Science.gov

Sample records for numerical integration methods

  1. Numerical methods for engine-airframe integration

    SciTech Connect

    Murthy, S.N.B.; Paynter, G.C.

    1986-01-01

    Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison of full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment.

  2. Automatic numerical integration methods for Feynman integrals through 3-loop

    NASA Astrophysics Data System (ADS)

    de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.

    2015-05-01

    We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.

  3. Numerical Integration

    ERIC Educational Resources Information Center

    Sozio, Gerry

    2009-01-01

    Senior secondary students cover numerical integration techniques in their mathematics courses. In particular, students would be familiar with the "midpoint rule," the elementary "trapezoidal rule" and "Simpson's rule." This article derives these techniques by methods which secondary students may not be familiar with and an approach that…

  4. Singularity Preserving Numerical Methods for Boundary Integral Equations

    NASA Technical Reports Server (NTRS)

    Kaneko, Hideaki (Principal Investigator)

    1996-01-01

    In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

  5. Comparison of four stable numerical methods for Abel's integral equation

    NASA Technical Reports Server (NTRS)

    Murio, Diego A.; Mejia, Carlos E.

    1991-01-01

    The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.

  6. Trigonometrically fitted two step hybrid method for the numerical integration of second order IVPs

    NASA Astrophysics Data System (ADS)

    Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.

    2016-06-01

    In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct trigonometrically fitted two step hybrid methods. We apply the new methods on the numerical integration of several test problems.

  7. Path Integrals and Exotic Options:. Methods and Numerical Results

    NASA Astrophysics Data System (ADS)

    Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.

    2005-09-01

    In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.

  8. An Improved Numerical Integration Method for Springback Predictions

    NASA Astrophysics Data System (ADS)

    Ibrahim, R.; Smith, L. M.; Golovashchenko, Sergey F.

    2011-08-01

    In this investigation, the focus is on the springback of steel sheets in V-die air bending. A full replication to a numerical integration algorithm presented rigorously in [1] to predict the springback in air bending was performed and confirmed successfully. Algorithm alteration and extensions were proposed here. The altered approach used in solving the moment equation numerically resulted in springback values much closer to the trend presented by the experimental data, Although investigation here extended to use a more realistic work-hardening model, the differences in the springback values obtained by both hardening models were almost negligible. The algorithm was extended to be applied on thin sheets down to 0.8 mm. Results show that this extension is possible as verified by FEA and other published experiments on TRIP steel sheets.

  9. Integrated numerical methods for hypersonic aircraft cooling systems analysis

    NASA Technical Reports Server (NTRS)

    Petley, Dennis H.; Jones, Stuart C.; Dziedzic, William M.

    1992-01-01

    Numerical methods have been developed for the analysis of hypersonic aircraft cooling systems. A general purpose finite difference thermal analysis code is used to determine areas which must be cooled. Complex cooling networks of series and parallel flow can be analyzed using a finite difference computer program. Both internal fluid flow and heat transfer are analyzed, because increased heat flow causes a decrease in the flow of the coolant. The steady state solution is a successive point iterative method. The transient analysis uses implicit forward-backward differencing. Several examples of the use of the program in studies of hypersonic aircraft and rockets are provided.

  10. Numerical integration of population models satisfying conservation laws: NSFD methods.

    PubMed

    Mickens, Ronald E

    2007-10-01

    Population models arising in ecology, epidemiology and mathematical biology may involve a conservation law, i.e. the total population is constant. In addition to these cases, other situations may occur for which the total population, asymptotically in time, approach a constant value. Since it is rarely the situation that the equations of motion can be analytically solved to obtain exact solutions, it follows that numerical techniques are needed to provide solutions. However, numerical procedures are only valid if they can reproduce fundamental properties of the differential equations modeling the phenomena of interest. We show that for population models, involving a dynamical conservation law the use of nonstandard finite difference (NSFD) methods allows the construction of discretization schemes such that they are dynamically consistent (DC) with the original differential equations. The paper will briefly discuss the NSFD methodology, the concept of DC, and illustrate their application to specific problems for population models. PMID:22876826

  11. Numerical Solutions of Electromagnetic Problems by Integral Equation Methods and Finite-Difference Time - Method.

    NASA Astrophysics Data System (ADS)

    Min, Xiaoyi

    This thesis first presents the study of the interaction of electromagnetic waves with three-dimensional heterogeneous, dielectric, magnetic, and lossy bodies by surface integral equation modeling. Based on the equivalence principle, a set of coupled surface integral equations is formulated and then solved numerically by the method of moments. Triangular elements are used to model the interfaces of the heterogeneous body, and vector basis functions are defined to expand the unknown current in the formulation. The validity of this formulation is verified by applying it to concentric spheres for which an exact solution exists. The potential applications of this formulation to a partially coated sphere and a homogeneous human body are discussed. Next, this thesis also introduces an efficient new set of integral equations for treating the scattering problem of a perfectly conducting body coated with a thin magnetically lossy layer. These electric field integral equations and magnetic field integral equations are numerically solved by the method of moments (MoM). To validate the derived integral equations, an alternative method to solve the scattering problem of an infinite circular cylinder coated with a thin magnetic lossy layer has also been developed, based on the eigenmode expansion. Results for the radar cross section and current densities via the MoM and the eigenmode expansion method are compared. The agreement is excellent. The finite difference time domain method is subsequently implemented to solve a metallic object coated with a magnetic thin layer and numerical results are compared with that by the MoM. Finally, this thesis presents an application of the finite-difference time-domain approach to the problem of electromagnetic receiving and scattering by a cavity -backed antenna situated on an infinite conducting plane. This application involves modifications of Yee's model, which applies the difference approximations of field derivatives to differential

  12. 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.

  13. An efficient step-size control method in numerical integration for astrodynamical equations

    NASA Astrophysics Data System (ADS)

    Liu, C. Z.; Cui, D. X.

    2002-11-01

    Using the curvature of the integral curve, a step-size control method is introduced in this paper. This method will prove to be the efficient scheme in the sense that it saves computation time and improve accuracy of numerical integration.

  14. Some numerical methods for integrating systems of first-order ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Clark, N. W.

    1969-01-01

    Report on numerical methods of integration includes the extrapolation methods of Bulirsch-Stoer and Neville. A comparison is made nith the Runge-Kutta and Adams-Moulton methods, and circumstances are discussed under which the extrapolation method may be preferred.

  15. Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

    NASA Technical Reports Server (NTRS)

    Sidi, A.; Israeli, M.

    1986-01-01

    High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

  16. Numerical solution of optimal control problems using multiple-interval integral Gegenbauer pseudospectral methods

    NASA Astrophysics Data System (ADS)

    Tang, Xiaojun

    2016-04-01

    The main purpose of this work is to provide multiple-interval integral Gegenbauer pseudospectral methods for solving optimal control problems. The latest developed single-interval integral Gauss/(flipped Radau) pseudospectral methods can be viewed as special cases of the proposed methods. We present an exact and efficient approach to compute the mesh pseudospectral integration matrices for the Gegenbauer-Gauss and flipped Gegenbauer-Gauss-Radau points. Numerical results on benchmark optimal control problems confirm the ability of the proposed methods to obtain highly accurate solutions.

  17. Conservation properties of numerical integration methods for systems of ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Rosenbaum, J. S.

    1976-01-01

    If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

  18. A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations

    NASA Technical Reports Server (NTRS)

    Radhakrishnan, K.

    1984-01-01

    The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.

  19. Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

    NASA Astrophysics Data System (ADS)

    Liu, Peigui; Elshall, Ahmed S.; Ye, Ming; Beerli, Peter; Zeng, Xiankui; Lu, Dan; Tao, Yuezan

    2016-02-01

    Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamic integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. The thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.

  20. Abstract Applets: A Method for Integrating Numerical Problem Solving into the Undergraduate Physics Curriculum

    SciTech Connect

    Peskin, Michael E

    2003-02-13

    In upper-division undergraduate physics courses, it is desirable to give numerical problem-solving exercises integrated naturally into weekly problem sets. I explain a method for doing this that makes use of the built-in class structure of the Java programming language. I also supply a Java class library that can assist instructors in writing programs of this type.

  1. Extended RKN-type methods for numerical integration of perturbed oscillators

    NASA Astrophysics Data System (ADS)

    Yang, Hongli; Wu, Xinyuan; You, Xiong; Fang, Yonglei

    2009-10-01

    In this paper, extended Runge-Kutta-Nyström-type methods for the numerical integration of perturbed oscillators with low frequencies are presented, which inherit the framework of RKN methods and make full use of the special feature of the true flows for both the internal stages and the updates. Following the approach of J. Butcher, E. Hairer and G. Wanner, we develop a new kind of tree set to derive order conditions for the extended Runge-Kutta-Nyström-type methods. The numerical stability and phase properties of the new methods are analyzed. Numerical experiments are accompanied to show the applicability and efficiency of our new methods in comparison with some well-known high quality methods proposed in the scientific literature.

  2. On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

    NASA Technical Reports Server (NTRS)

    Gottlieb, D.; Turkel, E.

