Assessment of numerical techniques for unsteady flow calculations

NASA Technical Reports Server (NTRS)

Hsieh, Kwang-Chung

1989-01-01

The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.

A numerically efficient finite element hydroelastic analysis. Volume 2: Implementation in NASTRAN, part 1

NASA Technical Reports Server (NTRS)

Coppolino, R. N.

1974-01-01

Details are presented of the implementation of the new formulation into NASTRAN including descriptions of the DMAP statements required for conversion of the program and details pertaining to problem definition and bulk data considerations. Details of the current 1/8-scale space shuttle external tank mathematical model, numerical results and analysis/test comparisons are also presented. The appendices include a description and listing of a FORTRAN program used to develop harmonic transformation bulk data (multipoint constraint statements) and sample bulk data information for a number of hydroelastic problems.

TOUGH Simulations of the Updegraff's Set of Fluid and Heat Flow Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moridis, G.J.; Pruess

1992-11-01

The TOUGH code [Pruess, 1987] for two-phase flow of water, air, and heat in penneable media has been exercised on a suite of test problems originally selected and simulated by C. D. Updegraff [1989]. These include five 'verification' problems for which analytical or numerical solutions are available, and three 'validation' problems that model laboratory fluid and heat flow experiments. All problems could be run without any code modifications (*). Good and efficient numerical performance, as well as accurate results were obtained throughout. Additional code verification and validation problems from the literature are briefly summarized, and suggestions are given for propermore » applications of TOUGH and related codes.« less

Computation of Pressurized Gas Bearings Using CE/SE Method

NASA Technical Reports Server (NTRS)

Cioc, Sorin; Dimofte, Florin; Keith, Theo G., Jr.; Fleming, David P.

2003-01-01

The space-time conservation element and solution element (CE/SE) method is extended to compute compressible viscous flows in pressurized thin fluid films. This numerical scheme has previously been used successfully to solve a wide variety of compressible flow problems, including flows with large and small discontinuities. In this paper, the method is applied to calculate the pressure distribution in a hybrid gas journal bearing. The formulation of the problem is presented, including the modeling of the feeding system. the numerical results obtained are compared with experimental data. Good agreement between the computed results and the test data were obtained, and thus validate the CE/SE method to solve such problems.

Human-computer interfaces applied to numerical solution of the Plateau problem

NASA Astrophysics Data System (ADS)

Elias Fabris, Antonio; Soares Bandeira, Ivana; Ramos Batista, Valério

2015-09-01

In this work we present a code in Matlab to solve the Problem of Plateau numerically, and the code will include human-computer interface. The Problem of Plateau has applications in areas of knowledge like, for instance, Computer Graphics. The solution method will be the same one of the Surface Evolver, but the difference will be a complete graphical interface with the user. This will enable us to implement other kinds of interface like ocular mouse, voice, touch, etc. To date, Evolver does not include any graphical interface, which restricts its use by the scientific community. Specially, its use is practically impossible for most of the Physically Challenged People.

SciCADE 95: International conference on scientific computation and differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1995-12-31

This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included.

The Social Problem-Solving Questionnaire: Evaluation of Psychometric Properties among Turkish Primary School Students

ERIC Educational Resources Information Center

Dereli Iman, Esra

2013-01-01

Problem Statement: Children, like adults, face numerous problems and conflicts in their everyday lives, including issues with peers, siblings, older children, parents, teachers, and other adults. The methods children use to solve such problems are more important than actually facing the problems. The lack of effective social problem-solving skills…

Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems

NASA Astrophysics Data System (ADS)

Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.

2015-10-01

In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of variables applied to the Helmholtz, Laplace, or Schrödinger equation leads to a multiparameter eigenvalue problem (MEP); important cases include Mathieu's system, Lamé's system, and a system of spheroidal wave functions. Although multiparameter approaches are exploited occasionally to solve such equations numerically, MEPs remain less well known, and the variety of available numerical methods is not wide. The classical approach of discretizing the equations using standard finite differences leads to algebraic MEPs with large matrices, which are difficult to solve efficiently. The aim of this paper is to change this perspective. We show that by combining spectral collocation methods and new efficient numerical methods for algebraic MEPs it is possible to solve such problems both very efficiently and accurately. We improve on several previous results available in the literature, and also present a MATLAB toolbox for solving a wide range of problems.

A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation

NASA Astrophysics Data System (ADS)

Mamehrashi, K.; Yousefi, S. A.

2017-02-01

This paper presents a numerical solution for solving a nonlinear 2-D optimal control problem (2DOP). The performance index of a nonlinear 2DOP is described with a state and a control function. Furthermore, dynamic constraint of the system is given by a classical diffusion equation. It is preferred to use the Ritz method for finding the numerical solution of the problem. The method is based upon the Legendre polynomial basis. By using this method, the given optimisation nonlinear 2DOP reduces to the problem of solving a system of algebraic equations. The benefit of the method is that it provides greater flexibility in which the given initial and boundary conditions of the problem are imposed. Moreover, compared with the eigenfunction method, the satisfactory results are obtained only in a small number of polynomials order. This numerical approach is applicable and effective for such a kind of nonlinear 2DOP. The convergence of the method is extensively discussed and finally two illustrative examples are included to observe the validity and applicability of the new technique developed in the current work.

Simulation of a class of hazardous situations in the ICS «INM RAS - Baltic Sea»

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Agoshkov, Valery; Aseev, Nikita; Parmuzin, Eugene; Sheloput, Tateana; Shutyaev, Victor

2017-04-01

Development of Informational Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in mathematical modeling, theory of adjoint equations and optimal control, inverse problems, numerical methods theory, numerical algebra, scientific computing and processing of satellite data. In this work the results on the ICS development for PC-ICS "INM RAS - Baltic Sea" are presented. We discuss practical problems studied by ICS. The System includes numerical model of the Baltic Sea thermodynamics, the new oil spill model describing the propagation of a slick at the Sea surface (Agoshkov, Aseev et al., 2014) and the optimal ship route calculating block (Agoshkov, Zayachkovsky et al., 2014). The ICS is based on the INMOM numerical model of the Baltic Sea thermodynamics (Zalesny et al., 2013). It is possible to calculate main hydrodynamic parameters (temperature, salinity, velocities, sea level) using user-friendly interface of the ICS. The System includes data assimilation procedures (Agoshkov, 2003, Parmuzin, Agoshkov, 2012) and one can use the block of variational assimilation of the sea surface temperature in order to obtain main hydrodynamic parameters. Main possibilities of the ICS and several numerical experiments are presented in the work. By the problem of risk control is meant a problem of determination of optimal resources quantity which are necessary for decreasing the risk to some acceptable value. Mass of oil slick is chosen as a function of control. For the realization of the random variable the quadratic "functional of cost" is introduced. It comprises cleaning costs and deviation of damage of oil pollution from its acceptable value. The problem of minimization of this functional is solved based on the methods of optimal control and the theory of adjoint equations. The solution of this problem is explicitly found. The study was supported by the Russian Foundation for Basic Research (project 16-31-00510) and by the Russian Science Foundation (project №14-11-00609). V. I. Agoshkov, Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). V. B. Zalesny, A. V. Gusev, V. O. Ivchenko, R. Tamsalu, and R. Aps, Numerical model of the Baltic Sea circulation. Russ. J. Numer. Anal. Math. Modelling 28 (2013), No. 1, 85-100. V.I. Agoshkov, A.O. Zayachkovskiy, R. Aps, P. Kujala, and J. Rytkönen. Risk theory based solution to the problem of optimal vessel route // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 69-78. Agoshkov, V., Aseev, N., Aps, R., Kujala, P., Rytkönen, J., Zalesny, V. The problem of control of oil pollution risk in the Baltic Sea // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 93-105. E. I. Parmuzin and V. I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling 27 (2012), No. 1, 69-94. Olof Liungman and Johan Mattsson. Scientic Documentation of Seatrack Web; physical processes, algorithms and references, 2011.

A Numerical Investigation of the Burnett Equations Based on the Second Law

NASA Technical Reports Server (NTRS)

Comeaux, Keith A.; Chapman, Dean R.; MacCormack, Robert W.; Edwards, Thomas A. (Technical Monitor)

1995-01-01

The Burnett equations have been shown to potentially violate the second law of thermodynamics. The objective of this investigation is to correlate the numerical problems experienced by the Burnett equations to the negative production of entropy. The equations have had a long history of numerical instability to small wavelength disturbances. Recently, Zhong corrected the instability problem and made solutions attainable for one dimensional shock waves and hypersonic blunt bodies. Difficulties still exist when attempting to solve hypersonic flat plate boundary layers and blunt body wake flows, however. Numerical experiments will include one-dimensional shock waves, quasi-one dimensional nozzles, and expanding Prandlt-Meyer flows and specifically examine the entropy production for these cases.

Numerical stability in problems of linear algebra.

NASA Technical Reports Server (NTRS)

Babuska, I.

1972-01-01

Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2002-01-01

This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations. Chapter 2

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2001-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Sandia National Laboratories analysis code data base

NASA Astrophysics Data System (ADS)

Peterson, C. W.

1994-11-01

Sandia National Laboratories' mission is to solve important problems in the areas of national defense, energy security, environmental integrity, and industrial technology. The laboratories' strategy for accomplishing this mission is to conduct research to provide an understanding of the important physical phenomena underlying any problem, and then to construct validated computational models of the phenomena which can be used as tools to solve the problem. In the course of implementing this strategy, Sandia's technical staff has produced a wide variety of numerical problem-solving tools which they use regularly in the design, analysis, performance prediction, and optimization of Sandia components, systems, and manufacturing processes. This report provides the relevant technical and accessibility data on the numerical codes used at Sandia, including information on the technical competency or capability area that each code addresses, code 'ownership' and release status, and references describing the physical models and numerical implementation.

Research in nonlinear structural and solid mechanics

NASA Technical Reports Server (NTRS)

Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)

1980-01-01

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

Three Years of Global Positioning System Experience on International Space Station

NASA Technical Reports Server (NTRS)

Gomez, Susan

2006-01-01

The International Space Station global positioning system (GPS) receiver was activated in April 2002. Since that time, numerous software anomalies surfaced that had to be worked around. Some of the software problems required waivers, such as the time function, while others required extensive operator intervention, such as numerous power cycles. Eventually enough anomalies surfaced that the three pieces of code included in the GPS unit have been re-written and the GPS units upgraded. The technical aspects of the problems are discussed, as well as the underlying causes that led to the delivery of a product that has had so many problems. The technical aspects of the problems included physical phenomena that were not well understood, such as the affect that the ionosphere would have on the GPS measurements. The underlying causes were traced to inappropriate use of legacy software, changing requirements, inadequate software processes, unrealistic schedules, incorrect contract type, and unclear ownership responsibilities..

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Numerical Inverse Scattering for the Toda Lattice

NASA Astrophysics Data System (ADS)

Bilman, Deniz; Trogdon, Thomas

2017-06-01

We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann-Hilbert (RH) problem numerically. Deformations for the RH problem are incorporated so that the IST can be evaluated in O(1) operations for arbitrary points in the ( n, t)-domain, including short- and long-time regimes. No time-stepping is required to compute the solution because ( n, t) appear as parameters in the associated RH problem. The solution of the Toda lattice is computed in long-time asymptotic regions where the asymptotics are not known rigorously.

International Symposium on Numerical Methods in Engineering, 5th, Ecole Polytechnique Federale de Lausanne, Switzerland, Sept. 11-15, 1989, Proceedings. Volumes 1 & 2

NASA Astrophysics Data System (ADS)

Gruber, Ralph; Periaux, Jaques; Shaw, Richard Paul

Recent advances in computational mechanics are discussed in reviews and reports. Topics addressed include spectral superpositions on finite elements for shear banding problems, strain-based finite plasticity, numerical simulation of hypersonic viscous continuum flow, constitutive laws in solid mechanics, dynamics problems, fracture mechanics and damage tolerance, composite plates and shells, contact and friction, metal forming and solidification, coupling problems, and adaptive FEMs. Consideration is given to chemical flows, convection problems, free boundaries and artificial boundary conditions, domain-decomposition and multigrid methods, combustion and thermal analysis, wave propagation, mixed and hybrid FEMs, integral-equation methods, optimization, software engineering, and vector and parallel computing.

Figurate Numbers in the Classroom.

ERIC Educational Resources Information Center

Norman, F. Alexander

1991-01-01

A series of activities involving figurate numbers that allow students at various levels to integrate numerical, geometric, arithmetic, patterning, measuring, and problem-solving skills are presented. A discussion of the geometric and numerical aspects of figurate numbers is included. Appended are IBM Logo procedures that will create pentagonal…

Hay preservation with propionic acid

USDA-ARS?s Scientific Manuscript database

Most hay producers are quite familiar with the problems associated with baling moist hays. Normally, these problems include spontaneous heating, increased evidence of mold, losses of dry matter (DM) during storage, poorer nutritive value, and (in extreme cases) spontaneous combustion. Numerous fact...

Cumulative reports and publications through December 31, 1989

NASA Technical Reports Server (NTRS)

1990-01-01

A complete list of reports from the Institute for Computer Applications in Science and Engineering (ICASE) is presented. The major categories of the current ICASE research program are: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effectual numerical methods; computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, structural analysis, and chemistry; computer systems and software, especially vector and parallel computers, microcomputers, and data management. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available.

Energy analysis in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-07-01

The gravity assist or flyby is investigated by analysing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. First, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighbourhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the Solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

Energy Analysis in the Elliptic Restricted Three-body Problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-05-01

The gravity assist or flyby is investigated by analyzing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. Firstly, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighborhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

Preservation of hay with propionic acid

USDA-ARS?s Scientific Manuscript database

Most hay producers are quite familiar with the problems associated with baling moist hays. Normally, these problems include spontaneous heating, increased evidence of mold, losses of dry matter (DM) during storage, poorer nutritive value, and (in extreme cases) spontaneous combustion. Numerous fact...

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent advances in the analytical and numerical treatment of physical and engineering problems are discussed in reviews and reports. Topics addressed include fluid mechanics, numerical methods for differential equations, FEM approaches, and boundary-element methods. Consideration is given to optimization, decision theory, stochastics, actuarial mathematics, applied mathematics and mathematical physics, and numerical analysis.

Methods for compressible multiphase flows and their applications

NASA Astrophysics Data System (ADS)

Kim, H.; Choe, Y.; Kim, H.; Min, D.; Kim, C.

2018-06-01

This paper presents an efficient and robust numerical framework to deal with multiphase real-fluid flows and their broad spectrum of engineering applications. A homogeneous mixture model incorporated with a real-fluid equation of state and a phase change model is considered to calculate complex multiphase problems. As robust and accurate numerical methods to handle multiphase shocks and phase interfaces over a wide range of flow speeds, the AUSMPW+_N and RoeM_N schemes with a system preconditioning method are presented. These methods are assessed by extensive validation problems with various types of equation of state and phase change models. Representative realistic multiphase phenomena, including the flow inside a thermal vapor compressor, pressurization in a cryogenic tank, and unsteady cavitating flow around a wedge, are then investigated as application problems. With appropriate physical modeling followed by robust and accurate numerical treatments, compressible multiphase flow physics such as phase changes, shock discontinuities, and their interactions are well captured, confirming the suitability of the proposed numerical framework to wide engineering applications.

A Numerical-Analytical Approach Based on Canonical Transformations for Computing Optimal Low-Thrust Transfers

NASA Astrophysics Data System (ADS)

da Silva Fernandes, S.; das Chagas Carvalho, F.; Bateli Romão, J. V.

2018-04-01

A numerical-analytical procedure based on infinitesimal canonical transformations is developed for computing optimal time-fixed low-thrust limited power transfers (no rendezvous) between coplanar orbits with small eccentricities in an inverse-square force field. The optimization problem is formulated as a Mayer problem with a set of non-singular orbital elements as state variables. Second order terms in eccentricity are considered in the development of the maximum Hamiltonian describing the optimal trajectories. The two-point boundary value problem of going from an initial orbit to a final orbit is solved by means of a two-stage Newton-Raphson algorithm which uses an infinitesimal canonical transformation. Numerical results are presented for some transfers between circular orbits with moderate radius ratio, including a preliminary analysis of Earth-Mars and Earth-Venus missions.

Using Written-Answer Questions To Complement Numerical Problems. Case Study: A Separation Processes Course.

ERIC Educational Resources Information Center

Iveson, Simon M.

2002-01-01

Describes the process and outcome of including in assignments and examinations some questions requiring written answers along with traditional questions requiring only numerical calculations. Lists questions used in a chemical engineering course on separation processes along with sample responses from students. Student feedback indicates a…

How to handle stuck pipe and fishing problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brouse, M.

1983-01-01

This paper presents valuable information on evaluating fishing problems, including a rule of thumb equation for estimating the number of days that should be spent fishing. Also given is a description and usage breakdown of the numerous tools available to the operator.

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjogreen, B.; Sandham, N. D.; Hadjadj, A.; Kwak, Dochan (Technical Monitor)

2000-01-01

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Probabilistic numerics and uncertainty in computations

PubMed Central

Hennig, Philipp; Osborne, Michael A.; Girolami, Mark

2015-01-01

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations. PMID:26346321

Probabilistic numerics and uncertainty in computations.

PubMed

Hennig, Philipp; Osborne, Michael A; Girolami, Mark

2015-07-08

We deliver a call to arms for probabilistic numerical methods : algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

Constant-concentration boundary condition: Lessons from the HYDROCOIN variable-density groundwater benchmark problem

USGS Publications Warehouse

Konikow, Leonard F.; Sanford, W.E.; Campbell, P.J.

1997-01-01

In a solute-transport model, if a constant-concentration boundary condition is applied at a node in an active flow field, a solute flux can occur by both advective and dispersive processes. The potential for advective release is demonstrated by reexamining the Hydrologic Code Intercomparison (HYDROCOIN) project case 5 problem, which represents a salt dome overlain by a shallow groundwater system. The resulting flow field includes significant salinity and fluid density variations. Several independent teams simulated this problem using finite difference or finite element numerical models. We applied a method-of-characteristics model (MOCDENSE). The previous numerical implementations by HYDROCOIN teams of a constant-concentration boundary to represent salt release by lateral dispersion only (as stipulated in the original problem definition) was flawed because this boundary condition allows the release of salt into the flow field by both dispersion and advection. When the constant-concentration boundary is modified to allow salt release by dispersion only, significantly less salt is released into the flow field. The calculated brine distribution for case 5 depends very little on which numerical model is used, as long as the selected model is solving the proper equations. Instead, the accuracy of the solution depends strongly on the proper conceptualization of the problem, including the detailed design of the constant-concentration boundary condition. The importance and sensitivity to the manner of specification of this boundary does not appear to have been recognized previously in the analysis of this problem.

Boundary elements; Proceedings of the Fifth International Conference, Hiroshima, Japan, November 8-11, 1983

NASA Astrophysics Data System (ADS)

Brebbia, C. A.; Futagami, T.; Tanaka, M.

The boundary-element method (BEM) in computational fluid and solid mechanics is examined in reviews and reports of theoretical studies and practical applications. Topics presented include the fundamental mathematical principles of BEMs, potential problems, EM-field problems, heat transfer, potential-wave problems, fluid flow, elasticity problems, fracture mechanics, plates and shells, inelastic problems, geomechanics, dynamics, industrial applications of BEMs, optimization methods based on the BEM, numerical techniques, and coupling.

On Numerical Heating

NASA Astrophysics Data System (ADS)

Liou, Meng-Sing

2013-11-01

The development of computational fluid dynamics over the last few decades has yielded enormous successes and capabilities that are being routinely employed today; however there remain some open problems to be properly resolved. One example is the so-called overheating problem, which can arise in two very different scenarios, from either colliding or receding streams. Common in both is a localized, numerically over-predicted temperature. Von Neumann reported the former, a compressive overheating, nearly 70 years ago and numerically smeared the temperature peak by introducing artificial diffusion. However, the latter is unphysical in an expansive (rarefying) situation; it still dogs every method known to the author. We will present a study aiming at resolving this overheating problem and we find that: (1) the entropy increase is one-to-one linked to the increase in the temperature rise and (2) the overheating is inevitable in the current computational fluid dynamics framework in practice. Finally we will show a simple hybrid method that fundamentally cures the overheating problem in a rarefying flow, but also retains the property of accurate shock capturing. Moreover, this remedy (enhancement of current numerical methods) can be included easily in the present Eulerian codes. This work is performed under NASA's Fundamental Aeronautics Program.

An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Han, Jianqiang; Tang, Huazhong

2007-01-01

This paper presents an adaptive moving mesh algorithm for two-dimensional (2D) ideal magnetohydrodynamics (MHD) that utilizes a staggered constrained transport technique to keep the magnetic field divergence-free. The algorithm consists of two independent parts: MHD evolution and mesh-redistribution. The first part is a high-resolution, divergence-free, shock-capturing scheme on a fixed quadrangular mesh, while the second part is an iterative procedure. In each iteration, mesh points are first redistributed, and then a conservative-interpolation formula is used to calculate the remapped cell-averages of the mass, momentum, and total energy on the resulting new mesh; the magnetic potential is remapped to the new mesh in a non-conservative way and is reconstructed to give a divergence-free magnetic field on the new mesh. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy, track and resolve strong shock waves in ideal MHD problems, and preserve divergence-free property of the magnetic field. Numerical examples include the smooth Alfvén wave problem, 2D and 2.5D shock tube problems, two rotor problems, the stringent blast problem, and the cloud-shock interaction problem.

Numerical method and FORTRAN program for the solution of an axisymmetric electrostatic collector design problem

NASA Technical Reports Server (NTRS)

Reese, O. W.

1972-01-01

The numerical calculation is described of the steady-state flow of electrons in an axisymmetric, spherical, electrostatic collector for a range of boundary conditions. The trajectory equations of motion are solved alternately with Poisson's equation for the potential field until convergence is achieved. A direct (noniterative) numerical technique is used to obtain the solution to Poisson's equation. Space charge effects are included for initial current densities as large as 100 A/sq cm. Ways of dealing successfully with the difficulties associated with these high densities are discussed. A description of the mathematical model, a discussion of numerical techniques, results from two typical runs, and the FORTRAN computer program are included.

Multigrid methods for isogeometric discretization

PubMed Central

Gahalaut, K.P.S.; Kraus, J.K.; Tomar, S.K.

2013-01-01

We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels ℓ, whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order p=4, and for C0 and Cp-1 smoothness. PMID:24511168

Generalized bipartite quantum state discrimination problems with sequential measurements

NASA Astrophysics Data System (ADS)

Nakahira, Kenji; Kato, Kentaro; Usuda, Tsuyoshi Sasaki

2018-02-01

We investigate an optimization problem of finding quantum sequential measurements, which forms a wide class of state discrimination problems with the restriction that only local operations and one-way classical communication are allowed. Sequential measurements from Alice to Bob on a bipartite system are considered. Using the fact that the optimization problem can be formulated as a problem with only Alice's measurement and is convex programming, we derive its dual problem and necessary and sufficient conditions for an optimal solution. Our results are applicable to various practical optimization criteria, including the Bayes criterion, the Neyman-Pearson criterion, and the minimax criterion. In the setting of the problem of finding an optimal global measurement, its dual problem and necessary and sufficient conditions for an optimal solution have been widely used to obtain analytical and numerical expressions for optimal solutions. Similarly, our results are useful to obtain analytical and numerical expressions for optimal sequential measurements. Examples in which our results can be used to obtain an analytical expression for an optimal sequential measurement are provided.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hart, William E.; Siirola, John Daniel

We describe new capabilities for modeling MPEC problems within the Pyomo modeling software. These capabilities include new modeling components that represent complementar- ity conditions, modeling transformations for re-expressing models with complementarity con- ditions in other forms, and meta-solvers that apply transformations and numeric optimization solvers to optimize MPEC problems. We illustrate the breadth of Pyomo's modeling capabil- ities for MPEC problems, and we describe how Pyomo's meta-solvers can perform local and global optimization of MPEC problems.

Preventing Alcohol-Related Problems on Campus: Vandalism.

ERIC Educational Resources Information Center

Epstein, Joel; Finn, Peter

This bulletin provides suggestions for the components of a comprehensive approach to reducing student vandalism on college and university campuses. Numerous facets of the problem are addressed, including: the association of binge drinking with vandalism and school policies that tolerate or even facilitate binge drinking; a school's drinking…

STAGS Example Problems Manual

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.; Rankin, Charles C.

2006-01-01

This document summarizes the STructural Analysis of General Shells (STAGS) development effort, STAGS performance for selected demonstration problems, and STAGS application problems illustrating selected advanced features available in the STAGS Version 5.0. Each problem is discussed including selected background information and reference solutions when available. The modeling and solution approach for each problem is described and illustrated. Numerical results are presented and compared with reference solutions, test data, and/or results obtained from mesh refinement studies. These solutions provide an indication of the overall capabilities of the STAGS nonlinear finite element analysis tool and provide users with representative cases, including input files, to explore these capabilities that may then be tailored to other applications.

Teens Parenting: The Challenge of Babies and Toddlers.

ERIC Educational Resources Information Center

Lindsay, Jeanne Warren

This parenting guide for teenage parents of infants and toddlers incorporates numerous comments from 61 teenage parents who chose to stay in school after the birth of their child. Specific problems confronting young parents are addressed. These problems include single parenthood, early marriage, and the advantages and disadvantages of living with…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flintoff, F.

With the advent of industrialisation and urbanisation, developing countries are faced with numerous problems, one of the biggest being the provision of an effective solid wastes system appropriate to their varying climates and economies. The problems facing third world countries are discussed, these include the lack of a network of district depots, inadequate automotive servicing facilities and technical expertise.

RIACS

NASA Technical Reports Server (NTRS)

Oliger, Joseph

1997-01-01

Topics considered include: high-performance computing; cognitive and perceptual prostheses (computational aids designed to leverage human abilities); autonomous systems. Also included: development of a 3D unstructured grid code based on a finite volume formulation and applied to the Navier-stokes equations; Cartesian grid methods for complex geometry; multigrid methods for solving elliptic problems on unstructured grids; algebraic non-overlapping domain decomposition methods for compressible fluid flow problems on unstructured meshes; numerical methods for the compressible navier-stokes equations with application to aerodynamic flows; research in aerodynamic shape optimization; S-HARP: a parallel dynamic spectral partitioner; numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains; application of high-order shock capturing schemes to direct simulation of turbulence; multicast technology; network testbeds; supercomputer consolidation project.

Numerical modeling of coupled variably saturated fluid flow and reactive transport with fast and slow chemical reactions

NASA Astrophysics Data System (ADS)

Yeh, Gour-Tsyh (George); Siegel, Malcolm D.; Li, Ming-Hsu

2001-02-01

The couplings among chemical reaction rates, advective and diffusive transport in fractured media or soils, and changes in hydraulic properties due to precipitation and dissolution within fractures and in rock matrix are important for both nuclear waste disposal and remediation of contaminated sites. This paper describes the development and application of LEHGC2.0, a mechanistically based numerical model for simulation of coupled fluid flow and reactive chemical transport, including both fast and slow reactions in variably saturated media. Theoretical bases and numerical implementations are summarized, and two example problems are demonstrated. The first example deals with the effect of precipitation/dissolution on fluid flow and matrix diffusion in a two-dimensional fractured media. Because of the precipitation and decreased diffusion of solute from the fracture into the matrix, retardation in the fractured medium is not as large as the case wherein interactions between chemical reactions and transport are not considered. The second example focuses on a complicated but realistic advective-dispersive-reactive transport problem. This example exemplifies the need for innovative numerical algorithms to solve problems involving stiff geochemical reactions.

Numerical Analysis Objects

NASA Astrophysics Data System (ADS)

Henderson, Michael

1997-08-01

The Numerical Analysis Objects project (NAO) is a project in the Mathematics Department of IBM's TJ Watson Research Center. While there are plenty of numerical tools available today, it is not an easy task to combine them into a custom application. NAO is directed at the dual problems of building applications from a set of tools, and creating those tools. There are several "reuse" projects, which focus on the problems of identifying and cataloging tools. NAO is directed at the specific context of scientific computing. Because the type of tools is restricted, problems such as tools with incompatible data structures for input and output, and dissimilar interfaces to tools which solve similar problems can be addressed. The approach we've taken is to define interfaces to those objects used in numerical analysis, such as geometries, functions and operators, and to start collecting (and building) a set of tools which use these interfaces. We have written a class library (a set of abstract classes and implementations) in C++ which demonstrates the approach. Besides the classes, the class library includes "stub" routines which allow the library to be used from C or Fortran, and an interface to a Visual Programming Language. The library has been used to build a simulator for petroleum reservoirs, using a set of tools for discretizing nonlinear differential equations that we have written, and includes "wrapped" versions of packages from the Netlib repository. Documentation can be found on the Web at "http://www.research.ibm.com/nao". I will describe the objects and their interfaces, and give examples ranging from mesh generation to solving differential equations.

Asymptotic analysis of dissipative waves with applications to their numerical simulation

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1990-01-01

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

Numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis - Stanford Univ., Mar. 1989

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.

1990-01-01

The current work is initiated in an effort to obtain an efficient, accurate, and robust algorithm for the numerical solution of the incompressible Navier-Stokes equations in two- and three-dimensional generalized curvilinear coordinates for both steady-state and time-dependent flow problems. This is accomplished with the use of the method of artificial compressibility and a high-order flux-difference splitting technique for the differencing of the convective terms. Time accuracy is obtained in the numerical solutions by subiterating the equations in psuedo-time for each physical time step. The system of equations is solved with a line-relaxation scheme which allows the use of very large pseudo-time steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. Numerous laminar test flow problems are computed and presented with a comparison against analytically known solutions or experimental results. These include the flow in a driven cavity, the flow over a backward-facing step, the steady and unsteady flow over a circular cylinder, flow over an oscillating plate, flow through a one-dimensional inviscid channel with oscillating back pressure, the steady-state flow through a square duct with a 90 degree bend, and the flow through an artificial heart configuration with moving boundaries. An adequate comparison with the analytical or experimental results is obtained in all cases. Numerical comparisons of the upwind differencing with central differencing plus artificial dissipation indicates that the upwind differencing provides a much more robust algorithm, which requires significantly less computing time. The time-dependent problems require on the order of 10 to 20 subiterations, indicating that the elliptical nature of the problem does require a substantial amount of computing effort.

LSENS: A General Chemical Kinetics and Sensitivity Analysis Code for homogeneous gas-phase reactions. Part 1: Theory and numerical solution procedures

NASA Technical Reports Server (NTRS)

Radhakrishnan, Krishnan

1994-01-01

LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 1 of a series of three reference publications that describe LENS, provide a detailed guide to its usage, and present many example problems. Part 1 derives the governing equations and describes the numerical solution procedures for the types of problems that can be solved. The accuracy and efficiency of LSENS are examined by means of various test problems, and comparisons with other methods and codes are presented. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions.

Active Problem Solving and Applied Research Methods in a Graduate Course on Numerical Methods

ERIC Educational Resources Information Center

Maase, Eric L.; High, Karen A.

2008-01-01

"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…

N-person differential games. Part 2: The penalty method

NASA Technical Reports Server (NTRS)

Chen, G.; Mills, W. H.; Zheng, Q.; Shaw, W. H.

1983-01-01

The equilibrium strategy for N-person differential games can be found by studying a min-max problem subject to differential systems constraints. The differential constraints are penalized and finite elements are used to compute numerical solutions. Convergence proof and error estimates are given. Numerical results are also included and compared with those obtained by the dual method.

Teaching Children How to Include the Inversion Principle in Their Reasoning about Quantitative Relations

ERIC Educational Resources Information Center

Nunes, Terezinha; Bryant, Peter; Evans, Deborah; Bell, Daniel; Barros, Rossana

2012-01-01

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research…

Propeller Study. Part 2: the Design of Propellers for Minimum Noise

NASA Technical Reports Server (NTRS)

Ormsbee, A. I.; Woan, C. J.

1977-01-01

The design of propellers which are efficient and yet produce minimum noise requires accurate determinations of both the flow over the propeller. Topics discussed in relating aerodynamic propeller design and propeller acoustics include the necessary approximations and assumptions involved, the coordinate systems and their transformations, the geometry of the propeller blade, and the problem formulations including the induced velocity, required in the determination of mean lines of blade sections, and the optimization of propeller noise. The numerical formulation for the lifting-line model are given. Some applications and numerical results are included.

Some unsolved problems in discrete mathematics and mathematical cybernetics

NASA Astrophysics Data System (ADS)

Korshunov, Aleksei D.

2009-10-01

There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

NASA Astrophysics Data System (ADS)

Witte, J. H.; Reisinger, C.

2010-09-01

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

On numerical modeling of one-dimensional geothermal histories

USGS Publications Warehouse

Haugerud, R.A.

1989-01-01

Numerical models of one-dimensional geothermal histories are one way of understanding the relations between tectonics and transient thermal structure in the crust. Such models can be powerful tools for interpreting geochronologic and thermobarometric data. A flexible program to calculate these models on a microcomputer is available and examples of its use are presented. Potential problems with this approach include the simplifying assumptions that are made, limitations of the numerical techniques, and the neglect of convective heat transfer. ?? 1989.

A New Homotopy Perturbation Scheme for Solving Singular Boundary Value Problems Arising in Various Physical Models

NASA Astrophysics Data System (ADS)

Roul, Pradip; Warbhe, Ujwal

2017-08-01

The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).

A novel numerical framework for self-similarity in plasticity: Wedge indentation in single crystals

NASA Astrophysics Data System (ADS)

Juul, K. J.; Niordson, C. F.; Nielsen, K. L.; Kysar, J. W.

2018-03-01

A novel numerical framework for analyzing self-similar problems in plasticity is developed and demonstrated. Self-similar problems of this kind include processes such as stationary cracks, void growth, indentation etc. The proposed technique offers a simple and efficient method for handling this class of complex problems by avoiding issues related to traditional Lagrangian procedures. Moreover, the proposed technique allows for focusing the mesh in the region of interest. In the present paper, the technique is exploited to analyze the well-known wedge indentation problem of an elastic-viscoplastic single crystal. However, the framework may be readily adapted to any constitutive law of interest. The main focus herein is the development of the self-similar framework, while the indentation study serves primarily as verification of the technique by comparing to existing numerical and analytical studies. In this study, the three most common metal crystal structures will be investigated, namely the face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close packed (HCP) crystal structures, where the stress and slip rate fields around the moving contact point singularity are presented.

Numerical electromagnetic frequency domain analysis with discrete exterior calculus

NASA Astrophysics Data System (ADS)

Chen, Shu C.; Chew, Weng Cho

2017-12-01

In this paper, we perform a numerical analysis in frequency domain for various electromagnetic problems based on discrete exterior calculus (DEC) with an arbitrary 2-D triangular or 3-D tetrahedral mesh. We formulate the governing equations in terms of DEC for 3-D and 2-D inhomogeneous structures, and also show that the charge continuity relation is naturally satisfied. Then we introduce a general construction for signed dual volume to incorporate material information and take into account the case when circumcenters fall outside triangles or tetrahedrons, which may lead to negative dual volume without Delaunay triangulation. Then we examine the boundary terms induced by the dual mesh and provide a systematical treatment of various boundary conditions, including perfect magnetic conductor (PMC), perfect electric conductor (PEC), Dirichlet, periodic, and absorbing boundary conditions (ABC) within this method. An excellent agreement is achieved through the numerical calculation of several problems, including homogeneous waveguides, microstructured fibers, photonic crystals, scattering by a 2-D PEC, and resonant cavities.

Generalized Differential Calculus and Applications to Optimization

NASA Astrophysics Data System (ADS)

Rector, Robert Blake Hayden

This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations research, including non-convex problems. Finally, an optimization framework is applied to solve a problem in electric power systems involving a smart solar inverter and battery storage system providing energy and ancillary services to the grid.

The P1-RKDG method for two-dimensional Euler equations of gas dynamics

NASA Technical Reports Server (NTRS)

Cockburn, Bernardo; Shu, Chi-Wang

1991-01-01

A class of nonlinearly stable Runge-Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws is investigated. Two dimensional Euler equations for gas dynamics are solved using P1 elements. The generalization of the local projections, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions is discussed. Numerical examples include the standard regular shock reflection problem, the forward facing step problem, and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of the approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods.

Relapse Prevention for Alcohol and Drug Problems: That Was Zen, This Is Tao

ERIC Educational Resources Information Center

Witkiewitz, Katie; Marlatt, Alan G.

2004-01-01

Relapse prevention, based on the cognitive-behavioral model of relapse, has become an adjunct to the treatment of numerous psychological problems, including (but not limited to) substance abuse, depression, sexual offending, and schizophrenia. This article provides an overview of the efficacy and effectiveness of relapse prevention in the…

Math Thinkercises. A Good Apple Math Activity Book for Students. Grades 4-8.

ERIC Educational Resources Information Center

Daniel, Becky

This booklet designed for students in grades 4-8 provides 52 activities, including puzzles and problems. Activities range from simple to complex, giving learners practice in finding patterns, numeration, permutation, and problem solving. Calculators should be available, and students should be encouraged to discuss solutions with classmates,…

A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case

NASA Astrophysics Data System (ADS)

Dudley Ward, N. F.; Lähivaara, T.; Eveson, S.

2017-12-01

In this paper, we consider a high-order discontinuous Galerkin (DG) method for modelling wave propagation in coupled poroelastic-elastic media. The upwind numerical flux is derived as an exact solution for the Riemann problem including the poroelastic-elastic interface. Attenuation mechanisms in both Biot's low- and high-frequency regimes are considered. The current implementation supports non-uniform basis orders which can be used to control the numerical accuracy element by element. In the numerical examples, we study the convergence properties of the proposed DG scheme and provide experiments where the numerical accuracy of the scheme under consideration is compared to analytic and other numerical solutions.

Force-controlled absorption in a fully-nonlinear numerical wave tank

NASA Astrophysics Data System (ADS)

Spinneken, Johannes; Christou, Marios; Swan, Chris

2014-09-01

An active control methodology for the absorption of water waves in a numerical wave tank is introduced. This methodology is based upon a force-feedback technique which has previously been shown to be very effective in physical wave tanks. Unlike other methods, an a-priori knowledge of the wave conditions in the tank is not required; the absorption controller being designed to automatically respond to a wide range of wave conditions. In comparison to numerical sponge layers, effective wave absorption is achieved on the boundary, thereby minimising the spatial extent of the numerical wave tank. In contrast to the imposition of radiation conditions, the scheme is inherently capable of absorbing irregular waves. Most importantly, simultaneous generation and absorption can be achieved. This is an important advance when considering inclusion of reflective bodies within the numerical wave tank. In designing the absorption controller, an infinite impulse response filter is adopted, thereby eliminating the problem of non-causality in the controller optimisation. Two alternative controllers are considered, both implemented in a fully-nonlinear wave tank based on a multiple-flux boundary element scheme. To simplify the problem under consideration, the present analysis is limited to water waves propagating in a two-dimensional domain. The paper presents an extensive numerical validation which demonstrates the success of the method for a wide range of wave conditions including regular, focused and random waves. The numerical investigation also highlights some of the limitations of the method, particularly in simultaneously generating and absorbing large amplitude or highly-nonlinear waves. The findings of the present numerical study are directly applicable to related fields where optimum absorption is sought; these include physical wavemaking, wave power absorption and a wide range of numerical wave tank schemes.

Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

NASA Astrophysics Data System (ADS)

Rahman, M. A.; Ahmed, U.; Uddin, M. S.

2013-08-01

A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

Advanced numerical methods for three dimensional two-phase flow calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toumi, I.; Caruge, D.

1997-07-01

This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses anmore » extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.« less

Extraction of gravitational waves in numerical relativity.

PubMed

Bishop, Nigel T; Rezzolla, Luciano

2016-01-01

A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to "extract" the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages.

