "Advanced Prediction Researches for Natural Disaster Prevention and Reduction," or the theme "Improvement of the tsunami forecasting system on the HPCI computer." The results of tsunami simulation using the K computer will be reported. We are going to apply it to a real problem of the disaster prevention in future.
Li, Bin; Sang, Jizhang; Zhang, Zhongping
2016-01-01
A critical requirement to achieve high efficiency of debris laser tracking is to have sufficiently accurate orbit predictions (OP) in both the pointing direction (better than 20 arc seconds) and distance from the tracking station to the debris objects, with the former more important than the latter because of the narrow laser beam. When the two line element (TLE) is used to provide the orbit predictions, the resultant pointing errors are usually on the order of tens to hundreds of arc seconds. In practice, therefore, angular observations of debris objects are first collected using an optical tracking sensor, and then used to guide the laser beam pointing to the objects. The manual guidance may cause interrupts to the laser tracking, and consequently loss of valuable laser tracking data. This paper presents a real-time orbit determination (OD) and prediction method to realize smooth and efficient debris laser tracking. The method uses TLE-computed positions and angles over a short-arc of less than 2 min as observations in an OD process where simplified force models are considered. After the OD convergence, the OP is performed from the last observation epoch to the end of the tracking pass. Simulation and real tracking data processing results show that the pointing prediction errors are usually less than 10″, and the distance errors less than 100 m, therefore, the prediction accuracy is sufficient for the blind laser tracking. PMID:27347958
[Malthus's Essay and Newton's Principia].
Nakanishi, Y
1989-05-01
The author examines a natural scientific approach to demography using the example of Malthus's "Essay on the Principle of Population." The work is analyzed and compared to Newton's "Philosophiae Naturalis Principia Mathematica." PMID:12342767
XMM-Newton publication statistics
NASA Astrophysics Data System (ADS)
Ness, J.-U.; Parmar, A. N.; Valencic, L. A.; Smith, R.; Loiseau, N.; Salama, A.; Ehle, M.; Schartel, N.
2014-02-01
We assessed the scientific productivity of XMM-Newton by examining XMM-Newton publications and data usage statistics. We analyse 3272 refereed papers, published until the end of 2012, that directly use XMM-Newton data. The SAO/NASA Astrophysics Data System (ADS) was used to provide additional information on each paper including the number of citations. For each paper, the XMM-Newton observation identifiers and instruments used to provide the scientific results were determined. The identifiers were used to access the XMM-{Newton} Science Archive (XSA) to provide detailed information on the observations themselves and on the original proposals. The information obtained from these sources was then combined to allow the scientific productivity of the mission to be assessed. Since around three years after the launch of XMM-Newton there have been around 300 refereed papers per year that directly use XMM-Newton data. After more than 13 years in operation, this rate shows no evidence that it is decreasing. Since 2002, around 100 scientists per year become lead authors for the first time on a refereed paper which directly uses XMM-Newton data. Each refereed XMM-Newton paper receives around four citations per year in the first few years with a long-term citation rate of three citations per year, more than five years after publication. About half of the articles citing XMM-Newton articles are not primarily X-ray observational papers. The distribution of elapsed time between observations taken under the Guest Observer programme and first article peaks at 2 years with a possible second peak at 3.25 years. Observations taken under the Target of Opportunity programme are published significantly faster, after one year on average. The fraction of science time taken until the end of 2009 that has been used in at least one article is {˜ 90} %. Most observations were used more than once, yielding on average a factor of two in usage on available observing time per year. About 20 % of
Space and motion in nature and Scripture: Galileo, Descartes, Newton.