    1980-01-01

    New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

  3. A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

    NASA Technical Reports Server (NTRS)

    Hu, Fang Q.

    1994-01-01

    It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

  4. A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations

    NASA Technical Reports Server (NTRS)

    Radhakrishnan, K.

    1984-01-01

    A comparison of the efficiency of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations is presented. The methods examined include two general-purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.

  5. Response sensitivity analysis of the dynamic milling process based on the numerical integration method

    NASA Astrophysics Data System (ADS)

    Ding, Ye; Zhu, Limin; Zhang, Xiaojian; Ding, Han

    2012-09-01

    As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.

  6. Two step hybrid methods of 7th and 8th order for the numerical integration of second order IVPs

    NASA Astrophysics Data System (ADS)

    Kalogiratou, Z.; Monovasilis, Th.; Simos, T. E.

    2016-06-01

    In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct two step hybrid methods with six and seven stages and seventh and eighth algebraic order. We apply the new methods on the numerical integration of several test problems.

  7. Rythmos Numerical Integration Package

    SciTech Connect

    Coffey, Todd S.; Bartlett, Roscoe A.

    2006-09-01

    Rythmos numerically integrates transient differential equations. The differential equations can be explicit or implicit ordinary differential equations ofr formulated as fully implicit differential-algebraic equations. Methods include backward Euler, forward Euler, explicit Runge-Kutta, and implicit BDF at this time. Native support for operator split methods and strict modularity are strong design goals. Forward sensitivity computations will be included in the first release with adjoint sensitivities coming in the near future. Rythmos heavily relies on Thyra for linear algebra and nonlinear solver interfaces to AztecOO, Amesos, IFPack, and NOX in Tilinos. Rythmos is specially suited for stiff differential equations and thos applictions where operator split methods have a big advantage, e.g. Computational fluid dynamics, convection-diffusion equations, etc.

  8. Rythmos Numerical Integration Package

    Energy Science and Technology Software Center (ESTSC)

    2006-09-01

    Rythmos numerically integrates transient differential equations. The differential equations can be explicit or implicit ordinary differential equations ofr formulated as fully implicit differential-algebraic equations. Methods include backward Euler, forward Euler, explicit Runge-Kutta, and implicit BDF at this time. Native support for operator split methods and strict modularity are strong design goals. Forward sensitivity computations will be included in the first release with adjoint sensitivities coming in the near future. Rythmos heavily relies on Thyra formore » linear algebra and nonlinear solver interfaces to AztecOO, Amesos, IFPack, and NOX in Tilinos. Rythmos is specially suited for stiff differential equations and thos applictions where operator split methods have a big advantage, e.g. Computational fluid dynamics, convection-diffusion equations, etc.« less

  9. Application of Numerical Integration and Data Fusion in Unit Vector Method

    NASA Astrophysics Data System (ADS)

    Zhang, J.

    2012-01-01

    The Unit Vector Method (UVM) is a series of orbit determination methods which are designed by Purple Mountain Observatory (PMO) and have been applied extensively. It gets the conditional equations for different kinds of data by projecting the basic equation to different unit vectors, and it suits for weighted process for different kinds of data. The high-precision data can play a major role in orbit determination, and accuracy of orbit determination is improved obviously. The improved UVM (PUVM2) promoted the UVM from initial orbit determination to orbit improvement, and unified the initial orbit determination and orbit improvement dynamically. The precision and efficiency are improved further. In this thesis, further research work has been done based on the UVM: Firstly, for the improvement of methods and techniques for observation, the types and decision of the observational data are improved substantially, it is also asked to improve the decision of orbit determination. The analytical perturbation can not meet the requirement. So, the numerical integration for calculating the perturbation has been introduced into the UVM. The accuracy of dynamical model suits for the accuracy of the real data, and the condition equations of UVM are modified accordingly. The accuracy of orbit determination is improved further. Secondly, data fusion method has been introduced into the UVM. The convergence mechanism and the defect of weighted strategy have been made clear in original UVM. The problem has been solved in this method, the calculation of approximate state transition matrix is simplified and the weighted strategy has been improved for the data with different dimension and different precision. Results of orbit determination of simulation and real data show that the work of this thesis is effective: (1) After the numerical integration has been introduced into the UVM, the accuracy of orbit determination is improved obviously, and it suits for the high-accuracy data of

  10. Numerical computation of unsteady laminar boundary layers with separation using two-parameter integral method

    NASA Astrophysics Data System (ADS)

    Akamatsu, T.; Matsushita, M.; Murata, S.

    1985-11-01

    A two-parameter integral method is presented which is applicable even to separated boundary layers. The governing equation system, which consists of three moment equations of the boundary layer equation, is shown to be classifiable as a quasi-linear hyperbolic system under the assumed velocity profile function. The governing system is numerically solved by a dissipative finite difference scheme in order to capture a discontinuous solution associated with the singularity of unsteady separation. The spontaneous generation of singularity associated with unsteady separation is confirmed as the focusing of characteristics. The starting flows of a circular and an elliptic cylinder are considered as definite examples. This method is found to give excellent results in comparison with exact methods, not only for practically important boundary layer quantities such as displacement thickness or skin friction coefficient, but also for generation of separation singularity.

  11. An integrated data-directed numerical method for estimating the undiscovered mineral endowment in a region

    USGS Publications Warehouse

    McCammon, R.B.; Finch, W.I.; Kork, J.O.; Bridges, N.J.

    1994-01-01

    An integrated data-directed numerical method has been developed to estimate the undiscovered mineral endowment within a given area. The method has been used to estimate the undiscovered uranium endowment in the San Juan Basin, New Mexico, U.S.A. The favorability of uranium concentration was evaluated in each of 2,068 cells defined within the Basin. Favorability was based on the correlated similarity of the geologic characteristics of each cell to the geologic characteristics of five area-related deposit models. Estimates of the undiscovered endowment for each cell were categorized according to deposit type, depth, and cutoff grade. The method can be applied to any mineral or energy commodity provided that the data collected reflect discovered endowment. ?? 1994 Oxford University Press.

  12. 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.

  13. Dynamics analysis of flexible mechanisms based on mixed numerical integration methods of Hilber-Huges-Taylor and Rossenbrock-Wanner

    SciTech Connect

    Ianakiev, A.; Esat, I.I.

    1995-09-01

    Numerical solution of dynamical systems with widely varying motion characteristics, such as relatively slow motion coupled with high frequency as it would be in flexible mechanisms, likely to pose problems. In this paper the mathematical model of a flexible mechanism is solved by using a mixed integration method that attempts to deal with the complexity of the coupled differential equations of the rigid-body and elastic motion. The mixed integration method consists of two integration methods (Rossenbrock-Wanner and Hilber-Hughes-Taylor methods) that have been combined in order to minimize the computational complexity required for the approximation of the real system. The a Hilber-Hughes-Taylor methods incorporates numerical damping that selectively affects only the higher modes of vibration. The improvement of the stability and the accuracy of the solution due to the numerical damping has been demonstrated via a numerical example that represents a stiff system. The example system was selected to contain a physically important low frequency and spurious highly frequency oscillations. The solution method filtered the high numerical oscillations from the response results. The Rossenbrock-Wanner integration technique was also presented. In this case it is also shown that fine adjustment of integration parameters could effect the degree of numerical damping. A mixed integration method, combination of the two found to give the best performance and accuracy in the case of stiff problems.

  14. Path-Integral Renormalization Group Method for Numerical Study of Strongly Correlated Electron Systems

    NASA Astrophysics Data System (ADS)

    Imada, Masatoshi; Kashima, Tsuyoshi

    2000-09-01

    A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after a numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from the optimized linear combination of retained states in the truncated Hilbert space with a numerically chosen basis. This algorithm does not suffer from the negative sign problem and can be applied to any type of Hamiltonian in any dimension. The efficiency is tested in examples of the Hubbard model where the basis of Slater determinants is numerically optimized. We show results on fast convergence and accuracy achieved with a small number of retained states.

  15. Numerical Modeling of 3-D Dynamics of Ultrasound Contrast Agent Microbubbles Using the Boundary Integral Method

    NASA Astrophysics Data System (ADS)

    Calvisi, Michael; Manmi, Kawa; Wang, Qianxi

    2014-11-01

    Ultrasound contrast agents (UCAs) are microbubbles stabilized with a shell typically of lipid, polymer, or protein and are emerging as a unique tool for noninvasive therapies ranging from gene delivery to tumor ablation. The nonspherical dynamics of contrast agents are thought to play an important role in both diagnostic and therapeutic applications, for example, causing the emission of subharmonic frequency components and enhancing the uptake of therapeutic agents across cell membranes and tissue interfaces. A three-dimensional model for nonspherical contrast agent dynamics based on the boundary integral method is presented. The effects of the encapsulating shell are approximated by adapting Hoff's model for thin-shell, spherical contrast agents to the nonspherical case. A high-quality mesh of the bubble surface is maintained by implementing a hybrid approach of the Lagrangian method and elastic mesh technique. Numerical analyses for the dynamics of UCAs in an infinite liquid and near a rigid wall are performed in parameter regimes of clinical relevance. The results show that the presence of a coating significantly reduces the oscillation amplitude and period, increases the ultrasound pressure amplitude required to incite jetting, and reduces the jet width and velocity.