Numerical implementation of multiple peeling theory and its application to spider web anchorages.

PubMed

Brely, Lucas; Bosia, Federico; Pugno, Nicola M

2015-02-06

Adhesion of spider web anchorages has been studied in recent years, including the specific functionalities achieved through different architectures. To better understand the delamination mechanisms of these and other biological or artificial fibrillar adhesives, and how their adhesion can be optimized, we develop a novel numerical model to simulate the multiple peeling of structures with arbitrary branching and adhesion angles, including complex architectures. The numerical model is based on a recently developed multiple peeling theory, which extends the energy-based single peeling theory of Kendall, and can be applied to arbitrarily complex structures. In particular, we numerically show that a multiple peeling problem can be treated as the superposition of single peeling configurations even for complex structures. Finally, we apply the developed numerical approach to study spider web anchorages, showing how their function is achieved through optimal geometrical configurations.

Numerical implementation of multiple peeling theory and its application to spider web anchorages

PubMed Central

Brely, Lucas; Bosia, Federico; Pugno, Nicola M.

2015-01-01

Adhesion of spider web anchorages has been studied in recent years, including the specific functionalities achieved through different architectures. To better understand the delamination mechanisms of these and other biological or artificial fibrillar adhesives, and how their adhesion can be optimized, we develop a novel numerical model to simulate the multiple peeling of structures with arbitrary branching and adhesion angles, including complex architectures. The numerical model is based on a recently developed multiple peeling theory, which extends the energy-based single peeling theory of Kendall, and can be applied to arbitrarily complex structures. In particular, we numerically show that a multiple peeling problem can be treated as the superposition of single peeling configurations even for complex structures. Finally, we apply the developed numerical approach to study spider web anchorages, showing how their function is achieved through optimal geometrical configurations. PMID:25657835

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration.

PubMed

Bearup, Daniel; Petrovskaya, Natalia; Petrovskii, Sergei

2015-05-01

Monitoring of pest insects is an important part of the integrated pest management. It aims to provide information about pest insect abundance at a given location. This includes data collection, usually using traps, and their subsequent analysis and/or interpretation. However, interpretation of trap count (number of insects caught over a fixed time) remains a challenging problem. First, an increase in either the population density or insects activity can result in a similar increase in the number of insects trapped (the so called "activity-density" problem). Second, a genuine increase of the local population density can be attributed to qualitatively different ecological mechanisms such as multiplication or immigration. Identification of the true factor causing an increase in trap count is important as different mechanisms require different control strategies. In this paper, we consider a mean-field mathematical model of insect trapping based on the diffusion equation. Although the diffusion equation is a well-studied model, its analytical solution in closed form is actually available only for a few special cases, whilst in a more general case the problem has to be solved numerically. We choose finite differences as the baseline numerical method and show that numerical solution of the problem, especially in the realistic 2D case, is not at all straightforward as it requires a sufficiently accurate approximation of the diffusion fluxes. Once the numerical method is justified and tested, we apply it to the corresponding boundary problem where different types of boundary forcing describe different scenarios of pest insect immigration and reveal the corresponding patterns in the trap count growth. Copyright © 2015 Elsevier Inc. All rights reserved.

A comparative analysis of numerical approaches to the mechanics of elastic sheets

NASA Astrophysics Data System (ADS)

Taylor, Michael; Davidovitch, Benny; Qiu, Zhanlong; Bertoldi, Katia

2015-06-01

Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of wrinkles in these problems has important implications in design and is an area of increasing interest in the fields of physics and engineering. In this work, several numerical approaches previously proposed to model equilibrium deformations in thin elastic sheets are compared. These include standard finite element-based static post-buckling approaches as well as a recently proposed method based on dynamic relaxation, which are applied to the problem of an annular sheet with opposed tractions where wrinkling is a key feature. Numerical solutions are compared to analytic predictions of the ground state, enabling a quantitative evaluation of the predictive power of the various methods. Results indicate that static finite element approaches produce local minima that are highly sensitive to initial imperfections, relying on a priori knowledge of the equilibrium wrinkling pattern to generate optimal results. In contrast, dynamic relaxation is much less sensitive to initial imperfections and can generate low-energy solutions for a wide variety of loading conditions without requiring knowledge of the equilibrium solution beforehand.

On numerical instabilities of Godunov-type schemes for strong shocks

NASA Astrophysics Data System (ADS)

Xie, Wenjia; Li, Wei; Li, Hua; Tian, Zhengyu; Pan, Sha

2017-12-01

It is well known that low diffusion Riemann solvers with minimal smearing on contact and shear waves are vulnerable to shock instability problems, including the carbuncle phenomenon. In the present study, we concentrate on exploring where the instability grows out and how the dissipation inherent in Riemann solvers affects the unstable behaviors. With the help of numerical experiments and a linearized analysis method, it has been found that the shock instability is strongly related to the unstable modes of intermediate states inside the shock structure. The consistency of mass flux across the normal shock is needed for a Riemann solver to capture strong shocks stably. The famous carbuncle phenomenon is interpreted as the consequence of the inconsistency of mass flux across the normal shock for a low diffusion Riemann solver. Based on the results of numerical experiments and the linearized analysis, a robust Godunov-type scheme with a simple cure for the shock instability is suggested. With only the dissipation corresponding to shear waves introduced in the vicinity of strong shocks, the instability problem is circumvented. Numerical results of several carefully chosen strong shock wave problems are investigated to demonstrate the robustness of the proposed scheme.

Numerical methods in heat transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, R.W.

1985-01-01

This third volume in the series in Numerical Methods in Engineering presents expanded versions of selected papers given at the Conference on Numerical Methods in Thermal Problems held in Venice in July 1981. In this reference work, contributors offer the current state of knowledge on the numerical solution of convective heat transfer problems and conduction heat transfer problems.

A POSTERIORI ERROR ANALYSIS OF TWO STAGE COMPUTATION METHODS WITH APPLICATION TO EFFICIENT DISCRETIZATION AND THE PARAREAL ALGORITHM.

PubMed

Chaudhry, Jehanzeb Hameed; Estep, Don; Tavener, Simon; Carey, Varis; Sandelin, Jeff

2016-01-01

We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute "dual-weighted" a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.

Numerical treatment of a geometrically nonlinear planar Cosserat shell model

NASA Astrophysics Data System (ADS)

Sander, Oliver; Neff, Patrizio; Bîrsan, Mircea

2016-05-01

We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general six-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements (GFEs), which leads to an objective discrete model which naturally allows arbitrarily large rotations. GFEs of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton's method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkling of thin elastic sheets in shear.

Potential flow about arbitrary biplane wing sections

NASA Technical Reports Server (NTRS)

Garrick, I E

1937-01-01

A rigorous treatment is given of the problem of determining the two-dimensional potential flow around arbitrary biplane cellules. The analysis involves the use of elliptic functions and is sufficiently general to include the effects of such elements as the section shapes, the chord ratio, gap, stagger, and decalage, which elements may be specified arbitrarily. The flow problem is resolved by making use of the methods of conformal representation. Thus the solution of the problem of transforming conformally two arbitrary contours into two circles is expressed by a pair of simultaneous integral equations, for which a method of numerical solution is outlined. As an example of the numerical process, the pressure distribution over certain arrangements of the NACA 4412 airfoil in biplane combinations is presented and compared with the monoplane pressure distribution.

2-dimensional implicit hydrodynamics on adaptive grids

NASA Astrophysics Data System (ADS)

Stökl, A.; Dorfi, E. A.

2007-12-01

We present a numerical scheme for two-dimensional hydrodynamics computations using a 2D adaptive grid together with an implicit discretization. The combination of these techniques has offered favorable numerical properties applicable to a variety of one-dimensional astrophysical problems which motivated us to generalize this approach for two-dimensional applications. Due to the different topological nature of 2D grids compared to 1D problems, grid adaptivity has to avoid severe grid distortions which necessitates additional smoothing parameters to be included into the formulation of a 2D adaptive grid. The concept of adaptivity is described in detail and several test computations demonstrate the effectivity of smoothing. The coupled solution of this grid equation together with the equations of hydrodynamics is illustrated by computation of a 2D shock tube problem.

The Osher scheme for non-equilibrium reacting flows

NASA Technical Reports Server (NTRS)

Suresh, Ambady; Liou, Meng-Sing

1992-01-01

An extension of the Osher upwind scheme to nonequilibrium reacting flows is presented. Owing to the presence of source terms, the Riemann problem is no longer self-similar and therefore its approximate solution becomes tedious. With simplicity in mind, a linearized approach which avoids an iterative solution is used to define the intermediate states and sonic points. The source terms are treated explicitly. Numerical computations are presented to demonstrate the feasibility, efficiency and accuracy of the proposed method. The test problems include a ZND (Zeldovich-Neumann-Doring) detonation problem for which spurious numerical solutions which propagate at mesh speed have been observed on coarse grids. With the present method, a change of limiter causes the solution to change from the physically correct CJ detonation solution to the spurious weak detonation solution.

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus

NASA Astrophysics Data System (ADS)

Atangana, Abdon

2016-10-01

In order to describe more complex problems using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with the generalized Mittag-Leffler function. The first order is included in the power law function and the second one is in the generalized Mittag-Leffler function. Each order therefore plays an important role while modeling, for instance, problems with two layers with different properties. This is the case, for instance, in thermal science for a reaction diffusion within a media with two different layers with different properties. Another case is that of groundwater flowing within an aquifer where geological formation is formed with two layers with different properties. The paper presents new fractional operators that will open new doors for research and investigations in modeling real world problems. Some useful properties of the new operators are presented, in particular their relationship with existing integral transforms, namely the Laplace, Sumudu, Mellin and Fourier transforms. The numerical approximation of the new fractional operators are presented. We apply the new fractional operators on the model of groundwater plume with degradation and limited sorption and solve the new model numerically with some numerical simulations. The numerical simulation leaves no doubt in believing that the new fractional operators are powerfull mathematical tools able to portray complexes real world problems.

Numerical methods for coupled fracture problems

NASA Astrophysics Data System (ADS)

Viesca, Robert C.; Garagash, Dmitry I.

2018-04-01

We consider numerical solutions in which the linear elastic response to an opening- or sliding-mode fracture couples with one or more processes. Classic examples of such problems include traction-free cracks leading to stress singularities or cracks with cohesive-zone strength requirements leading to non-singular stress distributions. These classical problems have characteristic square-root asymptotic behavior for stress, relative displacement, or their derivatives. Prior work has shown that such asymptotics lead to a natural quadrature of the singular integrals at roots of Chebyhsev polynomials of the first, second, third, or fourth kind. We show that such quadratures lead to convenient techniques for interpolation, differentiation, and integration, with the potential for spectral accuracy. We further show that these techniques, with slight amendment, may continue to be used for non-classical problems which lack the classical asymptotic behavior. We consider solutions to example problems of both the classical and non-classical variety (e.g., fluid-driven opening-mode fracture and fault shear rupture driven by thermal weakening), with comparisons to analytical solutions or asymptotes, where available.

The point explosion with radiation transport

NASA Astrophysics Data System (ADS)

Lin, Zhiwei; Zhang, Lu; Kuang, Longyu; Jiang, Shaoen

2017-10-01

Some amount of energy is released instantaneously at the origin to generate simultaneously a spherical radiative heat wave and a spherical shock wave in the point explosion with radiation transport, which is a complicated problem due to the competition between these two waves. The point explosion problem possesses self-similar solutions when only hydrodynamic motion or only heat conduction is considered, which are Sedov solution and Barenblatt solution respectively. The point explosion problem wherein both physical mechanisms of hydrodynamic motion and heat conduction are included has been studied by P. Reinicke and A.I. Shestakov. In this talk we numerically investigate the point explosion problem wherein both physical mechanisms of hydrodynamic motion and radiation transport are taken into account. The radiation transport equation in one dimensional spherical geometry has to be solved for this problem since the ambient medium is optically thin with respect to the initially extremely high temperature at the origin. The numerical results reveal a high compression of medium and a bi-peak structure of density, which are further theoretically analyzed at the end.

Proposal of a micromagnetic standard problem for ferromagnetic resonance simulations

NASA Astrophysics Data System (ADS)

Baker, Alexander; Beg, Marijan; Ashton, Gregory; Albert, Maximilian; Chernyshenko, Dmitri; Wang, Weiwei; Zhang, Shilei; Bisotti, Marc-Antonio; Franchin, Matteo; Hu, Chun Lian; Stamps, Robert; Hesjedal, Thorsten; Fangohr, Hans

2017-01-01

Nowadays, micromagnetic simulations are a common tool for studying a wide range of different magnetic phenomena, including the ferromagnetic resonance. A technique for evaluating reliability and validity of different micromagnetic simulation tools is the simulation of proposed standard problems. We propose a new standard problem by providing a detailed specification and analysis of a sufficiently simple problem. By analyzing the magnetization dynamics in a thin permalloy square sample, triggered by a well defined excitation, we obtain the ferromagnetic resonance spectrum and identify the resonance modes via Fourier transform. Simulations are performed using both finite difference and finite element numerical methods, with OOMMF and Nmag simulators, respectively. We report the effects of initial conditions and simulation parameters on the character of the observed resonance modes for this standard problem. We provide detailed instructions and code to assist in using the results for evaluation of new simulator tools, and to help with numerical calculation of ferromagnetic resonance spectra and modes in general.

Optimal control design of turbo spin‐echo sequences with applications to parallel‐transmit systems

PubMed Central

Hoogduin, Hans; Hajnal, Joseph V.; van den Berg, Cornelis A. T.; Luijten, Peter R.; Malik, Shaihan J.

2016-01-01

Purpose The design of turbo spin‐echo sequences is modeled as a dynamic optimization problem which includes the case of inhomogeneous transmit radiofrequency fields. This problem is efficiently solved by optimal control techniques making it possible to design patient‐specific sequences online. Theory and Methods The extended phase graph formalism is employed to model the signal evolution. The design problem is cast as an optimal control problem and an efficient numerical procedure for its solution is given. The numerical and experimental tests address standard multiecho sequences and pTx configurations. Results Standard, analytically derived flip angle trains are recovered by the numerical optimal control approach. New sequences are designed where constraints on radiofrequency total and peak power are included. In the case of parallel transmit application, the method is able to calculate the optimal echo train for two‐dimensional and three‐dimensional turbo spin echo sequences in the order of 10 s with a single central processing unit (CPU) implementation. The image contrast is maintained through the whole field of view despite inhomogeneities of the radiofrequency fields. Conclusion The optimal control design sheds new light on the sequence design process and makes it possible to design sequences in an online, patient‐specific fashion. Magn Reson Med 77:361–373, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine PMID:26800383

Numerical Analysis of Dusty-Gas Flows

NASA Astrophysics Data System (ADS)

Saito, T.

2002-02-01

This paper presents the development of a numerical code for simulating unsteady dusty-gas flows including shock and rarefaction waves. The numerical results obtained for a shock tube problem are used for validating the accuracy and performance of the code. The code is then extended for simulating two-dimensional problems. Since the interactions between the gas and particle phases are calculated with the operator splitting technique, we can choose numerical schemes independently for the different phases. A semi-analytical method is developed for the dust phase, while the TVD scheme of Harten and Yee is chosen for the gas phase. Throughout this study, computations are carried out on SGI Origin2000, a parallel computer with multiple of RISC based processors. The efficient use of the parallel computer system is an important issue and the code implementation on Origin2000 is also described. Flow profiles of both the gas and solid particles behind the steady shock wave are calculated by integrating the steady conservation equations. The good agreement between the pseudo-stationary solutions and those from the current numerical code validates the numerical approach and the actual coding. The pseudo-stationary shock profiles can also be used as initial conditions of unsteady multidimensional simulations.

Automated Acquisition Systems: Keynote Address.

ERIC Educational Resources Information Center

Boss, Richard D.

1980-01-01

The 1980s offer libraries numerous automated acquisitions alternatives, including turnkey systems from circulation system vendors and the acquisition subsystems of the bibliographic utilities. Integration of systems from several sources poses the principal problem. (Author/RAA)

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network.

PubMed

Landajuela, Mikel; Vergara, Christian; Gerbi, Antonello; Dedé, Luca; Formaggia, Luca; Quarteroni, Alfio

2018-03-25

In this work, we consider the numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bidomain equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical solution of the coupled problem, we consider a fixed-point iterative algorithm that enables a partitioned solution of the myocardium and Purkinje network problems. Different levels of myocardium-Purkinje network splitting are considered and analyzed. The results are compared with those obtained using standard strategies proposed in the literature to trigger the electrical activation. Finally, we present a numerical study that, although performed in an idealized computational domain, features all the physiological issues that characterize a heartbeat simulation, including the initiation of the signal in the Purkinje network and the systolic and diastolic phases. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

Spacelike matching to null infinity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zenginoglu, Anil; Tiglio, Manuel

2009-07-15

We present two methods to include the asymptotic domain of a background spacetime in null directions for numerical solutions of evolution equations so that both the radiation extraction problem and the outer boundary problem are solved. The first method is based on the geometric conformal approach, the second is a coordinate based approach. We apply these methods to the case of a massless scalar wave equation on a Kerr spacetime. Our methods are designed to allow existing codes to reach the radiative zone by including future null infinity in the computational domain with relatively minor modifications. We demonstrate the flexibilitymore » of the methods by considering both Boyer-Lindquist and ingoing Kerr coordinates near the black hole. We also confirm numerically predictions concerning tail decay rates for scalar fields at null infinity in Kerr spacetime due to Hod for the first time.« less

Epilepsy: A Spectrum Disorder

PubMed Central

Sirven, Joseph I.

2015-01-01

Epilepsy, a disorder of unprovoked seizures is a multifaceted disease affecting individuals of all ages with a particular predilection for the very young and old. In addition to seizures, many patients often report cognitive and psychiatric problems associated with both the seizures themselves and its therapy. Epilepsy has numerous etiologies both idiopathic and acquired with a wide range of therapeutic responses. Despite numerous treatments available to control repetitive seizures including medications, diets, immunotherapy, surgery, and neuromodulatory devices, a large percentage of patients continue to suffer the consequences of uncontrolled seizures, which include psychosocial stigma and death. PMID:26328931

Adaptive Numerical Dissipation Control in High Order Schemes for Multi-D Non-Ideal MHD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, B.

2005-01-01

The required type and amount of numerical dissipation/filter to accurately resolve all relevant multiscales of complex MHD unsteady high-speed shock/shear/turbulence/combustion problems are not only physical problem dependent, but also vary from one flow region to another. In addition, proper and efficient control of the divergence of the magnetic field (Div(B)) numerical error for high order shock-capturing methods poses extra requirements for the considered type of CPU intensive computations. The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multiresolution wavelets (WAV) (for the above types of flow feature). These filters also provide a natural and efficient way for the minimization of Div(B) numerical error.

Modelling groundwater fractal flow with fractional differentiation via Mittag-Leffler law

NASA Astrophysics Data System (ADS)

Ahokposi, D. P.; Atangana, Abdon; Vermeulen, D. P.

2017-04-01

Modelling the flow of groundwater within a network of fractures is perhaps one of the most difficult exercises within the field of geohydrology. This physical problem has attracted the attention of several scientists across the globe. Already two different types of differentiations have been used to attempt modelling this problem including the classical and the fractional differentiation. In this paper, we employed the most recent concept of differentiation based on the non-local and non-singular kernel called the generalized Mittag-Leffler function, to reshape the model of groundwater fractal flow. We presented the existence of positive solution of the new model. Using the fixed-point approach, we established the uniqueness of the positive solution. We solve the new model with three different numerical schemes including implicit, explicit and Crank-Nicholson numerical methods. Experimental data collected from four constant discharge tests conducted in a typical fractured crystalline rock aquifer of the Northern Limb (Bushveld Complex) in the Limpopo Province (South Africa) are compared with the numerical solutions. It is worth noting that the four boreholes (BPAC1, BPAC2, BPAC3, and BPAC4) are located on Faults.

TEMPEST/N33.5. Computational Fluid Dynamics Package For Incompressible, 3D, Time Dependent Pro

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trent, Dr.D.S.; Eyler, Dr.L.L.

TEMPESTN33.5 provides numerical solutions to general incompressible flow problems with coupled heat transfer in fluids and solids. Turbulence is created with a k-e model and gas, liquid or solid constituents may be included with the bulk flow. Problems may be modeled in Cartesian or cylindrical coordinates. Limitations include incompressible flow, Boussinesq approximation, and passive constituents. No direct steady state solution is available; steady state is obtained as the limit of a transient.

Systematic Approach for Calculating the Concentrations of Chemical Species in Multiequilibrium Problems: Inclusion of the Ionic Strength Effects

ERIC Educational Resources Information Center

Baeza-Baeza, Juan J.; Garcia-Alvarez-Coque, M. Celia

2012-01-01

A general systematic approach including ionic strength effects is proposed for the numerical calculation of concentrations of chemical species in multiequilibrium problems. This approach extends the versatility of the approach presented in a previous article and is applied using the Solver option of the Excel spreadsheet to solve real problems…

Rotordynamic Instability Problems in High-Performance Turbomachinery, 1988

NASA Technical Reports Server (NTRS)

1989-01-01

The continuing trend toward a unified view is supported with several developments in the design and manufacture of turbomachines with enhanced stability characteristics along with data and associated numerical/theoretical results. The intent is to provide a continuing impetus for an understanding and resolution of these problems. Topics addressed include: field experience, dampers, seals, impeller forces, bearings, and compressor and rotor modeling.

A Novel Numerical Method for Fuzzy Boundary Value Problems

NASA Astrophysics Data System (ADS)

Can, E.; Bayrak, M. A.; Hicdurmaz

2016-05-01

In the present paper, a new numerical method is proposed for solving fuzzy differential equations which are utilized for the modeling problems in science and engineering. Fuzzy approach is selected due to its important applications on processing uncertainty or subjective information for mathematical models of physical problems. A second-order fuzzy linear boundary value problem is considered in particular due to its important applications in physics. Moreover, numerical experiments are presented to show the effectiveness of the proposed numerical method on specific physical problems such as heat conduction in an infinite plate and a fin.

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1985-01-01

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

NASA Technical Reports Server (NTRS)

Szabo, Barna A.; Actis, Ricardo L.; Holzer, Stefan M.

1993-01-01

The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

New methods for the numerical integration of ordinary differential equations and their application to the equations of motion of spacecraft

NASA Technical Reports Server (NTRS)

Banyukevich, A.; Ziolkovski, K.

1975-01-01

A number of hybrid methods for solving Cauchy problems are described on the basis of an evaluation of advantages of single and multiple-point numerical integration methods. The selection criterion is the principle of minimizing computer time. The methods discussed include the Nordsieck method, the Bulirsch-Stoer extrapolation method, and the method of recursive Taylor-Steffensen power series.

Numerical Activities and Information Learned at Home Link to the Exact Numeracy Skills in 5–6 Years-Old Children

PubMed Central

Benavides-Varela, Silvia; Butterworth, Brian; Burgio, Francesca; Arcara, Giorgio; Lucangeli, Daniela; Semenza, Carlo

2016-01-01

It is currently accepted that certain activities within the family environment contribute to develop early numerical skills before schooling. However, it is unknown whether this early experience influences both the exact and the approximate representation of numbers, and if so, which is more important for numerical tasks. In the present study the mathematical performance of 110 children (mean age 5 years 11 months) was evaluated using a battery that included tests of approximate and exact numerical abilities, as well as everyday numerical problems. Moreover, children were assessed on their knowledge of number information learned at home. The parents of the participants provided information regarding daily activities of the children and socio-demographic characteristics of the family. The results showed that the amount of numerical information learned at home was a significant predictor of participants' performance on everyday numerical problems and exact number representations, even after taking account of age, memory span and socio-economic and educational status of the family. We also found that particular activities, such as board games, correlate with the children's counting skills, which are foundational for arithmetic. Crucially, tests relying on approximate representations were not predicted by the numerical knowledge acquired at home. The present research supports claims about the importance and nature of home experiences in the child's acquisition of mathematics. PMID:26903902

An iterative transformation procedure for numerical solution of flutter and similar characteristics-value problems

NASA Technical Reports Server (NTRS)

Gossard, Myron L

1952-01-01

An iterative transformation procedure suggested by H. Wielandt for numerical solution of flutter and similar characteristic-value problems is presented. Application of this procedure to ordinary natural-vibration problems and to flutter problems is shown by numerical examples. Comparisons of computed results with experimental values and with results obtained by other methods of analysis are made.

Optimization of the Bridgman crystal growth process

NASA Astrophysics Data System (ADS)

Margulies, M.; Witomski, P.; Duffar, T.

2004-05-01

A numerical optimization method of the vertical Bridgman growth configuration is presented and developed. It permits to optimize the furnace temperature field and the pulling rate versus time in order to decrease the radial thermal gradients in the sample. Some constraints are also included in order to insure physically realistic results. The model includes the two classical non-linearities associated to crystal growth processes, the radiative thermal exchange and the release of latent heat at the solid-liquid interface. The mathematical analysis and development of the problem is shortly described. On some examples, it is shown that the method works in a satisfactory way; however the results are dependent on the numerical parameters. Improvements of the optimization model, on the physical and numerical point of view, are suggested.

Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations

NASA Astrophysics Data System (ADS)

Husa, Sascha; Hinder, Ian; Lechner, Christiane

2006-06-01

We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert certain (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code for solving initial boundary value problems. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations. Program summaryTitle of program: Kranc Catalogue identifier: ADXS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXS_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computer for which the program is designed and others on which it has been tested: General computers which run Mathematica (for code generation) and Cactus (for numerical simulations), tested under Linux Programming language used: Mathematica, C, Fortran 90 Memory required to execute with typical data: This depends on the number of variables and gridsize, the included ADM example requires 4308 KB Has the code been vectorized or parallelized: The code is parallelized based on the Cactus framework. Number of bytes in distributed program, including test data, etc.: 1 578 142 Number of lines in distributed program, including test data, etc.: 11 711 Nature of physical problem: Solution of partial differential equations in three space dimensions, which are formulated as an initial value problem. In particular, the program is geared towards handling very complex tensorial equations as they appear, e.g., in numerical relativity. The worked out examples comprise the Klein-Gordon equations, the Maxwell equations, and the ADM formulation of the Einstein equations. Method of solution: The method of numerical solution is finite differencing and method of lines time integration, the numerical code is generated through a high level Mathematica interface. Restrictions on the complexity of the program: Typical numerical relativity applications will contain up to several dozen evolution variables and thousands of source terms, Cactus applications have shown scaling up to several thousand processors and grid sizes exceeding 500 3. Typical running time: This depends on the number of variables and the grid size: the included ADM example takes approximately 100 seconds on a 1600 MHz Intel Pentium M processor. Unusual features of the program: based on Mathematica and Cactus

Dynamical Approach Study of Spurious Numerics in Nonlinear Computations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi (Technical Monitor)

2002-01-01

The last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air and space transportation systems, and systems for planetary and atmospheric sciences, and in understanding the evolution and origin of life. The need to guarantee PAR becomes acute when computations offer the ONLY way of solving these types of data limited problems. Employing theory from nonlinear dynamical systems, some building blocks to ensure a higher level of confidence in PAR of numerical simulations have been revealed by the author and world expert collaborators in relevant fields. Five building blocks with supporting numerical examples were discussed. The next step is to utilize knowledge gained by including nonlinear dynamics, bifurcation and chaos theories as an integral part of the numerical process. The third step is to design integrated criteria for reliable and accurate algorithms that cater to the different multiscale nonlinear physics. This includes but is not limited to the construction of appropriate adaptive spatial and temporal discretizations that are suitable for the underlying governing equations. In addition, a multiresolution wavelets approach for adaptive numerical dissipation/filter controls for high speed turbulence, acoustics and combustion simulations will be sought. These steps are corner stones for guarding against spurious numerical solutions that are solutions of the discretized counterparts but are not solutions of the underlying governing equations.

A class of high resolution explicit and implicit shock-capturing methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Symbolic-numeric interface: A review

NASA Technical Reports Server (NTRS)

Ng, E. W.

1980-01-01

A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach.

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Mailhe, Laurie M.; Guzman, Jose J.

2002-01-01

In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.

Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay.

PubMed

Akimenko, Vitalii; Anguelov, Roumen

2017-12-01

In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density. The quasi-periodical travelling wave solutions are studied numerically for the autonomous system with the different values of time delays and for the system with oscillating death rate and birth modulus. In both cases it is observed three types of travelling wave solutions: harmonic oscillations, pulse sequence and single pulse.

An efficient multi-dimensional implementation of VSIAM3 and its applications to free surface flows

NASA Astrophysics Data System (ADS)

Yokoi, Kensuke; Furuichi, Mikito; Sakai, Mikio

2017-12-01

We propose an efficient multidimensional implementation of VSIAM3 (volume/surface integrated average-based multi-moment method). Although VSIAM3 is a highly capable fluid solver based on a multi-moment concept and has been used for a wide variety of fluid problems, VSIAM3 could not simulate some simple benchmark problems well (for instance, lid-driven cavity flows) due to relatively high numerical viscosity. In this paper, we resolve the issue by using the efficient multidimensional approach. The proposed VSIAM3 is shown to capture lid-driven cavity flows of the Reynolds number up to Re = 7500 with a Cartesian grid of 128 × 128, which was not capable for the original VSIAM3. We also tested the proposed framework in free surface flow problems (droplet collision and separation of We = 40 and droplet splashing on a superhydrophobic substrate). The numerical results by the proposed VSIAM3 showed reasonable agreements with these experiments. The proposed VSIAM3 could capture droplet collision and separation of We = 40 with a low numerical resolution (8 meshes for the initial diameter of droplets). We also simulated free surface flows including particles toward non-Newtonian flow applications. These numerical results have showed that the proposed VSIAM3 can robustly simulate interactions among air, particles (solid), and liquid.

Penny-shaped crack in a fiber-reinforced matrix. [elastostatics

NASA Technical Reports Server (NTRS)

Narayanan, T. V.; Erdogan, F.

1974-01-01

Using a slender inclusion model developed earlier, the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles, the problem was reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given, and distribution of the stress intensity factor along the crack border was obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.

Penny-shaped crack in a fiber-reinforced matrix

NASA Technical Reports Server (NTRS)

Narayanan, T. V.; Erdogan, F.

1975-01-01

Using the slender inclusion model developed earlier the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles the problem is reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given and distribution of the stress intensity factor along the crack border is obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.

Resolution of singularities for multi-loop integrals

NASA Astrophysics Data System (ADS)

Bogner, Christian; Weinzierl, Stefan

2008-04-01

We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to terminate. The program can be used to compute numerically the Laurent expansion of divergent multi-loop integrals regulated by dimensional regularisation. The symbolic and the numerical steps of the algorithm are combined into one program. Program summaryProgram title: sector_decomposition Catalogue identifier: AEAG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAG_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.: 47 506 No. of bytes in distributed program, including test data, etc.: 328 485 Distribution format: tar.gz Programming language: C++ Computer: all Operating system: Unix RAM: Depending on the complexity of the problem Classification: 4.4 External routines: GiNaC, available from http://www.ginac.de, GNU scientific library, available from http://www.gnu.org/software/gsl Nature of problem: Computation of divergent multi-loop integrals. Solution method: Sector decomposition. Restrictions: Only limited by the available memory and CPU time. Running time: Depending on the complexity of the problem.

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

DOE PAGES

Liu, Jianfeng; Laird, Carl Damon

2017-09-22

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Jianfeng; Laird, Carl Damon

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

Deployment, Foam Rigidization, and Structural Characterization of Inflatable Thin-Film Booms

NASA Technical Reports Server (NTRS)

Schnell, Andrew R.; Leigh, Larry M., Jr.; Tinker, Michael L.; McConnaughey, Paul R. (Technical Monitor)

2002-01-01

Detailed investigation of the construction, packaging/deployment, foam rigidization, and structural characterization of polyimide film inflatable booms is described. These structures have considerable potential for use in space with solar concentrators, solar sails, space power systems including solar arrays, and other future missions. Numerous thin-film booms or struts were successfully constructed, inflated, injected with foam, and rigidized. Both solid-section and annular test articles were fabricated, using Kapton polyimide film, various adhesives, Styrofoam end plugs, and polyurethane pressurized foam. Numerous inflation/deployment experiments were conducted and compared to computer simulations using the MSC/DYTRAN code. Finite element models were developed for several foam-rigidized struts and compared to model test results. Several problems encountered in the construction, deployment, and foam injection/rigidization process are described. Areas of difficulty included inadequate adhesive strength, cracking of the film arid leakage, excessive bending of the structure during deployment, problems with foam distribution and curing properties, and control of foam leakage following injection into the structure. Many of these problems were overcome in the course of the research.

Fluid dynamic problems associated with air-breathing propulsive systems

NASA Technical Reports Server (NTRS)

Chow, W. L.

1979-01-01

A brief account of research activities on problems related to air-breathing propulsion is made in this final report for the step funded research grant NASA NGL 14-005-140. Problems include the aircraft ejector-nozzle propulsive system, nonconstant pressure jet mixing process, recompression and reattachment of turbulent free shear layer, supersonic turbulent base pressure, low speed separated flows, transonic boattail flow with and without small angle of attack, transonic base pressures, Mach reflection of shocks, and numerical solution of potential equation through hodograph transformation.

An extended validation of the last generation of particle finite element method for free surface flows

NASA Astrophysics Data System (ADS)

Gimenez, Juan M.; González, Leo M.

2015-03-01

In this paper, a new generation of the particle method known as Particle Finite Element Method (PFEM), which combines convective particle movement and a fixed mesh resolution, is applied to free surface flows. This interesting variant, previously described in the literature as PFEM-2, is able to use larger time steps when compared to other similar numerical tools which implies shorter computational times while maintaining the accuracy of the computation. PFEM-2 has already been extended to free surface problems, being the main topic of this paper a deep validation of this methodology for a wider range of flows. To accomplish this task, different improved versions of discontinuous and continuous enriched basis functions for the pressure field have been developed to capture the free surface dynamics without artificial diffusion or undesired numerical effects when different density ratios are involved. A collection of problems has been carefully selected such that a wide variety of Froude numbers, density ratios and dominant dissipative cases are reported with the intention of presenting a general methodology, not restricted to a particular range of parameters, and capable of using large time-steps. The results of the different free-surface problems solved, which include: Rayleigh-Taylor instability, sloshing problems, viscous standing waves and the dam break problem, are compared to well validated numerical alternatives or experimental measurements obtaining accurate approximations for such complex flows.

Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction

PubMed Central

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-01-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality. PMID:23271835

Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction

NASA Astrophysics Data System (ADS)

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-11-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constraint involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the PAPA. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.

Buckling and Damage Resistance of Transversely-Loaded Composite Shells

NASA Technical Reports Server (NTRS)

Wardle, Brian L.

1998-01-01

Experimental and numerical work was conducted to better understand composite shell response to transverse loadings which simulate damage-causing impact events. The quasi-static, centered, transverse loading response of laminated graphite/epoxy shells in a [+/-45(sub n)/O(sub n)](sub s) layup having geometric characteristics of a commercial fuselage are studied. The singly-curved composite shell structures are hinged along the straight circumferential edges and are either free or simply supported along the curved axial edges. Key components of the shell response are response instabilities due to limit-point and/or bifurcation buckling. Experimentally, deflection-controlled shell response is characterized via load-deflection data, deformation-shape evolutions, and the resulting damage state. Finite element models are used to study the kinematically nonlinear shell response, including bifurcation, limit-points, and postbuckling. A novel technique is developed for evaluating bifurcation from nonlinear prebuckling states utilizing asymmetric spatial discretization to introduce numerical perturbations. Advantages of the asymmetric meshing technique (AMT) over traditional techniques include efficiency, robustness, ease of application, and solution of the actual (not modified) problems. The AMT is validated by comparison to traditional numerical analysis of a benchmark problem and verified by comparison to experimental data. Applying the technique, bifurcation in a benchmark shell-buckling problem is correctly identified. Excellent agreement between the numerical and experimental results are obtained for a number of composite shells although predictive capability decreases for stiffer (thicker) specimens which is attributed to compliance of the test fixture. Restraining the axial edge (simple support) has the effect of creating a more complex response which involves unstable bifurcation, limit-point buckling, and dynamic collapse. Such shells were noted to bifurcate into asymmetric deformation modes but were undamaged during testing. Shells in this study which were damaged were not observed to bifurcate. Thus, a direct link between bifurcation and atypical damage could not be established although the mechanism (bifurcation) was identified. Recommendations for further work in these related areas are provided and include extensions of the AMT to other shell geometries and structural problems.

Numerical methods for large-scale, time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Turkel, E.

1979-01-01

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Variational data assimilation system "INM RAS - Black Sea"

NASA Astrophysics Data System (ADS)

Parmuzin, Eugene; Agoshkov, Valery; Assovskiy, Maksim; Giniatulin, Sergey; Zakharova, Natalia; Kuimov, Grigory; Fomin, Vladimir

2013-04-01

Development of Informational-Computational Systems (ICS) for Data Assimilation Procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in: mathematical modeling; theory of adjoint equations and optimal control; inverse problems; numerical methods theory; numerical algebra and scientific computing. The problems discussed above are studied in the Institute of Numerical Mathematics of the Russian Academy of Science (INM RAS) in ICS for Personal Computers (PC). Special problems and questions arise while effective ICS versions for PC are being developed. These problems and questions can be solved with applying modern methods of numerical mathematics and by solving "parallelism problem" using OpenMP technology and special linear algebra packages. In this work the results on the ICS development for PC-ICS "INM RAS - Black Sea" are presented. In the work the following problems and questions are discussed: practical problems that can be studied by ICS; parallelism problems and their solutions with applying of OpenMP technology and the linear algebra packages used in ICS "INM - Black Sea"; Interface of ICS. The results of ICS "INM RAS - Black Sea" testing are presented. Efficiency of technologies and methods applied are discussed. The work was supported by RFBR, grants No. 13-01-00753, 13-05-00715 and by The Ministry of education and science of Russian Federation, project 8291, project 11.519.11.1005 References: [1] V.I. Agoshkov, M.V. Assovskii, S.A. Lebedev, Numerical simulation of Black Sea hydrothermodynamics taking into account tide-forming forces. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 5-31 [2] E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 69-94 [3] V.B. Zalesny, N.A. Diansky, V.V. Fomin, S.N. Moshonkin, S.G. Demyshev, Numerical model of the circulation of Black Sea and Sea of Azov. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 95-111 [4] V.I. Agoshkov, S.V. Giniatulin, G.V. Kuimov. OpenMP technology and linear algebra packages in the variation data assimilation systems. - Abstracts of the 1-st China-Russia Conference on Numerical Algebra with Applications in Radiactive Hydrodynamics, Beijing, China, October 16-18, 2012. [5] Zakharova N.B., Agoshkov V.I., Parmuzin E.I., The new method of ARGO buoys system observation data interpolation. Russian Journal of Numerical Analysis and Mathematical Modelling. Vol. 28, Issue 1, 2013.

Numerical Determination of Critical Conditions for Thermal Ignition

NASA Technical Reports Server (NTRS)

Luo, W.; Wake, G. C.; Hawk, C. W.; Litchford, R. J.

2008-01-01

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Numerical Computation of Sensitivities and the Adjoint Approach

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael

1997-01-01

We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the costate computed via the weak form of the adjoint problem and show the significance for the discrete adjoint problem.