Janiak, Andrew
2015-06-01
In the Scholium to the Definitions in Principia mathematica, Newton departs from his main task of discussing space, time and motion by suddenly mentioning the proper method for interpreting Scripture. This is surprising, and it has long been ignored by scholars. In this paper, I argue that the Scripture passage in the Scholium is actually far from incidental: it reflects Newton's substantive concern, one evident in correspondence and manuscripts from the 1680s, that any general understanding of space, time and motion must enable readers to recognize the veracity of Biblical claims about natural phenomena, including the motion of the earth. This substantive concern sheds new light on an aspect of Newton's project in the Scholium. It also underscores Newton's originality in dealing with the famous problem of reconciling theological and philosophical conceptions of nature in the seventeenth century. PMID:26227236
Spronck, Bart; Megens, Remco T A; Reesink, Koen D; Delhaas, Tammo
2016-04-01
When studying in vivo arterial mechanical behaviour using constitutive models, smooth muscle cells (SMCs) should be considered, while they play an important role in regulating arterial vessel tone. Current constitutive models assume a strictly circumferential SMC orientation, without any dispersion. We hypothesised that SMC orientation would show considerable dispersion in three dimensions and that helical dispersion would be greater than transversal dispersion. To test these hypotheses, we developed a method to quantify the 3D orientation of arterial SMCs. Fluorescently labelled SMC nuclei of left and right carotid arteries of ten mice were imaged using two-photon laser scanning microscopy. Arteries were imaged at a range of luminal pressures. 3D image processing was used to identify individual nuclei and their orientations. SMCs showed to be arranged in two distinct layers. Orientations were quantified by fitting a Bingham distribution to the observed orientations. As hypothesised, orientation dispersion was much larger helically than transversally. With increasing luminal pressure, transversal dispersion decreased significantly, whereas helical dispersion remained unaltered. Additionally, SMC orientations showed a statistically significant ([Formula: see text]) mean right-handed helix angle in both left and right arteries and in both layers, which is a relevant finding from a developmental biology perspective. In conclusion, vascular SMC orientation (1) can be quantified in 3D; (2) shows considerable dispersion, predominantly in the helical direction; and (3) has a distinct right-handed helical component in both left and right carotid arteries. The obtained quantitative distribution data are instrumental for constitutive modelling of the artery wall and illustrate the merit of our method. PMID:26174758
Smooth Programs and Languages.
ERIC Educational Resources Information Center
Foulk, Clinton R.; Juelich, Otto C.
A smooth program is defined to be one which is "go to"-free in the sense that it can be represented by a flowchart consisting only of concatenation, alternation, and interation elements. Three methods of eliminating the "go to" statement from a program have been proposed: (1) the introduction of additional Boolean variables or the equivalent…
NASA Astrophysics Data System (ADS)
Ginzburg, Vitalii L.
1987-01-01
The first edition of Newton's "Philosophiae Naturalis Principia Mathematica" was published in 1687. The present paper is dedicated to the tricentenary of this event, which is important not just in the history of physics, but of science generally. After the Introduction, the paper continues with the following Sections: Before Newton, Principia, Principia and the method of principles, The nature of gravitation, Critique of Newtonian mechanics and its subsequent development, On Newton, Concluding remarks.
Computing modified Newton directions using a partial Cholesky factorization
Forsgren, A. . Dept. of Mathematics); Gill, P.E. ); Murray, W. . Systems Optimization Lab.)
1993-03-01
The effectiveness of Newton's method for finding an unconstrained minimizer of a strictly convex twice continuously differentiable function has prompted the proposal of various modified Newton inetliods for the nonconvex case. Linesearch modified Newton methods utilize a linear combination of a descent direction and a direction of negative curvature. If these directions are sufficient in a certain sense, and a suitable linesearch is used, the resulting method will generate limit points that satisfy the second-order necessary conditions for optimality. We propose an efficient method for computing a descent direction and a direction of negative curvature that is based on a partial Cholesky factorization of the Hessian. This factorization not only gives theoretically satisfactory directions, but also requires only a partial pivoting strategy, i.e., the equivalent of only two rows of the Schur complement need be examined at each step.
Sebastian Schunert; Yousry Y. Azmy
2011-05-01
The quantification of the discretization error associated with the spatial discretization of the Discrete Ordinate(DO) equations in multidimensional Cartesian geometries is the central problem in error estimation of spatial discretization schemes for transport theory as well as computer code verification. Traditionally fine mesh solutions are employed as reference, because analytical solutions only exist in the absence of scattering. This approach, however, is inadequate when the discretization error associated with the reference solution is not small compared to the discretization error associated with the mesh under scrutiny. Typically this situation occurs if the mesh of interest is only a couple of refinement levels away from the reference solution or if the order of accuracy of the numerical method (and hence the reference as well) is lower than expected. In this work we present a Method of Manufactured Solutions (MMS) benchmark suite with variable order of smoothness of the underlying exact solution for two-dimensional Cartesian geometries which provides analytical solutions aver- aged over arbitrary orthogonal meshes for scattering and non-scattering media. It should be emphasized that the developed MMS benchmark suite first eliminates the aforementioned limitation of fine mesh reference solutions since it secures knowledge of the underlying true solution and second that it allows for an arbitrary order of smoothness of the underlying ex- act solution. The latter is of importance because even for smooth parameters and boundary conditions the DO equations can feature exact solution with limited smoothness. Moreover, the degree of smoothness is crucial for both the order of accuracy and the magnitude of the discretization error for any spatial discretization scheme.