  16. Cuba: Multidimensional numerical integration library

    NASA Astrophysics Data System (ADS)

    Hahn, Thomas

    2016-08-01

    The Cuba library offers four independent routines for multidimensional numerical integration: Vegas, Suave, Divonne, and Cuhre. The four algorithms work by very different methods, and can integrate vector integrands and have very similar Fortran, C/C++, and Mathematica interfaces. Their invocation is very similar, making it easy to cross-check by substituting one method by another. For further safeguarding, the output is supplemented by a chi-square probability which quantifies the reliability of the error estimate.

  17. Comparison of symbolic and numerical integration methods for an assumed-stress hybrid shell element

    NASA Technical Reports Server (NTRS)

    Rengarajan, Govind; Knight, Norman F., Jr.; Aminpour, Mohammad A.

    1993-01-01

    Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement-based formulations. However, a noteworthy factor in favor of hybrid elements is that numerical integration to generate element matrices can be entirely avoided by the use of symbolic integration. In this paper, the use of the symbolic computational approach is presented for an assumed-stress hybrid shell element with drilling degrees of freedom and the significant time savings achieved is demonstrated through an example.

  18. Numerical methods for the simulation of complex multi-body flows with applications for the integrated Space Shuttle vehicle

    NASA Technical Reports Server (NTRS)

    Chan, William M.

    1992-01-01

    The following papers are presented: (1) numerical methods for the simulation of complex multi-body flows with applications for the Integrated Space Shuttle vehicle; (2) a generalized scheme for 3-D hyperbolic grid generation; (3) collar grids for intersecting geometric components within the Chimera overlapped grid scheme; and (4) application of the Chimera overlapped grid scheme to simulation of Space Shuttle ascent flows.

  19. Time transformations and Cowell's method. [for numerical integration of satellite motion equations

    NASA Technical Reports Server (NTRS)

    Velez, C. E.; Hilinski, S.

    1978-01-01

    The precise numerical integration of Cowell's equations of satellite motion is frequently performed with an independent variable s defined by an equation of the form dt = cr to the n-th power ds, where t represents time, r the radial distance from the center of attraction, c is a constant, and n is a parameter. This has been primarily motivated by the 'uniformizing' effects of such a transformation resulting in desirable 'analytic' stepsize control for elliptical orbits. This report discusses the 'proper' choice of the parameter n defining the independent variable s for various types of orbits and perturbation models, and develops a criterion for its selection.

  20. ICM: an Integrated Compartment Method for numerically solving partial differential equations

    SciTech Connect

    Yeh, G.T.

    1981-05-01

    An integrated compartment method (ICM) is proposed to construct a set of algebraic equations from a system of partial differential equations. The ICM combines the utility of integral formulation of finite element approach, the simplicity of interpolation of finite difference approximation, and the flexibility of compartment analyses. The integral formulation eases the treatment of boundary conditions, in particular, the Neumann-type boundary conditions. The simplicity of interpolation provides great economy in computation. The flexibility of discretization with irregular compartments of various shapes and sizes offers advantages in resolving complex boundaries enclosing compound regions of interest. The basic procedures of ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. The Navier-Stokes equations are used as an example of how to derive the corresponding ICM alogrithm for a given set of partial differential equations. Because of the structure of the algorithm, the basic computer program remains the same for cases in one-, two-, or three-dimensional problems.

  1. High-performance Integrated numerical methods for Two-phase Flow in Heterogeneous Porous Media

    NASA Astrophysics Data System (ADS)

    Chueh, Chih-Che; Djilali, Ned; Bangerth, Wolfgang

    2010-11-01

    Modelling of two-phase flow in heterogeneous porous media has been playing a decisive role in a variety of areas. However, how to efficiently and accurately solve the governing equation in the flow in porous media remains a challenge. In order to ensure the accurate representative flow field and simultaneously increase the computational efficiency, we incorporate a number of state-of-the-art techniques into a numerical framework on which more complicated models in the field of multi-phase flow in porous media will be based. Such a numerical framework consists of a h-adaptive refinement method, an entropy-based artificial diffusive term, a new adaptive operator splitting method and efficient preconditioners. In particular, it is emphasized that we propose a new efficient adaptive operator splitting to avoid solving a time-consuming pressure-velocity part every saturation time step and, most importantly, we also provide a theoretically numerical analysis as well as proof. A few benchmarks will be demonstrated in the presentation.

  2. Runge-Kutta type methods with special properties for the numerical integration of ordinary differential equations

    NASA Astrophysics Data System (ADS)

    Kalogiratou, Z.; Monovasilis, Th.; Psihoyios, G.; Simos, T. E.

    2014-03-01

    In this work we review single step methods of the Runge-Kutta type with special properties. Among them are methods specially tuned to integrate problems that exhibit a pronounced oscillatory character and such problems arise often in celestial mechanics and quantum mechanics. Symplectic methods, exponentially and trigonometrically fitted methods, minimum phase-lag and phase-fitted methods are presented. These are Runge-Kutta, Runge-Kutta-Nyström and Partitioned Runge-Kutta methods. The theory of constructing such methods is given as well as several specific methods. In order to present the performance of the methods we have tested 58 methods from all categories. We consider the two dimensional harmonic oscillator, the two body problem, the pendulum problem and the orbital problem studied by Stiefel and Bettis. Also we have tested the methods on the computation of the eigenvalues of the one dimensional time independent Schrödinger equation with the harmonic oscillator, the doubly anharmonic oscillator and the exponential potentials.

  3. Numerical integral methods to study plasmonic modes in a photonic crystal waveguide with circular inclusions that involve a metamaterial

    NASA Astrophysics Data System (ADS)

    Mendoza-Suárez, A.; Pérez-Aguilar, H.

    2016-09-01

    We present several numerical integral methods for the study of a photonic crystal waveguide, formed by two parallel conducting plates and an array of circular inclusions involving a conducting material and a metamaterial. Band structures and reflectance were calculated, for infinite and finite photonic crystal waveguides, respectively. The numerical results obtained show that the numerical methods applied provide good accuracy and efficiency. An interesting detail that resulted from this study was the appearance of a propagating mode in a band gap due to defects in the middle of the photonic crystal waveguide. This is equivalent to dope a semiconductor to introduce allowed energy states within a band gap. Our main interest in this work is to model photonic crystal waveguides that involve left-handed materials (LHMs). For the specific LHM considered, a surface plasmon mode on the vacuum-LHM interface was found.

  4. Evaluation of 3 numerical methods for propulsion integration studies on transonic transport configurations

    NASA Technical Reports Server (NTRS)

    Yaros, S. F.; Carlson, J. R.; Chandrasekaran, B.

    1986-01-01

    An effort has been undertaken at the NASA Langley Research Center to assess the capabilities of available computational methods for use in propulsion integration design studies of transonic transport aircraft, particularly of pylon/nacelle combinations which exhibit essentially no interference drag. The three computer codes selected represent state-of-the-art computational methods for analyzing complex configurations at subsonic and transonic flight conditions. These are: EULER, a finitie volume solution of the Euler equation; VSAERO, a panel solution of the Laplace equation; and PPW, a finite difference solution of the small disturbance transonic equations. In general, all three codes have certain capabilities that allow them to be of some value in predicting the flows about transport configurations, but all have limitations. Until more accurate methods are available, careful application and interpretation of the results of these codes are needed.

  5. cuSwift --- a suite of numerical integration methods for modelling planetary systems implemented in C/CUDA

    NASA Astrophysics Data System (ADS)

    Hellmich, S.; Mottola, S.; Hahn, G.; Kührt, E.; Hlawitschka, M.

    2014-07-01

    Simulations of dynamical processes in planetary systems represent an important tool for studying the orbital evolution of the systems [1--3]. Using modern numerical integration methods, it is possible to model systems containing many thousands of objects over timescales of several hundred million years. However, in general, supercomputers are needed to get reasonable simulation results in acceptable execution times [3]. To exploit the ever-growing computation power of Graphics Processing Units (GPUs) in modern desktop computers, we implemented cuSwift, a library of numerical integration methods for studying long-term dynamical processes in planetary systems. cuSwift can be seen as a re-implementation of the famous SWIFT integrator package written by Hal Levison and Martin Duncan. cuSwift is written in C/CUDA and contains different integration methods for various purposes. So far, we have implemented three algorithms: a 15th-order Radau integrator [4], the Wisdom-Holman Mapping (WHM) integrator [5], and the Regularized Mixed Variable Symplectic (RMVS) Method [6]. These algorithms treat only the planets as mutually gravitationally interacting bodies whereas asteroids and comets (or other minor bodies of interest) are treated as massless test particles which are gravitationally influenced by the massive bodies but do not affect each other or the massive bodies. The main focus of this work is on the symplectic methods (WHM and RMVS) which use a larger time step and thus are capable of integrating many particles over a large time span. As an additional feature, we implemented the non-gravitational Yarkovsky effect as described by M. Brož [7]. With cuSwift, we show that the use of modern GPUs makes it possible to speed up these methods by more than one order of magnitude compared to the single-core CPU implementation, thereby enabling modest workstation computers to perform long-term dynamical simulations. We use these methods to study the influence of the Yarkovsky

  6. Numerical Integration: One Step at a Time

    ERIC Educational Resources Information Center

    Yang, Yajun; Gordon, Sheldon P.