Computational-hydrodynamic studies of the Noh compressible flow problem using non-ideal equations of state

NASA Astrophysics Data System (ADS)

Honnell, Kevin; Burnett, Sarah; Yorke, Chloe'; Howard, April; Ramsey, Scott

2017-06-01

The Noh problem is classic verification problem in the field of compressible flows. Simple to conceptualize, it is nonetheless difficult for numerical codes to predict correctly, making it an ideal code-verification test bed. In its original incarnation, the fluid is a simple ideal gas; once validated, however, these codes are often used to study highly non-ideal fluids and solids. In this work the classic Noh problem is extended beyond the commonly-studied polytropic ideal gas to more realistic equations of state (EOS) including the stiff gas, the Nobel-Abel gas, and the Carnahan-Starling hard-sphere fluid, thus enabling verification studies to be performed on more physically-realistic fluids. Exact solutions are compared with numerical results obtained from the Lagrangian hydrocode FLAG, developed at Los Alamos. For these more realistic EOSs, the simulation errors decreased in magnitude both at the origin and at the shock, but also spread more broadly about these points compared to the ideal EOS. The overall spatial convergence rate remained first order.

FASOR - A second generation shell of revolution code

NASA Technical Reports Server (NTRS)

Cohen, G. A.

1978-01-01

An integrated computer program entitled Field Analysis of Shells of Revolution (FASOR) currently under development for NASA is described. When completed, this code will treat prebuckling, buckling, initial postbuckling and vibrations under axisymmetric static loads as well as linear response and bifurcation under asymmetric static loads. Although these modes of response are treated by existing programs, FASOR extends the class of problems treated to include general anisotropy and transverse shear deformations of stiffened laminated shells. At the same time, a primary goal is to develop a program which is free of the usual problems of modeling, numerical convergence and ill-conditioning, laborious problem setup, limitations on problem size and interpretation of output. The field method is briefly described, the shell differential equations are cast in a suitable form for solution by this method and essential aspects of the input format are presented. Numerical results are given for both unstiffened and stiffened anisotropic cylindrical shells and compared with previously published analytical solutions.

Numeracy and Communication with Patients: They Are Counting on Us

PubMed Central

Paasche-Orlow, Michael K.; Remillard, Janine T.; Bennett, Ian M.; Ben-Joseph, Elana Pearl; Batista, Rosanna M.; Hyde, James; Rudd, Rima E.

2008-01-01

Patient-centered interactive communication between physicians and patients is recommended to improve the quality of medical care. Numerical concepts are important components of such exchanges and include arithmetic and use of percentages, as well as higher level tasks like estimation, probability, problem-solving, and risk assessment - the basis of preventive medicine. Difficulty with numerical concepts may impede communication. The current evidence on prevalence, measurement, and outcomes related to numeracy is presented, along with a summary of best practices for communication of numerical information. This information is integrated into a hierarchical model of mathematical concepts and skills, which can guide clinicians toward numerical communication that is easier to use with patients. PMID:18830764

Temperature distribution of thick thermoset composites

NASA Astrophysics Data System (ADS)

Guo, Zhan-Sheng; Du, Shanyi; Zhang, Boming

2004-05-01

The development of temperature distribution of thick polymeric matrix laminates during an autoclave vacuum bag process was measured and compared with numerically calculated results. The finite element formulation of the transient heat transfer problem was carried out for polymeric matrix composite materials from the heat transfer differential equations including internal heat generation produced by exothermic chemical reactions. Software based on the general finite element software package was developed for numerical simulation of the entire composite process. From the experimental and numerical results, it was found that the measured temperature profiles were in good agreement with the numerical ones, and conventional cure cycles recommended by prepreg manufacturers for thin laminates should be modified to prevent temperature overshoot.

Accelerating numerical solution of stochastic differential equations with CUDA

NASA Astrophysics Data System (ADS)

Januszewski, M.; Kostur, M.

2010-01-01

Numerical integration of stochastic differential equations is commonly used in many branches of science. In this paper we present how to accelerate this kind of numerical calculations with popular NVIDIA Graphics Processing Units using the CUDA programming environment. We address general aspects of numerical programming on stream processors and illustrate them by two examples: the noisy phase dynamics in a Josephson junction and the noisy Kuramoto model. In presented cases the measured speedup can be as high as 675× compared to a typical CPU, which corresponds to several billion integration steps per second. This means that calculations which took weeks can now be completed in less than one hour. This brings stochastic simulation to a completely new level, opening for research a whole new range of problems which can now be solved interactively. Program summaryProgram title: SDE Catalogue identifier: AEFG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Gnu GPL v3 No. of lines in distributed program, including test data, etc.: 978 No. of bytes in distributed program, including test data, etc.: 5905 Distribution format: tar.gz Programming language: CUDA C Computer: any system with a CUDA-compatible GPU Operating system: Linux RAM: 64 MB of GPU memory Classification: 4.3 External routines: The program requires the NVIDIA CUDA Toolkit Version 2.0 or newer and the GNU Scientific Library v1.0 or newer. Optionally gnuplot is recommended for quick visualization of the results. Nature of problem: Direct numerical integration of stochastic differential equations is a computationally intensive problem, due to the necessity of calculating multiple independent realizations of the system. We exploit the inherent parallelism of this problem and perform the calculations on GPUs using the CUDA programming environment. The GPU's ability to execute hundreds of threads simultaneously makes it possible to speed up the computation by over two orders of magnitude, compared to a typical modern CPU. Solution method: The stochastic Runge-Kutta method of the second order is applied to integrate the equation of motion. Ensemble-averaged quantities of interest are obtained through averaging over multiple independent realizations of the system. Unusual features: The numerical solution of the stochastic differential equations in question is performed on a GPU using the CUDA environment. Running time: < 1 minute

Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics

NASA Astrophysics Data System (ADS)

Kakhktsyan, V. M.; Khachatryan, A. Kh.

2013-07-01

A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.

Linear and nonlinear acoustic wave propagation in the atmosphere

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Yu, Ping

1988-01-01

The investigation of the acoustic wave propagation theory and numerical implementation for the situation of an isothermal atmosphere is described. A one-dimensional model to validate an asymptotic theory and a 3-D situation to relate to a realistic situation are considered. In addition, nonlinear wave propagation and the numerical treatment are included. It is known that the gravitational effects play a crucial role in the low frequency acoustic wave propagation. They propagate large distances and, as such, the numerical treatment of those problems become difficult in terms of posing boundary conditions which are valid for all frequencies.

REVIEWS OF TOPICAL PROBLEMS: Physical aspects of cryobiology

NASA Astrophysics Data System (ADS)

Zhmakin, A. I.

2008-03-01

Physical phenomena during biological freezing and thawing processes at the molecular, cellular, tissue, and organ levels are examined. The basics of cryosurgery and cryopreservation of cells and tissues are presented. Existing cryobiological models, including numerical ones, are reviewed.

The Function sin x/x.

ERIC Educational Resources Information Center

Gearhart, William B.; Shultz, Harris S.

1990-01-01

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

Numerical Boundary Conditions for Computational Aeroacoustics Benchmark Problems

NASA Technical Reports Server (NTRS)

Tam, Chritsopher K. W.; Kurbatskii, Konstantin A.; Fang, Jun

1997-01-01

Category 1, Problems 1 and 2, Category 2, Problem 2, and Category 3, Problem 2 are solved computationally using the Dispersion-Relation-Preserving (DRP) scheme. All these problems are governed by the linearized Euler equations. The resolution requirements of the DRP scheme for maintaining low numerical dispersion and dissipation as well as accurate wave speeds in solving the linearized Euler equations are now well understood. As long as 8 or more mesh points per wavelength is employed in the numerical computation, high quality results are assured. For the first three categories of benchmark problems, therefore, the real challenge is to develop high quality numerical boundary conditions. For Category 1, Problems 1 and 2, it is the curved wall boundary conditions. For Category 2, Problem 2, it is the internal radiation boundary conditions inside the duct. For Category 3, Problem 2, they are the inflow and outflow boundary conditions upstream and downstream of the blade row. These are the foci of the present investigation. Special nonhomogeneous radiation boundary conditions that generate the incoming disturbances and at the same time allow the outgoing reflected or scattered acoustic disturbances to leave the computation domain without significant reflection are developed. Numerical results based on these boundary conditions are provided.

Current issues and challenges in the management of bariatric patients.

PubMed

Bell, Sue Ellen

2005-01-01

Morbid obesity is an increasingly common healthcare problem, and providers and patients currently face numerous challenges in dealing with this problem effectively. Issues addressed in this article include the effect of stigma, the need for more evidence regarding effective management options, and the declining insurance coverage for bariatric surgery. The role of bariatric surgery in effective management of morbid obesity is discussed, along with the effect on and possible reasons for declining coverage. A comparison between benefits and coverage for bariatric surgery and angioplasty/stent placement is included.

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

NASA Astrophysics Data System (ADS)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

NASA Astrophysics Data System (ADS)

Bao, Weizhu; Jiang, Wei; Wang, Yan; Zhao, Quan

2017-02-01

We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th- or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.

Finite element solution of optimal control problems with inequality constraints

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.

1990-01-01

A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.

Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem

NASA Astrophysics Data System (ADS)

Farrés, Ariadna; Jorba, Àngel; Mondelo, Josep-Maria

2017-09-01

The Augmented Hill Three-Body problem is an extension of the classical Hill problem that, among other applications, has been used to model the motion of a solar sail around an asteroid. This model is a 3 degrees of freedom (3DoF) Hamiltonian system that depends on four parameters. This paper describes the bounded motions (periodic orbits and invariant tori) in an extended neighbourhood of some of the equilibrium points of the model. An interesting feature is the existence of equilibrium points with a 1:1 resonance, whose neighbourhood we also describe. The main tools used are the computation of periodic orbits (including their stability and bifurcations), the reduction of the Hamiltonian to centre manifolds at equilibria, and the numerical approximation of invariant tori. It is remarkable how the combination of these techniques allows the description of the dynamics of a 3DoF Hamiltonian system.

MFIX simulation of NETL/PSRI challenge problem of circulating fluidized bed

DOE PAGES

Li, Tingwen; Dietiker, Jean-François; Shahnam, Mehrdad

2012-12-01

In this paper, numerical simulations of NETL/PSRI challenge problem of circulating fluidized bed (CFB) using the open-source code Multiphase Flow with Interphase eXchange (MFIX) are reported. Two rounds of simulation results are reported including the first-round blind test and the second-round modeling refinement. Three-dimensional high fidelity simulations are conducted to model a 12-inch diameter pilot-scale CFB riser. Detailed comparisons between numerical results and experimental data are made with respect to axial pressure gradient profile, radial profiles of solids velocity and solids mass flux along different radial directions at various elevations for operating conditions covering different fluidization regimes. Overall, the numericalmore » results show that CFD can predict the complex gas–solids flow behavior in the CFB riser reasonably well. In addition, lessons learnt from modeling this challenge problem are presented.« less

Hybrid near-optimal aeroassisted orbit transfer plane change trajectories

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Duckeman, Gregory A.

1994-01-01

In this paper, a hybrid methodology is used to determine optimal open loop controls for the atmospheric portion of the aeroassisted plane change problem. The method is hybrid in the sense that it combines the features of numerical collocation with the analytically tractable portions of the problem which result when the two-point boundary value problem is cast in the form of a regular perturbation problem. Various levels of approximation are introduced by eliminating particular collocation parameters and their effect upon problem complexity and required number of nodes is discussed. The results include plane changes of 10, 20, and 30 degrees for a given vehicle.

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

NASA Astrophysics Data System (ADS)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to create technology «no frost», realizing a steady stream of direct and inverse problems: solving the direct problem, the visualization and comparison with observed data, to solve the inverse problem (correction of the model parameters). The main objective of further work is the creation of a workstation operating emergency tool that could be used by an emergency duty person in real time.

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1994-01-01

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

Classical problems in computational aero-acoustics

NASA Technical Reports Server (NTRS)

Hardin, Jay C.

1996-01-01

In relation to the expected problems in the development of computational aeroacoustics (CAA), the preliminary applications were to classical problems where the known analytical solutions could be used to validate the numerical results. Such comparisons were used to overcome the numerical problems inherent in these calculations. Comparisons were made between the various numerical approaches to the problems such as direct simulations, acoustic analogies and acoustic/viscous splitting techniques. The aim was to demonstrate the applicability of CAA as a tool in the same class as computational fluid dynamics. The scattering problems that occur are considered and simple sources are discussed.

A gradient based algorithm to solve inverse plane bimodular problems of identification

NASA Astrophysics Data System (ADS)

Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing

2018-02-01

This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.

Recent advances in reduction methods for nonlinear problems. [in structural mechanics

NASA Technical Reports Server (NTRS)

Noor, A. K.

1981-01-01

Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (1) selection of basis vectors in nonlinear static and dynamic problems, (2) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (3) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

A Conforming Multigrid Method for the Pure Traction Problem of Linear Elasticity: Mixed Formulation

NASA Technical Reports Server (NTRS)

Lee, Chang-Ock

1996-01-01

A multigrid method using conforming P-1 finite element is developed for the two-dimensional pure traction boundary value problem of linear elasticity. The convergence is uniform even as the material becomes nearly incompressible. A heuristic argument for acceleration of the multigrid method is discussed as well. Numerical results with and without this acceleration as well as performance estimates on a parallel computer are included.

Computation of rotor-stator interaction using the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Chen, Jen-Ping

1995-01-01

The numerical scheme presented belongs to a family of codes known as UNCLE (UNsteady Computation of fieLd Equations) as reported by Whitfield (1995), that is being used to solve problems in a variety of areas including compressible and incompressible flows. This derivation is specifically developed for general unsteady multi-blade-row turbomachinery problems. The scheme solves the Reynolds-averaged N-S equations with the Baldwin-Lomax turbulence model.

Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Radhakrishnan, Krishnan; Hindmarsh, Alan C.

1993-01-01

LSODE, the Livermore Solver for Ordinary Differential Equations, is a package of FORTRAN subroutines designed for the numerical solution of the initial value problem for a system of ordinary differential equations. It is particularly well suited for 'stiff' differential systems, for which the backward differentiation formula method of orders 1 to 5 is provided. The code includes the Adams-Moulton method of orders 1 to 12, so it can be used for nonstiff problems as well. In addition, the user can easily switch methods to increase computational efficiency for problems that change character. For both methods a variety of corrector iteration techniques is included in the code. Also, to minimize computational work, both the step size and method order are varied dynamically. This report presents complete descriptions of the code and integration methods, including their implementation. It also provides a detailed guide to the use of the code, as well as an illustrative example problem.

Extension and Validation of a Hybrid Particle-Finite Element Method for Hypervelocity Impact Simulation. Chapter 2

NASA Technical Reports Server (NTRS)

Fahrenthold, Eric P.; Shivarama, Ravishankar

2004-01-01

The hybrid particle-finite element method of Fahrenthold and Horban, developed for the simulation of hypervelocity impact problems, has been extended to include new formulations of the particle-element kinematics, additional constitutive models, and an improved numerical implementation. The extended formulation has been validated in three dimensional simulations of published impact experiments. The test cases demonstrate good agreement with experiment, good parallel speedup, and numerical convergence of the simulation results.

Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1992-01-01

A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

DROMO formulation for planar motions: solution to the Tsien problem

NASA Astrophysics Data System (ADS)

Urrutxua, Hodei; Morante, David; Sanjurjo-Rivo, Manuel; Peláez, Jesús

2015-06-01

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen's ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo-Stiefel methods.

Computational Physics.

ERIC Educational Resources Information Center

Borcherds, P. H.

1986-01-01

Describes an optional course in "computational physics" offered at the University of Birmingham. Includes an introduction to numerical methods and presents exercises involving fast-Fourier transforms, non-linear least-squares, Monte Carlo methods, and the three-body problem. Recommends adding laboratory work into the course in the…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, David

In the January 2002 edition of SIAM News, Nick Trefethen announced the '$100, 100-Digit Challenge'. In this note he presented ten easy-to-state but hard-to-solve problems of numerical analysis, and challenged readers to find each answer to ten-digit accuracy. Trefethen closed with the enticing comment: 'Hint: They're hard! If anyone gets 50 digits in total, I will be impressed.' This challenge obviously struck a chord in hundreds of numerical mathematicians worldwide, as 94 teams from 25 nations later submitted entries. Many of these submissions exceeded the target of 50 correct digits; in fact, 20 teams achieved a perfect score of 100more » correct digits. Trefethen had offered $100 for the best submission. Given the overwhelming response, a generous donor (William Browning, founder of Applied Mathematics, Inc.) provided additional funds to provide a $100 award to each of the 20 winning teams. Soon after the results were out, four participants, each from a winning team, got together and agreed to write a book about the problems and their solutions. The team is truly international: Bornemann is from Germany, Laurie is from South Africa, Wagon is from the USA, and Waldvogel is from Switzerland. This book provides some mathematical background for each problem, and then shows in detail how each of them can be solved. In fact, multiple solution techniques are mentioned in each case. The book describes how to extend these solutions to much larger problems and much higher numeric precision (hundreds or thousands of digit accuracy). The authors also show how to compute error bounds for the results, so that one can say with confidence that one's results are accurate to the level stated. Numerous numerical software tools are demonstrated in the process, including the commercial products Mathematica, Maple and Matlab. Computer programs that perform many of the algorithms mentioned in the book are provided, both in an appendix to the book and on a website. In the process, the authors take the reader on a wide-ranging tour of modern numerical mathematics, with enough background material so that even readers with little or no training in numerical analysis can follow. Here is a list of just a few of the topics visited: numerical quadrature (i.e., numerical integration), series summation, sequence extrapolation, contour integration, Fourier integrals, high-precision arithmetic, interval arithmetic, symbolic computing, numerical linear algebra, perturbation theory, Euler-Maclaurin summation, global minimization, eigenvalue methods, evolutionary algorithms, matrix preconditioning, random walks, special functions, elliptic functions, Monte-Carlo methods, and numerical differentiation.« less

Role of Brittle Behaviour of Soft Calcarenites Under Low Confinement: Laboratory Observations and Numerical Investigation

NASA Astrophysics Data System (ADS)

Lollino, Piernicola; Andriani, Gioacchino Francesco

2017-07-01

The strength decay that occurs in the post-peak stage, under low confinement stress, represents a key factor of the stress-strain behaviour of rocks. However, for soft rocks this issue is generally underestimated or even neglected in the solution of boundary value problems, as for example those concerning the stability of underground cavities or rocky cliffs. In these cases, the constitutive models frequently used in limit equilibrium analyses or more sophisticated numerical calculations are, respectively, rigid-plastic or elastic-perfectly plastic. In particular, most of commercial continuum-based numerical codes propose a variety of constitutive models, including elasticity, elasto-plasticity, strain-softening and elasto-viscoplasticity, which are not exhaustive in simulating the progressive failure mechanisms affecting brittle rock materials, these being characterized by material detachment and crack opening and propagation. As a consequence, a numerical coupling with mechanical joint propagation is needed to cope with fracture mechanics. Therefore, continuum-based applications that treat the simulation of the failure processes of intact rock masses at low stress levels may need the adoption of numerical techniques capable of implementing fracture mechanics and rock brittleness concepts, as it is shown in this paper. This work is aimed at highlighting, for some applications of rock mechanics, the essential role of post-peak brittleness of soft rocks by means of the application of a hybrid finite-discrete element method. This method allows for a proper simulation of the brittle rock behaviour and the related mechanism of fracture propagation. In particular, the paper presents two ideal problems, represented by a shallow underground cave and a vertical cliff, for which the evolution of the stability conditions is investigated by comparing the solutions obtained implementing different brittle material responses with those resulting from the assumption of perfectly plastic behaviour. To this purpose, a series of petrophysical and mechanical tests were conducted on samples of soft calcarenite belonging to the Calcarenite di Gravina Fm. (Apulia, Southern Italy), focusing specific attention on the post-peak behaviour of the material under three types of loading (compression, indirect tension and shear). Typical geometrical features representative of real rock engineering problems observed in Southern Italy were assumed in the problems examined. The numerical results indicate the impact of soft rock brittleness in the assessment of stability and highlight the need for the adoption of innovative numerical techniques to analyse these types of problems properly.

Hyperbolic heat conduction problems involving non-Fourier effects - Numerical simulations via explicit Lax-Wendroff/Taylor-Galerkin finite element formulations

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; Namburu, Raju R.

1989-01-01

Numerical simulations are presented for hyperbolic heat-conduction problems that involve non-Fourier effects, using explicit, Lax-Wendroff/Taylor-Galerkin FEM formulations as the principal computational tool. Also employed are smoothing techniques which stabilize the numerical noise and accurately predict the propagating thermal disturbances. The accurate capture of propagating thermal disturbances at characteristic time-step values is achieved; numerical test cases are presented which validate the proposed hyperbolic heat-conduction problem concepts.

Computational procedures for mixed equations with shock waves

NASA Technical Reports Server (NTRS)

Yu, N. J.; Seebass, R.

1974-01-01

This paper discusses the procedures we have developed to treat a canonical problem involving a mixed nonlinear equation with boundary data that imply a discontinuous solution. This equation arises in various physical contexts and is basic to the description of the nonlinear acoustic behavior of a shock wave near a caustic. The numerical scheme developed is of second order, treats discontinuities as such by applying the appropriate jump conditions across them, and eliminates the numerical dissipation and dispersion associated with large gradients. Our results are compared with the results of a first-order scheme and with those of a second-order scheme we have developed. The algorithm used here can easily be generalized to more complicated problems, including transonic flows with imbedded shocks.

A practical guide to the Piccolo autopilot

NASA Astrophysics Data System (ADS)

Mornhinweg, Anton

In support of a UAV contract the Piccolo SL and Piccolo II autopilots were installed and operated on various aircraft. Numerous problems with the autopilot setup and analysis processes were found along with numerous problems with documentation and autopilot system information. Major areas of concern are identified along with objectives to eliminate the major areas of concern. Piccolo simulator vehicle gain calculations and Piccolo generation 2 version 2.1.4 control laws are reverse engineered. A complete modeling guide is created. Methods are developed to perform and analyze doublet maneuvers. A series of flight procedures are outlined that include methods for tuning gains. A series of MATLAB graphical user interfaces were created to analyze flight data and pertinent control loop data for gain tuning.

Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Arnold, Andrea; Calvetti, Daniela; Somersalo, Erkki

2014-10-01

A commonly encountered problem in numerous areas of applications is to estimate the unknown coefficients of a dynamical system from direct or indirect observations at discrete times of some of the components of the state vector. A related problem is to estimate unobserved components of the state. An egregious example of such a problem is provided by metabolic models, in which the numerous model parameters and the concentrations of the metabolites in tissue are to be estimated from concentration data in the blood. A popular method for addressing similar questions in stochastic and turbulent dynamics is the ensemble Kalman filter (EnKF), a particle-based filtering method that generalizes classical Kalman filtering. In this work, we adapt the EnKF algorithm for deterministic systems in which the numerical approximation error is interpreted as a stochastic drift with variance based on classical error estimates of numerical integrators. This approach, which is particularly suitable for stiff systems where the stiffness may depend on the parameters, allows us to effectively exploit the parallel nature of particle methods. Moreover, we demonstrate how spatial prior information about the state vector, which helps the stability of the computed solution, can be incorporated into the filter. The viability of the approach is shown by computed examples, including a metabolic system modeling an ischemic episode in skeletal muscle, with a high number of unknown parameters.

Simulating propagation of coherent light in random media using the Fredholm type integral equation

NASA Astrophysics Data System (ADS)

Kraszewski, Maciej; Pluciński, Jerzy

2017-06-01

Studying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g. Radiative Transfer Theory and Monte Carlo methods) but they do not treat coherence properties of light directly. Some variations of these methods allows to predict behavior of coherent light but only for an averaged realization of the scattering medium. This limits their application in studying many physical phenomena connected to a specific distribution of scattering particles (e.g. laser speckle). In general, numerical simulation of coherent light propagation in a specific realization of random medium is a time- and memory-consuming problem. The goal of the presented research was to develop new efficient method for solving this problem. The method, presented in our earlier works, is based on solving the Fredholm type integral equation, which describes multiple light scattering process. This equation can be discretized and solved numerically using various algorithms e.g. by direct solving the corresponding linear equations system, as well as by using iterative or Monte Carlo solvers. Here we present recent development of this method including its comparison with well-known analytical results and a finite-difference type simulations. We also present extension of the method for problems of multiple scattering of a polarized light on large spherical particles that joins presented mathematical formalism with Mie theory.

A technique to remove the tensile instability in weakly compressible SPH

NASA Astrophysics Data System (ADS)

Xu, Xiaoyang; Yu, Peng

2018-01-01

When smoothed particle hydrodynamics (SPH) is directly applied for the numerical simulations of transient viscoelastic free surface flows, a numerical problem called tensile instability arises. In this paper, we develop an optimized particle shifting technique to remove the tensile instability in SPH. The basic equations governing free surface flow of an Oldroyd-B fluid are considered, and approximated by an improved SPH scheme. This includes the implementations of the correction of kernel gradient and the introduction of Rusanov flux into the continuity equation. To verify the effectiveness of the optimized particle shifting technique in removing the tensile instability, the impacting drop, the injection molding of a C-shaped cavity, and the extrudate swell, are conducted. The numerical results obtained are compared with those simulated by other numerical methods. A comparison among different numerical techniques (e.g., the artificial stress) to remove the tensile instability is further performed. All numerical results agree well with the available data.

FEMFLOW3D; a finite-element program for the simulation of three-dimensional aquifers; version 1.0

USGS Publications Warehouse

Durbin, Timothy J.; Bond, Linda D.

1998-01-01

This document also includes model validation, source code, and example input and output files. Model validation was performed using four test problems. For each test problem, the results of a model simulation with FEMFLOW3D were compared with either an analytic solution or the results of an independent numerical approach. The source code, written in the ANSI x3.9-1978 FORTRAN standard, and the complete input and output of an example problem are listed in the appendixes.

lsjk—a C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functions

NASA Astrophysics Data System (ADS)

Kalmykov, M. Yu.; Sheplyakov, A.

2005-10-01

Generalized log-sine functions Lsj(k)(θ) appear in higher order ɛ-expansion of different Feynman diagrams. We present an algorithm for the numerical evaluation of these functions for real arguments. This algorithm is implemented as a C++ library with arbitrary-precision arithmetics for integer 0⩽k⩽9 and j⩾2. Some new relations and representations of the generalized log-sine functions are given. Program summaryTitle of program:lsjk Catalogue number:ADVS Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVS Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing terms: GNU General Public License Computers:all Operating systems:POSIX Programming language:C++ Memory required to execute:Depending on the complexity of the problem, at least 32 MB RAM recommended No. of lines in distributed program, including testing data, etc.:41 975 No. of bytes in distributed program, including testing data, etc.:309 156 Distribution format:tar.gz Other programs called:The CLN library for arbitrary-precision arithmetics is required at version 1.1.5 or greater External files needed:none Nature of the physical problem:Numerical evaluation of the generalized log-sine functions for real argument in the region 0<θ<π. These functions appear in Feynman integrals Method of solution:Series representation for the real argument in the region 0<θ<π Restriction on the complexity of the problem:Limited up to Lsj(9)(θ), and j is an arbitrary integer number. Thus, all function up to the weight 12 in the region 0<θ<π can be evaluated. The algorithm can be extended up to higher values of k(k>9) without modification Typical running time:Depending on the complexity of problem. See text below.

Visualization in Science and the Arts.

ERIC Educational Resources Information Center

Roth, Susan King

Visualization as a factor of intelligence includes the mental manipulation of spatial configurations and has been associated with spatial abilities, creative thinking, and conceptual problem solving. There are numerous reports of scientists and mathematicians using visualization to anticipate transformation of the external world. Artists and…

Workplace Math I: Easing into Math.

ERIC Educational Resources Information Center

Wilson, Nancy; Goschen, Claire

This basic skills learning module includes instruction in performing basic computations, using general numerical concepts such as whole numbers, fractions, decimals, averages, ratios, proportions, percentages, and equivalents in practical situations. The problems are relevant to all aspects of the printing and manufacturing industry, with emphasis…

Numerical solution of the Navier-Stokes equations about three-dimensional configurations: A survey

NASA Technical Reports Server (NTRS)

Holst, Terry L.

1987-01-01

The numerical solution of the Navier-Stokes equations about three-dimensional configurations is reviewed. Formulational and computational requirements for the various Navier-Stokes approaches are examined for typical problems including the viscous flow field solution about a complete aerospace vehicle. Recent computed results, with experimental comparisons when available, are presented to highlight the presentation. The future of Navier-Stokes applications in three-dimensions is seen to be rapidly expanding across a broad front including internal and external flows, and flows across the entire speed regime from incompressible to hypersonic applications. Prospects for the future are described and recommendations for areas of concentrated research are indicated.

The Transport of Mass, Energy, and Entropy in Cryogenic Support Struts for Engineering Design

NASA Technical Reports Server (NTRS)

Elchert, J. P.

2012-01-01

Engineers working to understand and reduce cryogenic boil-off must solve a variety of transport problems. An important class of nonlinear problems involves the thermal and mechanical design of cryogenic struts. These classic problems are scattered about the literature and typically require too many resources to obtain. So, to save time for practicing engineers, the author presents this essay. Herein, a variety of new, old, and revisited analytical and finite difference solutions of the thermal problem are covered in this essay, along with commentary on approach and assumptions. This includes a few thermal radiation and conduction combined mode solutions with a discussion on insulation, optimum emissivity, and geometrical phenomenon. Solutions to cooling and heat interception problems are also presented, including a discussion of the entropy generation. The literature on the combined mechanical and thermal design of cryogenic support struts is reviewed with an introduction to the associated numerical methods.

The Transport of Mass, Energy, and Entropy in Cryogenic Support Struts for Engineering Design

NASA Technical Reports Server (NTRS)

Elchert, J. P.

2012-01-01

Engineers working to understand and reduce cryogenic boil-off must solve a. variety of transport problems. An important class of nonlinear problems involves the thermal and mechanical design of cryogenic struts. These classic problems are scattered about the literature and typically require too many resources to obtain. So, to save time for practicing engineers, the author presents this essay. Herein, a variety of new, old, and revisited analytical and finite difference solutions of the thermal problem are covered in this essay, along with commentary on approach and assumptions, This includes a few thermal radiation and conduction combined mode solution with a discussion on insulation, optimum emissivity, and geometrical phenomenon. Solutions to cooling and heat interception problems are also presented, including a discussion of the entropy generation. And the literature on the combined mechanical and thermal design of cryogenic support struts is reviewed with an introduction to the associated numerical methods.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent experimental, theoretical, and numerical investigations of problems in applied mechanics are discussed in reviews and reports. The fields covered include vibration and stability; the mechanics of elastic and plastic materials; fluid mechanics; the numerical treatment of differential equations; finite and boundary elements; optimization, decision theory, stochastics, and actuarial analysis; applied analysis and mathematical physics; and numerical analysis. Reviews are presented on mathematical applications of geometric-optics methods, biomechanics and implant technology, vibration theory in engineering, the stiffness and strength of damaged materials, and the existence of slow steady flows of viscoelastic fluids of integral type.

A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm

DOE PAGES

Lehe, Remi; Kirchen, Manuel; Andriyash, Igor A.; ...

2016-02-17

We propose a spectral Particle-In-Cell (PIC) algorithm that is based on the combination of a Hankel transform and a Fourier transform. For physical problems that have close-to-cylindrical symmetry, this algorithm can be much faster than full 3D PIC algorithms. In addition, unlike standard finite-difference PIC codes, the proposed algorithm is free of spurious numerical dispersion, in vacuum. This algorithm is benchmarked in several situations that are of interest for laser-plasma interactions. These benchmarks show that it avoids a number of numerical artifacts, that would otherwise affect the physics in a standard PIC algorithm - including the zero-order numerical Cherenkov effect.

Numerical Problems and Agent-Based Models for a Mass Transfer Course

ERIC Educational Resources Information Center

Murthi, Manohar; Shea, Lonnie D.; Snurr, Randall Q.

2009-01-01

Problems requiring numerical solutions of differential equations or the use of agent-based modeling are presented for use in a course on mass transfer. These problems were solved using the popular technical computing language MATLABTM. Students were introduced to MATLAB via a problem with an analytical solution. A more complex problem to which no…

A numerical solution of Duffing's equations including the prediction of jump phenomena

NASA Technical Reports Server (NTRS)

Moyer, E. T., Jr.; Ghasghai-Abdi, E.

1987-01-01

Numerical methodology for the solution of Duffing's differential equation is presented. Algorithms for the prediction of multiple equilibrium solutions and jump phenomena are developed. In addition, a filtering algorithm for producing steady state solutions is presented. The problem of a rigidly clamped circular plate subjected to cosinusoidal pressure loading is solved using the developed algorithms (the plate is assumed to be in the geometrically nonlinear range). The results accurately predict regions of solution multiplicity and jump phenomena.

A numerical method for the stress analysis of stiffened-shell structures under nonuniform temperature distributions

NASA Technical Reports Server (NTRS)

Heldenfels, Richard R

1951-01-01

A numerical method is presented for the stress analysis of stiffened-shell structures of arbitrary cross section under nonuniform temperature distributions. The method is based on a previously published procedure that is extended to include temperature effects and multicell construction. The application of the method to practical problems is discussed and an illustrative analysis is presented of a two-cell box beam under the combined action of vertical loads and a nonuniform temperature distribution.

A suite of benchmark and challenge problems for enhanced geothermal systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Mark; Fu, Pengcheng; McClure, Mark

A diverse suite of numerical simulators is currently being applied to predict or understand the performance of enhanced geothermal systems (EGS). To build confidence and identify critical development needs for these analytical tools, the United States Department of Energy, Geothermal Technologies Office sponsored a Code Comparison Study (GTO-CCS), with participants from universities, industry, and national laboratories. A principal objective for the study was to create a community forum for improvement and verification of numerical simulators for EGS modeling. Teams participating in the study were those representing U.S. national laboratories, universities, and industries, and each team brought unique numerical simulation capabilitiesmore » to bear on the problems. Two classes of problems were developed during the study, benchmark problems and challenge problems. The benchmark problems were structured to test the ability of the collection of numerical simulators to solve various combinations of coupled thermal, hydrologic, geomechanical, and geochemical processes. This class of problems was strictly defined in terms of properties, driving forces, initial conditions, and boundary conditions. The challenge problems were based on the enhanced geothermal systems research conducted at Fenton Hill, near Los Alamos, New Mexico, between 1974 and 1995. The problems involved two phases of research, stimulation, development, and circulation in two separate reservoirs. The challenge problems had specific questions to be answered via numerical simulation in three topical areas: 1) reservoir creation/stimulation, 2) reactive and passive transport, and 3) thermal recovery. Whereas the benchmark class of problems were designed to test capabilities for modeling coupled processes under strictly specified conditions, the stated objective for the challenge class of problems was to demonstrate what new understanding of the Fenton Hill experiments could be realized via the application of modern numerical simulation tools by recognized expert practitioners. We present the suite of benchmark and challenge problems developed for the GTO-CCS, providing problem descriptions and sample solutions.« less

Control optimization, stabilization and computer algorithms for aircraft applications

NASA Technical Reports Server (NTRS)

1975-01-01

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Polynomial modal analysis of slanted lamellar gratings.

PubMed

Granet, Gérard; Randriamihaja, Manjakavola Honore; Raniriharinosy, Karyl

2017-06-01

The problem of diffraction by slanted lamellar dielectric and metallic gratings in classical mounting is formulated as an eigenvalue eigenvector problem. The numerical solution is obtained by using the moment method with Legendre polynomials as expansion and test functions, which allows us to enforce in an exact manner the boundary conditions which determine the eigensolutions. Our method is successfully validated by comparison with other methods including in the case of highly slanted gratings.

Linear Matrix Inequality Method for a Quadratic Performance Index Minimization Problem with a class of Bilinear Matrix Inequality Conditions

NASA Astrophysics Data System (ADS)

Tanemura, M.; Chida, Y.

2016-09-01

There are a lot of design problems of control system which are expressed as a performance index minimization under BMI conditions. However, a minimization problem expressed as LMIs can be easily solved because of the convex property of LMIs. Therefore, many researchers have been studying transforming a variety of control design problems into convex minimization problems expressed as LMIs. This paper proposes an LMI method for a quadratic performance index minimization problem with a class of BMI conditions. The minimization problem treated in this paper includes design problems of state-feedback gain for switched system and so on. The effectiveness of the proposed method is verified through a state-feedback gain design for switched systems and a numerical simulation using the designed feedback gains.

Numerical methods for stiff systems of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Flaherty, J. E.; Omalley, R. E., Jr.

1983-01-01

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

A flux splitting scheme with high-resolution and robustness for discontinuities

NASA Technical Reports Server (NTRS)

Wada, Yasuhiro; Liou, Meng-Sing

1994-01-01

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

Reconstruction of local perturbations in periodic surfaces

NASA Astrophysics Data System (ADS)

Lechleiter, Armin; Zhang, Ruming

2018-03-01

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet-Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply the Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, showing the efficiency of the numerical method.

OpenGeoSys: Performance-Oriented Computational Methods for Numerical Modeling of Flow in Large Hydrogeological Systems

NASA Astrophysics Data System (ADS)

Naumov, D.; Fischer, T.; Böttcher, N.; Watanabe, N.; Walther, M.; Rink, K.; Bilke, L.; Shao, H.; Kolditz, O.

2014-12-01

OpenGeoSys (OGS) is a scientific open source code for numerical simulation of thermo-hydro-mechanical-chemical processes in porous and fractured media. Its basic concept is to provide a flexible numerical framework for solving multi-field problems for applications in geoscience and hydrology as e.g. for CO2 storage applications, geothermal power plant forecast simulation, salt water intrusion, water resources management, etc. Advances in computational mathematics have revolutionized the variety and nature of the problems that can be addressed by environmental scientists and engineers nowadays and an intensive code development in the last years enables in the meantime the solutions of much larger numerical problems and applications. However, solving environmental processes along the water cycle at large scales, like for complete catchment or reservoirs, stays computationally still a challenging task. Therefore, we started a new OGS code development with focus on execution speed and parallelization. In the new version, a local data structure concept improves the instruction and data cache performance by a tight bundling of data with an element-wise numerical integration loop. Dedicated analysis methods enable the investigation of memory-access patterns in the local and global assembler routines, which leads to further data structure optimization for an additional performance gain. The concept is presented together with a technical code analysis of the recent development and a large case study including transient flow simulation in the unsaturated / saturated zone of the Thuringian Syncline, Germany. The analysis is performed on a high-resolution mesh (up to 50M elements) with embedded fault structures.

The aerodynamics of propellers and rotors using an acoustic formulation in the time domain

NASA Technical Reports Server (NTRS)

Long, L. N.

1983-01-01

The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.

Numerical simulation of the hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor

NASA Astrophysics Data System (ADS)

Fortova, S. V.; Shepelev, V. V.; Troshkin, O. V.; Kozlov, S. A.

2017-09-01

The paper presents the results of numerical simulation of the development of hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor encountered in experiments [1-3]. For the numerical solution used the TPS software package (Turbulence Problem Solver) that implements a generalized approach to constructing computer programs for a wide range of problems of hydrodynamics, described by the system of equations of hyperbolic type. As numerical methods are used the method of large particles and ENO-scheme of the second order with Roe solver for the approximate solution of the Riemann problem.

Least-Squares Spectral Element Solutions to the CAA Workshop Benchmark Problems

NASA Technical Reports Server (NTRS)

Lin, Wen H.; Chan, Daniel C.

1997-01-01

This paper presents computed results for some of the CAA benchmark problems via the acoustic solver developed at Rocketdyne CFD Technology Center under the corporate agreement between Boeing North American, Inc. and NASA for the Aerospace Industry Technology Program. The calculations are considered as benchmark testing of the functionality, accuracy, and performance of the solver. Results of these computations demonstrate that the solver is capable of solving the propagation of aeroacoustic signals. Testing of sound generation and on more realistic problems is now pursued for the industrial applications of this solver. Numerical calculations were performed for the second problem of Category 1 of the current workshop problems for an acoustic pulse scattered from a rigid circular cylinder, and for two of the first CAA workshop problems, i. e., the first problem of Category 1 for the propagation of a linear wave and the first problem of Category 4 for an acoustic pulse reflected from a rigid wall in a uniform flow of Mach 0.5. The aim for including the last two problems in this workshop is to test the effectiveness of some boundary conditions set up in the solver. Numerical results of the last two benchmark problems have been compared with their corresponding exact solutions and the comparisons are excellent. This demonstrates the high fidelity of the solver in handling wave propagation problems. This feature lends the method quite attractive in developing a computational acoustic solver for calculating the aero/hydrodynamic noise in a violent flow environment.

Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM

NASA Astrophysics Data System (ADS)

Idelsohn, S. R.; Marti, J.; Souto-Iglesias, A.; Oñate, E.

2008-12-01

The paper aims to introduce new fluid structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular case for which experimental results are not much reported. This is the case of FSI including free surface flows. The possibilities of the Particle Finite Element Method (PFEM) [1] for the simulation of free surface flows is also tested. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Details of the input data for all the examples studied are given. The aim is to identifying benchmark problems for FSI including free surface flows for future comparisons between different numerical approaches.

Numerical Modeling of Electroacoustic Logging Including Joule Heating

NASA Astrophysics Data System (ADS)

Plyushchenkov, Boris D.; Nikitin, Anatoly A.; Turchaninov, Victor I.

It is well known that electromagnetic field excites acoustic wave in a porous elastic medium saturated with fluid electrolyte due to electrokinetic conversion effect. Pride's equations describing this process are written in isothermal approximation. Update of these equations, which allows to take influence of Joule heating on acoustic waves propagation into account, is proposed here. This update includes terms describing the initiation of additional acoustic waves excited by thermoelastic stresses and the heat conduction equation with right side defined by Joule heating. Results of numerical modeling of several problems of propagation of acoustic waves excited by an electric field source with and without consideration of Joule heating effect in their statements are presented. From these results, it follows that influence of Joule heating should be taken into account at the numerical simulation of electroacoustic logging and at the interpretation of its log data.

Numerical methods for stochastic differential equations

NASA Astrophysics Data System (ADS)

Kloeden, Peter; Platen, Eckhard

1991-06-01

The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to the peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, both theory and applications. The main emphasise is placed on the numerical methods needed to solve such equations. It assumes an undergraduate background in mathematical methods typical of engineers and physicists, through many chapters begin with a descriptive summary which may be accessible to others who only require numerical recipes. To help the reader develop an intuitive understanding of the underlying mathematicals and hand-on numerical skills exercises and over 100 PC Exercises (PC-personal computer) are included. The stochastic Taylor expansion provides the key tool for the systematic derivation and investigation of discrete time numerical methods for stochastic differential equations. The book presents many new results on higher order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extrapolation and variance-reduction methods. Besides serving as a basic text on such methods. the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable.

Parameter Estimation and Model Validation of Nonlinear Dynamical Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abarbanel, Henry; Gill, Philip

In the performance period of this work under a DOE contract, the co-PIs, Philip Gill and Henry Abarbanel, developed new methods for statistical data assimilation for problems of DOE interest, including geophysical and biological problems. This included numerical optimization algorithms for variational principles, new parallel processing Monte Carlo routines for performing the path integrals of statistical data assimilation. These results have been summarized in the monograph: “Predicting the Future: Completing Models of Observed Complex Systems” by Henry Abarbanel, published by Spring-Verlag in June 2013. Additional results and details have appeared in the peer reviewed literature.

Metal band drives in spacecraft mechanisms

NASA Technical Reports Server (NTRS)

Maus, Daryl

1993-01-01

Transmitting and changing the characteristics of force and stroke is a requirement in nearly all mechanisms. Examples include changing linear to rotary motion, providing a 90 deg change in direction, and amplifying stroke or force. Requirements for size, weight, efficiency and reliability create unique problems in spacecraft mechanisms. Flexible metal band and cam drive systems provide powerful solutions to these problems. Band drives, rack and pinion gears, and bell cranks are compared for effectiveness. Band drive issues are discussed including materials, bend radius, fabrication, attachment and reliability. Numerous mechanisms are shown which illustrate practical applications of band drives.

Multiple burn fuel-optimal orbit transfers: Numerical trajectory computation and neighboring optimal feedback guidance

NASA Technical Reports Server (NTRS)

Chuang, C.-H.; Goodson, Troy D.; Ledsinger, Laura A.

1995-01-01

This report describes current work in the numerical computation of multiple burn, fuel-optimal orbit transfers and presents an analysis of the second variation for extremal multiple burn orbital transfers as well as a discussion of a guidance scheme which may be implemented for such transfers. The discussion of numerical computation focuses on the use of multivariate interpolation to aid the computation in the numerical optimization. The second variation analysis includes the development of the conditions for the examination of both fixed and free final time transfers. Evaluations for fixed final time are presented for extremal one, two, and three burn solutions of the first variation. The free final time problem is considered for an extremal two burn solution. In addition, corresponding changes of the second variation formulation over thrust arcs and coast arcs are included. The guidance scheme discussed is an implicit scheme which implements a neighboring optimal feedback guidance strategy to calculate both thrust direction and thrust on-off times.

Using Mobile Phone Technology in EFL Classes

ERIC Educational Resources Information Center

Sad, Süleyman Nihat

2008-01-01

Teachers of English as a foreign language (EFL) who want to develop successful lessons face numerous challenges, including large class sizes and inadequate instructional materials and technological support. Another problem is unmotivated students who refuse to participate in class activities. According to Harmer (2007), uncooperative and…

Numerical grid generation techniques. [conference

NASA Technical Reports Server (NTRS)

1980-01-01

The state of the art in topology and flow geometry is presented. Solution techniques for partial differential equations are reviewed and included developments in coordinate transformations, conformal mapping, and invariant imbeddings. Applications of these techniques in fluid mechanics, flow geometry, boundary value problems, and fluidics are presented.

Submission of nucleotide sequence eimeria acervulina profilin to genbank database

USDA-ARS?s Scientific Manuscript database

Poultry coccidiosis, caused by intestinal protozoa Eimeria, is a severe problem for the poultry industry, leading to a substantial economic burden of over three billion dollars worldwide. Conventional vaccines including live vaccines and attenuated vaccines could cause mild to severe reactions Numer...

Geometrically derived difference formulae for the numerical integration of trajectory problems

NASA Technical Reports Server (NTRS)

Mcleod, R. J. Y.; Sanz-Serna, J. M.

1981-01-01

The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested.

Generalized Pattern Search methods for a class of nonsmooth optimization problems with structure

NASA Astrophysics Data System (ADS)

Bogani, C.; Gasparo, M. G.; Papini, A.

2009-07-01

We propose a Generalized Pattern Search (GPS) method to solve a class of nonsmooth minimization problems, where the set of nondifferentiability is included in the union of known hyperplanes and, therefore, is highly structured. Both unconstrained and linearly constrained problems are considered. At each iteration the set of poll directions is enforced to conform to the geometry of both the nondifferentiability set and the boundary of the feasible region, near the current iterate. This is the key issue to guarantee the convergence of certain subsequences of iterates to points which satisfy first-order optimality conditions. Numerical experiments on some classical problems validate the method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jo, J.C.; Shin, W.K.; Choi, C.Y.

Transient heat transfer problems with phase changes (Stefan problems) occur in many engineering situations, including potential core melting and solidification during pressurized-water-reactor severe accidents, ablation of thermal shields, melting and solidification of alloys, and many others. This article addresses the numerical analysis of nonlinear transient heat transfer with melting or solidification. An effective and simple procedure is presented for the simulation of the motion of the boundary and the transient temperature field during the phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual-reciprocity boundary-element method. The dual-reciprocity boundary-element approach providedmore » in this article is much simpler than the usual boundary-element method in applying a reciprocity principle and an available technique for dealing with the domain integral of the boundary element formulation simultaneously. In this article, attention is focused on two-dimensional melting (ablation)/solidification problems for simplicity. The accuracy and effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of some examples of one-phase ablation/solidification problems with their known semianalytical or numerical solutions where available.« less

Investigation of instability of displacement front in non-isothermal flow problems

NASA Astrophysics Data System (ADS)

Syulyukina, Natalia; Pergament, Anna

2012-11-01

In this paper, we investigate the issues of front instability arising in non-isothermal flow displacement processes. The problem of two-phase flow of immiscible fluids, oil and water, is considered, including sources and dependence of viscosity on temperature. Three-dimensional problem with perturbation close to the injection well was considered to find the characteristic scale of the instability. As a result of numerical calculations, theoretical studies on the development of the instability due to the fact that the viscosity of the displacing fluid is less than the viscosity of the displaced have been confirmed. The influence of temperature on the evolution of the instability was considered. For this purpose, the dependence of oil viscosity on temperature has been added to the problem. Numerical calculations were carried out for different values of temperature and it was shown that with increasing of production rate. Thus, it has been demonstrated that the selection of the optimal temperature for injected fluids a possible way for stimulation of oil production also delaying the field water-flooding. This work was supporting by the RFBR grant 12-01-00793-a.

Three-dimensional geoelectric modelling with optimal work/accuracy rate using an adaptive wavelet algorithm

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H. R.; Vorloeper, J.; Dahmen, W.

2010-08-01

Despite the ever-increasing power of modern computers, realistic modelling of complex 3-D earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modelling approaches includes either finite difference or non-adaptive finite element algorithms and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behaviour of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modelled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet-based approach that is applicable to a large range of problems, also including nonlinear problems. In comparison with earlier applications of adaptive solvers to geophysical problems we employ here a new adaptive scheme whose core ingredients arose from a rigorous analysis of the overall asymptotically optimal computational complexity, including in particular, an optimal work/accuracy rate. Our adaptive wavelet algorithm offers several attractive features: (i) for a given subsurface model, it allows the forward modelling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient and (iii) the modelling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving 3-D geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best-fitting subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectric modelling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with high spatial variability of electrical conductivities. The linear dependence of the modelling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementation.

Optimal Routing and Control of Multiple Agents Moving in a Transportation Network and Subject to an Arrival Schedule and Separation Constraints

NASA Technical Reports Server (NTRS)

Sadovsky, A. V.; Davis, D.; Isaacson, D. R.

2012-01-01

We address the problem of navigating a set of moving agents, e.g. automated guided vehicles, through a transportation network so as to bring each agent to its destination at a specified time. Each pair of agents is required to be separated by a minimal distance, generally agent-dependent, at all times. The speed range, initial position, required destination, and required time of arrival at destination for each agent are assumed provided. The movement of each agent is governed by a controlled differential equation (state equation). The problem consists in choosing for each agent a path and a control strategy so as to meet the constraints and reach the destination at the required time. This problem arises in various fields of transportation, including Air Traffic Management and train coordination, and in robotics. The main contribution of the paper is a model that allows to recast this problem as a decoupled collection of problems in classical optimal control and is easily generalized to the case when inertia cannot be neglected. Some qualitative insight into solution behavior is obtained using the Pontryagin Maximum Principle. Sample numerical solutions are computed using a numerical optimal control solver.

Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities?

PubMed

Fuchs, Lynn S; Geary, David C; Compton, Donald L; Fuchs, Douglas; Hamlett, Carol L; Seethaler, Pamela M; Bryant, Joan D; Schatschneider, Christopher

2010-11-01

The purpose of this study was to examine the interplay between basic numerical cognition and domain-general abilities (such as working memory) in explaining school mathematics learning. First graders (N = 280; mean age = 5.77 years) were assessed on 2 types of basic numerical cognition, 8 domain-general abilities, procedural calculations, and word problems in fall and then reassessed on procedural calculations and word problems in spring. Development was indexed by latent change scores, and the interplay between numerical and domain-general abilities was analyzed by multiple regression. Results suggest that the development of different types of formal school mathematics depends on different constellations of numerical versus general cognitive abilities. When controlling for 8 domain-general abilities, both aspects of basic numerical cognition were uniquely predictive of procedural calculations and word problems development. Yet, for procedural calculations development, the additional amount of variance explained by the set of domain-general abilities was not significant, and only counting span was uniquely predictive. By contrast, for word problems development, the set of domain-general abilities did provide additional explanatory value, accounting for about the same amount of variance as the basic numerical cognition variables. Language, attentive behavior, nonverbal problem solving, and listening span were uniquely predictive.

Numerical Modeling of the Photothermal Processing for Bubble Forming around Nanowire in a Liquid

PubMed Central

Chaari, Anis; Giraud-Moreau, Laurence

2014-01-01

An accurate computation of the temperature is an important factor in determining the shape of a bubble around a nanowire immersed in a liquid. The study of the physical phenomenon consists in solving a photothermic coupled problem between light and nanowire. The numerical multiphysic model is used to study the variations of the temperature and the shape of the created bubble by illumination of the nanowire. The optimization process, including an adaptive remeshing scheme, is used to solve the problem through a finite element method. The study of the shape evolution of the bubble is made taking into account the physical and geometrical parameters of the nanowire. The relation between the sizes and shapes of the bubble and nanowire is deduced. PMID:24795538

Reservoir computing on the hypersphere

NASA Astrophysics Data System (ADS)

Andrecut, M.

Reservoir Computing (RC) refers to a Recurrent Neural Network (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a classifier (the hidden-output readout layer). Here, we focus on the sequence learning problem, and we explore a different approach to RC. More specifically, we remove the nonlinear neural activation function, and we consider an orthogonal reservoir acting on normalized states on the unit hypersphere. Surprisingly, our numerical results show that the system’s memory capacity exceeds the dimensionality of the reservoir, which is the upper bound for the typical RC approach based on Echo State Networks (ESNs). We also show how the proposed system can be applied to symmetric cryptography problems, and we include a numerical implementation.

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bokanowski, Olivier, E-mail: boka@math.jussieu.fr; Picarelli, Athena, E-mail: athena.picarelli@inria.fr; Zidani, Hasnaa, E-mail: hasnaa.zidani@ensta.fr

2015-02-15

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system ofmore » controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.« less

Numerical modeling of spray combustion with an advanced VOF method

NASA Technical Reports Server (NTRS)

Chen, Yen-Sen; Shang, Huan-Min; Shih, Ming-Hsin; Liaw, Paul

1995-01-01

This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.

A fully-implicit high-order system thermal-hydraulics model for advanced non-LWR safety analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Rui

An advanced system analysis tool is being developed for advanced reactor safety analysis. This paper describes the underlying physics and numerical models used in the code, including the governing equations, the stabilization schemes, the high-order spatial and temporal discretization schemes, and the Jacobian Free Newton Krylov solution method. The effects of the spatial and temporal discretization schemes are investigated. Additionally, a series of verification test problems are presented to confirm the high-order schemes. Furthermore, it is demonstrated that the developed system thermal-hydraulics model can be strictly verified with the theoretical convergence rates, and that it performs very well for amore » wide range of flow problems with high accuracy, efficiency, and minimal numerical diffusions.« less

A fully-implicit high-order system thermal-hydraulics model for advanced non-LWR safety analyses

DOE PAGES

Hu, Rui

2016-11-19

An advanced system analysis tool is being developed for advanced reactor safety analysis. This paper describes the underlying physics and numerical models used in the code, including the governing equations, the stabilization schemes, the high-order spatial and temporal discretization schemes, and the Jacobian Free Newton Krylov solution method. The effects of the spatial and temporal discretization schemes are investigated. Additionally, a series of verification test problems are presented to confirm the high-order schemes. Furthermore, it is demonstrated that the developed system thermal-hydraulics model can be strictly verified with the theoretical convergence rates, and that it performs very well for amore » wide range of flow problems with high accuracy, efficiency, and minimal numerical diffusions.« less

Inversion of geophysical potential field data using the finite element method

NASA Astrophysics Data System (ADS)

Lamichhane, Bishnu P.; Gross, Lutz

2017-12-01

The inversion of geophysical potential field data can be formulated as an optimization problem with a constraint in the form of a partial differential equation (PDE). It is common practice, if possible, to provide an analytical solution for the forward problem and to reduce the problem to a finite dimensional optimization problem. In an alternative approach the optimization is applied to the problem and the resulting continuous problem which is defined by a set of coupled PDEs is subsequently solved using a standard PDE discretization method, such as the finite element method (FEM). In this paper, we show that under very mild conditions on the data misfit functional and the forward problem in the three-dimensional space, the continuous optimization problem and its FEM discretization are well-posed including the existence and uniqueness of respective solutions. We provide error estimates for the FEM solution. A main result of the paper is that the FEM spaces used for the forward problem and the Lagrange multiplier need to be identical but can be chosen independently from the FEM space used to represent the unknown physical property. We will demonstrate the convergence of the solution approximations in a numerical example. The second numerical example which investigates the selection of FEM spaces, shows that from the perspective of computational efficiency one should use 2 to 4 times finer mesh for the forward problem in comparison to the mesh of the physical property.

A numerical solution of a singular boundary value problem arising in boundary layer theory.

PubMed

Hu, Jiancheng

2016-01-01

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

Controlling Reflections from Mesh Refinement Interfaces in Numerical Relativity

NASA Technical Reports Server (NTRS)

Baker, John G.; Van Meter, James R.

2005-01-01

A leading approach to improving the accuracy on numerical relativity simulations of black hole systems is through fixed or adaptive mesh refinement techniques. We describe a generic numerical error which manifests as slowly converging, artificial reflections from refinement boundaries in a broad class of mesh-refinement implementations, potentially limiting the effectiveness of mesh- refinement techniques for some numerical relativity applications. We elucidate this numerical effect by presenting a model problem which exhibits the phenomenon, but which is simple enough that its numerical error can be understood analytically. Our analysis shows that the effect is caused by variations in finite differencing error generated across low and high resolution regions, and that its slow convergence is caused by the presence of dramatic speed differences among propagation modes typical of 3+1 relativity. Lastly, we resolve the problem, presenting a class of finite-differencing stencil modifications which eliminate this pathology in both our model problem and in numerical relativity examples.

Benchmark Problems of the Geothermal Technologies Office Code Comparison Study

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Mark D.; Podgorney, Robert; Kelkar, Sharad M.

A diverse suite of numerical simulators is currently being applied to predict or understand the performance of enhanced geothermal systems (EGS). To build confidence and identify critical development needs for these analytical tools, the United States Department of Energy, Geothermal Technologies Office has sponsored a Code Comparison Study (GTO-CCS), with participants from universities, industry, and national laboratories. A principal objective for the study was to create a community forum for improvement and verification of numerical simulators for EGS modeling. Teams participating in the study were those representing U.S. national laboratories, universities, and industries, and each team brought unique numerical simulationmore » capabilities to bear on the problems. Two classes of problems were developed during the study, benchmark problems and challenge problems. The benchmark problems were structured to test the ability of the collection of numerical simulators to solve various combinations of coupled thermal, hydrologic, geomechanical, and geochemical processes. This class of problems was strictly defined in terms of properties, driving forces, initial conditions, and boundary conditions. Study participants submitted solutions to problems for which their simulation tools were deemed capable or nearly capable. Some participating codes were originally developed for EGS applications whereas some others were designed for different applications but can simulate processes similar to those in EGS. Solution submissions from both were encouraged. In some cases, participants made small incremental changes to their numerical simulation codes to address specific elements of the problem, and in other cases participants submitted solutions with existing simulation tools, acknowledging the limitations of the code. The challenge problems were based on the enhanced geothermal systems research conducted at Fenton Hill, near Los Alamos, New Mexico, between 1974 and 1995. The problems involved two phases of research, stimulation, development, and circulation in two separate reservoirs. The challenge problems had specific questions to be answered via numerical simulation in three topical areas: 1) reservoir creation/stimulation, 2) reactive and passive transport, and 3) thermal recovery. Whereas the benchmark class of problems were designed to test capabilities for modeling coupled processes under strictly specified conditions, the stated objective for the challenge class of problems was to demonstrate what new understanding of the Fenton Hill experiments could be realized via the application of modern numerical simulation tools by recognized expert practitioners.« less

New Additions to the Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment.

PubMed

Coll-Font, Jaume; Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrel J; Wang, Dafang; Brooks, Dana H; van Dam, Peter; Macleod, Rob S

2014-09-01

Cardiac electrical imaging often requires the examination of different forward and inverse problem formulations based on mathematical and numerical approximations of the underlying source and the intervening volume conductor that can generate the associated voltages on the surface of the body. If the goal is to recover the source on the heart from body surface potentials, the solution strategy must include numerical techniques that can incorporate appropriate constraints and recover useful solutions, even though the problem is badly posed. Creating complete software solutions to such problems is a daunting undertaking. In order to make such tools more accessible to a broad array of researchers, the Center for Integrative Biomedical Computing (CIBC) has made an ECG forward/inverse toolkit available within the open source SCIRun system. Here we report on three new methods added to the inverse suite of the toolkit. These new algorithms, namely a Total Variation method, a non-decreasing TMP inverse and a spline-based inverse, consist of two inverse methods that take advantage of the temporal structure of the heart potentials and one that leverages the spatial characteristics of the transmembrane potentials. These three methods further expand the possibilities of researchers in cardiology to explore and compare solutions to their particular imaging problem.

SUBOPT: A CAD program for suboptimal linear regulators

NASA Technical Reports Server (NTRS)

Fleming, P. J.

1985-01-01

An interactive software package which provides design solutions for both standard linear quadratic regulator (LQR) and suboptimal linear regulator problems is described. Intended for time-invariant continuous systems, the package is easily modified to include sampled-data systems. LQR designs are obtained by established techniques while the large class of suboptimal problems containing controller and/or performance index options is solved using a robust gradient minimization technique. Numerical examples demonstrate features of the package and recent developments are described.

Cumulative reports and publications through December 31, 1991

NASA Technical Reports Server (NTRS)

1992-01-01

A reports and publications list is given from the Institute for Computer Applications in Science and Engineering (ICASE) through December 31, 1991. The major categories of the current ICASE research program are; numerical methods, control and parameter identification problems, computational problems in engineering and the physical sciences, and computer systems and software. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when available.

Bonded half planes containing an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Aksogan, O.

1973-01-01

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin transforms, the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given include the stress intensity factors, tHe strain energy release rates, and tHe probable cleavage angles giving the direction of crack propagation.

Constructing space difference schemes which satisfy a cell entropy inequality

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1989-01-01

A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Battered Agency Syndrome: The Challenge to Agencies Serving Low-Income Communities.

ERIC Educational Resources Information Center

Reed, Diane; Lally, J. Ronald; Quiett, Douglas

Community-based social service agencies working in low-income communities increasingly function with inadequate support and encounter numerous oppressive external and internal conditions that compromise organizational and staff well-being. Working with many such agencies, WestEd identified stressors that included funding problems, unrealistic…

Group Therapy Techniques for Sexually Abused Preteen Girls.

ERIC Educational Resources Information Center

Berman, Pearl

1990-01-01

Describes an open-ended, structured, highly intensive therapy group for sexually abused preteen girls that was the primary mode of treatment for 11 girls from low-income, rural White families with numerous problems. Unique features of the group included simultaneous group and individualized goals. (Author/BB)

Numerical Differentiation of Noisy, Nonsmooth Data

DOE PAGES

Chartrand, Rick

2011-01-01

We consider the problem of differentiating a function specified by noisy data. Regularizing the differentiation process avoids the noise amplification of finite-difference methods. We use total-variation regularization, which allows for discontinuous solutions. The resulting simple algorithm accurately differentiates noisy functions, including those which have a discontinuous derivative.

Reformulation of the covering and quantizer problems as ground states of interacting particles.

PubMed

Torquato, S

2010-11-01

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d-dimensional Euclidean space R(d) interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in R(d) that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the "void" nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their "dual" solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4 , depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the quantizer error using sphere-packing solutions, which are generally substantially sharper than an existing upper bound in low to moderately large dimensions. We also demonstrate that disordered saturated sphere packings yield relatively good quantizers. Finally, we remark on possible applications of our results for the detection of gravitational waves.

Reformulation of the covering and quantizer problems as ground states of interacting particles

NASA Astrophysics Data System (ADS)

Torquato, S.

2010-11-01

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d -dimensional Euclidean space Rd interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in Rd that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the “void” nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their “dual” solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4 , depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the quantizer error using sphere-packing solutions, which are generally substantially sharper than an existing upper bound in low to moderately large dimensions. We also demonstrate that disordered saturated sphere packings yield relatively good quantizers. Finally, we remark on possible applications of our results for the detection of gravitational waves.

Competitive Facility Location with Fuzzy Random Demands

NASA Astrophysics Data System (ADS)

Uno, Takeshi; Katagiri, Hideki; Kato, Kosuke

2010-10-01

This paper proposes a new location problem of competitive facilities, e.g. shops, with uncertainty and vagueness including demands for the facilities in a plane. By representing the demands for facilities as fuzzy random variables, the location problem can be formulated as a fuzzy random programming problem. For solving the fuzzy random programming problem, first the α-level sets for fuzzy numbers are used for transforming it to a stochastic programming problem, and secondly, by using their expectations and variances, it can be reformulated to a deterministic programming problem. After showing that one of their optimal solutions can be found by solving 0-1 programming problems, their solution method is proposed by improving the tabu search algorithm with strategic oscillation. The efficiency of the proposed method is shown by applying it to numerical examples of the facility location problems.

An analytic-geometric model of the effect of spherically distributed injection errors for Galileo and Ulysses spacecraft - The multi-stage problem

NASA Technical Reports Server (NTRS)

Longuski, James M.; Mcronald, Angus D.

1988-01-01

In previous work the problem of injecting the Galileo and Ulysses spacecraft from low earth orbit into their respective interplanetary trajectories has been discussed for the single stage (Centaur) vehicle. The central issue, in the event of spherically distributed injection errors, is what happens to the vehicle? The difficulties addressed in this paper involve the multi-stage problem since both Galileo and Ulysses will be utilizing the two-stage IUS system. Ulysses will also include a third stage: the PAM-S. The solution is expressed in terms of probabilities for total percentage of escape, orbit decay and reentry trajectories. Analytic solutions are found for Hill's Equations of Relative Motion (more recently called Clohessy-Wiltshire Equations) for multi-stage injections. These solutions are interpreted geometrically on the injection sphere. The analytic-geometric models compare well with numerical solutions, provide insight into the behavior of trajectories mapped on the injection sphere and simplify the numerical two-dimensional search for trajectory families.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques.

PubMed

Vilas, Carlos; Balsa-Canto, Eva; García, Maria-Sonia G; Banga, Julio R; Alonso, Antonio A

2012-07-02

Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations.This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.

Domain decomposition method for the Baltic Sea based on theory of adjoint equation and inverse problem.

NASA Astrophysics Data System (ADS)

Lezina, Natalya; Agoshkov, Valery

2017-04-01

Domain decomposition method (DDM) allows one to present a domain with complex geometry as a set of essentially simpler subdomains. This method is particularly applied for the hydrodynamics of oceans and seas. In each subdomain the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations is solved. The problem of obtaining solution in the whole domain is that it is necessary to combine solutions in subdomains. For this purposes iterative algorithm is created and numerical experiments are conducted to investigate an effectiveness of developed algorithm using DDM. For symmetric operators in DDM, Poincare-Steklov's operators [1] are used, but for the problems of the hydrodynamics, it is not suitable. In this case for the problem, adjoint equation method [2] and inverse problem theory are used. In addition, it is possible to create algorithms for the parallel calculations using DDM on multiprocessor computer system. DDM for the model of the Baltic Sea dynamics is numerically studied. The results of numerical experiments using DDM are compared with the solution of the system of hydrodynamic equations in the whole domain. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments). [1] V.I. Agoshkov, Domain Decompositions Methods in the Mathematical Physics Problem // Numerical processes and systems, No 8, Moscow, 1991 (in Russian). [2] V.I. Agoshkov, Optimal Control Approaches and Adjoint Equations in the Mathematical Physics Problem, Institute of Numerical Mathematics, RAS, Moscow, 2003 (in Russian).

An Investigation into Students' Difficulties in Numerical Problem Solving Questions in High School Biology Using a Numeracy Framework

ERIC Educational Resources Information Center

Scott, Fraser J.

2016-01-01

The "mathematics problem" is a well-known source of difficulty for students attempting numerical problem solving questions in the context of science education. This paper illuminates this problem from a biology education perspective by invoking Hogan's numeracy framework. In doing so, this study has revealed that the contextualisation of…

Numerical simulation of transient, incongruent vaporization induced by high power laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsai, C.H.

1981-01-01

A mathematical model and numerical calculations were developed to solve the heat and mass transfer problems specifically for uranum oxide subject to laser irradiation. It can easily be modified for other heat sources or/and other materials. In the uranium-oxygen system, oxygen is the preferentially vaporizing component, and as a result of the finite mobility of oxygen in the solid, an oxygen deficiency is set up near the surface. Because of the bivariant behavior of uranium oxide, the heat transfer problem and the oxygen diffusion problem are coupled and a numerical method of simultaneously solving the two boundary value problems ismore » studied. The temperature dependence of the thermal properties and oxygen diffusivity, as well as the highly ablative effect on the surface, leads to considerable non-linearities in both the governing differential equations and the boundary conditions. Based on the earlier work done in this laboratory by Olstad and Olander on Iron and on Zirconium hydride, the generality of the problem is expanded and the efficiency of the numerical scheme is improved. The finite difference method, along with some advanced numerical techniques, is found to be an efficient way to solve this problem.« less

Viscous flow computations using a second-order upwind differencing scheme

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1988-01-01

In the present computations of a wide range of fluid flow problems by means of the primitive variables-incorporating Navier-Stokes equations, a mixed second-order upwinding scheme approximates the convective terms of the transport equations and the scheme's accuracy is verified for convection-dominated high Re number flow problems. An adaptive dissipation scheme is used as a monotonic supersonic shock flow capture mechanism. Many benchmark fluid flow problems, including the compressible and incompressible, laminar and turbulent, over a wide range of M and Re numbers, are presently studied to verify the accuracy and robustness of this numerical method.

Stress-free end problem in layered materials

NASA Technical Reports Server (NTRS)

Erdogan, F.; Bakioglu, M.

1977-01-01

In this paper the plane elastostatic problem for a medium which consists of periodically arranged two sets of bonded dissimilar layers or strips is considered. First it is assumed that one set of strips contains a crack which crosses the bimaterial interfaces. Then, by letting the collinear cracks join, the stress-free end problem is formulated. The singular behavior of the solutions at the point on intersection of the stress-free boundary and the interfaces is examined and appropriate stress intensity factors are defined. The results of some numerical examples are then presented which include the cases of both plane stress and plane strain.

SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-09-01

This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

Assessment of Efficiency and Performance in Tsunami Numerical Modeling with GPU

NASA Astrophysics Data System (ADS)

Yalciner, Bora; Zaytsev, Andrey

2017-04-01

Non-linear shallow water equations (NSWE) are used to solve the propagation and coastal amplification of long waves and tsunamis. Leap Frog scheme of finite difference technique is one of the satisfactory numerical methods which is widely used in these problems. Tsunami numerical models are necessary for not only academic but also operational purposes which need faster and accurate solutions. Recent developments in information technology provide considerably faster numerical solutions in this respect and are becoming one of the crucial requirements. Tsunami numerical code NAMI DANCE uses finite difference numerical method to solve linear and non-linear forms of shallow water equations for long wave problems, specifically for tsunamis. In this study, the new code is structured for Graphical Processing Unit (GPU) using CUDA API. The new code is applied to different (analytical, experimental and field) benchmark problems of tsunamis for tests. One of those applications is 2011 Great East Japan tsunami which was instrumentally recorded on various types of gauges including tide and wave gauges and offshore GPS buoys cabled Ocean Bottom Pressure (OBP) gauges and DART buoys. The accuracy of the results are compared with the measurements and fairly well agreements are obtained. The efficiency and performance of the code is also compared with the version using multi-core Central Processing Unit (CPU). Dependence of simulation speed with GPU on linear or non-linear solutions is also investigated. One of the results is that the simulation speed is increased up to 75 times comparing to the process time in the computer using single 4/8 thread multi-core CPU. The results are presented with comparisons and discussions. Furthermore how multi-dimensional finite difference problems fits towards GPU architecture is also discussed. The research leading to this study has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement No: 603839 (Project ASTARTE-Assessment, Strategy and Risk Reduction for Tsunamis in Europe). PARI, Japan and NOAA, USA are acknowledged for the data of the measurements. Prof. Ahmet C. Yalciner is also acknowledged for his long term and sustained support to the authors.

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

NASA Astrophysics Data System (ADS)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

NASA Technical Reports Server (NTRS)

Cerro, J. A.; Scotti, S. J.

1991-01-01

Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.

A Series of MATLAB Learning Modules to Enhance Numerical Competency in Applied Marine Sciences

NASA Astrophysics Data System (ADS)

Fischer, A. M.; Lucieer, V.; Burke, C.

2016-12-01

Enhanced numerical competency to navigate the massive data landscapes are critical skills students need to effectively explore, analyse and visualize complex patterns in high-dimensional data for addressing the complexity of many of the world's problems. This is especially the case for interdisciplinary, undergraduate applied marine science programs, where students are required to demonstrate competency in methods and ideas across multiple disciplines. In response to this challenge, we have developed a series of repository-based data exploration, analysis and visualization modules in MATLAB for integration across various attending and online classes within the University of Tasmania. The primary focus of these modules is to teach students to collect, aggregate and interpret data from large on-line marine scientific data repositories to, 1) gain technical skills in discovering, accessing, managing and visualising large, numerous data sources, 2) interpret, analyse and design approaches to visualise these data, and 3) to address, through numerical approaches, complex, real-world problems, that the traditional scientific methods cannot address. All modules, implemented through a MATLAB live script, include a short recorded lecture to introduce the topic, a handout that gives an overview of the activities, an instructor's manual with a detailed methodology and discussion points, a student assessment (quiz and level-specific challenge task), and a survey. The marine science themes addressed through these modules include biodiversity, habitat mapping, algal blooms and sea surface temperature change and utilize a series of marine science and oceanographic data portals. Through these modules students, with minimal experience in MATLAB or numerical methods are introduced to array indexing, concatenation, sorting, and reshaping, principal component analysis, spectral analysis and unsupervised classification within the context of oceanographic processes, marine geology and marine community ecology.

Parameter assessment for virtual Stackelberg game in aerodynamic shape optimization

NASA Astrophysics Data System (ADS)

Wang, Jing; Xie, Fangfang; Zheng, Yao; Zhang, Jifa

2018-05-01

In this paper, parametric studies of virtual Stackelberg game (VSG) are conducted to assess the impact of critical parameters on aerodynamic shape optimization, including design cycle, split of design variables and role assignment. Typical numerical cases, including the inverse design and drag reduction design of airfoil, have been carried out. The numerical results confirm the effectiveness and efficiency of VSG. Furthermore, the most significant parameters are identified, e.g. the increase of design cycle can improve the optimization results but it will also add computational burden. These studies will maximize the productivity of the effort in aerodynamic optimization for more complicated engineering problems, such as the multi-element airfoil and wing-body configurations.

Application of triggered lightning numerical models to the F106B and extension to other aircraft

NASA Technical Reports Server (NTRS)

Ng, Poh H.; Dalke, Roger A.; Horembala, Jim; Rudolph, Terence; Perala, Rodney A.

1988-01-01

The goal of the F106B Thunderstorm Research Program is to characterize the lightning environment for aircraft in flight. This report describes the application of numerical electromagnetic models to this problem. Topics include: (1) Extensive application of linear triggered lightning to F106B data; (2) Electrostatic analysis of F106B field mill data; (3) Application of subgrid modeling to F106B nose region, including both static and nonlinear models; (4) Extension of F106B results to other aircraft of varying sizes and shapes; and (5) Application of nonlinear model to interaction of F106B with lightning leader-return stroke event.

Designing Adaptive Low Dissipative High Order Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, B.; Parks, John W. (Technical Monitor)

2002-01-01

Proper control of the numerical dissipation/filter to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical dissipation/filter are not only physical problem dependent, but also vary from one flow region to another. This is particularly true for unsteady high-speed shock/shear/boundary-layer/turbulence/acoustics interactions and/or combustion problems since the dynamics of the nonlinear effect of these flows are not well-understood. Even with extensive grid refinement, it is of paramount importance to have proper control on the type and amount of numerical dissipation/filter in regions where it is needed.

Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

DTIC Science & Technology

2018-03-14

pricing, Appl. Math . Comp. Vol.305, 174-187 (2017) 5. W. Li, S. Wang, Pricing European options with proportional transaction costs and stochastic...for fractional differential equation. Numer. Math . Theor. Methods Appl. 5, 229–241, 2012. [23] Kilbas A.A. and Marzan, S.A., Cauchy problem for...numerical technique for solving fractional optimal control problems, Comput. Math . Appl., 62, Issue 3, 1055–1067, 2011. [26] Lotfi A., Yousefi SA., Dehghan M

Numerical Optimization Using Computer Experiments

NASA Technical Reports Server (NTRS)

Trosset, Michael W.; Torczon, Virginia

1997-01-01

Engineering design optimization often gives rise to problems in which expensive objective functions are minimized by derivative-free methods. We propose a method for solving such problems that synthesizes ideas from the numerical optimization and computer experiment literatures. Our approach relies on kriging known function values to construct a sequence of surrogate models of the objective function that are used to guide a grid search for a minimizer. Results from numerical experiments on a standard test problem are presented.

Problems with numerical techniques: Application to mid-loop operation transients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bryce, W.M.; Lillington, J.N.

1997-07-01

There has been an increasing need to consider accidents at shutdown which have been shown in some PSAs to provide a significant contribution to overall risk. In the UK experience has been gained at three levels: (1) Assessment of codes against experiments; (2) Plant studies specifically for Sizewell B; and (3) Detailed review of modelling to support the plant studies for Sizewell B. The work has largely been carried out using various versions of RELAP5 and SCDAP/RELAP5. The paper details some of the problems that have needed to be addressed. It is believed by the authors that these kinds ofmore » problems are probably generic to most of the present generation system thermal-hydraulic codes for the conditions present in mid-loop transients. Thus as far as possible these problems and solutions are proposed in generic terms. The areas addressed include: condensables at low pressure, poor time step calculation detection, water packing, inadequate physical modelling, numerical heat transfer and mass errors. In general single code modifications have been proposed to solve the problems. These have been very much concerned with means of improving existing models rather than by formulating a completely new approach. They have been produced after a particular problem has arisen. Thus, and this has been borne out in practice, the danger is that when new transients are attempted, new problems arise which then also require patching.« less

Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felício B.

2017-12-01

Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner-Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

An Empirical Comparison of Seven Iterative and Evolutionary Function Optimization Heuristics

NASA Technical Reports Server (NTRS)

Baluja, Shumeet

1995-01-01

This report is a repository of the results obtained from a large scale empirical comparison of seven iterative and evolution-based optimization heuristics. Twenty-seven static optimization problems, spanning six sets of problem classes which are commonly explored in genetic algorithm literature, are examined. The problem sets include job-shop scheduling, traveling salesman, knapsack, binpacking, neural network weight optimization, and standard numerical optimization. The search spaces in these problems range from 2368 to 22040. The results indicate that using genetic algorithms for the optimization of static functions does not yield a benefit, in terms of the final answer obtained, over simpler optimization heuristics. Descriptions of the algorithms tested and the encodings of the problems are described in detail for reproducibility.

BAS Brings Continuous Savings to Nebraska School District.

ERIC Educational Resources Information Center

Energy Management Technology, 1985

1985-01-01

Discusses advantages of a building automation system (BAS) used for monitoring and controlling 16 buildings (1,000,000 square feet). Problems solved and savings occurred with air handlers, indoor pool, minerals in boilers, and service tunnels. The system included numerous advantages for operators and paid for itself in 15 months. (DH)

Orange-fleshed sweet potatoes are an excellent source of vitamin A

USDA-ARS?s Scientific Manuscript database

Vitamin A is an essential vitamin required for growth, vision, and immune function. Vitamin A deficiency is a public health problem in numerous countries. 208 million women and children suffer from vitamin A deficiency worldwide. Several carotenoids, including beta-carotene, can be converted to vi...