    2016-01-01

    This article looks at the effects that adding a single extra subdivision has on the level of accuracy of some common numerical integration routines. Instead of automatically doubling the number of subdivisions for a numerical integration rule, we investigate what happens with a systematic method of judiciously selecting one extra subdivision for…

  7. Integrating experimental and numerical methods for a scenario-based quantitative assessment of subsurface energy storage options

    NASA Astrophysics Data System (ADS)

    Kabuth, Alina; Dahmke, Andreas; Hagrey, Said Attia al; Berta, Márton; Dörr, Cordula; Koproch, Nicolas; Köber, Ralf; Köhn, Daniel; Nolde, Michael; Tilmann Pfeiffer, Wolf; Popp, Steffi; Schwanebeck, Malte; Bauer, Sebastian

    2016-04-01

    Within the framework of the transition to renewable energy sources ("Energiewende"), the German government defined the target of producing 60 % of the final energy consumption from renewable energy sources by the year 2050. However, renewable energies are subject to natural fluctuations. Energy storage can help to buffer the resulting time shifts between production and demand. Subsurface geological structures provide large potential capacities for energy stored in the form of heat or gas on daily to seasonal time scales. In order to explore this potential sustainably, the possible induced effects of energy storage operations have to be quantified for both specified normal operation and events of failure. The ANGUS+ project therefore integrates experimental laboratory studies with numerical approaches to assess subsurface energy storage scenarios and monitoring methods. Subsurface storage options for gas, i.e. hydrogen, synthetic methane and compressed air in salt caverns or porous structures, as well as subsurface heat storage are investigated with respect to site prerequisites, storage dimensions, induced effects, monitoring methods and integration into spatial planning schemes. The conceptual interdisciplinary approach of the ANGUS+ project towards the integration of subsurface energy storage into a sustainable subsurface planning scheme is presented here, and this approach is then demonstrated using the examples of two selected energy storage options: Firstly, the option of seasonal heat storage in a shallow aquifer is presented. Coupled thermal and hydraulic processes induced by periodic heat injection and extraction were simulated in the open-source numerical modelling package OpenGeoSys. Situations of specified normal operation as well as cases of failure in operational storage with leaking heat transfer fluid are considered. Bench-scale experiments provided parameterisations of temperature dependent changes in shallow groundwater hydrogeochemistry. As a

  8. Numerical integration of subtraction terms

    NASA Astrophysics Data System (ADS)

    Seth, Satyajit; Weinzierl, Stefan

    2016-06-01

    Numerical approaches to higher-order calculations often employ subtraction terms, both for the real emission and the virtual corrections. These subtraction terms have to be added back. In this paper we show that at NLO the real subtraction terms, the virtual subtraction terms, the integral representations of the field renormalization constants and—in the case of initial-state partons—the integral representation for the collinear counterterm can be grouped together to give finite integrals, which can be evaluated numerically. This is useful for an extension towards next-to-next-to-leading order.

  9. Mosaic-skeleton method as applied to the numerical solution of three-dimensional Dirichlet problems for the Helmholtz equation in integral form

    NASA Astrophysics Data System (ADS)

    Kashirin, A. A.; Smagin, S. I.; Taltykina, M. Yu.

    2016-04-01

    Interior and exterior three-dimensional Dirichlet problems for the Helmholtz equation are solved numerically. They are formulated as equivalent boundary Fredholm integral equations of the first kind and are approximated by systems of linear algebraic equations, which are then solved numerically by applying an iteration method. The mosaic-skeleton method is used to speed up the solution procedure.

  10. Computational and numerical aspects of using the integral equation method for adhesive layer fracture mechanics analysis

    SciTech Connect

    Giurgiutiu, V.; Ionita, A.; Dillard, D.A.; Graffeo, J.K.

    1996-12-31

    Fracture mechanics analysis of adhesively bonded joints has attracted considerable attention in recent years. A possible approach to the analysis of adhesive layer cracks is to study a brittle adhesive between 2 elastic half-planes representing the substrates. A 2-material 3-region elasticity problem is set up and has to be solved. A modeling technique based on the work of Fleck, Hutchinson, and Suo is used. Two complex potential problems using Muskelishvili`s formulation are set up for the 3-region, 2-material model: (a) a distribution of edge dislocations is employed to simulate the crack and its near field; and (b) a crack-free problem is used to simulate the effect of the external loading applied in the far field. Superposition of the two problems is followed by matching tractions and displacements at the bimaterial boundaries. The Cauchy principal value integral is used to treat the singularities. Imposing the traction-free boundary conditions over the entire crack length yielded a linear system of two integral equations. The parameters of the problem are Dundurs` elastic mismatch coefficients, {alpha} and {beta}, and the ratio c/H representing the geometric position of the crack in the adhesive layer.

  11. Fast methods to numerically integrate the Reynolds equation for gas fluid films

    NASA Technical Reports Server (NTRS)

    Dimofte, Florin

    1992-01-01

    The alternating direction implicit (ADI) method is adopted, modified, and applied to the Reynolds equation for thin, gas fluid films. An efficient code is developed to predict both the steady-state and dynamic performance of an aerodynamic journal bearing. An alternative approach is shown for hybrid journal gas bearings by using Liebmann's iterative solution (LIS) for elliptic partial differential equations. The results are compared with known design criteria from experimental data. The developed methods show good accuracy and very short computer running time in comparison with methods based on an inverting of a matrix. The computer codes need a small amount of memory and can be run on either personal computers or on mainframe systems.

  12. Numerical integration of a relativistic two-body problem via a multiple scales method

    NASA Astrophysics Data System (ADS)

    Abouelmagd, Elbaz I.; Elshaboury, S. M.; Selim, H. H.

    2016-01-01

    We offer an analytical study on the dynamics of a two-body problem perturbed by small post-Newtonian relativistic term. We prove that, while the angular momentum is not conserved, the motion is planar. We also show that the energy is subject to small changes due to the relativistic effect. We also offer a periodic solution to this problem, obtained by a method based on the separation of time scales. We demonstrate that our solution is more general than the method developed in the book by Brumberg (Essential Relativistic Celestial Mechanics, Hilger, Bristol, 1991). The practical applicability of this model may be in studies of the long-term evolution of relativistic binaries (neutron stars or black holes).

  13. Fresnel Integral Equations: Numerical Properties

    SciTech Connect

    Adams, R J; Champagne, N J II; Davis, B A

    2003-07-22

    A spatial-domain solution to the problem of electromagnetic scattering from a dielectric half-space is outlined. The resulting half-space operators are referred to as Fresnel surface integral operators. When used as preconditioners for nonplanar geometries, the Fresnel operators yield surface Fresnel integral equations (FIEs) which are stable with respect to dielectric constant, discretization, and frequency. Numerical properties of the formulations are discussed.

  14. Numerical modeling of the 3D dynamics of ultrasound contrast agent microbubbles using the boundary integral method

    NASA Astrophysics Data System (ADS)

    Wang, Qianxi; Manmi, Kawa; Calvisi, Michael L.

    2015-02-01

    Ultrasound contrast agents (UCAs) are microbubbles stabilized with a shell typically of lipid, polymer, or protein and are emerging as a unique tool for noninvasive therapies ranging from gene delivery to tumor ablation. While various models have been developed to describe the spherical oscillations of contrast agents, the treatment of nonspherical behavior has received less attention. However, the nonspherical dynamics of contrast agents are thought to play an important role in therapeutic applications, for example, enhancing the uptake of therapeutic agents across cell membranes and tissue interfaces, and causing tissue ablation. In this paper, a model for nonspherical contrast agent dynamics based on the boundary integral method is described. The effects of the encapsulating shell are approximated by adapting Hoff's model for thin-shell, spherical contrast agents. A high-quality mesh of the bubble surface is maintained by implementing a hybrid approach of the Lagrangian method and elastic mesh technique. The numerical model agrees well with a modified Rayleigh-Plesset equation for encapsulated spherical bubbles. Numerical analyses of the dynamics of UCAs in an infinite liquid and near a rigid wall are performed in parameter regimes of clinical relevance. The oscillation amplitude and period decrease significantly due to the coating. A bubble jet forms when the amplitude of ultrasound is sufficiently large, as occurs for bubbles without a coating; however, the threshold amplitude required to incite jetting increases due to the coating. When a UCA is near a rigid boundary subject to acoustic forcing, the jet is directed towards the wall if the acoustic wave propagates perpendicular to the boundary. When the acoustic wave propagates parallel to the rigid boundary, the jet direction has components both along the wave direction and towards the boundary that depend mainly on the dimensionless standoff distance of the bubble from the boundary. In all cases, the jet

  15. A control volume method on an icosahedral grid for numerical integration of the shallow-water equations on the sphere

    SciTech Connect

    Chern, I-Liang

    1994-08-01

    Two versions of a control volume method on a symmetrized icosahedral grid are proposed for solving the shallow-water equations on a sphere. One version expresses of the equations in the 3-D Cartersian coordinate system, while the other expresses the equations in the northern/southern polar sterographic coordinate systems. The pole problem is avoided because of these expressions in both versions and the quasi-homogenity of the icosahedral grid. Truncation errors and convergence tests of the numerical gradient and divergent operators associated with this method are studied. A convergence tests of the numerical gradient and divergent operators associated with this method are studied. A convergence test for a steady zonal flow is demonstrated. Several simulations of Rossby-Haurwitz waves with various numbers are also performed.