The Schrodinger Eigenvalue March

ERIC Educational Resources Information Center

Tannous, C.; Langlois, J.

2011-01-01

A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…

Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-03-09

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3Dmore » code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.« less

Unconditionally energy stable time stepping scheme for Cahn–Morral equation: Application to multi-component spinodal decomposition and optimal space tiling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tavakoli, Rouhollah, E-mail: rtavakoli@sharif.ir

An unconditionally energy stable time stepping scheme is introduced to solve Cahn–Morral-like equations in the present study. It is constructed based on the combination of David Eyre's time stepping scheme and Schur complement approach. Although the presented method is general and independent of the choice of homogeneous free energy density function term, logarithmic and polynomial energy functions are specifically considered in this paper. The method is applied to study the spinodal decomposition in multi-component systems and optimal space tiling problems. A penalization strategy is developed, in the case of later problem, to avoid trivial solutions. Extensive numerical experiments demonstrate themore » success and performance of the presented method. According to the numerical results, the method is convergent and energy stable, independent of the choice of time stepsize. Its MATLAB implementation is included in the appendix for the numerical evaluation of algorithm and reproduction of the presented results. -- Highlights: •Extension of Eyre's convex–concave splitting scheme to multiphase systems. •Efficient solution of spinodal decomposition in multi-component systems. •Efficient solution of least perimeter periodic space partitioning problem. •Developing a penalization strategy to avoid trivial solutions. •Presentation of MATLAB implementation of the introduced algorithm.« less

Testing density-dependent groundwater models: Two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

USGS Publications Warehouse

Weatherill, D.; Simmons, C.T.; Voss, C.I.; Robinson, N.I.

2004-01-01

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA-A model for saturated-unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4??2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature. ?? 2004 Elsevier Ltd. All rights reserved.

Numerical optimization methods for controlled systems with parameters

NASA Astrophysics Data System (ADS)

Tyatyushkin, A. I.

2017-10-01

First- and second-order numerical methods for optimizing controlled dynamical systems with parameters are discussed. In unconstrained-parameter problems, the control parameters are optimized by applying the conjugate gradient method. A more accurate numerical solution in these problems is produced by Newton's method based on a second-order functional increment formula. Next, a general optimal control problem with state constraints and parameters involved on the righthand sides of the controlled system and in the initial conditions is considered. This complicated problem is reduced to a mathematical programming one, followed by the search for optimal parameter values and control functions by applying a multimethod algorithm. The performance of the proposed technique is demonstrated by solving application problems.

Solving traveling salesman problems with DNA molecules encoding numerical values.

PubMed

Lee, Ji Youn; Shin, Soo-Yong; Park, Tai Hyun; Zhang, Byoung-Tak

2004-12-01

We introduce a DNA encoding method to represent numerical values and a biased molecular algorithm based on the thermodynamic properties of DNA. DNA strands are designed to encode real values by variation of their melting temperatures. The thermodynamic properties of DNA are used for effective local search of optimal solutions using biochemical techniques, such as denaturation temperature gradient polymerase chain reaction and temperature gradient gel electrophoresis. The proposed method was successfully applied to the traveling salesman problem, an instance of optimization problems on weighted graphs. This work extends the capability of DNA computing to solving numerical optimization problems, which is contrasted with other DNA computing methods focusing on logical problem solving.

Reactive transport codes for subsurface environmental simulation

DOE PAGES

Steefel, C. I.; Appelo, C. A. J.; Arora, B.; ...

2014-09-26

A general description of the mathematical and numerical formulations used in modern numerical reactive transport codes relevant for subsurface environmental simulations is presented. The formulations are followed by short descriptions of commonly used and available subsurface simulators that consider continuum representations of flow, transport, and reactions in porous media. These formulations are applicable to most of the subsurface environmental benchmark problems included in this special issue. The list of codes described briefly here includes PHREEQC, HPx, PHT3D, OpenGeoSys (OGS), HYTEC, ORCHESTRA, TOUGHREACT, eSTOMP, HYDROGEOCHEM, CrunchFlow, MIN3P, and PFLOTRAN. The descriptions include a high-level list of capabilities for each of themore » codes, along with a selective list of applications that highlight their capabilities and historical development.« less

Intellectual Abilities That Discriminate Good and Poor Problem Solvers.

ERIC Educational Resources Information Center

Meyer, Ruth Ann

1981-01-01

This study compared good and poor fourth-grade problem solvers on a battery of 19 "reference" tests for verbal, induction, numerical, word fluency, memory, perceptual speed, and simple visualization abilities. Results suggest verbal, numerical, and especially induction abilities are important to successful mathematical problem solving.…

Validation of numerical models for flow simulation in labyrinth seals

NASA Astrophysics Data System (ADS)

Frączek, D.; Wróblewski, W.

2016-10-01

CFD results were compared with the results of experiments for the flow through the labyrinth seal. RANS turbulence models (k-epsilon, k-omega, SST and SST-SAS) were selected for the study. Steady and transient results were analyzed. ANSYS CFX was used for numerical computation. The analysis included flow through sealing section with the honeycomb land. Leakage flows and velocity profiles in the seal were compared. In addition to the comparison of computational models, the divergence of modeling and experimental results has been determined. Tips for modeling these problems were formulated.

Vortex sheet modeling with higher order curved panels. Ph.D Thesis Final Technical Report

NASA Technical Reports Server (NTRS)

Nagati, M. G.

1985-01-01

A numerical technique is presented for modeling the vortex sheet with a deformable surface definition, along which a continuous vortex strength distribution in the spanwise direction is applied, so that by repeatedly modifying its shape, its true configuration is approached, in the proximity of its generating wing. Design problems requiring the inclusion of a realistic configuration of the vortex sheet are numerous. Examples discussed include: control effectiveness and stability derivatives, longitudinal stability, lateral stability, canards, propellers and helicopter rotors, and trailing vortex hazards.

Analysis of supersonic combustion flow fields with embedded subsonic regions

NASA Technical Reports Server (NTRS)

Dash, S.; Delguidice, P.

1972-01-01

The viscous characteristic analysis for supersonic chemically reacting flows was extended to include provisions for analyzing embedded subsonic regions. The numerical method developed to analyze this mixed subsonic-supersonic flow fields is described. The boundary conditions are discussed related to the supersonic-subsonic and subsonic-supersonic transition, as well as a heuristic description of several other numerical schemes for analyzing this problem. An analysis of shock waves generated either by pressure mismatch between the injected fluid and surrounding flow or by chemical heat release is also described.

Optimal placement of excitations and sensors for verification of large dynamical systems

NASA Technical Reports Server (NTRS)

Salama, M.; Rose, T.; Garba, J.

1987-01-01

The computationally difficult problem of the optimal placement of excitations and sensors to maximize the observed measurements is studied within the framework of combinatorial optimization, and is solved numerically using a variation of the simulated annealing heuristic algorithm. Results of numerical experiments including a square plate and a 960 degrees-of-freedom Control of Flexible Structure (COFS) truss structure, are presented. Though the algorithm produces suboptimal solutions, its generality and simplicity allow the treatment of complex dynamical systems which would otherwise be difficult to handle.

A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

NASA Astrophysics Data System (ADS)

Chernogorova, Tatiana; Vulkov, Lubin

2009-11-01

This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

Merging Black Holes

NASA Technical Reports Server (NTRS)

Centrella, Joan; Baker, John G.; Kelly, Bernard J.; vanMeter, James R.

2010-01-01

Black-hole mergers take place in regions of very strong and dynamical gravitational fields, and are among the strongest sources of gravitational radiation. Probing these mergers requires solving the full set of Einstein's equations of general relativity numerically. For more than 40 years, progress towards this goal has been very slow, as numerical relativists encountered a host of difficult problems. Recently, several breakthroughs have led to dramatic progress, enabling stable and accurate calculations of black-hole mergers. This article presents an overview of this field, including impacts on astrophysics and applications in gravitational wave data analysis.

General method and thermodynamic tables for computation of equilibrium composition and temperature of chemical reactions

NASA Technical Reports Server (NTRS)

Huff, Vearl N; Gordon, Sanford; Morrell, Virginia E

1951-01-01

A rapidly convergent successive approximation process is described that simultaneously determines both composition and temperature resulting from a chemical reaction. This method is suitable for use with any set of reactants over the complete range of mixture ratios as long as the products of reaction are ideal gases. An approximate treatment of limited amounts of liquids and solids is also included. This method is particularly suited to problems having a large number of products of reaction and to problems that require determination of such properties as specific heat or velocity of sound of a dissociating mixture. The method presented is applicable to a wide variety of problems that include (1) combustion at constant pressure or volume; and (2) isentropic expansion to an assigned pressure, temperature, or Mach number. Tables of thermodynamic functions needed with this method are included for 42 substances for convenience in numerical computations.

A new shock-capturing numerical scheme for ideal hydrodynamics

NASA Astrophysics Data System (ADS)

Fecková, Z.; Tomášik, B.

2015-05-01

We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave propagation and the shock tube problem. Low numerical viscosity and high precision are attained with proper discretization.

NSR&D FY17 Report: CartaBlanca Capability Enhancements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Long, Christopher Curtis; Dhakal, Tilak Raj; Zhang, Duan Zhong

Over the last several years, particle technology in the CartaBlanca code has been matured and has been successfully applied to a wide variety of physical problems. It has been shown that the particle methods, especially Los Alamos's dual domain material point method, is capable of computing many problems involves complex physics, chemistries accompanied by large material deformations, where the traditional finite element or Eulerian method encounter significant difficulties. In FY17, the CartaBlanca code has been enhanced with physical models and numerical algorithms. We started out to compute penetration and HE safety problems. Most of the year we focused on themore » TEPLA model improvement testing against the sweeping wave experiment by Gray et al., because it was found that pore growth and material failure are essentially important for our tasks and needed to be understood for modeling the penetration and the can experiments efficiently. We extended the TEPLA mode from the point view of ensemble phase average to include the effects of nite deformation. It is shown that the assumed pore growth model in TEPLA is actually an exact result from the theory. Alone this line, we then generalized the model to include finite deformations to consider nonlinear dynamics of large deformation. The interaction between the HE product gas and the solid metal is based on the multi-velocity formation. Our preliminary numerical results suggest good agreement between the experiment and the numerical results, pending further verification. To improve the parallel processing capabilities of the CartaBlanca code, we are actively working with the Next Generation Code (NGC) project to rewrite selected packages using C++. This work is expected to continue in the following years. This effort also makes the particle technology developed with CartaBlanca project available to other part of the laboratory. Working with the NGC project and rewriting some parts of the code also given us an opportunity to improve our numerical implementations of the method and to take advantage of recently advances in the numerical methods, such as multiscale algorithms.« less

Hamilton's Equations with Euler Parameters for Rigid Body Dynamics Modeling. Chapter 3

NASA Technical Reports Server (NTRS)

Shivarama, Ravishankar; Fahrenthold, Eric P.

2004-01-01

A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

Progress toward a circulation atlas for application to coastal water siting problems

NASA Technical Reports Server (NTRS)

Munday, J. C., Jr.; Gordon, H. H.

1978-01-01

Circulation data needed to resolve coastal siting problems are assembled from historical hydrographic and remote sensing studies in the form of a Circulation Atlas. Empirical data are used instead of numerical model simulations to achieve fine resolution and include fronts and convergence zones. Eulerian and Langrangian data are collected, transformed, and combined into trajectory maps and current vector maps as a function of tidal phase and wind vector. Initial Atlas development is centered on the Elizabeth River, Hampton Roads, Virgina.

Discrete-continuous variable structural synthesis using dual methods

NASA Technical Reports Server (NTRS)

Schmit, L. A.; Fleury, C.

1980-01-01

Approximation concepts and dual methods are extended to solve structural synthesis problems involving a mix of discrete and continuous sizing type of design variables. Pure discrete and pure continuous variable problems can be handled as special cases. The basic mathematical programming statement of the structural synthesis problem is converted into a sequence of explicit approximate primal problems of separable form. These problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple nonnegativity constraints on the dual variables. A newly devised gradient projection type of algorithm called DUAL 1, which includes special features for handling dual function gradient discontinuities that arise from the discrete primal variables, is used to find the solution of each dual problem. Computational implementation is accomplished by incorporating the DUAL 1 algorithm into the ACCESS 3 program as a new optimizer option. The power of the method set forth is demonstrated by presenting numerical results for several example problems, including a pure discrete variable treatment of a metallic swept wing and a mixed discrete-continuous variable solution for a thin delta wing with fiber composite skins.

Adaptivity and smart algorithms for fluid-structure interaction

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley

1990-01-01

This paper reviews new approaches in CFD which have the potential for significantly increasing current capabilities of modeling complex flow phenomena and of treating difficult problems in fluid-structure interaction. These approaches are based on the notions of adaptive methods and smart algorithms, which use instantaneous measures of the quality and other features of the numerical flowfields as a basis for making changes in the structure of the computational grid and of algorithms designed to function on the grid. The application of these new techniques to several problem classes are addressed, including problems with moving boundaries, fluid-structure interaction in high-speed turbine flows, flow in domains with receding boundaries, and related problems.

Parallel Algorithm Solves Coupled Differential Equations

NASA Technical Reports Server (NTRS)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Galois groups of Schubert problems via homotopy computation

NASA Astrophysics Data System (ADS)

Leykin, Anton; Sottile, Frank

2009-09-01

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of the Schubert problem of 3-planes in mathbb{C}^8 meeting 15 fixed 5-planes non-trivially is the full symmetric group S_{6006} .

Analysis of composite ablators using massively parallel computation

NASA Technical Reports Server (NTRS)

Shia, David

1995-01-01

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Advanced development of BEM for elastic and inelastic dynamic analysis of solids

NASA Technical Reports Server (NTRS)

Banerjee, P. K.; Ahmad, S.; Wang, H. C.

1989-01-01

Direct Boundary Element formulations and their numerical implementation for periodic and transient elastic as well as inelastic transient dynamic analyses of two-dimensional, axisymmetric and three-dimensional solids are presented. The inelastic formulation is based on an initial stress approach and is the first of its kind in the field of Boundary Element Methods. This formulation employs the Navier-Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution, and the divergence theorem, together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of the small displacement theory of elastoplasticity. The dynamic (periodic, transient as well as nonlinear transient) formulations have been applied to a range of problems. The numerical formulations presented here are included in the BEST3D and GPBEST systems.

Automated generation of influence functions for planar crack problems

NASA Technical Reports Server (NTRS)

Sire, Robert A.; Harris, David O.; Eason, Ernest D.

1989-01-01

A numerical procedure for the generation of influence functions for Mode I planar problems is described. The resulting influence functions are in a form for convenient evaluation of stress-intensity factors for complex stress distributions. Crack surface displacements are obtained by a least-squares solution of the Williams eigenfunction expansion for displacements in a cracked body. Discrete values of the influence function, evaluated using the crack surface displacements, are curve fit using an assumed functional form. The assumed functional form includes appropriate limit-behavior terms for very deep and very shallow cracks. Continuous representation of the influence function provides a convenient means for evaluating stress-intensity factors for arbitrary stress distributions by numerical integration. The procedure is demonstrated for an edge-cracked strip and a radially cracked disk. Comparisons with available published results demonstrate the accuracy of the procedure.

Numerical marching techniques for fluid flows with heat transfer

NASA Technical Reports Server (NTRS)

Hornbeck, R. W.

1973-01-01

The finite difference formulation and method of solution is presented for a wide variety of fluid flow problems with associated heat transfer. Only a few direct results from these formulations are given as examples, since the book is intended primarily to serve a discussion of the techniques and as a starting point for further investigations; however, the formulations are sufficiently complete that a workable computer program may be written from them. In the appendixes a number of topics are discussed which are of interest with respect to the finite difference equations presented. These include a very rapid method for solving certain sets of linear algebraic equations, a discussion of numerical stability, the inherent error in flow rate for confined flow problems, and a method for obtaining high accuracy with a relatively small number of mesh points.

Advances in Numerical Boundary Conditions for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.

1997-01-01

Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.

How number line estimation skills relate to neural activations in single digit subtraction problems

PubMed Central

Berteletti, I.; Man, G.; Booth, J.R.

2014-01-01

The Number Line (NL) task requires judging the relative numerical magnitude of a number and estimating its value spatially on a continuous line. Children's skill on this task has been shown to correlate with and predict future mathematical competence. Neurofunctionally, this task has been shown to rely on brain regions involved in numerical processing. However, there is no direct evidence that performance on the NL task is related to brain areas recruited during arithmetical processing and that these areas are domain-specific to numerical processing. In this study, we test whether 8- to 14-year-old's behavioral performance on the NL task is related to fMRI activation during small and large single-digit subtraction problems. Domain-specific areas for numerical processing were independently localized through a numerosity judgment task. Results show a direct relation between NL estimation performance and the amount of the activation in key areas for arithmetical processing. Better NL estimators showed a larger problem size effect than poorer NL estimators in numerical magnitude (i.e., intraparietal sulcus) and visuospatial areas (i.e., posterior superior parietal lobules), marked by less activation for small problems. In addition, the direction of the activation with problem size within the IPS was associated to differences in accuracies for small subtraction problems. This study is the first to show that performance in the NL task, i.e. estimating the spatial position of a number on an interval, correlates with brain activity observed during single-digit subtraction problem in regions thought to be involved numerical magnitude and spatial processes. PMID:25497398

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

NASA Astrophysics Data System (ADS)

D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

2018-05-01

In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

Excore Modeling with VERAShift

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pandya, Tara M.; Evans, Thomas M.

It is important to be able to accurately predict the neutron flux outside the immediate reactor core for a variety of safety and material analyses. Monte Carlo radiation transport calculations are required to produce the high fidelity excore responses. Under this milestone VERA (specifically the VERAShift package) has been extended to perform excore calculations by running radiation transport calculations with Shift. This package couples VERA-CS with Shift to perform excore tallies for multiple state points concurrently, with each component capable of parallel execution on independent domains. Specifically, this package performs fluence calculations in the core barrel and vessel, or, performsmore » the requested tallies in any user-defined excore regions. VERAShift takes advantage of the general geometry package in Shift. This gives VERAShift the flexibility to explicitly model features outside the core barrel, including detailed vessel models, detectors, and power plant details. A very limited set of experimental and numerical benchmarks is available for excore simulation comparison. The Consortium for the Advanced Simulation of Light Water Reactors (CASL) has developed a set of excore benchmark problems to include as part of the VERA-CS verification and validation (V&V) problems. The excore capability in VERAShift has been tested on small representative assembly problems, multiassembly problems, and quarter-core problems. VERAView has also been extended to visualize these vessel fluence results from VERAShift. Preliminary vessel fluence results for quarter-core multistate calculations look very promising. Further development is needed to determine the details relevant to excore simulations. Validation of VERA for fluence and excore detectors still needs to be performed against experimental and numerical results.« less

Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity

NASA Astrophysics Data System (ADS)

Avitabile, Daniele; Bridges, Thomas J.

2010-06-01

Numerical integration of complex linear systems of ODEs depending analytically on an eigenvalue parameter are considered. Complex orthogonalization, which is required to stabilize the numerical integration, results in non-analytic systems. It is shown that properties of eigenvalues are still efficiently recoverable by extracting information from a non-analytic characteristic function. The orthonormal systems are constructed using the geometry of Stiefel bundles. Different forms of continuous orthogonalization in the literature are shown to correspond to different choices of connection one-form on the Stiefel bundle. For the numerical integration, Gauss-Legendre Runge-Kutta algorithms are the principal choice for preserving orthogonality, and performance results are shown for a range of GLRK methods. The theory and methods are tested by application to example boundary value problems including the Orr-Sommerfeld equation in hydrodynamic stability.

Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0

NASA Astrophysics Data System (ADS)

Borowka, Sophia; Carter, Jonathon; Heinrich, Gudrun

2013-02-01

We present the program SecDec 2.0, which contains various new features. First, it allows the numerical evaluation of multi-loop integrals with no restriction on the kinematics. Dimensionally regulated ultraviolet and infrared singularities are isolated via sector decomposition, while threshold singularities are handled by a deformation of the integration contour in the complex plane. As an application, we present numerical results for various massive two-loop four-point diagrams. SecDec 2.0 also contains new useful features for the calculation of more general parameter integrals, related for example to phase space integrals. Program summaryProgram title: SecDec 2.0 Catalogue identifier: AEIR_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIR_v2_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.: 156829 No. of bytes in distributed program, including test data, etc.: 2137907 Distribution format: tar.gz Programming language: Wolfram Mathematica, Perl, Fortran/C++. Computer: From a single PC to a cluster, depending on the problem. Operating system: Unix, Linux. RAM: Depending on the complexity of the problem Classification: 4.4, 5, 11.1. Catalogue identifier of previous version: AEIR_v1_0 Journal reference of previous version: Comput. Phys. Comm. 182(2011)1566 Does the new version supersede the previous version?: Yes Nature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories. Numerical integration in the presence of integrable singularities (e.g., kinematic thresholds). Solution method: Algebraic extraction of singularities in dimensional regularization using iterated sector decomposition. This leads to a Laurent series in the dimensional regularization parameter ɛ, where the coefficients are finite integrals over the unit hypercube. Those integrals are evaluated numerically by Monte Carlo integration. The integrable singularities are handled by choosing a suitable integration contour in the complex plane, in an automated way. Reasons for new version: In the previous version the calculation of multi-scale integrals was restricted to the Euclidean region. Now multi-loop integrals with arbitrary physical kinematics can be evaluated. Another major improvement is the possibility of full parallelization. Summary of revisions: No restriction on the kinematics for multi-loop integrals. The integrand can be constructed from the topological cuts of the diagram. Possibility of full parallelization. Numerical integration of multi-loop integrals written in C++ rather than Fortran. Possibility to loop over ranges of parameters. Restrictions: Depending on the complexity of the problem, limited by memory and CPU time. The restriction that multi-scale integrals could only be evaluated at Euclidean points is superseded in version 2.0. Running time: Between a few minutes and several days, depending on the complexity of the problem. Test runs provided take only seconds.

Process Guide for Deburring Technologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frey, David L.

This report is an updated and consolidated view of the current deburring processes at the Kansas City Plant (KCP). It includes specific examples of current burr problems and the methods used for their detection. Also included is a pictorial review of the large variety of available deburr tools, along with a complete numerical listing of existing tools and their descriptions. The process for deburring all the major part feature categories is discussed.

Effect of correlations on controllability transition in network control

PubMed Central

Nie, Sen; Wang, Xu-Wen; Wang, Bing-Hong; Jiang, Luo-Luo

2016-01-01

The network control problem has recently attracted an increasing amount of attention, owing to concerns including the avoidance of cascading failures of power-grids and the management of ecological networks. It has been proven that numerical control can be achieved if the number of control inputs exceeds a certain transition point. In the present study, we investigate the effect of degree correlation on the numerical controllability in networks whose topological structures are reconstructed from both real and modeling systems, and we find that the transition point of the number of control inputs depends strongly on the degree correlation in both undirected and directed networks with moderately sparse links. More interestingly, the effect of the degree correlation on the transition point cannot be observed in dense networks for numerical controllability, which contrasts with the corresponding result for structural controllability. In particular, for directed random networks and scale-free networks, the influence of the degree correlation is determined by the types of correlations. Our approach provides an understanding of control problems in complex sparse networks. PMID:27063294

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

Procurement Ethics: Have We Resolved the Army’s Expeditionary Contracting Problems?

DTIC Science & Technology

2011-03-11

Distribution A: Unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT The United States Army discovered numerous occurrences of unethical behavior by...The United States Army discovered numerous occurrences of unethical behavior by contracting officials and contractors while providing contracting...ARMY’S EXPEDITIONARY CONTRACTING PROBLEMS? The United States Army discovered numerous occurrences of unethical behavior by contracting officials

Problem-Based Instructional Strategy and Numerical Ability as Determinants of Senior Secondary Achievement in Mathematics

ERIC Educational Resources Information Center

Badru, Ademola K.

2016-01-01

The study investigated Problem-based Instructional Strategy and Numerical ability as determinants of Senior Secondary Achievement in Mathematics. This study used 4 x 2 x 2 non-randomised control group Pretest-Posttest Quasi-experimental Factorial design. It consisted of two independent variables (treatment and Numerical ability) and one moderating…

Numerical solutions of a control problem governed by functional differential equations

NASA Technical Reports Server (NTRS)

Banks, H. T.; Thrift, P. R.; Burns, J. A.; Cliff, E. M.

1978-01-01

A numerical procedure is proposed for solving optimal control problems governed by linear retarded functional differential equations. The procedure is based on the idea of 'averaging approximations', due to Banks and Burns (1975). For illustration, numerical results generated on an IBM 370/158 computer, which demonstrate the rapid convergence of the method are presented.

An efficient numerical algorithm for transverse impact problems

NASA Technical Reports Server (NTRS)

Sankar, B. V.; Sun, C. T.

1985-01-01

Transverse impact problems in which the elastic and plastic indentation effects are considered, involve a nonlinear integral equation for the contact force, which, in practice, is usually solved by an iterative scheme with small increments in time. In this paper, a numerical method is proposed wherein the iterations of the nonlinear problem are separated from the structural response computations. This makes the numerical procedures much simpler and also efficient. The proposed method is applied to some impact problems for which solutions are available, and they are found to be in good agreement. The effect of the magnitude of time increment on the results is also discussed.

Efficient numerical method for solving Cauchy problem for the Gamma equation

NASA Astrophysics Data System (ADS)

Koleva, Miglena N.

2011-12-01

In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black-Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ = VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard-Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non-differentiable functions. Results of numerical simulations are given.

Numerical method for solving the nonlinear four-point boundary value problems

NASA Astrophysics Data System (ADS)

Lin, Yingzhen; Lin, Jinnan

2010-12-01

In this paper, a new reproducing kernel space is constructed skillfully in order to solve a class of nonlinear four-point boundary value problems. The exact solution of the linear problem can be expressed in the form of series and the approximate solution of the nonlinear problem is given by the iterative formula. Compared with known investigations, the advantages of our method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Meanwhile we present the convergent theorem, complexity analysis and error estimation. The performance of the new method is illustrated with several numerical examples.

Reconstruction of structural damage based on reflection intensity spectra of fiber Bragg gratings

NASA Astrophysics Data System (ADS)

Huang, Guojun; Wei, Changben; Chen, Shiyuan; Yang, Guowei

2014-12-01

We present an approach for structural damage reconstruction based on the reflection intensity spectra of fiber Bragg gratings (FBGs). Our approach incorporates the finite element method, transfer matrix (T-matrix), and genetic algorithm to solve the inverse photo-elastic problem of damage reconstruction, i.e. to identify the location, size, and shape of a defect. By introducing a parameterized characterization of the damage information, the inverse photo-elastic problem is reduced to an optimization problem, and a relevant computational scheme was developed. The scheme iteratively searches for the solution to the corresponding direct photo-elastic problem until the simulated and measured (or target) reflection intensity spectra of the FBGs near the defect coincide within a prescribed error. Proof-of-concept validations of our approach were performed numerically and experimentally using both holed and cracked plate samples as typical cases of plane-stress problems. The damage identifiability was simulated by changing the deployment of the FBG sensors, including the total number of sensors and their distance to the defect. Both the numerical and experimental results demonstrate that our approach is effective and promising. It provides us with a photo-elastic method for developing a remote, automatic damage-imaging technique that substantially improves damage identification for structural health monitoring.

Fully-coupled analysis of jet mixing problems. Three-dimensional PNS model, SCIP3D

NASA Technical Reports Server (NTRS)

Wolf, D. E.; Sinha, N.; Dash, S. M.

1988-01-01

Numerical procedures formulated for the analysis of 3D jet mixing problems, as incorporated in the computer model, SCIP3D, are described. The overall methodology closely parallels that developed in the earlier 2D axisymmetric jet mixing model, SCIPVIS. SCIP3D integrates the 3D parabolized Navier-Stokes (PNS) jet mixing equations, cast in mapped cartesian or cylindrical coordinates, employing the explicit MacCormack Algorithm. A pressure split variant of this algorithm is employed in subsonic regions with a sublayer approximation utilized for treating the streamwise pressure component. SCIP3D contains both the ks and kW turbulence models, and employs a two component mixture approach to treat jet exhausts of arbitrary composition. Specialized grid procedures are used to adjust the grid growth in accordance with the growth of the jet, including a hybrid cartesian/cylindrical grid procedure for rectangular jets which moves the hybrid coordinate origin towards the flow origin as the jet transitions from a rectangular to circular shape. Numerous calculations are presented for rectangular mixing problems, as well as for a variety of basic unit problems exhibiting overall capabilities of SCIP3D.

Multiple equilibria, bifurcations and selection scenarios in cosymmetric problem of thermal convection in porous medium

NASA Astrophysics Data System (ADS)

Govorukhin, Vasily N.; Shevchenko, Igor V.

2017-12-01

We study convection in a two-dimensional container of porous material saturated with fluid and heated from below. This problem belongs to the class of dynamical systems with nontrivial cosymmetry. The cosymmetry gives rise to a hidden parameter in the system and continuous families of infinitely many equilibria, and leads to non-trivial bifurcations. In this article we present our numerical studies that demonstrate nonlinear phenomena resulting from the existence of cosymmetry. We give a comprehensive picture of different bifurcations which occur in cosymmetric dynamical systems and in the convection problem. It includes internal and external (as an invariant set) bifurcations of one-parameter families of equilibria, as well as bifurcations leading to periodic, quasiperiodic and chaotic behaviour. The existence of infinite number of stable steady-state regimes begs the important question as to which of them can realize in physical experiments. In this paper, this question (known as the selection problem) is studied in detail. In particular, we show that the selection scenarios strongly depend on the initial temperature distribution of the fluid. The calculations are carried out by the global cosymmetry-preserving Galerkin method, and numerical methods used to analyse cosymmetric systems are also described.

Solving transient acoustic boundary value problems with equivalent sources using a lumped parameter approach.

PubMed

Fahnline, John B

2016-12-01

An equivalent source method is developed for solving transient acoustic boundary value problems. The method assumes the boundary surface is discretized in terms of triangular or quadrilateral elements and that the solution is represented using the acoustic fields of discrete sources placed at the element centers. Also, the boundary condition is assumed to be specified for the normal component of the surface velocity as a function of time, and the source amplitudes are determined to match the known elemental volume velocity vector at a series of discrete time steps. Equations are given for marching-on-in-time schemes to solve for the source amplitudes at each time step for simple, dipole, and tripole source formulations. Several example problems are solved to illustrate the results and to validate the formulations, including problems with closed boundary surfaces where long-time numerical instabilities typically occur. A simple relationship between the simple and dipole source amplitudes in the tripole source formulation is derived so that the source radiates primarily in the direction of the outward surface normal. The tripole source formulation is shown to eliminate interior acoustic resonances and long-time numerical instabilities.

Direct Numerical Simulation of Fingering Instabilities in Coating Flows

NASA Astrophysics Data System (ADS)

Eres, Murat H.; Schwartz, Leonard W.

1998-11-01

We consider stability and finger formation in free surface flows. Gravity driven downhill drainage and temperature gradient driven climbing flows are two examples of such problems. The former situation occurs when a mound of viscous liquid on a vertical wall is allowed to flow. Constant surface shear stress due to temperature gradients (Marangoni stress) can initiate the latter problem. The evolution equations are derived using the lubrication approximation. We also include the effects of finite-contact angles in the evolution equations using a disjoining pressure model. Evolution equations for both problems are solved using an efficient alternating-direction-implicit method. For both problems a one-dimensional base state is established, that is steady in a moving reference frame. This base state is unstable to transverse perturbations. The transverse wavenumbers for the most rapidly growing modes are found through direct numerical solution of the nonlinear evolution equations, and are compared with published experimental results. For a range of finite equilibrium contact angles, the fingers can grow without limit leading to semi-finite steady fingers in a moving coordinate system. A computer generated movie of the nonlinear simulation results, for several sets of input parameters, will be shown.

Solving ODE Initial Value Problems With Implicit Taylor Series Methods

NASA Technical Reports Server (NTRS)

Scott, James R.

2000-01-01

In this paper we introduce a new class of numerical methods for integrating ODE initial value problems. Specifically, we propose an extension of the Taylor series method which significantly improves its accuracy and stability while also increasing its range of applicability. To advance the solution from t (sub n) to t (sub n+1), we expand a series about the intermediate point t (sub n+mu):=t (sub n) + mu h, where h is the stepsize and mu is an arbitrary parameter called an expansion coefficient. We show that, in general, a Taylor series of degree k has exactly k expansion coefficients which raise its order of accuracy. The accuracy is raised by one order if k is odd, and by two orders if k is even. In addition, if k is three or greater, local extrapolation can be used to raise the accuracy two additional orders. We also examine stability for the problem y'= lambda y, Re (lambda) less than 0, and identify several A-stable schemes. Numerical results are presented for both fixed and variable stepsizes. It is shown that implicit Taylor series methods provide an effective integration tool for most problems, including stiff systems and ODE's with a singular point.

Word problems: a review of linguistic and numerical factors contributing to their difficulty

PubMed Central

Daroczy, Gabriella; Wolska, Magdalena; Meurers, Walt Detmar; Nuerk, Hans-Christoph

2015-01-01

Word problems (WPs) belong to the most difficult and complex problem types that pupils encounter during their elementary-level mathematical development. In the classroom setting, they are often viewed as merely arithmetic tasks; however, recent research shows that a number of linguistic verbal components not directly related to arithmetic contribute greatly to their difficulty. In this review, we will distinguish three components of WP difficulty: (i) the linguistic complexity of the problem text itself, (ii) the numerical complexity of the arithmetic problem, and (iii) the relation between the linguistic and numerical complexity of a problem. We will discuss the impact of each of these factors on WP difficulty and motivate the need for a high degree of control in stimuli design for experiments that manipulate WP difficulty for a given age group. PMID:25883575

Locating CVBEM collocation points for steady state heat transfer problems

USGS Publications Warehouse

Hromadka, T.V.

1985-01-01

The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.

A Flux-Corrected Transport Based Hydrodynamic Model for the Plasmasphere Refilling Problem following Geomagnetic Storms

NASA Astrophysics Data System (ADS)

Chatterjee, K.; Schunk, R. W.

2017-12-01

The refilling of the plasmasphere following a geomagnetic storm remains one of the longstanding problems in the area of ionosphere-magnetosphere coupling. Both diffusion and hydrodynamic approximations have been adopted for the modeling and solution of this problem. The diffusion approximation neglects the nonlinear inertial term in the momentum equation and so this approximation is not rigorously valid immediately after the storm. Over the last few years, we have developed a hydrodynamic refilling model using the flux-corrected transport method, a numerical method that is extremely well suited to handling nonlinear problems with shocks and discontinuities. The plasma transport equations are solved along 1D closed magnetic field lines that connect conjugate ionospheres and the model currently includes three ion (H+, O+, He+) and two neutral (O, H) species. In this work, each ion species under consideration has been modeled as two separate streams emanating from the conjugate hemispheres and the model correctly predicts supersonic ion speeds and the presence of high levels of Helium during the early hours of refilling. The ultimate objective of this research is the development of a 3D model for the plasmasphere refilling problem and with additional development, the same methodology can potentially be applied to the study of other complex space plasma coupling problems in closed flux tube geometries. Index Terms: 2447 Modeling and forecasting [IONOSPHERE] 2753 Numerical modeling [MAGNETOSPHERIC PHYSICS] 7959 Models [SPACE WEATHER

Beyond Introductory Programming: Success Factors for Advanced Programming

ERIC Educational Resources Information Center

Hoskey, Arthur; Maurino, Paula San Millan

2011-01-01

Numerous studies document high drop-out and failure rates for students in computer programming classes. Studies show that even when some students pass programming classes, they still do not know how to program. Many factors have been considered to explain this problem including gender, age, prior programming experience, major, math background,…

Longitudinal Associations of Alcohol Involvement with Subjective Well-Being in Adolescence and Prediction to Alcohol Problems in Early Adulthood

ERIC Educational Resources Information Center

Mason, W. Alex; Spoth, Richard L.

2011-01-01

Adolescent alcohol involvement is associated with numerous negative outcomes, but also appears to have positive correlates, including subjective well-being. Additional research is needed to understand these paradoxical findings. The current study examines alcohol use, adverse alcohol-related (and other substance-related) consequences, and…

Collaborative Learning in Online Study Groups: An Evolutionary Game Theory Perspective

ERIC Educational Resources Information Center

Chiong, Raymond; Jovanovic, Jelena

2012-01-01

Educational benefits of online collaborative group work have been confirmed in numerous research studies. Most frequently cited advantages include the development of skills of critical thinking and problem solving as well as skills of self-reflection and co-construction of knowledge and meaning. However, the establishment and maintenance of active…

The Association between Students' Number Knowledge and Social Disadvantage at School Entry

ERIC Educational Resources Information Center

Gould, Peter

2014-01-01

At the start of the Kindergarten year in New South Wales (NSW) government schools, teachers gather information on several aspects of children's number knowledge to guide their teaching programs. This includes knowledge of the sequence of words used for counting, numeral identification, and using counting to solve problems. This study investigated…

Comparitive Study of High-Order Positivity-Preserving WENO Schemes

NASA Technical Reports Server (NTRS)

Kotov, D. V.; Yee, H. C.; Sjogreen, B.

2014-01-01

In gas dynamics and magnetohydrodynamics flows, physically, the density ? and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order Weighted Essentially Non-Oscillatory (WENO) schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative ? may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more di cult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium ow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case as well as for the case consisting of two species and one reaction.. This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

Robust and Simple Non-Reflecting Boundary Conditions for the Euler Equations: A New Approach Based on the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Himansu, Ananda; Loh, Ching-Yuen; Wang, Xiao-Yen; Yu, Shang-Tao

2003-01-01

This paper reports on a significant advance in the area of non-reflecting boundary conditions (NRBCs) for unsteady flow computations. As a part of the development of the space-time conservation element and solution element (CE/SE) method, sets of NRBCs for 1D Euler problems are developed without using any characteristics-based techniques. These conditions are much simpler than those commonly reported in the literature, yet so robust that they are applicable to subsonic, transonic and supersonic flows even in the presence of discontinuities. In addition, the straightforward multidimensional extensions of the present 1D NRBCs have been shown numerically to be equally simple and robust. The paper details the theoretical underpinning of these NRBCs, and explains their unique robustness and accuracy in terms of the conservation of space-time fluxes. Some numerical results for an extended Sod's shock-tube problem, illustrating the effectiveness of the present NRBCs are included, together with an associated simple Fortran computer program. As a preliminary to the present development, a review of the basic CE/SE schemes is also included.

Relational complexity modulates activity in the prefrontal cortex during numerical inductive reasoning: an fMRI study.

PubMed

Feng, Xiao; Peng, Li; Chang-Quan, Long; Yi, Lei; Hong, Li

2014-09-01

Most previous studies investigating relational reasoning have used visuo-spatial materials. This fMRI study aimed to determine how relational complexity affects brain activity during inductive reasoning, using numerical materials. Three numerical relational levels of the number series completion task were adopted for use: 0-relational (e.g., "23 23 23"), 1-relational ("32 30 28") and 2-relational ("12 13 15") problems. The fMRI results revealed that the bilateral dorsolateral prefrontal cortex (DLPFC) showed enhanced activity associated with relational complexity. Bilateral inferior parietal lobule (IPL) activity was greater during the 1- and 2-relational level problems than during the 0-relational level problems. In addition, the left fronto-polar cortex (FPC) showed selective activity during the 2-relational level problems. The bilateral DLPFC may be involved in the process of hypothesis generation, whereas the bilateral IPL may be sensitive to calculation demands. Moreover, the sensitivity of the left FPC to the multiple relational problems may be related to the integration of numerical relations. The present study extends our knowledge of the prefrontal activity pattern underlying numerical relational processing. Copyright © 2014 Elsevier B.V. All rights reserved.