  16. Effects of aliasing on numerical integration.

    SciTech Connect

    Edwards, Timothy S.

    2005-02-01

    During the course of processing acceleration data from mechanical systems it is often desirable to integrate the data to obtain velocity or displacement waveforms. However, those who have attempted these operations may be painfully aware that the integrated records often yield unrealistic residual values. This is true whether the data has been obtained experimentally or through numerical simulation such as Runge-Kutta integration or the explicit finite element method. In the case of experimentally obtained data, the integration errors are usually blamed on accelerometer zero shift or amplifier saturation. In the case of simulation data, incorrect integrations are often incorrectly blamed on the integration algorithm itself. This work demonstrates that seemingly small aliased content can cause appreciable errors in the integrated waveforms and explores the unavoidable source of aliasing in both experiment and simulation-the sampling operation. Numerical analysts are often puzzled as to why the integrated acceleration from their simulation does not match the displacement output from the same simulation. This work shows that these strange results can be caused by aliasing induced by interpolation of the model output during sampling regularization.

  17. Numerical methods for the simulation of complex multi-body flows with applications for the integrated Space Shuttle vehicle

    NASA Technical Reports Server (NTRS)

    Chan, William M.

    1992-01-01

    This project forms part of the long term computational effort to simulate the time dependent flow over the integrated Space Shuttle vehicle (orbiter, solid rocket boosters (SRB's), external tank (ET), and attach hardware) during its ascent mode for various nominal and abort flight conditions. Due to the limitations of experimental data such as wind tunnel wall effects and the difficulty of safely obtaining valid flight data, numerical simulations are undertaken to supplement the existing data base. This data can then be used to predict the aerodynamic behavior over a wide range of flight conditions. Existing computational results show relatively good overall comparison with experiments but further refinement is required to reduce numerical errors and to obtain finer agreements over a larger parameter space. One of the important goals of this project is to obtain better comparisons between numerical simulations and experiments. In the simulations performed so far, the geometry has been simplified in various ways to reduce the complexity so that useful results can be obtained in a reasonable time frame due to limitations in computer resources. In this project, the finer details of the major components of the Space Shuttle are modeled better by including more complexity in the geometry definition. Smaller components not included in early Space Shuttle simulations will now be modeled and gridded.

  18. Theoretical, experimental and numerical methods for investigating the characteristics of laser radiation scattered in the integrated-optical waveguide with three-dimensional irregularities

    SciTech Connect

    Egorov, Alexander A

    2011-07-31

    We consider theoretical, experimental and numerical methods which make it possible to analyse the key characteristics of laser radiation scattered in the integrated-optical waveguide with three-dimensional irregularities. The main aspects of the three-dimensional vector electrodynamic problem of waveguide scattering are studied. The waveguide light scattering method is presented and its main advantages over the methods of single scattering of laser radiation are discussed. The experimental setup and results of measurements are described. Theoretical and experimental results confirming the validity of the vector theory of three-dimensional waveguide scattering of laser radiation developed by the author are compared for the first time. (fiber and integrated optics)

  19. Numerical multi-loop integrals and applications

    NASA Astrophysics Data System (ADS)

    Freitas, A.

    2016-09-01

    Higher-order radiative corrections play an important role in precision studies of the electroweak and Higgs sector, as well as for the detailed understanding of large backgrounds to new physics searches. For corrections beyond the one-loop level and involving many independent mass and momentum scales, it is in general not possible to find analytic results, so that one needs to resort to numerical methods instead. This article presents an overview of a variety of numerical loop integration techniques, highlighting their range of applicability, suitability for automatization, and numerical precision and stability. In a second part of this article, the application of numerical loop integration methods in the area of electroweak precision tests is illustrated. Numerical methods were essential for obtaining full two-loop predictions for the most important precision observables within the Standard Model. The theoretical foundations for these corrections will be described in some detail, including aspects of the renormalization, resummation of leading log contributions, and the evaluation of the theory uncertainty from missing higher orders.

  20. 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.

  1. The Fourier transform method and the SD-bar approach for the analytical and numerical treatment of multicenter overlap-like quantum similarity integrals

    SciTech Connect

    Safouhi, Hassan . E-mail: hassan.safouhi@ualberta.ca; Berlu, Lilian

    2006-07-20

    Molecular overlap-like quantum similarity measurements imply the evaluation of overlap integrals of two molecular electronic densities related by Dirac delta function. When the electronic densities are expanded over atomic orbitals using the usual LCAO-MO approach (linear combination of atomic orbitals), overlap-like quantum similarity integrals could be expressed in terms of four-center overlap integrals. It is shown that by introducing the Fourier transform of delta Dirac function in the integrals and using the Fourier transform approach combined with the so-called B functions, one can obtain analytic expressions of the integrals under consideration. These analytic expressions involve highly oscillatory semi-infinite spherical Bessel functions, which are the principal source of severe numerical and computational difficulties. In this work, we present a highly efficient algorithm for a fast and accurate numerical evaluation of these multicenter overlap-like quantum similarity integrals over Slater type functions. This algorithm is based on the SD-bar approach due to Safouhi. Recurrence formulae are used for a better control of the degree of accuracy and for a better stability of the algorithm. The numerical result section shows the efficiency of our algorithm, compared with the alternatives using the one-center two-range expansion method, which led to very complicated analytic expressions, the epsilon algorithm and the nonlinear D-bar transformation.

  2. Integrating a Numerical Taxonomic Method and Molecular Phylogeny for Species Delimitation of Melampsora Species (Melampsoraceae, Pucciniales) on Willows in China

    PubMed Central

    Zhao, Peng; Wang, Qing-Hong; Tian, Cheng-Ming; Kakishima, Makoto

    2015-01-01

    The species in genus Melampsora are the causal agents of leaf rust diseases on willows in natural habitats and plantations. However, the classification and recognition of species diversity are challenging because morphological characteristics are scant and morphological variation in Melampsora on willows has not been thoroughly evaluated. Thus, the taxonomy of Melampsora species on willows remains confused, especially in China where 31 species were reported based on either European or Japanese taxonomic systems. To clarify the species boundaries of Melampsora species on willows in China, we tested two approaches for species delimitation inferred from morphological and molecular variations. Morphological species boundaries were determined based on numerical taxonomic analyses of morphological characteristics in the uredinial and telial stages by cluster analysis and one-way analysis of variance. Phylogenetic species boundaries were delineated based on the generalized mixed Yule-coalescent (GMYC) model analysis of the sequences of the internal transcribed spacer (ITS1 and ITS2) regions including the 5.8S and D1/D2 regions of the large nuclear subunit of the ribosomal RNA gene. Numerical taxonomic analyses of 14 morphological characteristics recognized in the uredinial-telial stages revealed 22 morphological species, whereas the GMYC results recovered 29 phylogenetic species. In total, 17 morphological species were in concordance with the phylogenetic species and 5 morphological species were in concordance with 12 phylogenetic species. Both the morphological and molecular data supported 14 morphological characteristics, including 5 newly recognized characteristics and 9 traditionally emphasized characteristics, as effective for the differentiation of Melampsora species on willows in China. Based on the concordance and discordance of the two species delimitation approaches, we concluded that integrative taxonomy by using both morphological and molecular variations was

  3. Numerical Analysis of the Symmetric Methods

    NASA Astrophysics Data System (ADS)

    Xu, Ji-Hong; Zhang, A.-Li

    1995-03-01

    Aimed at the initial value problem of the particular second-order ordinary differential equations,y ″=f(x, y), the symmetric methods (Quinlan and Tremaine, 1990) and our methods (Xu and Zhang, 1994) have been compared in detail by integrating the artificial earth satellite orbits in this paper. In the end, we point out clearly that the integral accuracy of numerical integration of the satellite orbits by applying our methods is obviously higher than that by applying the same order formula of the symmetric methods when the integration time-interval is not greater than 12000 periods.

  4. Towards an integrated numerical simulator for crack-seal vein microstructure: Coupling phase-field with the Discrete Element Method

    NASA Astrophysics Data System (ADS)

    Virgo, Simon; Ankit, Kumar; Nestler, Britta; Urai, Janos L.