A Fixed-point Scheme for the Numerical Construction of Magnetohydrostatic Atmospheres in Three Dimensions

NASA Astrophysics Data System (ADS)

Gilchrist, S. A.; Braun, D. C.; Barnes, G.

2016-12-01

Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin ( Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.

Numerical Ergonomics Analysis in Operation Environment of CNC Machine

NASA Astrophysics Data System (ADS)

Wong, S. F.; Yang, Z. X.

2010-05-01

The performance of operator will be affected by different operation environments [1]. Moreover, poor operation environment may cause health problems of the operator [2]. Physical and psychological considerations are two main factors that will affect the performance of operator under different conditions of operation environment. In this paper, applying scientific and systematic methods find out the pivot elements in the field of physical and psychological factors. There are five main factors including light, temperature, noise, air flow and space that are analyzed. A numerical ergonomics model has been built up regarding the analysis results which can support to advance the design of operation environment. Moreover, the output of numerical ergonomic model can provide the safe, comfortable, more productive conditions for the operator.

Numerical Study of Tip Vortex Flows

NASA Technical Reports Server (NTRS)

Dacles-Mariani, Jennifer; Hafez, Mohamed

1998-01-01

This paper presents an overview and summary of the many different research work related to tip vortex flows and wake/trailing vortices as applied to practical engineering problems. As a literature survey paper, it outlines relevant analytical, theoretical, experimental and computational study found in literature. It also discusses in brief some of the fundamental aspects of the physics and its complexities. An appendix is also included. The topics included in this paper are: 1) Analytical Vortices; 2) Experimental Studies; 3) Computational Studies; 4) Wake Vortex Control and Management; 5) Wake Modeling; 6) High-Lift Systems; 7) Issues in Numerical Studies; 8) Instabilities; 9) Related Topics; 10) Visualization Tools for Vertical Flows; 11) Further Work Needed; 12) Acknowledgements; 13) References; and 14) Appendix.

Nonlinear Transient Problems Using Structure Compatible Heat Transfer Code

NASA Technical Reports Server (NTRS)

Hou, Gene

2000-01-01

The report documents the recent effort to enhance a transient linear heat transfer code so as to solve nonlinear problems. The linear heat transfer code was originally developed by Dr. Kim Bey of NASA Largely and called the Structure-Compatible Heat Transfer (SCHT) code. The report includes four parts. The first part outlines the formulation of the heat transfer problem of concern. The second and the third parts give detailed procedures to construct the nonlinear finite element equations and the required Jacobian matrices for the nonlinear iterative method, Newton-Raphson method. The final part summarizes the results of the numerical experiments on the newly enhanced SCHT code.

Dual methods and approximation concepts in structural synthesis

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins.

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

A fast direct solver for boundary value problems on locally perturbed geometries

NASA Astrophysics Data System (ADS)

Zhang, Yabin; Gillman, Adrianna

2018-03-01

Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

Computational Studies of Strongly Correlated Quantum Matter

NASA Astrophysics Data System (ADS)

Shi, Hao

The study of strongly correlated quantum many-body systems is an outstanding challenge. Highly accurate results are needed for the understanding of practical and fundamental problems in condensed-matter physics, high energy physics, material science, quantum chemistry and so on. Our familiar mean-field or perturbative methods tend to be ineffective. Numerical simulations provide a promising approach for studying such systems. The fundamental difficulty of numerical simulation is that the dimension of the Hilbert space needed to describe interacting systems increases exponentially with the system size. Quantum Monte Carlo (QMC) methods are one of the best approaches to tackle the problem of enormous Hilbert space. They have been highly successful for boson systems and unfrustrated spin models. For systems with fermions, the exchange symmetry in general causes the infamous sign problem, making the statistical noise in the computed results grow exponentially with the system size. This hinders our understanding of interesting physics such as high-temperature superconductivity, metal-insulator phase transition. In this thesis, we present a variety of new developments in the auxiliary-field quantum Monte Carlo (AFQMC) methods, including the incorporation of symmetry in both the trial wave function and the projector, developing the constraint release method, using the force-bias to drastically improve the efficiency in Metropolis framework, identifying and solving the infinite variance problem, and sampling Hartree-Fock-Bogoliubov wave function. With these developments, some of the most challenging many-electron problems are now under control. We obtain an exact numerical solution of two-dimensional strongly interacting Fermi atomic gas, determine the ground state properties of the 2D Fermi gas with Rashba spin-orbit coupling, provide benchmark results for the ground state of the two-dimensional Hubbard model, and establish that the Hubbard model has a stripe order in the underdoped region.

Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube

NASA Astrophysics Data System (ADS)

Zhou, Guangzhao; Xu, Kun; Liu, Feng

2018-01-01

The flow in a shock tube is extremely complex with dynamic multi-scale structures of sharp fronts, flow separation, and vortices due to the interaction of the shock wave, the contact surface, and the boundary layer over the side wall of the tube. Prediction and understanding of the complex fluid dynamics are of theoretical and practical importance. It is also an extremely challenging problem for numerical simulation, especially at relatively high Reynolds numbers. Daru and Tenaud ["Evaluation of TVD high resolution schemes for unsteady viscous shocked flows," Comput. Fluids 30, 89-113 (2001)] proposed a two-dimensional model problem as a numerical test case for high-resolution schemes to simulate the flow field in a square closed shock tube. Though many researchers attempted this problem using a variety of computational methods, there is not yet an agreed-upon grid-converged solution of the problem at the Reynolds number of 1000. This paper presents a rigorous grid-convergence study and the resulting grid-converged solutions for this problem by using a newly developed, efficient, and high-order gas-kinetic scheme. Critical data extracted from the converged solutions are documented as benchmark data. The complex fluid dynamics of the flow at Re = 1000 are discussed and analyzed in detail. Major phenomena revealed by the numerical computations include the downward concentration of the fluid through the curved shock, the formation of the vortices, the mechanism of the shock wave bifurcation, the structure of the jet along the bottom wall, and the Kelvin-Helmholtz instability near the contact surface. Presentation and analysis of those flow processes provide important physical insight into the complex flow physics occurring in a shock tube.

Mathematical modeling of heat transfer problems in the permafrost

NASA Astrophysics Data System (ADS)

Gornov, V. F.; Stepanov, S. P.; Vasilyeva, M. V.; Vasilyev, V. I.

2014-11-01

In this work we present results of numerical simulation of three-dimensional temperature fields in soils for various applied problems: the railway line in the conditions of permafrost for different geometries, the horizontal tunnel underground storage and greenhouses of various designs in the Far North. Mathematical model of the process is described by a nonstationary heat equation with phase transitions of pore water. The numerical realization of the problem is based on the finite element method using a library of scientific computing FEniCS. For numerical calculations we use high-performance computing systems.

Milne, a routine for the numerical solution of Milne's problem

NASA Astrophysics Data System (ADS)

Rawat, Ajay; Mohankumar, N.

2010-11-01

The routine Milne provides accurate numerical values for the classical Milne's problem of neutron transport for the planar one speed and isotropic scattering case. The solution is based on the Case eigen-function formalism. The relevant X functions are evaluated accurately by the Double Exponential quadrature. The calculated quantities are the extrapolation distance and the scalar and the angular fluxes. Also, the H function needed in astrophysical calculations is evaluated as a byproduct. Program summaryProgram title: Milne Catalogue identifier: AEGS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGS_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.: 701 No. of bytes in distributed program, including test data, etc.: 6845 Distribution format: tar.gz Programming language: Fortran 77 Computer: PC under Linux or Windows Operating system: Ubuntu 8.04 (Kernel version 2.6.24-16-generic), Windows-XP Classification: 4.11, 21.1, 21.2 Nature of problem: The X functions are integral expressions. The convergence of these regular and Cauchy Principal Value integrals are impaired by the singularities of the integrand in the complex plane. The DE quadrature scheme tackles these singularities in a robust manner compared to the standard Gauss quadrature. Running time: The test included in the distribution takes a few seconds to run.

Numerical solution of 2D-vector tomography problem using the method of approximate inverse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna

2016-08-10

We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.

Comparing Psychology Undergraduates' Performance in Probabilistic Reasoning under Verbal-Numerical and Graphical-Pictorial Problem Presentation Format: What Is the Role of Individual and Contextual Dimensions?

ERIC Educational Resources Information Center

Agus, Mirian; Peró-Cebollero, Maribel; Penna, Maria Pietronilla; Guàrdia-Olmos, Joan

2015-01-01

This study aims to investigate about the existence of a graphical facilitation effect on probabilistic reasoning. Measures of undergraduates' performances on problems presented in both verbal-numerical and graphical-pictorial formats have been related to visuo-spatial and numerical prerequisites, to statistical anxiety, to attitudes towards…

Numerical solution of the electron transport equation

NASA Astrophysics Data System (ADS)

Woods, Mark

The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

Transport in Dynamical Astronomy and Multibody Problems

NASA Astrophysics Data System (ADS)

Dellnitz, Michael; Junge, Oliver; Koon, Wang Sang; Lekien, Francois; Lo, Martin W.; Marsden, Jerrold E.; Padberg, Kathrin; Preis, Robert; Ross, Shane D.; Thiere, Bianca

We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing key dynamical features, including almost invariant sets, resonance regions as well as transport rates and bottlenecks between regions in dynamical systems. This methodology can be applied to a variety of multibody problems, including those in molecular modeling, chemical reaction rates and dynamical astronomy. In this paper we focus on problems in dynamical astronomy to illustrate the power of the combination of these different numerical tools and their applicability. In particular, we compute transport rates between two resonance regions for the three-body system consisting of the Sun, Jupiter and a third body (such as an asteroid). These resonance regions are appropriate for certain comets and asteroids.

On the numerical treatment of selected oscillatory evolutionary problems

NASA Astrophysics Data System (ADS)

Cardone, Angelamaria; Conte, Dajana; D'Ambrosio, Raffaele; Paternoster, Beatrice

2017-07-01

We focus on evolutionary problems whose qualitative behaviour is known a-priori and exploited in order to provide efficient and accurate numerical schemes. For classical numerical methods, depending on constant coefficients, the required computational effort could be quite heavy, due to the necessary employ of very small stepsizes needed to accurately reproduce the qualitative behaviour of the solution. In these situations, it may be convenient to use special purpose formulae, i.e. non-polynomially fitted formulae on basis functions adapted to the problem (see [16, 17] and references therein). We show examples of special purpose strategies to solve two families of evolutionary problems exhibiting periodic solutions, i.e. partial differential equations and Volterra integral equations.

Handwritten numeral databases of Indian scripts and multistage recognition of mixed numerals.

PubMed

Bhattacharya, Ujjwal; Chaudhuri, B B

2009-03-01

This article primarily concerns the problem of isolated handwritten numeral recognition of major Indian scripts. The principal contributions presented here are (a) pioneering development of two databases for handwritten numerals of two most popular Indian scripts, (b) a multistage cascaded recognition scheme using wavelet based multiresolution representations and multilayer perceptron classifiers and (c) application of (b) for the recognition of mixed handwritten numerals of three Indian scripts Devanagari, Bangla and English. The present databases include respectively 22,556 and 23,392 handwritten isolated numeral samples of Devanagari and Bangla collected from real-life situations and these can be made available free of cost to researchers of other academic Institutions. In the proposed scheme, a numeral is subjected to three multilayer perceptron classifiers corresponding to three coarse-to-fine resolution levels in a cascaded manner. If rejection occurred even at the highest resolution, another multilayer perceptron is used as the final attempt to recognize the input numeral by combining the outputs of three classifiers of the previous stages. This scheme has been extended to the situation when the script of a document is not known a priori or the numerals written on a document belong to different scripts. Handwritten numerals in mixed scripts are frequently found in Indian postal mails and table-form documents.

Bio-Inspired Functional Surfaces Based on Laser-Induced Periodic Surface Structures

PubMed Central

Müller, Frank A.; Kunz, Clemens; Gräf, Stephan

2016-01-01

Nature developed numerous solutions to solve various technical problems related to material surfaces by combining the physico-chemical properties of a material with periodically aligned micro/nanostructures in a sophisticated manner. The utilization of ultra-short pulsed lasers allows mimicking numerous of these features by generating laser-induced periodic surface structures (LIPSS). In this review paper, we describe the physical background of LIPSS generation as well as the physical principles of surface related phenomena like wettability, reflectivity, and friction. Then we introduce several biological examples including e.g., lotus leafs, springtails, dessert beetles, moth eyes, butterfly wings, weevils, sharks, pangolins, and snakes to illustrate how nature solves technical problems, and we give a comprehensive overview of recent achievements related to the utilization of LIPSS to generate superhydrophobic, anti-reflective, colored, and drag resistant surfaces. Finally, we conclude with some future developments and perspectives related to forthcoming applications of LIPSS-based surfaces. PMID:28773596

Practical Bayesian tomography

NASA Astrophysics Data System (ADS)

Granade, Christopher; Combes, Joshua; Cory, D. G.

2016-03-01

In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we address all three problems. First, we use modern statistical methods, as pioneered by Huszár and Houlsby (2012 Phys. Rev. A 85 052120) and by Ferrie (2014 New J. Phys. 16 093035), to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first priors on quantum states and channels that allow for including useful experimental insight. Finally, we develop a method that allows tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.

A new 3D immersed boundary method for non-Newtonian fluid-structure-interaction with application

NASA Astrophysics Data System (ADS)

Zhu, Luoding

2017-11-01

Motivated by fluid-structure-interaction (FSI) phenomena in life sciences (e.g., motions of sperm and cytoskeleton in complex fluids), we introduce a new immersed boundary method for FSI problems involving non-Newtonian fluids in three dimensions. The non-Newtonian fluids are modelled by the FENE-P model (including the Oldroyd-B model as an especial case) and numerically solved by a lattice Boltzmann scheme (the D3Q7 model). The fluid flow is modelled by the lattice Boltzmann equations and numerically solved by the D3Q19 model. The deformable structure and the fluid-structure-interaction are handled by the immersed boundary method. As an application, we study a FSI toy problem - interaction of an elastic plate (flapped at its leading edge and restricted nowhere else) with a non-Newtonian fluid in a 3D flow. Thanks to the support of NSF-DMS support under research Grant 1522554.

Some problems in applications of the linear variational method

NASA Astrophysics Data System (ADS)

Pupyshev, Vladimir I.; Montgomery, H. E.

2015-09-01

The linear variational method is a standard computational method in quantum mechanics and quantum chemistry. As taught in most classes, the general guidance is to include as many basis functions as practical in the variational wave function. However, if it is desired to study the patterns of energy change accompanying the change of system parameters such as the shape and strength of the potential energy, the problem becomes more complicated. We use one-dimensional systems with a particle in a rectangular or in a harmonic potential confined in an infinite rectangular box to illustrate situations where a variational calculation can give incorrect results. These situations result when the energy of the lowest eigenvalue is strongly dependent on the parameters that describe the shape and strength of the potential. The numerical examples described in this work are provided as cautionary notes for practitioners of numerical variational calculations.

Efficient Trajectory Propagation for Orbit Determination Problems

NASA Technical Reports Server (NTRS)

Roa, Javier; Pelaez, Jesus

2015-01-01

Regularized formulations of orbital motion apply a series of techniques to improve the numerical integration of the orbit. Despite their advantages and potential applications little attention has been paid to the propagation of the partial derivatives of the corresponding set of elements or coordinates, required in many orbit-determination scenarios and optimization problems. This paper fills this gap by presenting the general procedure for integrating the state-transition matrix of the system together with the nominal trajectory using regularized formulations and different sets of elements. The main difficulty comes from introducing an independent variable different from time, because the solution needs to be synchronized. The correction of the time delay is treated from a generic perspective not focused on any particular formulation. The synchronization using time-elements is also discussed. Numerical examples include strongly-perturbed orbits in the Pluto system, motivated by the recent flyby of the New Horizons spacecraft, together with a geocentric flyby of the NEAR spacecraft.

Variational Approach to Enhanced Sampling and Free Energy Calculations

NASA Astrophysics Data System (ADS)

Valsson, Omar; Parrinello, Michele

2014-08-01

The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo simulations, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to alleviate this problem. Many are based on the introduction of a bias potential which is a function of a small number of collective variables. However constructing such a bias is not simple. Here we introduce a functional of the bias potential and an associated variational principle. The bias that minimizes the functional relates in a simple way to the free energy surface. This variational principle can be turned into a practical, efficient, and flexible sampling method. A number of numerical examples are presented which include the determination of a three-dimensional free energy surface. We argue that, beside being numerically advantageous, our variational approach provides a convenient and novel standpoint for looking at the sampling problem.

Incompressible Navier-Stokes Computations with Heat Transfer

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan; Rogers, Stuart; Kutler, Paul (Technical Monitor)

1994-01-01

The existing pseudocompressibility method for the system of incompressible Navier-Stokes equations is extended to heat transfer problems by including the energy equation. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. Both forced and natural convection problems are examined. Numerical results from turbulent reattaching flow behind a backward-facing step will be compared against experimental measurements for the forced convection case. The validity of Boussinesq approximation to simplify the buoyancy force term will be investigated. The natural convective flow structure generated by heat transfer in a vertical rectangular cavity will be studied. The numerical results will be compared by experimental measurements by Morrison and Tran.

A Continuing Search for a Near-Perfect Numerical Flux Scheme. Part 1; [AUSM+

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1994-01-01

While enjoying demonstrated improvement in accuracy, efficiency, and robustness over existing schemes, the Advection Upstream Splitting Scheme (AUSM) was found to have some deficiencies in extreme cases. This recent progress towards improving the AUSM while retaining its advantageous features is described. The new scheme, termed AUSM+, features: unification of velocity and Mach number splitting; exact capture of a single stationary shock; and improvement in accuracy. A general construction of the AUSM+ scheme is layed out and then focus is on the analysis of the a scheme and its mathematical properties, heretofore unreported. Monotonicity and positivity are proved, and a CFL-like condition is given for first and second order schemes and for generalized curvilinear co-ordinates. Finally, results of numerical tests on many problems are given to confirm the capability and improvements on a variety of problems including those failed by prominent schemes.

Bio-Inspired Functional Surfaces Based on Laser-Induced Periodic Surface Structures.

PubMed

Müller, Frank A; Kunz, Clemens; Gräf, Stephan

2016-06-15

Nature developed numerous solutions to solve various technical problems related to material surfaces by combining the physico-chemical properties of a material with periodically aligned micro/nanostructures in a sophisticated manner. The utilization of ultra-short pulsed lasers allows mimicking numerous of these features by generating laser-induced periodic surface structures (LIPSS). In this review paper, we describe the physical background of LIPSS generation as well as the physical principles of surface related phenomena like wettability, reflectivity, and friction. Then we introduce several biological examples including e.g., lotus leafs, springtails, dessert beetles, moth eyes, butterfly wings, weevils, sharks, pangolins, and snakes to illustrate how nature solves technical problems, and we give a comprehensive overview of recent achievements related to the utilization of LIPSS to generate superhydrophobic, anti-reflective, colored, and drag resistant surfaces. Finally, we conclude with some future developments and perspectives related to forthcoming applications of LIPSS-based surfaces.

Adaptable structural synthesis using advanced analysis and optimization coupled by a computer operating system

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, J.; Bhat, R. B.

1979-01-01

A finite element program is linked with a general purpose optimization program in a 'programing system' which includes user supplied codes that contain problem dependent formulations of the design variables, objective function and constraints. The result is a system adaptable to a wide spectrum of structural optimization problems. In a sample of numerical examples, the design variables are the cross-sectional dimensions and the parameters of overall shape geometry, constraints are applied to stresses, displacements, buckling and vibration characteristics, and structural mass is the objective function. Thin-walled, built-up structures and frameworks are included in the sample. Details of the system organization and characteristics of the component programs are given.

Crystal Growth and Fluid Mechanics Problems in Directional Solidification

NASA Technical Reports Server (NTRS)

Tanveer, Saleh A.; Baker, Gregory R.; Foster, Michael R.

2001-01-01

Our work in directional solidification has been in the following areas: (1) Dynamics of dendrites including rigorous mathematical analysis of the resulting equations; (2) Examination of the near-structurally unstable features of the mathematically related Hele-Shaw dynamics; (3) Numerical studies of steady temperature distribution in a vertical Bridgman device; (4) Numerical study of transient effects in a vertical Bridgman device; (5) Asymptotic treatment of quasi-steady operation of a vertical Bridgman furnace for large Rayleigh numbers and small Biot number in 3D; and (6) Understanding of Mullins-Sererka transition in a Bridgman device with fluid dynamics is accounted for.

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

NASA Technical Reports Server (NTRS)

1982-01-01

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

Magnesium: Nutrition and Homoeostasis.

PubMed

Vormann, Jürgen

2016-01-01

The essential mineral magnesium is involved in numerous physiological processes. Recommended dietary intake is often not met and a low magnesium status increases the risk for various diseases. Magnesium status is regulated by several magnesium transport systems either in cellular or paracellular pathways. Numerous drugs either interfere with magnesium absorption in the intestines or the reabsorption from primary urine in the kidney. Low magnesium status has been identified as a significant risk factor for several diseases, including type-2 diabetes, cardiovascular diseases, arrhythmias, as well as general muscular and neurological problems. Therefore, an adequate magnesium supply would be of special benefit to our overall health.

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Universitaet Regensburg, Regensburg, West Germany, April 16-19, 1984, Proceedings

NASA Astrophysics Data System (ADS)

Problems in applied mathematics and mechanics are addressed in reviews and reports. Areas covered are vibration and stability, elastic and plastic mechanics, fluid mechanics, the numerical treatment of differential equations (general theory and finite-element methods in particular), optimization, decision theory, stochastics, actuarial mathematics, applied analysis and mathematical physics, and numerical analysis. Included are major lectures on separated flows, the transition regime of rarefied-gas dynamics, recent results in nonlinear elasticity, fluid-elastic vibration, the new computer arithmetic, and unsteady wave propagation in layered elastic bodies.

Numerical simulation of swept-wing flows

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1991-01-01

Efforts of the last six months to computationally model the transition process characteristics of flow over swept wings are described. Specifically, the crossflow instability and crossflow/Tollmien-Schlichting wave interactions are analyzed through the numerical solution of the full 3D Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiment. The leading edge region of a swept wing is considered in a 3D spatial simulation with random disturbances as the initial conditions.

Analytical formulation of selected activities of the remote manipulator system

NASA Technical Reports Server (NTRS)

Zimmerman, K. J.

1977-01-01

Existing analysis of Orbiter-RMS-Payload kinematics were surveyed, including equations dealing with the two body kinematics in the presence of a massless RMS and compares analytical explicit solutions with numerical solutions. For the following operational phases of the RMS numerical demonstration, problems are provided: (1) payload capture; (2) payload stowage and removal from cargo bay; and (3) payload deployment. The equation of motion provided accounted for RMS control forces and torque moments and could be extended to RMS flexibility and control loop simulation without increasing the degrees of freedom of the two body system.

Transport Phenomena in Thin Rotating Liquid Films Including: Nucleate Boiling

NASA Technical Reports Server (NTRS)

Faghri, Amir

2005-01-01

In this grant, experimental, numerical and analytical studies of heat transfer in a thin liquid film flowing over a rotating disk have been conducted. Heat transfer coefficients were measured experimentally in a rotating disk heat transfer apparatus where the disk was heated from below with electrical resistance heaters. The heat transfer measurements were supplemented by experimental characterization of the liquid film thickness using a novel laser based technique. The heat transfer measurements show that the disk rotation plays an important role on enhancement of heat transfer primarily through the thinning of the liquid film. Experiments covered both momentum and rotation dominated regimes of the flow and heat transfer in this apparatus. Heat transfer measurements have been extended to include evaporation and nucleate boiling and these experiments are continuing in our laboratory. Empirical correlations have also been developed to provide useful information for design of compact high efficiency heat transfer devices. The experimental work has been supplemented by numerical and analytical analyses of the same problem. Both numerical and analytical results have been found to agree reasonably well with the experimental results on liquid film thickness and heat transfer Coefficients/Nusselt numbers. The numerical simulations include the free surface liquid film flow and heat transfer under disk rotation including the conjugate effects. The analytical analysis utilizes an integral boundary layer approach from which

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

NASA Astrophysics Data System (ADS)

Schaerer, Roman Pascal; Bansal, Pratyuksh; Torrilhon, Manuel

2017-07-01

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) [13], we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

Finite element modeling of mass transport in high-Péclet cardiovascular flows

NASA Astrophysics Data System (ADS)

Hansen, Kirk; Arzani, Amirhossein; Shadden, Shawn

2016-11-01

Mass transport plays an important role in many important cardiovascular processes, including thrombus formation and atherosclerosis. These mass transport problems are characterized by Péclet numbers of up to 108, leading to several numerical difficulties. The presence of thin near-wall concentration boundary layers requires very fine mesh resolution in these regions, while large concentration gradients within the flow cause numerical stabilization issues. In this work, we will discuss some guidelines for solving mass transport problems in cardiovascular flows using a stabilized Galerkin finite element method. First, we perform mesh convergence studies in a series of idealized and patient-specific geometries to determine the required near-wall mesh resolution for these types of problems, using both first- and second-order tetrahedral finite elements. Second, we investigate the use of several boundary condition types at outflow boundaries where backflow during some parts of the cardiac cycle can lead to convergence issues. Finally, we evaluate the effect of reducing Péclet number by increasing mass diffusivity as has been proposed by some researchers. This work was supported by the NSF GRFP and NSF Career Award #1354541.

Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation

NASA Astrophysics Data System (ADS)

Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo

2015-10-01

The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.

Numerical Modeling of Ablation Heat Transfer

NASA Technical Reports Server (NTRS)

Ewing, Mark E.; Laker, Travis S.; Walker, David T.

2013-01-01

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

A comparison of numerical methods for the prediction of two-dimensional heat transfer in an electrothermal deicer pad. M.S. Thesis. Final Contractor Report

NASA Technical Reports Server (NTRS)

Wright, William B.

1988-01-01

Transient, numerical simulations of the deicing of composite aircraft components by electrothermal heating have been performed in a 2-D rectangular geometry. Seven numerical schemes and four solution methods were used to find the most efficient numerical procedure for this problem. The phase change in the ice was simulated using the Enthalpy method along with the Method for Assumed States. Numerical solutions illustrating deicer performance for various conditions are presented. Comparisons are made with previous numerical models and with experimental data. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

Enhanced Verification Test Suite for Physics Simulation Codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamm, J R; Brock, J S; Brandon, S T

2008-10-10

This document discusses problems with which to augment, in quantity and in quality, the existing tri-laboratory suite of verification problems used by Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratory (LLNL), and Sandia National Laboratories (SNL). The purpose of verification analysis is demonstrate whether the numerical results of the discretization algorithms in physics and engineering simulation codes provide correct solutions of the corresponding continuum equations. The key points of this document are: (1) Verification deals with mathematical correctness of the numerical algorithms in a code, while validation deals with physical correctness of a simulation in a regime of interest.more » This document is about verification. (2) The current seven-problem Tri-Laboratory Verification Test Suite, which has been used for approximately five years at the DOE WP laboratories, is limited. (3) Both the methodology for and technology used in verification analysis have evolved and been improved since the original test suite was proposed. (4) The proposed test problems are in three basic areas: (a) Hydrodynamics; (b) Transport processes; and (c) Dynamic strength-of-materials. (5) For several of the proposed problems we provide a 'strong sense verification benchmark', consisting of (i) a clear mathematical statement of the problem with sufficient information to run a computer simulation, (ii) an explanation of how the code result and benchmark solution are to be evaluated, and (iii) a description of the acceptance criterion for simulation code results. (6) It is proposed that the set of verification test problems with which any particular code be evaluated include some of the problems described in this document. Analysis of the proposed verification test problems constitutes part of a necessary--but not sufficient--step that builds confidence in physics and engineering simulation codes. More complicated test cases, including physics models of greater sophistication or other physics regimes (e.g., energetic material response, magneto-hydrodynamics), would represent a scientifically desirable complement to the fundamental test cases discussed in this report. The authors believe that this document can be used to enhance the verification analyses undertaken at the DOE WP Laboratories and, thus, to improve the quality, credibility, and usefulness of the simulation codes that are analyzed with these problems.« less

An accurate boundary element method for the exterior elastic scattering problem in two dimensions

NASA Astrophysics Data System (ADS)

Bao, Gang; Xu, Liwei; Yin, Tao

2017-11-01

This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller [1] boundary integral formulation, and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula [2] is employed for the numerical evaluation of hyper-singular boundary integral operator. A new computational approach is employed based on the series expansions of Hankel functions for the computation of weakly-singular boundary integral operators during the reduction of corresponding Galerkin equations into a discrete linear system. The effectiveness of proposed numerical methods is demonstrated using several numerical examples.

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Touma, Rony; Zeidan, Dia

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potentialmore » of the proposed scheme.« less

Special data base of Informational - Computational System 'INM RAS - Black Sea' for solving inverse and data assimilation problems

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Piskovatsky, Nicolay; Gusev, Anatoly

2014-05-01

Development of Informational-Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in: mathematical modeling; theory of adjoint equations and optimal control; inverse problems; numerical methods theory; numerical algebra and scientific computing. The above problems are studied in the Institute of Numerical Mathematics of the Russian Academy of Science (INM RAS) in ICS for personal computers. In this work the results on the Special data base development for ICS "INM RAS - Black Sea" are presented. In the presentation the input information for ICS is discussed, some special data processing procedures are described. In this work the results of forecast using ICS "INM RAS - Black Sea" with operational observation data assimilation are presented. This study was supported by the Russian Foundation for Basic Research (project No 13-01-00753) and by Presidium Program of Russian Academy of Sciences (project P-23 "Black sea as an imitational ocean model"). References 1. V.I. Agoshkov, M.V. Assovskii, S.A. Lebedev, Numerical simulation of Black Sea hydrothermodynamics taking into account tide-forming forces. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 5-31. 2. E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 69-94. 3. V.B. Zalesny, N.A. Diansky, V.V. Fomin, S.N. Moshonkin, S.G. Demyshev, Numerical model of the circulation of Black Sea and Sea of Azov. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 95-111. 4. Agoshkov V.I.,Assovsky M.B., Giniatulin S. V., Zakharova N.B., Kuimov G.V., Parmuzin E.I., Fomin V.V. Informational Computational system of variational assimilation of observation data "INM RAS - Black sea"// Ecological safety of coastal and shelf zones and complex use of shelf resources: Collection of scientific works. Issue 26, Volume 2. - National Academy of Sciences of Ukraine, Marine Hydrophysical Institute, Sebastopol, 2012. Pages 352-360. (In russian)

Wavelet-based Adaptive Mesh Refinement Method for Global Atmospheric Chemical Transport Modeling

NASA Astrophysics Data System (ADS)

Rastigejev, Y.

2011-12-01

Numerical modeling of global atmospheric chemical transport presents enormous computational difficulties, associated with simulating a wide range of time and spatial scales. The described difficulties are exacerbated by the fact that hundreds of chemical species and thousands of chemical reactions typically are used for chemical kinetic mechanism description. These computational requirements very often forces researches to use relatively crude quasi-uniform numerical grids with inadequate spatial resolution that introduces significant numerical diffusion into the system. It was shown that this spurious diffusion significantly distorts the pollutant mixing and transport dynamics for typically used grid resolution. The described numerical difficulties have to be systematically addressed considering that the demand for fast, high-resolution chemical transport models will be exacerbated over the next decade by the need to interpret satellite observations of tropospheric ozone and related species. In this study we offer dynamically adaptive multilevel Wavelet-based Adaptive Mesh Refinement (WAMR) method for numerical modeling of atmospheric chemical evolution equations. The adaptive mesh refinement is performed by adding and removing finer levels of resolution in the locations of fine scale development and in the locations of smooth solution behavior accordingly. The algorithm is based on the mathematically well established wavelet theory. This allows us to provide error estimates of the solution that are used in conjunction with an appropriate threshold criteria to adapt the non-uniform grid. Other essential features of the numerical algorithm include: an efficient wavelet spatial discretization that allows to minimize the number of degrees of freedom for a prescribed accuracy, a fast algorithm for computing wavelet amplitudes, and efficient and accurate derivative approximations on an irregular grid. The method has been tested for a variety of benchmark problems including numerical simulation of transpacific traveling pollution plumes. The generated pollution plumes are diluted due to turbulent mixing as they are advected downwind. Despite this dilution, it was recently discovered that pollution plumes in the remote troposphere can preserve their identity as well-defined structures for two weeks or more as they circle the globe. Present Global Chemical Transport Models (CTMs) implemented for quasi-uniform grids are completely incapable of reproducing these layered structures due to high numerical plume dilution caused by numerical diffusion combined with non-uniformity of atmospheric flow. It is shown that WAMR algorithm solutions of comparable accuracy as conventional numerical techniques are obtained with more than an order of magnitude reduction in number of grid points, therefore the adaptive algorithm is capable to produce accurate results at a relatively low computational cost. The numerical simulations demonstrate that WAMR algorithm applied the traveling plume problem accurately reproduces the plume dynamics unlike conventional numerical methods that utilizes quasi-uniform numerical grids.

Treating convection in sequential solvers

NASA Technical Reports Server (NTRS)

Shyy, Wei; Thakur, Siddharth

1992-01-01

The treatment of the convection terms in the sequential solver, a standard procedure found in virtually all pressure based algorithms, to compute the flow problems with sharp gradients and source terms is investigated. Both scalar model problems and one-dimensional gas dynamics equations have been used to study the various issues involved. Different approaches including the use of nonlinear filtering techniques and adoption of TVD type schemes have been investigated. Special treatments of the source terms such as pressure gradients and heat release have also been devised, yielding insight and improved accuracy of the numerical procedure adopted.

Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. III - Impact/contact simulations

NASA Technical Reports Server (NTRS)

Nakajima, Yukio; Padovan, Joe

1987-01-01

In a three-part series of papers, a generalized finite element methodology is formulated to handle traveling load problems involving large deformation fields in structure composed of viscoelastic media. The main thrust of this paper is to develop an overall finite element methodology and associated solution algorithms to handle the transient aspects of moving problems involving contact impact type loading fields. Based on the methodology and algorithms formulated, several numerical experiments are considered. These include the rolling/sliding impact of tires with road obstructions.

Inverse kinematics of a dual linear actuator pitch/roll heliostat

NASA Astrophysics Data System (ADS)

Freeman, Joshua; Shankar, Balakrishnan; Sundaram, Ganesh

2017-06-01

This work presents a simple, computationally efficient inverse kinematics solution for a pitch/roll heliostat using two linear actuators. The heliostat design and kinematics have been developed, modeled and tested using computer simulation software. A physical heliostat prototype was fabricated to validate the theoretical computations and data. Pitch/roll heliostats have numerous advantages including reduced cost potential and reduced space requirements, with a primary disadvantage being the significantly more complicated kinematics, which are solved here. Novel methods are applied to simplify the inverse kinematics problem which could be applied to other similar problems.

Self-tuning regulators for multicyclic control of helicopter vibration

NASA Technical Reports Server (NTRS)

Johnson, W.

1982-01-01

A class of algorithms for the multicyclic control of helicopter vibration and loads is derived and discussed. This class is characterized by a linear, quasi-static, frequency-domain model of the helicopter response to control; identification of the helicopter model by least-squared-error or Kalman filter methods; and a minimum variance or quadratic performance function controller. Previous research on such controllers is reviewed. The derivations and discussions cover the helicopter model; the identification problem, including both off-line and on-line (recursive) algorithms; the control problem, including both open-loop and closed-loop feedback; and the various regulator configurations possible within this class. Conclusions from analysis and numerical simulations of the regulators provide guidance in the design and selection of algorithms for further development, including wind tunnel and flight tests.

Numerical modeling of the acoustic wave propagation across a homogenized rigid microstructure in the time domain

NASA Astrophysics Data System (ADS)

Lombard, Bruno; Maurel, Agnès; Marigo, Jean-Jacques

2017-04-01

Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded. This paper aims (i) to propose a numerical method able to handle the jump conditions in order to simulate the homogenized problem in the time domain, (ii) to inspect the validity of the homogenized problem when compared to the real one. For this purpose, we adapt the Explicit Simplified Interface Method originally developed for standard jump conditions across a zero-thickness interface. Doing so allows us to handle arbitrary-shaped interfaces on a Cartesian grid with the same efficiency and accuracy of the numerical scheme than those obtained in a homogeneous medium. Numerical experiments are performed to test the properties of the numerical method and to inspect the validity of the homogenization problem.

Complete Numerical Solution of the Diffusion Equation of Random Genetic Drift

PubMed Central

Zhao, Lei; Yue, Xingye; Waxman, David

2013-01-01

A numerical method is presented to solve the diffusion equation for the random genetic drift that occurs at a single unlinked locus with two alleles. The method was designed to conserve probability, and the resulting numerical solution represents a probability distribution whose total probability is unity. We describe solutions of the diffusion equation whose total probability is unity as complete. Thus the numerical method introduced in this work produces complete solutions, and such solutions have the property that whenever fixation and loss can occur, they are automatically included within the solution. This feature demonstrates that the diffusion approximation can describe not only internal allele frequencies, but also the boundary frequencies zero and one. The numerical approach presented here constitutes a single inclusive framework from which to perform calculations for random genetic drift. It has a straightforward implementation, allowing it to be applied to a wide variety of problems, including those with time-dependent parameters, such as changing population sizes. As tests and illustrations of the numerical method, it is used to determine: (i) the probability density and time-dependent probability of fixation for a neutral locus in a population of constant size; (ii) the probability of fixation in the presence of selection; and (iii) the probability of fixation in the presence of selection and demographic change, the latter in the form of a changing population size. PMID:23749318

Does the Acquisition of Mathematical Knowledge Make Students Better Problem Solvers? An Examination of Third Graders' Solutions of Division-with-Remainder (DWR) Problems.

ERIC Educational Resources Information Center

Guerrero, Lourdes; Rivera, Antonio

Fourteen third graders were given numerical computation and division-with-remainder (DWR) problems both before and after they were taught the division algorithm in classrooms. Their solutions were examined. The results show that students' initial acquisition of the division algorithm did improve their performance in numerical division computations…

Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers.

PubMed

Zhang, Yong-Tao; Shi, Jing; Shu, Chi-Wang; Zhou, Ye

2003-10-01

A quantitative study is carried out in this paper to investigate the size of numerical viscosities and the resolution power of high-order weighted essentially nonoscillatory (WENO) schemes for solving one- and two-dimensional Navier-Stokes equations for compressible gas dynamics with high Reynolds numbers. A one-dimensional shock tube problem, a one-dimensional example with parameters motivated by supernova and laser experiments, and a two-dimensional Rayleigh-Taylor instability problem are used as numerical test problems. For the two-dimensional Rayleigh-Taylor instability problem, or similar problems with small-scale structures, the details of the small structures are determined by the physical viscosity (therefore, the Reynolds number) in the Navier-Stokes equations. Thus, to obtain faithful resolution to these small-scale structures, the numerical viscosity inherent in the scheme must be small enough so that the physical viscosity dominates. A careful mesh refinement study is performed to capture the threshold mesh for full resolution, for specific Reynolds numbers, when WENO schemes of different orders of accuracy are used. It is demonstrated that high-order WENO schemes are more CPU time efficient to reach the same resolution, both for the one-dimensional and two-dimensional test problems.

Eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method

NASA Astrophysics Data System (ADS)

Bekhoucha, F.; Rechak, S.; Cadou, J. M.

2016-12-01

In this paper, free vibrations of a rotating clamped Euler-Bernoulli beams with uniform cross section are studied using continuation method, namely asymptotic numerical method. The governing equations of motion are derived using Lagrange's method. The kinetic and strain energy expression are derived from Rayleigh-Ritz method using a set of hybrid variables and based on a linear deflection assumption. The derived equations are transformed in two eigenvalue problems, where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms. While the second is standard eigenvalue problem and corresponds to the flapping motion. Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method. New method proposed for the solution of the linear gyroscopic system based on an augmented system, which transforms the original problem to a standard form with real symmetric matrices. By using some techniques to resolve these singular problems by the continuation method, evolution curves of the natural frequencies against dimensionless angular velocity are determined. At high angular velocity, some singular points, due to the linear elastic assumption, are computed. Numerical tests of convergence are conducted and the obtained results are compared to the exact values. Results obtained by continuation are compared to those computed with discrete eigenvalue problem.

Tying Early Childhood Education More Closely to Schooling: Promise, Perils and Practical Problems

ERIC Educational Resources Information Center

Halpern, Robert

2013-01-01

Background: Over the past decade or so, the idea of joining early childhood education (ECE) and schooling has gained currency in the educational reform arena. Numerous education reform proposals and plans include ECE as a component. Scores of school districts around the country have added preschool classrooms to at least some of their elementary…

What Learning Looks Like: Mediated Learning in Theory and Practice, K-6

ERIC Educational Resources Information Center

Feuerstein, Reuven; Lewin-Benham, Ann

2012-01-01

In this unique collaboration, the authors bring to life the theory of mediated learning. Through numerous examples and scenarios from classrooms and museums, they show how mediated learning helps children to become more effective learners. Readers learn the steps in the process, including analyzing the child's problem, teaching the child to focus…

Statistics of stable marriages

NASA Astrophysics Data System (ADS)

Dzierzawa, Michael; Oméro, Marie-José

2000-11-01

In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and analytical methods. Generalizations of the model including singles and unequal numbers of men and women are also investigated.

Petroleum accounting principles, procedures, and issues

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brock, H.R.; Klingstedt, J.P.; Jones, D.M.

1985-01-01

This book begins with the basics and leads one through the complexities of accounting and reporting for the industry. It presents the material one needs as an accountant in the petroleum industry. Examples deal with real problems and issues. It also includes numerous illustrations and examples, as well as sample forms, lease agreements, and industry and governmental regulations.

On a problem of reconstruction of a discontinuous function by its Radon transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Derevtsov, Evgeny Yu.; Maltseva, Svetlana V.; Svetov, Ivan E.

A problem of reconstruction of a discontinuous function by its Radon transform is considered. One of the approaches to the numerical solution for the problem consists in the next sequential steps: a visualization of a set of breaking points; an identification of this set; a determination of jump values; an elimination of discontinuities. We consider three of listed problems except the problem of jump values. The problems are investigated by mathematical modeling using numerical experiments. The results of simulation are satisfactory and allow to hope for the further development of the approach.

The stability issues in problems of mathematical modeling

NASA Astrophysics Data System (ADS)

Mokin, A. Yu.; Savenkova, N. P.; Udovichenko, N. S.

2018-03-01

In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

University Students' Problem Posing Abilities and Attitudes towards Mathematics.

ERIC Educational Resources Information Center

Grundmeier, Todd A.

2002-01-01

Explores the problem posing abilities and attitudes towards mathematics of students in a university pre-calculus class and a university mathematical proof class. Reports a significant difference in numeric posing versus non-numeric posing ability in both classes. (Author/MM)

Solving fractional optimal control problems within a Chebyshev-Legendre operational technique

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Ezz-Eldien, S. S.; Doha, E. H.; Abdelkawy, M. A.; Baleanu, D.

2017-06-01

In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre-Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.

Numerical Solution of the Electron Transport Equation in the Upper Atmosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woods, Mark Christopher; Holmes, Mark; Sailor, William C

A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplifieed problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other to at least two significant digits.

Variational data assimilation for limited-area models: solution of the open boundary control problem and its application for the Gulf of Finland

NASA Astrophysics Data System (ADS)

Sheloput, Tatiana; Agoshkov, Valery

2017-04-01

The problem of modeling water areas with `liquid' (open) lateral boundaries is discussed. There are different known methods dealing with open boundaries in limited-area models, and one of the most efficient is data assimilation. Although this method is popular, there are not so many articles concerning its implementation for recovering boundary functions. However, the problem of specifying boundary conditions at the open boundary of a limited area is still actual and important. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. It is based on the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations. The splitting method that is used for time approximation in the model allows to consider the data assimilation problem as a sequence of linear problems. One of such `simple' temperature (salinity) assimilation problem is investigated in the study. Using well known techniques of study and solution of inverse problems and optimal control problems [1], we propose an iterative solution algorithm and we obtain conditions for existence of the solution, for unique and dense solvability of the problem and for convergence of the iterative algorithm. The investigation shows that if observations satisfy certain conditions, the proposed algorithm converges to the solution of the boundary control problem. Particularly, it converges when observational data are given on the `liquid' boundary [2]. Theoretical results are confirmed by the results of numerical experiments. The numerical algorithm was implemented to water area of the Baltic Sea. Two numerical experiments were carried out in the Gulf of Finland: one with the application of the assimilation procedure and the other without. The analyses have shown that the surface temperature field in the first experiment is close to the observed one, while the result of the second experiment misfits. Number of iterations depends on the regularisation parameter, but generally the algorithm converges after 10 iterations. The results of the numerical experiments show that the usage of the proposed method makes sense. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments) and by the Russian Foundation for Basic Research (project 16-01-00548, the formulation of the problem and its study). [1] Agoshkov V. I. Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). [2] Agoshkov V.I., Sheloput T.O. The study and numerical solution of the problem of heat and salinity transfer assuming 'liquid' boundaries // Russ. J. Numer. Anal. Math. Modelling. 2016. Vol. 31, No. 2. P. 71-80.

The Root Cause of the Overheating Problem

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

2017-01-01

Previously we identified the receding flow, where two fluid streams recede from each other, as an open numerical problem, because all well-known numerical fluxes give an anomalous temperature rise, thus called the overheating problem. This phenomenon, although presented in several textbooks, and many previous publications, has scarcely been satisfactorily addressed and the root cause of the overheating problem not well understood. We found that this temperature rise was solely connected to entropy rise and proposed to use the method of characteristics to eradicate the problem. However, the root cause of the entropy production was still unclear. In the present study, we identify the cause of this problem: the entropy rise is rooted in the pressure flux in a finite volume formulation and is implanted at the first time step. It is found theoretically inevitable for all existing numerical flux schemes used in the finite volume setting, as confirmed by numerical tests. This difficulty cannot be eliminated by manipulating time step, grid size, spatial accuracy, etc, although the rate of overheating depends on the flux scheme used. Finally, we incorporate the entropy transport equation, in place of the energy equation, to ensure preservation of entropy, thus correcting this temperature anomaly. Its applicability is demonstrated for some relevant 1D and 2D problems. Thus, the present study validates that the entropy generated ab initio is the genesis of the overheating problem.

Propagation of Axisymmetric Electroelastic Waves in a Hollow Layered Cylinder Under Mechanical Excitation

NASA Astrophysics Data System (ADS)

Grigorenko, A. Ya.; Loza, I. A.

2017-09-01

The problem on propagation of axisymmetric electroelastic waves in a hollow layered cylinder made of metallic and radially polarized piezoceramic layers is solved. The lateral surfaces of the cylinder are free of electrodes. The outside surface is free of mechanical loads, while the inside one undergoes harmonically varying pressure Pe. The problem was solved with a numerical-analytical method. By representing the components of the stress tensor, displacement vectors, electric-flux density, and electrostatic potential by traveling waves, the original electroelastic problem in partial derivatives is reduced to an inhomogeneous boundary-value problem for ordinary differential equations. To solve the problem, the stable numerical discrete-orthogonalization method is used. The results of the kinematic analysis of the layered cylinder both with metallic and piezoceramic (PZT 4) layers are presented. The numerical results are analyzed.

Adaptive Wavelet Modeling of Geophysical Data

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H.; Dahmen, W.; Vorloeper, J.

2009-12-01

Despite the ever-increasing power of modern computers, realistic modeling of complex three-dimensional Earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modeling approaches includes either finite difference or non-adaptive finite element algorithms, and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behavior of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modeled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet based approach that is applicable to a large scope of problems, also including nonlinear problems. To the best of our knowledge such algorithms have not yet been applied in geophysics. Adaptive wavelet algorithms offer several attractive features: (i) for a given subsurface model, they allow the forward modeling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient, and (iii) the modeling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving three-dimensional geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best fit subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectrical modeling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with spatially highly variable electrical conductivities. The linear dependency of the modeling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementation.

The numerical-analytical implementation of the cross-sections method to the open waveguide transition of the "horn" type

NASA Astrophysics Data System (ADS)

Divakov, Dmitriy; Malykh, Mikhail; Sevastianov, Leonid; Sevastianov, Anton; Tiutiunnik, Anastasiia

2017-04-01

In the paper we construct a method for approximate solution of the waveguide problem for guided modes of an open irregular waveguide transition. The method is based on straightening of the curved waveguide boundaries by introducing new variables and applying the Kantorovich method to the problem formulated in the new variables to get a system of ordinary second-order differential equations. In the method, the boundary conditions are formulated by analogy with the partial radiation conditions in the similar problem for closed waveguide transitions. The method is implemented in the symbolic-numeric form using the Maple computer algebra system. The coefficient matrices of the system of differential equations and boundary conditions are calculated symbolically, and then the obtained boundary-value problem is solved numerically using the finite difference method. The chosen coordinate functions of Kantorovich expansions provide good conditionality of the coefficient matrices. The numerical experiment simulating the propagation of guided modes in the open waveguide transition confirms the validity of the method proposed to solve the problem.

Recovery of time-dependent volatility in option pricing model

NASA Astrophysics Data System (ADS)

Deng, Zui-Cha; Hon, Y. C.; Isakov, V.

2016-11-01

In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective. The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CityU 101112) and grants from the NNSF of China (Nos. 11261029, 11461039), and NSF grants DMS 10-08902 and 15-14886 and by Emylou Keith and Betty Dutcher Distinguished Professorship at the Wichita State University (USA).

Numerical Solution of Time-Dependent Problems with a Fractional-Power Elliptic Operator

NASA Astrophysics Data System (ADS)

Vabishchevich, P. N.

2018-03-01

A time-dependent problem in a bounded domain for a fractional diffusion equation is considered. The first-order evolution equation involves a fractional-power second-order elliptic operator with Robin boundary conditions. A finite-element spatial approximation with an additive approximation of the operator of the problem is used. The time approximation is based on a vector scheme. The transition to a new time level is ensured by solving a sequence of standard elliptic boundary value problems. Numerical results obtained for a two-dimensional model problem are presented.

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

The solution of non-linear hyperbolic equation systems by the finite element method

NASA Technical Reports Server (NTRS)

Loehner, R.; Morgan, K.; Zienkiewicz, O. C.

1984-01-01

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Numerical treatment of free surface problems in ferrohydrodynamics

NASA Astrophysics Data System (ADS)

Lavrova, O.; Matthies, G.; Mitkova, T.; Polevikov, V.; Tobiska, L.

2006-09-01

The numerical treatment of free surface problems in ferrohydrodynamics is considered. Starting from the general model, special attention is paid to field-surface and flow-surface interactions. Since in some situations these feedback interactions can be partly or even fully neglected, simpler models can be derived. The application of such models to the numerical simulation of dissipative systems, rotary shaft seals, equilibrium shapes of ferrofluid drops, and pattern formation in the normal-field instability of ferrofluid layers is given. Our numerical strategy is able to recover solitary surface patterns which were discovered recently in experiments.

The minimal residual QR-factorization algorithm for reliably solving subset regression problems

NASA Technical Reports Server (NTRS)

Verhaegen, M. H.

1987-01-01

A new algorithm to solve test subset regression problems is described, called the minimal residual QR factorization algorithm (MRQR). This scheme performs a QR factorization with a new column pivoting strategy. Basically, this strategy is based on the change in the residual of the least squares problem. Furthermore, it is demonstrated that this basic scheme might be extended in a numerically efficient way to combine the advantages of existing numerical procedures, such as the singular value decomposition, with those of more classical statistical procedures, such as stepwise regression. This extension is presented as an advisory expert system that guides the user in solving the subset regression problem. The advantages of the new procedure are highlighted by a numerical example.

Numerical formulation for the prediction of solid/liquid change of a binary alloy

NASA Technical Reports Server (NTRS)

Schneider, G. E.; Tiwari, S. N.

1990-01-01

A computational model is presented for the prediction of solid/liquid phase change energy transport including the influence of free convection fluid flow in the liquid phase region. The computational model considers the velocity components of all non-liquid phase change material control volumes to be zero but fully solves the coupled mass-momentum problem within the liquid region. The thermal energy model includes the entire domain and uses an enthalpy like model and a recently developed method for handling the phase change interface nonlinearity. Convergence studies are performed and comparisons made with experimental data for two different problem specifications. The convergence studies indicate that grid independence was achieved and the comparison with experimental data indicates excellent quantitative prediction of the melt fraction evolution. Qualitative data is also provided in the form of velocity vector diagrams and isotherm plots for selected times in the evolution of both problems. The computational costs incurred are quite low by comparison with previous efforts on solving these problems.

Wavelet-based identification of rotor blades in passage-through-resonance tests

NASA Astrophysics Data System (ADS)

Carassale, Luigi; Marrè-Brunenghi, Michela; Patrone, Stefano

2018-01-01

Turbine blades are critical components in turbo engines and their design process usually includes experimental tests in order to validate and/or update numerical models. These tests are generally carried out on full-scale rotors having some blades instrumented with strain gauges and usually involve a run-up or a run-down phase. The quantification of damping in these conditions is rather challenging for several reasons. In this work, we show through numerical simulations that the usual identification procedures lead to a systematic overestimation of damping due both to the finite sweep velocity, as well as to the variation of the blade natural frequencies with the rotation speed. To overcome these problems, an identification procedure based on the continuous wavelet transform is proposed and validated through numerical simulation.

Numerical simulation of nonequilibrium flows by using the state-to-state approach in commercial software

NASA Astrophysics Data System (ADS)

Kunova, O. V.; Shoev, G. V.; Kudryavtsev, A. N.

2017-01-01

Nonequilibrium flows of a two-component oxygen mixture O2/O behind a shock wave are studied with due allowance for the state-to-state vibrational and chemical kinetics. The system of gas-dynamic equations is supplemented with kinetic equations including contributions of VT (TV)-exchange and dissociation processes. A method of the numerical solution of this system with the use of the ANSYS Fluent commercial software package is proposed, which is used in a combination with the authors' code that takes into account nonequilibrium kinetics. The computed results are compared with parameters obtained by solving the problem in the shock-fitting formulation. The vibrational temperature is compared with experimental data. The numerical tool proposed in the present paper is applied to study the flow around a cylinder.

Thermochemical nonequilibrium in atomic hydrogen at elevated temperatures

NASA Technical Reports Server (NTRS)

Scott, R. K.

1972-01-01

A numerical study of the nonequilibrium flow of atomic hydrogen in a cascade arc was performed to obtain insight into the physics of the hydrogen cascade arc. A rigorous mathematical model of the flow problem was formulated, incorporating the important nonequilibrium transport phenomena and atomic processes which occur in atomic hydrogen. Realistic boundary conditions, including consideration of the wall electrostatic sheath phenomenon, were included in the model. The governing equations of the asymptotic region of the cascade arc were obtained by writing conservation of mass and energy equations for the electron subgas, an energy conservation equation for heavy particles and an equation of state. Finite-difference operators for variable grid spacing were applied to the governing equations and the resulting system of strongly coupled, stiff equations were solved numerically by the Newton-Raphson method.

SIAM Conference on Parallel Processing for Scientific Computing, 4th, Chicago, IL, Dec. 11-13, 1989, Proceedings

NASA Technical Reports Server (NTRS)

Dongarra, Jack (Editor); Messina, Paul (Editor); Sorensen, Danny C. (Editor); Voigt, Robert G. (Editor)

1990-01-01

Attention is given to such topics as an evaluation of block algorithm variants in LAPACK and presents a large-grain parallel sparse system solver, a multiprocessor method for the solution of the generalized Eigenvalue problem on an interval, and a parallel QR algorithm for iterative subspace methods on the CM2. A discussion of numerical methods includes the topics of asynchronous numerical solutions of PDEs on parallel computers, parallel homotopy curve tracking on a hypercube, and solving Navier-Stokes equations on the Cedar Multi-Cluster system. A section on differential equations includes a discussion of a six-color procedure for the parallel solution of elliptic systems using the finite quadtree structure, data parallel algorithms for the finite element method, and domain decomposition methods in aerodynamics. Topics dealing with massively parallel computing include hypercube vs. 2-dimensional meshes and massively parallel computation of conservation laws. Performance and tools are also discussed.

A simple iterative independent component analysis algorithm for vibration source signal identification of complex structures

NASA Astrophysics Data System (ADS)

Lee, Dong-Sup; Cho, Dae-Seung; Kim, Kookhyun; Jeon, Jae-Jin; Jung, Woo-Jin; Kang, Myeng-Hwan; Kim, Jae-Ho

2015-01-01

Independent Component Analysis (ICA), one of the blind source separation methods, can be applied for extracting unknown source signals only from received signals. This is accomplished by finding statistical independence of signal mixtures and has been successfully applied to myriad fields such as medical science, image processing, and numerous others. Nevertheless, there are inherent problems that have been reported when using this technique: instability and invalid ordering of separated signals, particularly when using a conventional ICA technique in vibratory source signal identification of complex structures. In this study, a simple iterative algorithm of the conventional ICA has been proposed to mitigate these problems. The proposed method to extract more stable source signals having valid order includes an iterative and reordering process of extracted mixing matrix to reconstruct finally converged source signals, referring to the magnitudes of correlation coefficients between the intermediately separated signals and the signals measured on or nearby sources. In order to review the problems of the conventional ICA technique and to validate the proposed method, numerical analyses have been carried out for a virtual response model and a 30 m class submarine model. Moreover, in order to investigate applicability of the proposed method to real problem of complex structure, an experiment has been carried out for a scaled submarine mockup. The results show that the proposed method could resolve the inherent problems of a conventional ICA technique.

ICASE semiannual report, April 1 - September 30, 1989

NASA Technical Reports Server (NTRS)

1990-01-01

The Institute conducts unclassified basic research in applied mathematics, numerical analysis, and computer science in order to extend and improve problem-solving capabilities in science and engineering, particularly in aeronautics and space. The major categories of the current Institute for Computer Applications in Science and Engineering (ICASE) research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification problems, with emphasis on effective numerical methods; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers. ICASE reports are considered to be primarily preprints of manuscripts that have been submitted to appropriate research journals or that are to appear in conference proceedings.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Verification and benchmark testing of the NUFT computer code

NASA Astrophysics Data System (ADS)

Lee, K. H.; Nitao, J. J.; Kulshrestha, A.

1993-10-01

This interim report presents results of work completed in the ongoing verification and benchmark testing of the NUFT (Nonisothermal Unsaturated-saturated Flow and Transport) computer code. NUFT is a suite of multiphase, multicomponent models for numerical solution of thermal and isothermal flow and transport in porous media, with application to subsurface contaminant transport problems. The code simulates the coupled transport of heat, fluids, and chemical components, including volatile organic compounds. Grid systems may be cartesian or cylindrical, with one-, two-, or fully three-dimensional configurations possible. In this initial phase of testing, the NUFT code was used to solve seven one-dimensional unsaturated flow and heat transfer problems. Three verification and four benchmarking problems were solved. In the verification testing, excellent agreement was observed between NUFT results and the analytical or quasianalytical solutions. In the benchmark testing, results of code intercomparison were very satisfactory. From these testing results, it is concluded that the NUFT code is ready for application to field and laboratory problems similar to those addressed here. Multidimensional problems, including those dealing with chemical transport, will be addressed in a subsequent report.

Crisis phenomena among African adolescents.

PubMed

Pretorius, J W; Ferreira, G V; Edwards, D N

1999-01-01

This study investigated inadequate parent-child relationships, problems with regard to sexuality, and substance abuse among African university students. They reported experiencing positive aspects of the parent-child relationship, such as acceptance, love, understanding, encouragement, and guidance, as well as negative aspects, including inadequate communication and parents' authoritarian attitudes. Numerous sexual issues and the abuse of alcohol and other drugs were perceived as serious problems among teenagers in general. Although an inadequate parent-child relationship appears to contribute to substance abuse and sexuality problems, it cannot be regarded as solely responsible, as a multitude of factors also play a role. The results indicate the need for life-skills training for both adolescents and parents, particularly regarding communication.

An inverse finance problem for estimation of the volatility

NASA Astrophysics Data System (ADS)

Neisy, A.; Salmani, K.

2013-01-01

Black-Scholes model, as a base model for pricing in derivatives markets has some deficiencies, such as ignoring market jumps, and considering market volatility as a constant factor. In this article, we introduce a pricing model for European-Options under jump-diffusion underlying asset. Then, using some appropriate numerical methods we try to solve this model with integral term, and terms including derivative. Finally, considering volatility as an unknown parameter, we try to estimate it by using our proposed model. For the purpose of estimating volatility, in this article, we utilize inverse problem, in which inverse problem model is first defined, and then volatility is estimated using minimization function with Tikhonov regularization.

Finite horizon optimum control with and without a scrap value

NASA Astrophysics Data System (ADS)

Neck, R.; Blueschke-Nikolaeva, V.; Blueschke, D.

2017-06-01

In this paper, we study the effects of scrap values on the solutions of optimal control problems with finite time horizon. We show how to include a scrap value, either for the state variables or for the state and the control variables, in the OPTCON2 algorithm for the optimal control of dynamic economic systems. We ask whether the introduction of a scrap value can serve as a substitute for an infinite horizon in economic policy optimization problems where the latter option is not available. Using a simple numerical macroeconomic model, we demonstrate that the introduction of a scrap value cannot induce control policies which can be expected for problems with an infinite time horizon.

Workshop report on large-scale matrix diagonalization methods in chemistry theory institute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bischof, C.H.; Shepard, R.L.; Huss-Lederman, S.

The Large-Scale Matrix Diagonalization Methods in Chemistry theory institute brought together 41 computational chemists and numerical analysts. The goal was to understand the needs of the computational chemistry community in problems that utilize matrix diagonalization techniques. This was accomplished by reviewing the current state of the art and looking toward future directions in matrix diagonalization techniques. This institute occurred about 20 years after a related meeting of similar size. During those 20 years the Davidson method continued to dominate the problem of finding a few extremal eigenvalues for many computational chemistry problems. Work on non-diagonally dominant and non-Hermitian problems asmore » well as parallel computing has also brought new methods to bear. The changes and similarities in problems and methods over the past two decades offered an interesting viewpoint for the success in this area. One important area covered by the talks was overviews of the source and nature of the chemistry problems. The numerical analysts were uniformly grateful for the efforts to convey a better understanding of the problems and issues faced in computational chemistry. An important outcome was an understanding of the wide range of eigenproblems encountered in computational chemistry. The workshop covered problems involving self- consistent-field (SCF), configuration interaction (CI), intramolecular vibrational relaxation (IVR), and scattering problems. In atomic structure calculations using the Hartree-Fock method (SCF), the symmetric matrices can range from order hundreds to thousands. These matrices often include large clusters of eigenvalues which can be as much as 25% of the spectrum. However, if Cl methods are also used, the matrix size can be between 10{sup 4} and 10{sup 9} where only one or a few extremal eigenvalues and eigenvectors are needed. Working with very large matrices has lead to the development of« less

Application of artificial intelligence to impulsive orbital transfers

NASA Technical Reports Server (NTRS)

Burns, Rowland E.

1987-01-01

A generalized technique for the numerical solution of any given class of problems is presented. The technique requires the analytic (or numerical) solution of every applicable equation for all variables that appear in the problem. Conditional blocks are employed to rapidly expand the set of known variables from a minimum of input. The method is illustrated via the use of the Hohmann transfer problem from orbital mechanics.

A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems

NASA Astrophysics Data System (ADS)

Pan, Kejia; He, Dongdong; Hu, Hongling; Ren, Zhengyong

2017-09-01

In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H3-regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems.

Bi-criteria travelling salesman subtour problem with time threshold

NASA Astrophysics Data System (ADS)

Kumar Thenepalle, Jayanth; Singamsetty, Purusotham

2018-03-01

This paper deals with the bi-criteria travelling salesman subtour problem with time threshold (BTSSP-T), which comes from the family of the travelling salesman problem (TSP) and is NP-hard in the strong sense. The problem arises in several application domains, mainly in routing and scheduling contexts. Here, the model focuses on two criteria: total travel distance and gains attained. The BTSSP-T aims to determine a subtour that starts and ends at the same city and visits a subset of cities at a minimum travel distance with maximum gains, such that the time spent on the tour does not exceed the predefined time threshold. A zero-one integer-programming problem is adopted to formulate this model with all practical constraints, and it includes a finite set of feasible solutions (one for each tour). Two algorithms, namely, the Lexi-Search Algorithm (LSA) and the Tabu Search (TS) algorithm have been developed to solve the BTSSP-T problem. The proposed LSA implicitly enumerates the feasible patterns and provides an efficient solution with backtracking, whereas the TS, which is metaheuristic, will give the better approximate solution. A numerical example is demonstrated in order to understand the search mechanism of the LSA. Numerical experiments are carried out in the MATLAB environment, on the different benchmark instances available in the TSPLIB domain as well as on randomly generated test instances. The experimental results show that the proposed LSA works better than the TS algorithm in terms of solution quality and, computationally, both LSA and TS are competitive.

Inverse problems and optimal experiment design in unsteady heat transfer processes identification

NASA Technical Reports Server (NTRS)

Artyukhin, Eugene A.

1991-01-01

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

Problems Associated with Grid Convergence of Functionals

NASA Technical Reports Server (NTRS)

Salas, Manuel D.; Atkins, Harld L.

2008-01-01

The current use of functionals to evaluate order-of-convergence of a numerical scheme can lead to incorrect values. The problem comes about because of interplay between the errors from the evaluation of the functional, e.g., quadrature error, and from the numerical scheme discretization. Alternative procedures for deducing the order-property of a scheme are presented. The problem is studied within the context of the inviscid supersonic flow over a blunt body; however, the problem and solutions presented are not unique to this example.

On Problems Associated with Grid Convergence of Functionals

NASA Technical Reports Server (NTRS)

Salas, Manuael D.; Atkins, Harold L

2009-01-01

The current use of functionals to evaluate order-of-convergence of a numerical scheme can lead to incorrect values. The problem comes about because of interplay between the errors from the evaluation of the functional, e.g., quadrature error, and from the numerical scheme discretization. Alternative procedures for deducing the order property of a scheme are presented. The problems are studied within the context of the inviscid supersonic flow over a blunt body; however, the problems and solutions presented are not unique to this example.

Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives

NASA Astrophysics Data System (ADS)

Antunes, Pedro R. S.; Ferreira, Rui A. C.

2017-07-01

In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented -RBF method. Several examples illustrate the good performance of the numerical method.

Optimality conditions for the numerical solution of optimization problems with PDE constraints :

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguilo Valentin, Miguel Alejandro; Ridzal, Denis

2014-03-01

A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.

An accurate method for solving a class of fractional Sturm-Liouville eigenvalue problems

NASA Astrophysics Data System (ADS)

Kashkari, Bothayna S. H.; Syam, Muhammed I.

2018-06-01

This article is devoted to both theoretical and numerical study of the eigenvalues of nonsingular fractional second-order Sturm-Liouville problem. In this paper, we implement a fractional-order Legendre Tau method to approximate the eigenvalues. This method transforms the Sturm-Liouville problem to a sparse nonsingular linear system which is solved using the continuation method. Theoretical results for the considered problem are provided and proved. Numerical results are presented to show the efficiency of the proposed method.

The contact sport of rough surfaces

NASA Astrophysics Data System (ADS)

Carpick, Robert W.

2018-01-01

Describing the way two surfaces touch and make contact may seem simple, but it is not. Fully describing the elastic deformation of ideally smooth contacting bodies, under even low applied pressure, involves second-order partial differential equations and fourth-rank elastic constant tensors. For more realistic rough surfaces, the problem becomes a multiscale exercise in surface-height statistics, even before including complex phenomena such as adhesion, plasticity, and fracture. A recent research competition, the “Contact Mechanics Challenge” (1), was designed to test various approximate methods for solving this problem. A hypothetical rough surface was generated, and the community was invited to model contact with this surface with competing theories for the calculation of properties, including contact area and pressure. A supercomputer-generated numerical solution was kept secret until competition entries were received. The comparison of results (2) provides insights into the relative merits of competing models and even experimental approaches to the problem.

Periodontal disease.

PubMed

Niemiec, Brook A

2008-05-01

Periodontal disease is the most commonly diagnosed problem in small animal veterinary medicine. In the vast majority of cases, however, there are little to no outward clinical signs of the disease process, and, therefore, therapy often comes very late in the disease course. Consequently, periodontal disease is also the most undertreated animal health problem. In addition, unchecked periodontal disease has numerous dire consequences both locally and systemically. These consequences are detailed in the article and should be utilized to educate clients and encourage compliance of therapeutic recommendations. The local consequences include oronasal fistulas, class II perio-endo lesions, pathologic fractures, ocular problems, osteomyelitis, and an increased incidence of oral cancer. Systemic diseases linked to periodontal disease include: renal, hepatic, pulmonary, and cardiac diseases; osteoporosis, adverse pregnancy effects, and diabetes mellitus. Before the discussion of consequences, this article covers the pathogenesis of periodontal disease, followed by clinical features and diagnostic tests.

Elasto-plastic bending of cracked plates, including the effects of crack closure. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Jones, D. P.

1972-01-01

A capability for solving elasto-plastic plate bending problems is developed using assumptions consistent with Kirchhoff plate theory. Both bending and extensional modes of deformation are admitted with the two modes becoming coupled as yielding proceeds. Equilibrium solutions are obtained numerically by determination of the stationary point of a functional which is analogous to the potential strain energy. The stationary value of the functional for each load increment is efficiently obtained through use of the conjugate gradient. This technique is applied to the problem of a large centrally through cracked plate subject to remote circular bending. Comparison is drawn between two cases of the bending problem. The first neglects the possibility of crack face interference with bending, and the second includes a kinematic prohibition against the crack face from passing through the symmetry plane. Results are reported which isolate the effects of elastoplastic flow and crack closure.

Ductile failure X-prize.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cox, James V.; Wellman, Gerald William; Emery, John M.

2011-09-01

Fracture or tearing of ductile metals is a pervasive engineering concern, yet accurate prediction of the critical conditions of fracture remains elusive. Sandia National Laboratories has been developing and implementing several new modeling methodologies to address problems in fracture, including both new physical models and new numerical schemes. The present study provides a double-blind quantitative assessment of several computational capabilities including tearing parameters embedded in a conventional finite element code, localization elements, extended finite elements (XFEM), and peridynamics. For this assessment, each of four teams reported blind predictions for three challenge problems spanning crack initiation and crack propagation. After predictionsmore » had been reported, the predictions were compared to experimentally observed behavior. The metal alloys for these three problems were aluminum alloy 2024-T3 and precipitation hardened stainless steel PH13-8Mo H950. The predictive accuracies of the various methods are demonstrated, and the potential sources of error are discussed.« less

Variational data assimilation problem for the Baltic Sea thermodynamics

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Agoshkov, Valery; Parmuzin, Eugene

2015-04-01

The most versatile and promising technology for solving problems of monitoring and analysis of the natural environment is a four-dimensional variational data assimilation of observation data. In such problems not only the development and justification of algorithms for numerical solution of variational data assimilation problems but the properties of the optimal solution play an important role. In this work the variational data assimilation problems in the Baltic Sea water area were formulated and studied. Numerical experiments on restoring the ocean heat flux and obtaining solution of the system (temperature, salinity, velocity, and sea surface height) in the Baltic Sea primitive equation hydrodynamics model with assimilation procedure were carried out. In the calculations we used daily sea surface temperature observation from Danish meteorological Institute, prepared on the basis of measurements of the radiometer (AVHRR, AATSR and AMSRE) and spectroradiometer (SEVIRI and MODIS). The spatial resolution of the model grid with respect to the horizontal variables amounted to 0.0625x0.03125 degree. The results of the numerical experiments are presented. This study was supported by the Russian Foundation for Basic Research (project 13-01-00753, project 14-01-31195) and project 14-11-00609 by the Russian Science Foundation. References: 1 E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 69-94 2 Zakharova N.B., Agoshkov V.I., Parmuzin E.I., The new method of ARGO buoys system observation data interpolation. Russian Journal of Numerical Analysis and Mathematical Modelling. Vol. 28, Issue 1, 2013. 3 Zalesny V.B., Gusev A.V., Chernobay S.Yu., Aps R., Tamsalu R., Kujala P., Rytkönen J. The Bal-tic Sea circulation modelling and assessment of marine pollution, Russ. J. Numer. Analysis and Math. Modelling, 2014, V 29, No. 2, pp. 129-138.

Analysis of Students’ Incorrect Answers on the Topic of Roman Numerals in The Fourth-Grade of Primary School

NASA Astrophysics Data System (ADS)

Selvianiresa, D.; Jupri, Al

2017-02-01

Mathematics has an important role in solving problems related to mathematical symbols. Mathematics topics are related to the daily life of students, as well as mathematics in the primary school level. In this paper, we report the results of research that aims to understand the difficulties of primary school students towards mathematics, especially on the topic of Roman numerals. The subject of this research included 38 students of fourth grade students from a primary school in the city of Bandung. The results showed that the teacher is more likely do the learning to deliver topic directly to students, rather than having to relatethe learning with a real context. In addition, after the teacher gave some exercises to students, we observed that there are some students’ answers that are unpredictable and made errors. Unexpected answers are caused by student’s unconscientious, misunderstanding, or inability to memorize in seven Roman numeral in general. The results of this analysis can be used to develop teacher competence in the teaching and learning process in the future. In this way, we expect the teacher can prepare various student responses to the given problems in the learning process.

The numerical modelling and process simulation for the fault diagnosis of rotary kiln incinerator.

PubMed

Roh, S D; Kim, S W; Cho, W S

2001-10-01

The numerical modelling and process simulation for the fault diagnosis of rotary kiln incinerator were accomplished. In the numerical modelling, two models applied to the modelling within the kiln are the combustion chamber model including the mass and energy balance equations for two combustion chambers and 3D thermal model. The combustion chamber model predicts temperature within the kiln, flue gas composition, flux and heat of combustion. Using the combustion chamber model and 3D thermal model, the production-rules for the process simulation can be obtained through interrelation analysis between control and operation variables. The process simulation of the kiln is operated with the production-rules for automatic operation. The process simulation aims to provide fundamental solutions to the problems in incineration process by introducing an online expert control system to provide an integrity in process control and management. Knowledge-based expert control systems use symbolic logic and heuristic rules to find solutions for various types of problems. It was implemented to be a hybrid intelligent expert control system by mutually connecting with the process control systems which has the capability of process diagnosis, analysis and control.

Mathematical and Numerical Techniques in Energy and Environmental Modeling

NASA Astrophysics Data System (ADS)

Chen, Z.; Ewing, R. E.

Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

NASA Technical Reports Server (NTRS)

Pandya, Shishir A.; Venkateswaran, Sankaran; Pulliam, Thomas H.; Kwak, Dochan (Technical Monitor)

2003-01-01

Preconditioning methods have become the method of choice for the solution of flowfields involving the simultaneous presence of low Mach and transonic regions. It is well known that these methods are important for insuring accurate numerical discretization as well as convergence efficiency over various operating conditions such as low Mach number, low Reynolds number and high Strouhal numbers. For unsteady problems, the preconditioning is introduced within a dual-time framework wherein the physical time-derivatives are used to march the unsteady equations and the preconditioned time-derivatives are used for purposes of numerical discretization and iterative solution. In this paper, we describe the implementation of the preconditioned dual-time methodology in the OVERFLOW code. To demonstrate the performance of the method, we employ both simple and practical unsteady flowfields, including vortex propagation in a low Mach number flow, flowfield of an impulsively started plate (Stokes' first problem) arid a cylindrical jet in a low Mach number crossflow with ground effect. All the results demonstrate that the preconditioning algorithm is responsible for improvements to both numerical accuracy and convergence efficiency and, thereby, enables low Mach number unsteady computations to be performed at a fraction of the cost of traditional time-marching methods.

A numerical approach to finding general stationary vacuum black holes

NASA Astrophysics Data System (ADS)

Adam, Alexander; Kitchen, Sam; Wiseman, Toby

2012-08-01

The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon, this equation has previously been shown to be elliptic, and Ricci flow and Newton’s method provide good numerical algorithms to solve it. Here we extend these techniques to the arbitrary cohomogeneity stationary case which must be treated in Lorentzian signature. For stationary spacetimes with globally timelike Killing vector the Harmonic Einstein equation is elliptic. In the presence of horizons and ergo-regions it is less obviously so. Motivated by the Rigidity theorem we study a class of stationary black hole spacetimes which is general enough to include many interesting higher dimensional solutions. We argue the Harmonic Einstein equation consistently truncates to this class of spacetimes giving an elliptic problem. The Killing horizons and axes of rotational symmetry are boundaries for this problem and we determine boundary conditions there. As a simple example we numerically construct 4D rotating black holes in a cavity using Anderson’s boundary conditions. We demonstrate both Newton’s method and Ricci flow to find these Lorentzian solutions.

Numerical solutions of nonlinear STIFF initial value problems by perturbed functional iterations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1982-01-01

Numerical solution of nonlinear stiff initial value problems by a perturbed functional iterative scheme is discussed. The algorithm does not fully linearize the system and requires only the diagonal terms of the Jacobian. Some examples related to chemical kinetics are presented.

An accelerated lambda iteration method for multilevel radiative transfer. I - Non-overlapping lines with background continuum

NASA Technical Reports Server (NTRS)

Rybicki, G. B.; Hummer, D. G.

1991-01-01

A method is presented for solving multilevel transfer problems when nonoverlapping lines and background continuum are present and active continuum transfer is absent. An approximate lambda operator is employed to derive linear, 'preconditioned', statistical-equilibrium equations. A method is described for finding the diagonal elements of the 'true' numerical lambda operator, and therefore for obtaining the coefficients of the equations. Iterations of the preconditioned equations, in conjunction with the transfer equation's formal solution, are used to solve linear equations. Some multilevel problems are considered, including an eleven-level neutral helium atom. Diagonal and tridiagonal approximate lambda operators are utilized in the problems to examine the convergence properties of the method, and it is found to be effective for the line transfer problems.

Vortex generator design for aircraft inlet distortion as a numerical optimization problem

NASA Technical Reports Server (NTRS)

Anderson, Bernhard H.; Levy, Ralph

1991-01-01

Aerodynamic compatibility of aircraft/inlet/engine systems is a difficult design problem for aircraft that must operate in many different flight regimes. Takeoff, subsonic cruise, supersonic cruise, transonic maneuvering, and high altitude loiter each place different constraints on inlet design. Vortex generators, small wing like sections mounted on the inside surfaces of the inlet duct, are used to control flow separation and engine face distortion. The design of vortex generator installations in an inlet is defined as a problem addressable by numerical optimization techniques. A performance parameter is suggested to account for both inlet distortion and total pressure loss at a series of design flight conditions. The resulting optimization problem is difficult since some of the design parameters take on integer values. If numerical procedures could be used to reduce multimillion dollar development test programs to a small set of verification tests, numerical optimization could have a significant impact on both cost and elapsed time to design new aircraft.