    2016-04-01

    Crack-seal veins form in a complex interplay of coupled thermal, hydraulic, mechanical and chemical processes. Their formation and cyclic growth involves brittle fracturing and dilatancy, phases of increased fluid flow and the growth of crystals that fill the voids and reestablish the mechanical strength. Existing numerical models of vein formation focus on selected aspects of the coupled process. Until today, no model exists that is able to use a realistic representation of the fracturing AND sealing processes, simultaneously. To address this challenge, we propose the bidirectional coupling of two numerical methods that have proven themselves as very powerful to model the fundamental processes acting in crack-seal systems: Phase-field and the Discrete Element Method (DEM). The phase-field Method was recently successfully extended to model the precipitation of quartz crystals from an aqueous solution and applied to model the sealing of a vein over multiple opening events (Ankit et al., 2013; Ankit et al., 2015a; Ankit et al., 2015b). The advantage over former, purely kinematic approaches is that in phase-field, the crystal growth is modeled based on thermodynamic and kinetic principles. Different driving forces for microstructure evolution, such as chemical bulk free energy, interfacial energy, elastic strain energy and different transport processes, such as mass diffusion and advection, can be coupled and the effect on the evolution process can be studied in 3D. The Discrete Element Method was already used in several studies to model the fracturing of rocks and the incremental growth of veins by repeated fracturing (Virgo et al., 2013; Virgo et al., 2014). Materials in DEM are represented by volumes of packed spherical particles and the response to the material to stress is modeled by interaction of the particles with their nearest neighbours. For rocks, in 3D, the method provides a realistic brittle failure behaviour. Exchange Routines are being developed that

  5. Efficient numerical evaluation of Feynman integrals

    NASA Astrophysics Data System (ADS)

    Li, Zhao; Wang, Jian; Yan, Qi-Shu; Zhao, Xiaoran

    2016-03-01

    Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass. Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)

  6. Numerical integration of ordinary differential equations of various orders

    NASA Technical Reports Server (NTRS)

    Gear, C. W.

    1969-01-01

    Report describes techniques for the numerical integration of differential equations of various orders. Modified multistep predictor-corrector methods for general initial-value problems are discussed and new methods are introduced.

  7. NMR signal for particles diffusing under potentials: From path integrals and numerical methods to a model of diffusion anisotropy

    NASA Astrophysics Data System (ADS)

    Yolcu, Cem; Memiç, Muhammet; Şimşek, Kadir; Westin, Carl-Fredrik; Özarslan, Evren

    2016-05-01

    We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using path integral methods. Explicit relationships are derived for commonly employed gradient waveforms involving pulsed and oscillating gradients. The Bloch-Torrey equation, describing the temporal evolution of magnetization, is modified by incorporating potentials. A general solution to this equation is obtained for the case of parabolic potential by adopting the multiple correlation function (MCF) formalism, which has been used in the past to quantify the effects of restricted diffusion. Both analytical and MCF results were found to be in agreement with random walk simulations. A multidimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike the case of traditional methods that employ a diffusion tensor, anisotropy originates from the tensorial force constant, and bulk diffusivity is retained in the formulation. Our findings suggest that some features of the NMR signal that have traditionally been attributed to restricted diffusion are accommodated by the Hookean model. Under certain conditions, the formalism can be envisioned to provide a viable approximation to the mathematically more challenging restricted diffusion problems.

  8. A numerical method for integrating the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes

    NASA Technical Reports Server (NTRS)

    Emukashvily, I. M.

    1982-01-01

    An extension of the method of moments is developed for the numerical integration of the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes. The number density function n sub k (x,t) in each separate droplet packet between droplet mass grid points (x sub k, x sub k+1) is represented by an expansion in orthogonal polynomials with a given weighting function. In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved and the problem of solving the kinetic equations is replaced by one of solving a set of coupled differential equations for the number density function moments. The method is tested against analytic solutions of the corresponding kinetic equations. Numerical results are obtained for different coalescence/breakup and condensation/evaporation kernels and for different initial droplet spectra. Also droplet mass grid intervals, weighting functions, and time steps are varied.

  9. Numerical study identifying the factors causing the significant underestimation of the specific discharge estimated using the modified integral pumping test method in a laboratory experiment

    NASA Astrophysics Data System (ADS)

    Sun, Kerang

    2015-09-01

    A three-dimensional finite element model is constructed to simulate the experimental conditions presented in a paper published in this journal [Goltz et al., 2009. Validation of two innovative methods to measure contaminant mass flux in groundwater. Journal of Contaminant Hydrology 106 (2009) 51-61] where the modified integral pumping test (MIPT) method was found to significantly underestimate the specific discharge in an artificial aquifer. The numerical model closely replicates the experimental configuration with explicit representation of the pumping well column and skin, allowing for the model to simulate the wellbore flow in the pumping well as an integral part of the porous media flow in the aquifer using the equivalent hydraulic conductivity approach. The equivalent hydraulic conductivity is used to account for head losses due to friction within the wellbore of the pumping well. Applying the MIPT method on the model simulated piezometric heads resulted in a specific discharge that underestimates the true specific discharge in the experimental aquifer by 18.8%, compared with the 57% underestimation of mass flux by the experiment reported by Goltz et al. (2009). Alternative simulation shows that the numerical model is capable of approximately replicating the experiment results when the equivalent hydraulic conductivity is reduced by an order of magnitude, suggesting that the accuracy of the MIPT estimation could be improved by expanding the physical meaning of the equivalent hydraulic conductivity to account for other factors such as orifice losses in addition to frictional losses within the wellbore. Numerical experiments also show that when applying the MIPT method to estimate hydraulic parameters, use of depth-integrated piezometric head instead of the head near the pump intake can reduce the estimation error resulting from well losses, but not the error associated with the well not being fully screened.

  10. Numerical study identifying the factors causing the significant underestimation of the specific discharge estimated using the modified integral pumping test method in a laboratory experiment.

    PubMed

    Sun, Kerang

    2015-09-01

    A three-dimensional finite element model is constructed to simulate the experimental conditions presented in a paper published in this journal [Goltz et al., 2009. Validation of two innovative methods to measure contaminant mass flux in groundwater. Journal of Contaminant Hydrology 106 (2009) 51-61] where the modified integral pumping test (MIPT) method was found to significantly underestimate the specific discharge in an artificial aquifer. The numerical model closely replicates the experimental configuration with explicit representation of the pumping well column and skin, allowing for the model to simulate the wellbore flow in the pumping well as an integral part of the porous media flow in the aquifer using the equivalent hydraulic conductivity approach. The equivalent hydraulic conductivity is used to account for head losses due to friction within the wellbore of the pumping well. Applying the MIPT method on the model simulated piezometric heads resulted in a specific discharge that underestimates the true specific discharge in the experimental aquifer by 18.8%, compared with the 57% underestimation of mass flux by the experiment reported by Goltz et al. (2009). Alternative simulation shows that the numerical model is capable of approximately replicating the experiment results when the equivalent hydraulic conductivity is reduced by an order of magnitude, suggesting that the accuracy of the MIPT estimation could be improved by expanding the physical meaning of the equivalent hydraulic conductivity to account for other factors such as orifice losses in addition to frictional losses within the wellbore. Numerical experiments also show that when applying the MIPT method to estimate hydraulic parameters, use of depth-integrated piezometric head instead of the head near the pump intake can reduce the estimation error resulting from well losses, but not the error associated with the well not being fully screened. PMID:26210034

  11. Path-Integral Renormalization Group Method for Numerical Study on Ground States of Strongly Correlated Electronic Systems

    NASA Astrophysics Data System (ADS)

    Kashima, Tsuyoshi; Imada, Masatoshi

    2001-08-01

    A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two procedures lead to a better approximation. The first is a numerical renormalization, which optimizes the chosen basis and projects onto the ground state within the fixed dimension, L, of the Hilbert space. The second is an increase of the dimension of the truncated Hilbert space, which enables the linear combination to converge to a better approximation. The extrapolation L→∞ after the convergence removes the approximation error systematically. This algorithm does not suffer from the negative sign problem and can be applied to systems in any spatial dimension and arbitrary lattice structure. The efficiency is tested and the implementation explained for two-dimensional Hubbard models where Slater determinants are employed as chosen basis. Our results with less than 400 chosen basis indicate good accuracy within the errorbar of the best available results as those of the quantum Monte Carlo for energy and other physical quantities.

  12. An Integrative Theory of Numerical Development

    ERIC Educational Resources Information Center

    Siegler, Robert; Lortie-Forgues, Hugues

    2014-01-01

    Understanding of numerical development is growing rapidly, but the volume and diversity of findings can make it difficult to perceive any coherence in the process. The integrative theory of numerical development posits that a coherent theme is present, however--progressive broadening of the set of numbers whose magnitudes can be accurately…

  13. Numerical methods in structural mechanics

    NASA Astrophysics Data System (ADS)

    Obraztsov, I. F.

    The papers contained in this volume focus on numerical, numerical-analytical, and theoretical methods for dealing with strength, stability, and dynamics problems in the design of the structural elements of flight vehicles. Topics discussed include the solution of homogeneous boundary value problems for systems of ordinary differential equations modified by a difference factorization method, a study of the rupture strength of a welded joint between plates, singular solutions in mixed problems for a wedge and a half-strip, and a thermoelasticity problem for an open-profile cylindrical shell with a localized temperature field.

  14. Numerical methods for turbulent flow

    NASA Astrophysics Data System (ADS)

    Turner, James C., Jr.

    1988-09-01

    It has generally become accepted that the Navier-Strokes equations predict the dynamic behavior of turbulent as well as laminar flows of a fluid at a point in space away form a discontinuity such as a shock wave. Turbulence is also closely related to the phenomena of non-uniqueness of solutions of the Navier-Strokes equations. These second order, nonlinear partial differential equations can be solved analytically for only a few simple flows. Turbulent flow fields are much to complex to lend themselves to these few analytical methods. Numerical methods, therefore, offer the only possibility of achieving a solution of turbulent flow equations. In spite of recent advances in computer technology, the direct solution, by discrete methods, of the Navier-Strokes equations for turbulent flow fields is today, and in the foreseeable future, impossible. Thus the only economically feasible way to solve practical turbulent flow problems numerically is to use statistically averaged equations governing mean-flow quantities. The objective is to study some recent developments relating to the use of numerical methods to study turbulent flow.

  15. Numerical methods for molecular dynamics

    SciTech Connect

    Skeel, R.D.

    1991-01-01

    This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.

  16. Translation and integration of numerical atomic orbitals in linear molecules.

    PubMed

    Heinäsmäki, Sami

    2014-02-14

    We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively. PMID:24527905

  17. Translation and integration of numerical atomic orbitals in linear molecules

    NASA Astrophysics Data System (ADS)

    Heinäsmäki, Sami

    2014-02-01

    We present algorithms for translation and integration of atomic orbitals for LCAO calculations in linear molecules. The method applies to arbitrary radial functions given on a numerical mesh. The algorithms are based on pseudospectral differentiation matrices in two dimensions and the corresponding two-dimensional Gaussian quadratures. As a result, multicenter overlap and Coulomb integrals can be evaluated effectively.

  18. On Numerical Methods For Hypersonic Turbulent Flows

    NASA Astrophysics Data System (ADS)

    Yee, H. C.; Sjogreen, B.; Shu, C. W.; Wang, W.; Magin, T.; Hadjadj, A.

    2011-05-01

    Proper control of numerical dissipation in numerical methods beyond the standard shock-capturing dissipation at discontinuities is an essential element for accurate and stable simulation of hypersonic turbulent flows, including combustion, and thermal and chemical nonequilibrium flows. Unlike rapidly developing shock interaction flows, turbulence computations involve long time integrations. Improper control of numerical dissipation from one time step to another would be compounded over time, resulting in the smearing of turbulent fluctuations to an unrecognizable form. Hypersonic turbulent flows around re- entry space vehicles involve mixed steady strong shocks and turbulence with unsteady shocklets that pose added computational challenges. Stiffness of the source terms and material mixing in combustion pose yet other types of numerical challenges. A low dissipative high order well- balanced scheme, which can preserve certain non-trivial steady solutions of the governing equations exactly, may help minimize some of these difficulties. For stiff reactions it is well known that the wrong propagation speed of discontinuities occurs due to the under-resolved numerical solutions in both space and time. Schemes to improve the wrong propagation speed of discontinuities for systems of stiff reacting flows remain a challenge for algorithm development. Some of the recent algorithm developments for direct numerical simulations (DNS) and large eddy simulations (LES) for the subject physics, including the aforementioned numerical challenges, will be discussed.

  19. Highly Parallel, High-Precision Numerical Integration

    SciTech Connect

    Bailey, David H.; Borwein, Jonathan M.

    2005-04-22

    This paper describes a scheme for rapidly computing numerical values of definite integrals to very high accuracy, ranging from ordinary machine precision to hundreds or thousands of digits, even for functions with singularities or infinite derivatives at endpoints. Such a scheme is of interest not only in computational physics and computational chemistry, but also in experimental mathematics, where high-precision numerical values of definite integrals can be used to numerically discover new identities. This paper discusses techniques for a parallel implementation of this scheme, then presents performance results for 1-D and 2-D test suites. Results are also given for a certain problem from mathematical physics, which features a difficult singularity, confirming a conjecture to 20,000 digit accuracy. The performance rate for this latter calculation on 1024 CPUs is 690 Gflop/s. We believe that this and one other 20,000-digit integral evaluation that we report are the highest-precision non-trivial numerical integrations performed to date.

  20. Numerical methods for multibody systems

    NASA Technical Reports Server (NTRS)

    Glowinski, Roland; Nasser, Mahmoud G.

    1994-01-01

    This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.

  1. Numerical solution of boundary-integral equations for molecular electrostatics.

    PubMed

    Bardhan, Jaydeep P

    2009-03-01

    Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived. PMID:19275391

  2. Numerical Methods for Stochastic Partial Differential Equations

    SciTech Connect

    Sharp, D.H.; Habib, S.; Mineev, M.B.

    1999-07-08

    This is the final report of a Laboratory Directed Research and Development (LDRD) project at the Los Alamos National laboratory (LANL). The objectives of this proposal were (1) the development of methods for understanding and control of spacetime discretization errors in nonlinear stochastic partial differential equations, and (2) the development of new and improved practical numerical methods for the solutions of these equations. The authors have succeeded in establishing two methods for error control: the functional Fokker-Planck equation for calculating the time discretization error and the transfer integral method for calculating the spatial discretization error. In addition they have developed a new second-order stochastic algorithm for multiplicative noise applicable to the case of colored noises, and which requires only a single random sequence generation per time step. All of these results have been verified via high-resolution numerical simulations and have been successfully applied to physical test cases. They have also made substantial progress on a longstanding problem in the dynamics of unstable fluid interfaces in porous media. This work has lead to highly accurate quasi-analytic solutions of idealized versions of this problem. These may be of use in benchmarking numerical solutions of the full stochastic PDEs that govern real-world problems.

  3. Numerical methods used in fusion science numerical modeling

    NASA Astrophysics Data System (ADS)

    Yagi, M.

    2015-04-01

    The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.

  4. Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes

    NASA Technical Reports Server (NTRS)

    Abrams, D.; Williams, C.

    1999-01-01

    We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.

  5. RELAP-7 Numerical Stabilization: Entropy Viscosity Method

    SciTech Connect

    R. A. Berry; M. O. Delchini; J. Ragusa

    2014-06-01

    The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.

  6. Integrated optical circuits for numerical computation

    NASA Technical Reports Server (NTRS)

    Verber, C. M.; Kenan, R. P.

    1983-01-01

    The development of integrated optical circuits (IOC) for numerical-computation applications is reviewed, with a focus on the use of systolic architectures. The basic architecture criteria for optical processors are shown to be the same as those proposed by Kung (1982) for VLSI design, and the advantages of IOCs over bulk techniques are indicated. The operation and fabrication of electrooptic grating structures are outlined, and the application of IOCs of this type to an existing 32-bit, 32-Mbit/sec digital correlator, a proposed matrix multiplier, and a proposed pipeline processor for polynomial evaluation is discussed. The problems arising from the inherent nonlinearity of electrooptic gratings are considered. Diagrams and drawings of the application concepts are provided.

  7. Numerical evaluation of Feynman path integrals

    NASA Astrophysics Data System (ADS)

    Baird, William Hugh

    1999-11-01

    The notion of path integration developed by Feynman, while an incredibly successful method of solving quantum mechanical problems, leads to frequently intractable integrations over an infinite number of paths. Two methods now exist which sidestep this difficulty by defining "densities" of actions which give the relative number of paths found at different values of the action. These densities are sampled by computer generation of paths and the propagators are found to a high degree of accuracy for the case of a particle on the infinite half line and in a finite square well in one dimension. The problem of propagation within a two dimensional radial well is also addressed as the precursor to the problem of a particle in a stadium (quantum billiard).

  8. REVA DATA INTEGRATION METHODS

    EPA Science Inventory

    The core of the research effort in the Regional Vulnerability Assessment Program (ReVA) is a set of data integration methods ranging from simple overlays to complex multivariate statistics. These methods are described in the EPA publication titled, "Regional Vulnerability Assess...

  9. Numerical integration of ordinary differential equations on manifolds

    NASA Astrophysics Data System (ADS)

    Crouch, P. E.; Grossman, R.

    1993-12-01

    This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions” defined by nonvanishing Lie brackets.

  10. Stability of numerical integration techniques for transient rotor dynamics

    NASA Technical Reports Server (NTRS)

    Kascak, A. F.

    1977-01-01

    A finite element model of a rotor bearing system was analyzed to determine the stability limits of the forward, backward, and centered Euler; Runge-Kutta; Milne; and Adams numerical integration techniques. The analysis concludes that the highest frequency mode determines the maximum time step for a stable solution. Thus, the number of mass elements should be minimized. Increasing the damping can sometimes cause numerical instability. For a uniform shaft, with 10 mass elements, operating at approximately the first critical speed, the maximum time step for the Runge-Kutta, Milne, and Adams methods is that which corresponds to approximately 1 degree of shaft movement. This is independent of rotor dimensions.