An efficient numerical method for the solution of the problem of elasticity for 3D-homogeneous elastic medium with cracks and inclusions

NASA Astrophysics Data System (ADS)

Kanaun, S.; Markov, A.

2017-06-01

An efficient numerical method for solution of static problems of elasticity for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Finite number of heterogeneous inclusions and planar parallel cracks of arbitrary shapes is considered. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. For the numerical solution of these equations, a class of Gaussian approximating functions is used. The method based on these functions is mesh free. For such functions, the elements of the matrix of the discretized system are combinations of explicit analytical functions and five standard 1D-integrals that can be tabulated. Thus, the numerical integration is excluded from the construction of the matrix of the discretized problem. For regular node grids, the matrix of the discretized system has Toeplitz's properties, and Fast Fourier Transform technique can be used for calculation matrix-vector products of such matrices.

Piezoelectric Vibration Damping Study for Rotating Composite Fan Blades

NASA Technical Reports Server (NTRS)

Min, James B.; Duffy, Kirsten P.; Choi, Benjamin B.; Provenza, Andrew J.; Kray, Nicholas

2012-01-01

Resonant vibrations of aircraft engine blades cause blade fatigue problems in engines, which can lead to thicker and aerodynamically lower performing blade designs, increasing engine weight, fuel burn, and maintenance costs. In order to mitigate undesirable blade vibration levels, active piezoelectric vibration control has been investigated, potentially enabling thinner blade designs for higher performing blades and minimizing blade fatigue problems. While the piezoelectric damping idea has been investigated by other researchers over the years, very little study has been done including rotational effects. The present study attempts to fill this void. The particular objectives of this study were: (a) to develop and analyze a multiphysics piezoelectric finite element composite blade model for harmonic forced vibration response analysis coupled with a tuned RLC circuit for rotating engine blade conditions, (b) to validate a numerical model with experimental test data, and (c) to achieve a cost-effective numerical modeling capability which enables simulation of rotating blades within the NASA Glenn Research Center (GRC) Dynamic Spin Rig Facility. A numerical and experimental study for rotating piezoelectric composite subscale fan blades was performed. It was also proved that the proposed numerical method is feasible and effective when applied to the rotating blade base excitation model. The experimental test and multiphysics finite element modeling technique described in this paper show that piezoelectric vibration damping can significantly reduce vibrations of aircraft engine composite fan blades.

Semiannual report, 1 April - 30 September 1991

NASA Technical Reports Server (NTRS)

1991-01-01

The major categories of the current Institute for Computer Applications in Science and Engineering (ICASE) research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification problems, with emphasis on effective numerical methods; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software for parallel computers. Research in these areas is discussed.

NOR-USA Scientific Traverse of East Antarctica: Science and Logistics on a Three-Month Expedition Across Antarctica's Farthest Frontier

NASA Technical Reports Server (NTRS)

Albert, Mary R.

2012-01-01

Dr. Albert's current research is centered on transfer processes in porous media, including air-snow exchange in the Polar Regions and in soils in temperate areas. Her research includes field measurements, laboratory experiments, and theoretical modeling. Mary conducts field and laboratory measurements of the physical properties of natural terrain surfaces, including permeability, microstructure, and thermal conductivity. Mary uses the measurements to examine the processes of diffusion and advection of heat, mass, and chemical transport through snow and other porous media. She has developed numerical models for investigation of a variety of problems, from interstitial transport to freezing of flowing liquids. These models include a two-dimensional finite element code for air flow with heat, water vapor, and chemical transport in porous media, several multidimensional codes for diffusive transfer, as well as a computational fluid dynamics code for analysis of turbulent water flow in moving-boundary phase change problems.

Modified Finite Particle Methods for Stokes problems

NASA Astrophysics Data System (ADS)

Montanino, A.; Asprone, D.; Reali, A.; Auricchio, F.

2018-04-01

The Modified Finite Particle Method (MFPM) is a numerical method belonging to the class of meshless methods, nowadays widely investigated due to their characteristic of being capable to easily model large deformation and fluid-dynamic problems. Here we use the MFPM to approximate the Stokes problem. Since the classical formulation of the Stokes problem may lead to pressure spurious oscillations, we investigate alternative formulations and focus on how MFPM discretization behaves in those situations. Some of the investigated formulations, in fact, do not enforce strongly the incompressibility constraint, and therefore an important issue of the present work is to verify if the MFPM is able to correctly reproduce the incompressibility in those cases. The numerical results show that for the formulations in which the incompressibility constraint is properly satisfied from a numerical point of view, the expected second-order is achieved, both in static and in dynamic problems.

Multidisciplinary Optimization of a Transport Aircraft Wing using Particle Swarm Optimization

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Venter, Gerhard

2002-01-01

The purpose of this paper is to demonstrate the application of particle swarm optimization to a realistic multidisciplinary optimization test problem. The paper's new contributions to multidisciplinary optimization is the application of a new algorithm for dealing with the unique challenges associated with multidisciplinary optimization problems, and recommendations as to the utility of the algorithm in future multidisciplinary optimization applications. The selected example is a bi-level optimization problem that demonstrates severe numerical noise and has a combination of continuous and truly discrete design variables. The use of traditional gradient-based optimization algorithms is thus not practical. The numerical results presented indicate that the particle swarm optimization algorithm is able to reliably find the optimum design for the problem presented here. The algorithm is capable of dealing with the unique challenges posed by multidisciplinary optimization as well as the numerical noise and truly discrete variables present in the current example problem.

Mixed Arlequin method for multiscale poromechanics problems: Mixed Arlequin method for multiscale poromechanics problems

DOE PAGES

Sun, WaiChing; Cai, Zhijun; Choo, Jinhyun

2016-11-18

An Arlequin poromechanics model is introduced to simulate the hydro-mechanical coupling effects of fluid-infiltrated porous media across different spatial scales within a concurrent computational framework. A two-field poromechanics problem is first recast as the twofold saddle point of an incremental energy functional. We then introduce Lagrange multipliers and compatibility energy functionals to enforce the weak compatibility of hydro-mechanical responses in the overlapped domain. Here, to examine the numerical stability of this hydro-mechanical Arlequin model, we derive a necessary condition for stability, the twofold inf–sup condition for multi-field problems, and establish a modified inf–sup test formulated in the product space ofmore » the solution field. We verify the implementation of the Arlequin poromechanics model through benchmark problems covering the entire range of drainage conditions. Finally, through these numerical examples, we demonstrate the performance, robustness, and numerical stability of the Arlequin poromechanics model.« less

Dynamic earthquake rupture simulation on nonplanar faults embedded in 3D geometrically complex, heterogeneous Earth models

NASA Astrophysics Data System (ADS)

Duru, K.; Dunham, E. M.; Bydlon, S. A.; Radhakrishnan, H.

2014-12-01

Dynamic propagation of shear ruptures on a frictional interface is a useful idealization of a natural earthquake.The conditions relating slip rate and fault shear strength are often expressed as nonlinear friction laws.The corresponding initial boundary value problems are both numerically and computationally challenging.In addition, seismic waves generated by earthquake ruptures must be propagated, far away from fault zones, to seismic stations and remote areas.Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods.We present a numerical method for:a) enforcing nonlinear friction laws, in a consistent and provably stable manner, suitable for efficient explicit time integration;b) dynamic propagation of earthquake ruptures along rough faults; c) accurate propagation of seismic waves in heterogeneous media with free surface topography.We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts finite differences in space. The finite difference stencils are 6th order accurate in the interior and 3rd order accurate close to the boundaries. Boundary and interface conditions are imposed weakly using penalties. By deriving semi-discrete energy estimates analogous to the continuous energy estimates we prove numerical stability. Time stepping is performed with a 4th order accurate explicit low storage Runge-Kutta scheme. We have performed extensive numerical experiments using a slip-weakening friction law on non-planar faults, including recent SCEC benchmark problems. We also show simulations on fractal faults revealing the complexity of rupture dynamics on rough faults. We are presently extending our method to rate-and-state friction laws and off-fault plasticity.

Comparative Study on High-Order Positivity-preserving WENO Schemes

NASA Technical Reports Server (NTRS)

Kotov, D. V.; Yee, H. C.; Sjogreen, B.

2013-01-01

In gas dynamics and magnetohydrodynamics flows, physically, the density and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order WENO schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more difficult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium flow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case (LeVeque & Yee 1990) as well as for the case consisting of two species and one reaction (Wang et al. 2012). For further information concerning this issue see (LeVeque & Yee 1990; Griffiths et al. 1992; Lafon & Yee 1996; Yee et al. 2012). This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

An analysis of hypercritical states in elastic and inelastic systems

NASA Astrophysics Data System (ADS)

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

Numerical methods for the inverse problem of density functional theory

DOE PAGES

Jensen, Daniel S.; Wasserman, Adam

2017-07-17

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Numerical methods for the inverse problem of density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jensen, Daniel S.; Wasserman, Adam

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Transient well flow in layered aquifer systems: the uniform well-face drawdown solution

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1999-11-01

Previously a hybrid analytical-numerical solution for the general problem of computing transient well flow in vertically heterogeneous aquifers was proposed by the author. The radial component of flow was treated analytically, while the finite-difference technique was used for the vertical flow component only. In the present work the hybrid solution has been modified by replacing the previously assumed uniform well-face gradient (UWG) boundary condition in such a way that the drawdown remains uniform along the well screen. The resulting uniform well-face drawdown (UWD) solution also includes the effects of a finite diameter well, wellbore storage and a thin skin, while partial penetration and vertical heterogeneity are accommodated by the one-dimensional discretization. Solutions are proposed for well flow caused by constant, variable and slug discharges. The model was verified by comparing wellbore drawdowns and well-face flux distributions with published numerical solutions. Differences between UWG and UWD well flow will occur in all situations with vertical flow components near the well, which is demonstrated by considering: (1) partially penetrating wells in confined aquifers, (2) fully penetrating wells in unconfined aquifers with delayed response and (3) layered aquifers and leaky multiaquifer systems. The presented solution can be a powerful tool for solving many well-hydraulic problems, including well tests, flowmeter tests, slug tests and pumping tests. A computer program for the analysis of pumping tests, based on the hybrid analytical-numerical technique and UWG or UWD conditions, is available from the author.

Comparison of PASCAL and FORTRAN for solving problems in the physical sciences

NASA Technical Reports Server (NTRS)

Watson, V. R.

1981-01-01

The paper compares PASCAL and FORTRAN for problem solving in the physical sciences, due to requests NASA has received to make PASCAL available on the Numerical Aerodynamic Simulator (scheduled to be operational in 1986). PASCAL disadvantages include the lack of scientific utility procedures equivalent to the IBM scientific subroutine package or the IMSL package which are available in FORTRAN. Advantages include a well-organized, easy to read and maintain writing code, range checking to prevent errors, and a broad selection of data types. It is concluded that FORTRAN may be the better language, although ADA (patterned after PASCAL) may surpass FORTRAN due to its ability to add complex and vector math, and the specify the precision and range of variables.

Error and Uncertainty Quantification in the Numerical Simulation of Complex Fluid Flows

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2010-01-01

The failure of numerical simulation to predict physical reality is often a direct consequence of the compounding effects of numerical error arising from finite-dimensional approximation and physical model uncertainty resulting from inexact knowledge and/or statistical representation. In this topical lecture, we briefly review systematic theories for quantifying numerical errors and restricted forms of model uncertainty occurring in simulations of fluid flow. A goal of this lecture is to elucidate both positive and negative aspects of applying these theories to practical fluid flow problems. Finite-element and finite-volume calculations of subsonic and hypersonic fluid flow are presented to contrast the differing roles of numerical error and model uncertainty. for these problems.

Evaluation of Optimal Formulas for Gravitational Tensors up to Gravitational Curvatures of a Tesseroid

NASA Astrophysics Data System (ADS)

Deng, Xiao-Le; Shen, Wen-Bin

2018-01-01

The forward modeling of the topographic effects of the gravitational parameters in the gravity field is a fundamental topic in geodesy and geophysics. Since the gravitational effects, including for instance the gravitational potential (GP), the gravity vector (GV) and the gravity gradient tensor (GGT), of the topographic (or isostatic) mass reduction have been expanded by adding the gravitational curvatures (GC) in geoscience, it is crucial to find efficient numerical approaches to evaluate these effects. In this paper, the GC formulas of a tesseroid in Cartesian integral kernels are derived in 3D/2D forms. Three generally used numerical approaches for computing the topographic effects (e.g., GP, GV, GGT, GC) of a tesseroid are studied, including the Taylor Series Expansion (TSE), Gauss-Legendre Quadrature (GLQ) and Newton-Cotes Quadrature (NCQ) approaches. Numerical investigations show that the GC formulas in Cartesian integral kernels are more efficient if compared to the previously given GC formulas in spherical integral kernels: by exploiting the 3D TSE second-order formulas, the computational burden associated with the former is 46%, as an average, of that associated with the latter. The GLQ behaves better than the 3D/2D TSE and NCQ in terms of accuracy and computational time. In addition, the effects of a spherical shell's thickness and large-scale geocentric distance on the GP, GV, GGT and GC functionals have been studied with the 3D TSE second-order formulas as well. The relative approximation errors of the GC functionals are larger with the thicker spherical shell, which are the same as those of the GP, GV and GGT. Finally, the very-near-area problem and polar singularity problem have been considered by the numerical methods of the 3D TSE, GLQ and NCQ. The relative approximation errors of the GC components are larger than those of the GP, GV and GGT, especially at the very near area. Compared to the GC formulas in spherical integral kernels, these new GC formulas can avoid the polar singularity problem.

Full wave description of VLF wave penetration through the ionosphere

NASA Astrophysics Data System (ADS)

Kuzichev, Ilya; Shklyar, David

2010-05-01

Of the many problems in whistler study, wave propagation through the ionosphere is among the most important, and the most difficult at the same time. Both satellite and ground-based investigations of VLF waves include considerations of this problem, and it has been in the focus of research since the beginning of whistler study (Budden [1985]; Helliwell [1965]). The difficulty in considering VLF wave passage through the ionosphere is, after all, due to fast variation of the lower ionosphere parameters as compared to typical VLF wave number. This makes irrelevant the consideration in the framework of geometrical optics, which, along with a smooth variations of parameters, is always based on a particular dispersion relation. Although the full wave analysis in the framework of cold plasma approximation does not require slow variations of plasma parameters, and does not assume any particular wave mode, the fact that the wave of a given frequency belongs to different modes in various regions makes numerical solution of the field equations not simple. More specifically, as is well known (e.g. Ginzburg and Rukhadze [1972]), in a cold magnetized plasma, there are, in general, two wave modes related to a given frequency. Both modes, however, do not necessarily correspond to propagating waves. In particular, in the frequency range related to whistler waves, the other mode is evanescent, i.e. it has a negative value of N2 (the refractive index squared). It means that one of solutions of the relevant differential equations is exponentially growing, which makes a straightforward numerical approach to these equations despairing. This well known difficulty in the problem under discussion is usually identified as numerical swamping (Budden [1985]). Resolving the problem of numerical swamping becomes, in fact, a key point in numerical study of wave passage through the ionosphere. As it is typical of work based on numerical simulations, its essential part remains virtually hidden. Then, every researcher, in order to get quantitative characteristics of the process, such as transmission and reflection coefficients, needs to go through the whole problem. That is why the number of publications dealing with VLF wave transmission through the ionosphere does not run short. In this work, we develop a new approach to the problem, such that its intrinsic difficulty is resolved analytically, while numerical calculations are reduced to stable equations solvable with the help of a routine program. Using this approach, the field of VLF wave incident on the ionosphere from above is calculated as a function of height, and reflection coefficients for different frequencies and angles of incidence are obtained. In particular, for small angles of incidence, for which incident waves reach the ground, the reflection coefficient appears to be an oscillating function of frequency. Another goal of the work is to present all equations and related formulae in an undisguised form, in order that the problem may be solved in a straightforward way, once the ionospheric plasma parameters are given. References Budden, K.G. (1985), The Propagation of Radio Waves, Cambridge Univ. Press, Cambridge, U.K. Ginzburg, V.L., and Rukhadze, A.A. (1972), Waves in Magnetoactive Plasma. In Handbuch der Physik (ed. S. Flügge). Vol. 49, Part IV, p. 395, Springer Verlag, Berlin. Helliwell, R. A. (1965), Whistlers and Related Ionospheric Phenomena, Stanford University Press, Stanford, California.

Comment on “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition” by A. Aziz, Comm. Nonlinear Sci. Numer. Simul. 2009;14:1064-8

NASA Astrophysics Data System (ADS)

Magyari, Eugen

2011-01-01

In a recent paper published in this Journal the title problem has been investigated numerically. In the present paper the exact solution for the temperature boundary layer is given in terms of the solution of the flow problem (the Blasius problem) in a compact integral form.

LSENS, a general chemical kinetics and sensitivity analysis code for homogeneous gas-phase reactions. 2: Code description and usage

NASA Technical Reports Server (NTRS)

Radhakrishnan, Krishnan; Bittker, David A.

1994-01-01

LSENS, the Lewis General Chemical Kinetics Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 2 of a series of three reference publications that describe LSENS, provide a detailed guide to its usage, and present many example problems. Part 2 describes the code, how to modify it, and its usage, including preparation of the problem data file required to execute LSENS. Code usage is illustrated by several example problems, which further explain preparation of the problem data file and show how to obtain desired accuracy in the computed results. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions. Part 1 (NASA RP-1328) derives the governing equations describes the numerical solution procedures for the types of problems that can be solved by lSENS. Part 3 (NASA RP-1330) explains the kinetics and kinetics-plus-sensitivity-analysis problems supplied with LSENS and presents sample results.

Inversion of Robin coefficient by a spectral stochastic finite element approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Semismooth Newton method for gradient constrained minimization problem

NASA Astrophysics Data System (ADS)

Anyyeva, Serbiniyaz; Kunisch, Karl

2012-08-01

In this paper we treat a gradient constrained minimization problem, particular case of which is the elasto-plastic torsion problem. In order to get the numerical approximation to the solution we have developed an algorithm in an infinite dimensional space framework using the concept of the generalized (Newton) differentiation. Regularization was done in order to approximate the problem with the unconstrained minimization problem and to make the pointwise maximum function Newton differentiable. Using semismooth Newton method, continuation method was developed in function space. For the numerical implementation the variational equations at Newton steps are discretized using finite elements method.

Comprehension and computation in Bayesian problem solving

PubMed Central

Johnson, Eric D.; Tubau, Elisabet

2015-01-01

Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian inferences relative to normalized formats (e.g., probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e., transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct vs. incorrect reasoners depart, and how individual differences might influence this time point. PMID:26283976

A supersonic, three-dimensional code for flow over blunt bodies: User's manual

NASA Technical Reports Server (NTRS)

Chaussee, D. S.; Mcmillan, O. J.

1980-01-01

A computer code is described which may be used to calculate the steady, supersonic, three-dimensional, inviscid flow over blunt bodies. The theoretical and numerical formulation of the problem is given (shock-capturing, downstream marching), including exposition of the boundary and initial conditions. The overall flow logic of the program, its usage, accuracy, and limitations are discussed.

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-04-01

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integrationmore » methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.« less

A Semi-implicit Method for Resolution of Acoustic Waves in Low Mach Number Flows

NASA Astrophysics Data System (ADS)

Wall, Clifton; Pierce, Charles D.; Moin, Parviz

2002-09-01

A semi-implicit numerical method for time accurate simulation of compressible flow is presented. By extending the low Mach number pressure correction method, a Helmholtz equation for pressure is obtained in the case of compressible flow. The method avoids the acoustic CFL limitation, allowing a time step restricted only by the convective velocity, resulting in significant efficiency gains. Use of a discretization that is centered in both time and space results in zero artificial damping of acoustic waves. The method is attractive for problems in which Mach numbers are low, and the acoustic waves of most interest are those having low frequency, such as acoustic combustion instabilities. Both of these characteristics suggest the use of time steps larger than those allowable by an acoustic CFL limitation. In some cases it may be desirable to include a small amount of numerical dissipation to eliminate oscillations due to small-wavelength, high-frequency, acoustic modes, which are not of interest; therefore, a provision for doing this in a controlled manner is included in the method. Results of the method for several model problems are presented, and the performance of the method in a large eddy simulation is examined.

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods

PubMed Central

Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev

2013-01-01

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L2-norm regularization. However, sparse representation methods via L1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72–88, 2013. PMID:23847452

Robust and Simple Non-Reflecting Boundary Conditions for the Euler Equations - A New Approach based on the Space-Time CE/SE Method

NASA Technical Reports Server (NTRS)

Chang, S.-C.; Himansu, A.; Loh, C.-Y.; Wang, X.-Y.; Yu, S.-T.J.

2005-01-01

This paper reports on a significant advance in the area of nonreflecting boundary conditions (NRBCs) for unsteady flow computations. As a part of t he development of t he space-time conservation element and solution element (CE/SE) method, sets of NRBCs for 1D Euler problems are developed without using any characteristics- based techniques. These conditions are much simpler than those commonly reported in the literature, yet so robust that they are applicable to subsonic, transonic and supersonic flows even in the presence of discontinuities. In addition, the straightforward multidimensional extensions of the present 1D NRBCs have been shown numerically to be equally simple and robust. The paper details the theoretical underpinning of these NRBCs, and explains t heir unique robustness and accuracy in terms of t he conservation of space-time fluxes. Some numerical results for an extended Sod's shock-tube problem, illustrating the effectiveness of the present NRBCs are included, together with an associated simple Fortran computer program. As a preliminary to the present development, a review of the basic CE/SE schemes is also included.

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods.

PubMed

Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev

2013-05-01

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L 2 -norm regularization. However, sparse representation methods via L 1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L 1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72-88, 2013.

Numerical System Solver Developed for the National Cycle Program

NASA Technical Reports Server (NTRS)

Binder, Michael P.

1999-01-01

As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.

Traveling-Wave Solutions of the Kolmogorov-Petrovskii-Piskunov Equation

NASA Astrophysics Data System (ADS)

Pikulin, S. V.

2018-02-01

We consider quasi-stationary solutions of a problem without initial conditions for the Kolmogorov-Petrovskii-Piskunov (KPP) equation, which is a quasilinear parabolic one arising in the modeling of certain reaction-diffusion processes in the theory of combustion, mathematical biology, and other areas of natural sciences. A new efficiently numerically implementable analytical representation is constructed for self-similar plane traveling-wave solutions of the KPP equation with a special right-hand side. Sufficient conditions for an auxiliary function involved in this representation to be analytical for all values of its argument, including the endpoints, are obtained. Numerical results are obtained for model examples.

Socio-economic applications of finite state mean field games.

PubMed

Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese

2014-11-13

In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Numerical modelling of surface waves generated by low frequency electromagnetic field for silicon refinement process

NASA Astrophysics Data System (ADS)

Geža, V.; Venčels, J.; Zāģeris, Ģ.; Pavlovs, S.

2018-05-01

One of the most perspective methods to produce SoG-Si is refinement via metallurgical route. The most critical part of this route is refinement from boron and phosphorus, therefore, approach under development will address this problem. An approach of creating surface waves on silicon melt’s surface is proposed in order to enlarge its area and accelerate removal of boron via chemical reactions and evaporation of phosphorus. A two dimensional numerical model is created which include coupling of electromagnetic and fluid dynamic simulations with free surface dynamics. First results show behaviour similar to experimental results from literature.

An Introduction to Numerical Control. Problems for Numerical Control Part Programming.

ERIC Educational Resources Information Center

Campbell, Clifton P.

This combination text and workbook is intended to introduce industrial arts students to numerical control part programming. Discussed in the first section are the impact of numerical control, training efforts, numerical control in established programs, related information for drafting, and the Cartesian Coordinate System and dimensioning…

Spectral Elements Analysis for Viscoelastic Fluids at High Weissenberg Number Using Logarithmic conformation Tensor Model

NASA Astrophysics Data System (ADS)

Jafari, Azadeh; Deville, Michel O.; Fiétier, Nicolas

2008-09-01

This study discusses the capability of the constitutive laws for the matrix logarithm of the conformation tensor (LCT model) within the framework of the spectral elements method. The high Weissenberg number problems (HWNP) usually produce a lack of convergence of the numerical algorithms. Even though the question whether the HWNP is a purely numerical problem or rather a breakdown of the constitutive law of the model has remained somewhat of a mystery, it has been recognized that the selection of an appropriate constitutive equation constitutes a very crucial step although implementing a suitable numerical technique is still important for successful discrete modeling of non-Newtonian flows. The LCT model formulation of the viscoelastic equations originally suggested by Fattal and Kupferman is applied for 2-dimensional (2D) FENE-CR model. The Planar Poiseuille flow is considered as a benchmark problem to test this representation at high Weissenberg number. The numerical results are compared with numerical solution of the standard constitutive equation.

Code Verification of the HIGRAD Computational Fluid Dynamics Solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Buren, Kendra L.; Canfield, Jesse M.; Hemez, Francois M.

2012-05-04

The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) solver of the compressible Navier-Stokes equations developed at the Los Alamos National Laboratory, and used to simulate various phenomena such as the propagation of wildfires and atmospheric hydrodynamics. Code verification efforts, as described in this report, are an important first step to establish the credibility of numerical simulations. They provide evidence that the mathematical formulation is properly implemented without significant mistakes that would adversely impact the application of interest. Highly accurate analytical solutions are derived for four code verificationmore » test problems that exercise different aspects of the code. These test problems are referred to as: (i) the quiet start, (ii) the passive advection, (iii) the passive diffusion, and (iv) the piston-like problem. These problems are simulated using HIGRAD with different levels of mesh discretization and the numerical solutions are compared to their analytical counterparts. In addition, the rates of convergence are estimated to verify the numerical performance of the solver. The first three test problems produce numerical approximations as expected. The fourth test problem (piston-like) indicates the extent to which the code is able to simulate a 'mild' discontinuity, which is a condition that would typically be better handled by a Lagrangian formulation. The current investigation concludes that the numerical implementation of the solver performs as expected. The quality of solutions is sufficient to provide credible simulations of fluid flows around wind turbines. The main caveat associated to these findings is the low coverage provided by these four problems, and somewhat limited verification activities. A more comprehensive evaluation of HIGRAD may be beneficial for future studies.« less

Renewable Hydrogen-Economically Viable: Integration into the U.S. Transportation Sector

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kurtz, Jennifer; Peters, Mike; Muratori, Matteo

The U.S. transportation sector is expected to meet numerous goals in differing applications. These goals address security, safety, fuel source, emissions reductions, advanced mobility models, and improvements in quality and accessibility. Solutions to meeting these goals include a variety of alternative-fuel technologies, including batteries, fuel cells, synthetic fuels, and biofuels, as well as modifying how current transportation systems are used and integrating new systems, such as storing renewable energy. Overall, there are many combinations of problems, objectives, and solutions.

A validated non-linear Kelvin-Helmholtz benchmark for numerical hydrodynamics

NASA Astrophysics Data System (ADS)

Lecoanet, D.; McCourt, M.; Quataert, E.; Burns, K. J.; Vasil, G. M.; Oishi, J. S.; Brown, B. P.; Stone, J. M.; O'Leary, R. M.

2016-02-01

The non-linear evolution of the Kelvin-Helmholtz instability is a popular test for code verification. To date, most Kelvin-Helmholtz problems discussed in the literature are ill-posed: they do not converge to any single solution with increasing resolution. This precludes comparisons among different codes and severely limits the utility of the Kelvin-Helmholtz instability as a test problem. The lack of a reference solution has led various authors to assert the accuracy of their simulations based on ad hoc proxies, e.g. the existence of small-scale structures. This paper proposes well-posed two-dimensional Kelvin-Helmholtz problems with smooth initial conditions and explicit diffusion. We show that in many cases numerical errors/noise can seed spurious small-scale structure in Kelvin-Helmholtz problems. We demonstrate convergence to a reference solution using both ATHENA, a Godunov code, and DEDALUS, a pseudo-spectral code. Problems with constant initial density throughout the domain are relatively straightforward for both codes. However, problems with an initial density jump (which are the norm in astrophysical systems) exhibit rich behaviour and are more computationally challenging. In the latter case, ATHENA simulations are prone to an instability of the inner rolled-up vortex; this instability is seeded by grid-scale errors introduced by the algorithm, and disappears as resolution increases. Both ATHENA and DEDALUS exhibit late-time chaos. Inviscid simulations are riddled with extremely vigorous secondary instabilities which induce more mixing than simulations with explicit diffusion. Our results highlight the importance of running well-posed test problems with demonstrated convergence to a reference solution. To facilitate future comparisons, we include as supplementary material the resolved, converged solutions to the Kelvin-Helmholtz problems in this paper in machine-readable form.

Electrostatic point charge fitting as an inverse problem: Revealing the underlying ill-conditioning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ivanov, Maxim V.; Talipov, Marat R.; Timerghazin, Qadir K., E-mail: qadir.timerghazin@marquette.edu

2015-10-07

Atom-centered point charge (PC) model of the molecular electrostatics—a major workhorse of the atomistic biomolecular simulations—is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. To reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem and construct an analytical model with the point charges spherically arranged according to Lebedev quadrature which is naturally suited for the inverse electrostatic problem. This analytical model is contrastedmore » to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and is related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field.« less

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schaerer, Roman Pascal, E-mail: schaerer@mathcces.rwth-aachen.de; Bansal, Pratyuksh; Torrilhon, Manuel

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) , we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropymore » distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.« less

Two-way ANOVA Problems with Simple Numbers.

ERIC Educational Resources Information Center

Read, K. L. Q.; Shihab, L. H.

1998-01-01

Describes how to construct simple numerical examples in two-way ANOVAs, specifically randomized blocks, balanced two-way layouts, and Latin squares. Indicates that working through simple numerical problems is helpful to students meeting a technique for the first time and should be followed by computer-based analysis of larger, real datasets when…

On the numerical treatment of Coulomb forces in scattering problems

NASA Astrophysics Data System (ADS)

Randazzo, J. M.; Ancarani, L. U.; Colavecchia, F. D.; Gasaneo, G.; Frapiccini, A. L.

2012-11-01

We investigate the limiting procedures to obtain Coulomb interactions from short-range potentials. The application of standard techniques used for the two-body case (exponential and sharp cutoff) to the three-body break-up problem is illustrated numerically by considering the Temkin-Poet (TP) model of e-H processes.

Numerical experiments on the accuracy of ENO and modified ENO schemes

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1990-01-01

Further numerical experiments are made assessing an accuracy degeneracy phenomena. A modified essentially non-oscillatory (ENO) scheme is proposed, which recovers the correct order of accuracy for all the test problems with smooth initial conditions and gives comparable results with the original ENO schemes for discontinuous problems.

Mesh and Time-Step Independent Computational Fluid Dynamics (CFD) Solutions

ERIC Educational Resources Information Center

Nijdam, Justin J.

2013-01-01

A homework assignment is outlined in which students learn Computational Fluid Dynamics (CFD) concepts of discretization, numerical stability and accuracy, and verification in a hands-on manner by solving physically realistic problems of practical interest to engineers. The students solve a transient-diffusion problem numerically using the common…

Quantitative Relationships Involving Additive Differences: Numerical Resilience

ERIC Educational Resources Information Center

Ramful, Ajay; Ho, Siew Yin

2014-01-01

This case study describes the ways in which problems involving additive differences with unknown starting quantities, constrain the problem solver in articulating the inherent quantitative relationship. It gives empirical evidence to show how numerical reasoning takes over as a Grade 6 student instantiates the quantitative relation by resorting to…

AN ACCURATE AND EFFICIENT ALGORITHM FOR NUMERICAL SIMULATION OF CONDUCTION-TYPE PROBLEMS. (R824801)

EPA Science Inventory

Abstract

A modification of the finite analytic numerical method for conduction-type (diffusion) problems is presented. The finite analytic discretization scheme is derived by means of the Fourier series expansion for the most general case of nonuniform grid and variabl...

Method for the numerical integration of equations of perturbed satellite motion in problems of space geodesy

NASA Astrophysics Data System (ADS)

Plakhov, Iu. V.; Mytsenko, A. V.; Shel'Pov, V. A.

A numerical integration method is developed that is more accurate than Everhart's (1974) implicit single-sequence approach for integrating orbits. This method can be used to solve problems of space geodesy based on the use of highly precise laser observations.

A Numerical Study of Hypersonic Forebody/Inlet Integration Problem

NASA Technical Reports Server (NTRS)

Kumar, Ajay

1991-01-01

A numerical study of hypersonic forebody/inlet integration problem is presented in the form of the view-graphs. The following topics are covered: physical/chemical modeling; solution procedure; flow conditions; mass flow rate at inlet face; heating and skin friction loads; 3-D forebogy/inlet integration model; and sensitivity studies.

The Visual Effects of Intraocular Colored Filters

PubMed Central

Hammond, Billy R.

2012-01-01

Modern life is associated with a myriad of visual problems, most notably refractive conditions such as myopia. Human ingenuity has addressed such problems using strategies such as spectacle lenses or surgical correction. There are other visual problems, however, that have been present throughout our evolutionary history and are not as easily solved by simply correcting refractive error. These problems include issues like glare disability and discomfort arising from intraocular scatter, photostress with the associated transient loss in vision that arises from short intense light exposures, or the ability to see objects in the distance through a veil of atmospheric haze. One likely biological solution to these more long-standing problems has been the use of colored intraocular filters. Many species, especially diurnal, incorporate chromophores from numerous sources (e.g., often plant pigments called carotenoids) into ocular tissues to improve visual performance outdoors. This review summarizes information on the utility of such filters focusing on chromatic filtering by humans. PMID:24278692

Inverse problem of the vibrational band gap of periodically supported beam

NASA Astrophysics Data System (ADS)

Shi, Xiaona; Shu, Haisheng; Dong, Fuzhen; Zhao, Lei

2017-04-01

The researches of periodic structures have a long history with the main contents confined in the field of forward problem. In this paper, the inverse problem is considered and an overall frame is proposed which includes two main stages, i.e., the band gap criterion and its optimization. As a preliminary investigation, the inverse problem of the flexural vibrational band gap of a periodically supported beam is analyzed. According to existing knowledge of its forward problem, the band gap criterion is given in implicit form. Then, two cases with three independent parameters, namely the double supported case and the triple one, are studied in detail and the explicit expressions of the feasible domain are constructed by numerical fitting. Finally, the parameter optimization of the double supported case with three variables is conducted using genetic algorithm aiming for the best mean attenuation within specified frequency band.

Geometrically derived difference formulae for the numerical integration of trajectory problems

NASA Technical Reports Server (NTRS)

Mcleod, R. J. Y.; Sanz-Serna, J. M.

1982-01-01

An initial value problem for the autonomous system of ordinary differential equations dy/dt = f(y), where y is a vector, is considered. In a number of practical applications the interest lies in obtaining the curve traced by the solution y. These applications include the computation of trajectories in mechanical problems. The term 'trajectory problem' is employed to refer to these cases. Lambert and McLeod (1979) have introduced a method involving local rotation of the axes in the y-plane for the two-dimensional case. The present investigation continues the study of difference schemes specifically derived for trajectory problems. A simple geometrical way of constructing such methods is presented, and the local accuracy of the schemes is investigated. A circularly exact, fixed-step predictor-corrector algorithm is defined, and a variable-step version of a circularly exact algorithm is presented.

The linear Boltzmann equation in slab geometry - Development and verification of a reliable and efficient solution

NASA Technical Reports Server (NTRS)

Stamnes, K.; Lie-Svendsen, O.; Rees, M. H.

1991-01-01

The linear Boltzmann equation can be cast in a form mathematically identical to the radiation-transport equation. A multigroup procedure is used to reduce the energy (or velocity) dependence of the transport equation to a series of one-speed problems. Each of these one-speed problems is equivalent to the monochromatic radiative-transfer problem, and existing software is used to solve this problem in slab geometry. The numerical code conserves particles in elastic collisions. Generic examples are provided to illustrate the applicability of this approach. Although this formalism can, in principle, be applied to a variety of test particle or linearized gas dynamics problems, it is particularly well-suited to study the thermalization of suprathermal particles interacting with a background medium when the thermal motion of the background cannot be ignored. Extensions of the formalism to include external forces and spherical geometry are also feasible.

Ethical issues of global corporatization: agriculture and beyond.

PubMed

Pimentel, D

2004-03-01

The world food supply has become inadequate for more than half the world population, as evidenced by a recent report of the World Health Organization that indicated that more than 3 billion people are malnourished. This is the largest number of malnourished ever reported. Per capita food production, especially cereal grains, has been declining for nearly 2 decades, despite new biotechnology and other agricultural technologies. Rapid human population growth, compounded by diminishing availability of fertile cropland, freshwater, and fossil fuels, is intensifying the emerging problems in all food production systems. Numerous ethical issues are related to the problem of malnutrition, including global corporatization.

The exact fundamental solution for the Benes tracking problem

NASA Astrophysics Data System (ADS)

Balaji, Bhashyam

2009-05-01

The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.

Algorithms for elasto-plastic-creep postbuckling

NASA Technical Reports Server (NTRS)

Padovan, J.; Tovichakchaikul, S.

1984-01-01

This paper considers the development of an improved constrained time stepping scheme which can efficiently and stably handle the pre-post-buckling behavior of general structure subject to high temperature environments. Due to the generality of the scheme, the combined influence of elastic-plastic behavior can be handled in addition to time dependent creep effects. This includes structural problems exhibiting indefinite tangent properties. To illustrate the capability of the procedure, several benchmark problems employing finite element analyses are presented. These demonstrate the numerical efficiency and stability of the scheme. Additionally, the potential influence of complex creep histories on the buckling characteristics is considered.

Parallel Implementation of Numerical Solution of Few-Body Problem Using Feynman's Continual Integrals

NASA Astrophysics Data System (ADS)

Naumenko, Mikhail; Samarin, Viacheslav

2018-02-01

Modern parallel computing algorithm has been applied to the solution of the few-body problem. The approach is based on Feynman's continual integrals method implemented in C++ programming language using NVIDIA CUDA technology. A wide range of 3-body and 4-body bound systems has been considered including nuclei described as consisting of protons and neutrons (e.g., 3,4He) and nuclei described as consisting of clusters and nucleons (e.g., 6He). The correctness of the results was checked by the comparison with the exactly solvable 4-body oscillatory system and experimental data.

Solution methods for one-dimensional viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, John M.; Simitses, George J.

1987-01-01

A recently developed differential methodology for solution of one-dimensional nonlinear viscoelastic problems is presented. Using the example of an eccentrically loaded cantilever beam-column, the results from the differential formulation are compared to results generated using a previously published integral solution technique. It is shown that the results obtained from these distinct methodologies exhibit a surprisingly high degree of correlation with one another. A discussion of the various factors affecting the numerical accuracy and rate of convergence of these two procedures is also included. Finally, the influences of some 'higher order' effects, such as straining along the centroidal axis are discussed.

Zdeněk Kopal: Numerical Analyst

NASA Astrophysics Data System (ADS)

Křížek, M.

2015-07-01

We give a brief overview of Zdeněk Kopal's life, his activities in the Czech Astronomical Society, his collaboration with Vladimír Vand, and his studies at Charles University, Cambridge, Harvard, and MIT. Then we survey Kopal's professional life. He published 26 monographs and 20 conference proceedings. We will concentrate on Kopal's extensive monograph Numerical Analysis (1955, 1961) that is widely accepted to be the first comprehensive textbook on numerical methods. It describes, for instance, methods for polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations with initial or boundary conditions, and numerical solution of integral and integro-differential equations. Special emphasis will be laid on error analysis. Kopal himself applied numerical methods to celestial mechanics, in particular to the N-body problem. He also used Fourier analysis to investigate light curves of close binaries to discover their properties. This is, in fact, a problem from mathematical analysis.

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

NASA Astrophysics Data System (ADS)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.