  11. A Collocation Method for Volterra Integral Equations

    NASA Astrophysics Data System (ADS)

    Kolk, Marek

    2010-09-01

    We propose a piecewise polynomial collocation method for solving linear Volterra integral equations of the second kind with logarithmic kernels which, in addition to a diagonal singularity, may have a singularity at the initial point of the interval of integration. An attainable order of the convergence of the method is studied. We illustrate our results with a numerical example.

  12. Zero initial partial derivatives of satellite orbits with respect to force parameters nullify the mathematical basis of the numerical integration method for the determination of standard gravity models from space geodetic measurements

    NASA Astrophysics Data System (ADS)

    Xu, Peiliang

    2015-04-01

    Satellite orbits have been routinely used to produce models of the Earth's gravity field. The numerical integration method is most widely used by almost all major institutions to determine standard gravity models from space geodetic measurements. As a basic component of the method, the partial derivatives of a satellite orbit with respect to the force parameters to be determined, namely, the unknown harmonic coefficients of the gravitational model, have been first computed by setting the initial values of partial derivatives to zero. In this talk, we first design some simple mathematical examples to show that setting the initial values of partial derivatives to zero is generally erroneous mathematically. We then prove that it is prohibited physically. In other words, setting the initial values of partial derivatives to zero violates the physics of motion of celestial bodies. To conclude, the numerical integration method, as is widely used today by major institutions to produce standard satellite gravity models, is simply incorrect mathematically. As a direct consequence, further work is required to confirm whether the numerical integration method can still be used as a mathematical foundation to produce standard satellite gravity models. More details can be found in Xu (2009, Sci China Ser D-Earth Sci, 52, 562-566).

  13. Applying integrals of motion to the numerical solution of differential equations

    NASA Technical Reports Server (NTRS)

    Jezewski, D. J.

    1979-01-01

    A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

  14. Numerical modeling and environmental isotope methods in integrated mine-water management: a case study from the Witwatersrand basin, South Africa

    NASA Astrophysics Data System (ADS)

    Mengistu, Haile; Tessema, Abera; Abiye, Tamiru; Demlie, Molla; Lin, Haili

    2015-05-01

    Improved groundwater flow conceptualization was achieved using environmental stable isotope (ESI) and hydrochemical information to complete a numerical groundwater flow model with reasonable certainty. The study aimed to assess the source of excess water at a pumping shaft located near the town of Stilfontein, North West Province, South Africa. The results indicate that the water intercepted at Margaret Shaft comes largely from seepage of a nearby mine tailings dam (Dam 5) and from the upper dolomite aquifer. If pumping at the shaft continues at the current rate and Dam 5 is decommissioned, neighbouring shallow farm boreholes would dry up within approximately 10 years. Stable isotope data of shaft water indicate that up to 50 % of the pumped water from Margaret Shaft is recirculated, mainly from Dam 5. The results are supplemented by tritium data, demonstrating that recent recharge is taking place through open fractures as well as man-made underground workings, whereas hydrochemical data of fissure water samples from roughly 950 m below ground level exhibit mine-water signatures. Pumping at the shaft, which captures shallow groundwater as well as seepage from surface dams, is a highly recommended option for preventing flooding of downstream mines. The results of this research highlight the importance of additional methods (ESI and hydrochemical analyses) to improve flow conceptualization and numerical modelling.

  15. Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals

    NASA Technical Reports Server (NTRS)

    Fink, Patrick W.; Wilton, Donald R.; Khayat, Michael A.

    2007-01-01

    Recently, significant progress has been made in the handling of singular and nearly-singular potential integrals that commonly arise in the Boundary Element Method (BEM). To facilitate object-oriented programming and handling of higher order basis functions, cancellation techniques are favored over techniques involving singularity subtraction. However, gradients of the Newton-type potentials, which produce hypersingular kernels, are also frequently required in BEM formulations. As is the case with the potentials, treatment of the near-hypersingular integrals has proven more challenging than treating the limiting case in which the observation point approaches the surface. Historically, numerical evaluation of these near-hypersingularities has often involved a two-step procedure: a singularity subtraction to reduce the order of the singularity, followed by a boundary contour integral evaluation of the extracted part. Since this evaluation necessarily links basis function, Green s function, and the integration domain (element shape), the approach ill fits object-oriented programming concepts. Thus, there is a need for cancellation-type techniques for efficient numerical evaluation of the gradient of the potential. Progress in the development of efficient cancellation-type procedures for the gradient potentials was recently presented. To the extent possible, a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. However, since the gradient kernel involves singularities of different orders, we also require that the transformation leaves remaining terms that are analytic. The terms "normal" and "tangential" are used herein with reference to the source element. Also, since computational formulations often involve the numerical evaluation of both potentials and their gradients, it is highly desirable that a single integration procedure efficiently handles both.

  16. Error Estimates for Numerical Integration Rules

    ERIC Educational Resources Information Center

    Mercer, Peter R.

    2005-01-01

    The starting point for this discussion of error estimates is the fact that integrals that arise in Fourier series have properties that can be used to get improved bounds. This idea is extended to more general situations.

  17. Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics

    SciTech Connect

    Klein, R I; Stone, J M

    2007-11-20

    We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.

  18. The development of accurate and efficient methods of numerical quadrature

    NASA Technical Reports Server (NTRS)

    Feagin, T.

    1973-01-01

    Some new methods for performing numerical quadrature of an integrable function over a finite interval are described. Each method provides a sequence of approximations of increasing order to the value of the integral. Each approximation makes use of all previously computed values of the integrand. The points at which new values of the integrand are computed are selected in such a way that the order of the approximation is maximized. The methods are compared with the quadrature methods of Clenshaw and Curtis, Gauss, Patterson, and Romberg using several examples.

  19. Research on the Evolutionary Strategy Based on AIS and Its Application on Numerical Integration

    NASA Astrophysics Data System (ADS)

    Bei, Li

    Based on the features of artificial immune system, a new evolutionary strategy is proposed in order to calculate the numerical integration of functions. This evolutionary strategy includes the mechanisms of swarm searching and constructing the fitness function. Finally, numerical examples are given for verifying the effectiveness of evolutionary strategy. The results show that the performance of evolutionary strategy is satisfactory and more accurate than traditional methods of numerical integration, such as trapezoid formula and Simpson formula.

  20. Accelerated adaptive integration method.

    PubMed

    Kaus, Joseph W; Arrar, Mehrnoosh; McCammon, J Andrew

    2014-05-15

    Conformational changes that occur upon ligand binding may be too slow to observe on the time scales routinely accessible using molecular dynamics simulations. The adaptive integration method (AIM) leverages the notion that when a ligand is either fully coupled or decoupled, according to λ, barrier heights may change, making some conformational transitions more accessible at certain λ values. AIM adaptively changes the value of λ in a single simulation so that conformations sampled at one value of λ seed the conformational space sampled at another λ value. Adapting the value of λ throughout a simulation, however, does not resolve issues in sampling when barriers remain high regardless of the λ value. In this work, we introduce a new method, called Accelerated AIM (AcclAIM), in which the potential energy function is flattened at intermediate values of λ, promoting the exploration of conformational space as the ligand is decoupled from its receptor. We show, with both a simple model system (Bromocyclohexane) and the more complex biomolecule Thrombin, that AcclAIM is a promising approach to overcome high barriers in the calculation of free energies, without the need for any statistical reweighting or additional processors. PMID:24780083

  1. Accelerated Adaptive Integration Method

    PubMed Central

    2015-01-01

    Conformational changes that occur upon ligand binding may be too slow to observe on the time scales routinely accessible using molecular dynamics simulations. The adaptive integration method (AIM) leverages the notion that when a ligand is either fully coupled or decoupled, according to λ, barrier heights may change, making some conformational transitions more accessible at certain λ values. AIM adaptively changes the value of λ in a single simulation so that conformations sampled at one value of λ seed the conformational space sampled at another λ value. Adapting the value of λ throughout a simulation, however, does not resolve issues in sampling when barriers remain high regardless of the λ value. In this work, we introduce a new method, called Accelerated AIM (AcclAIM), in which the potential energy function is flattened at intermediate values of λ, promoting the exploration of conformational space as the ligand is decoupled from its receptor. We show, with both a simple model system (Bromocyclohexane) and the more complex biomolecule Thrombin, that AcclAIM is a promising approach to overcome high barriers in the calculation of free energies, without the need for any statistical reweighting or additional processors. PMID:24780083

  2. A numerical method of detecting singularity

    NASA Technical Reports Server (NTRS)

    Laporte, M.; Vignes, J.

    1978-01-01

    A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.

  3. A numerical method for predicting hypersonic flowfields

    NASA Technical Reports Server (NTRS)

    Maccormack, Robert W.; Candler, Graham V.

    1989-01-01

    The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.

  4. Numerical simulation of scattering of acoustic waves by inelastic bodies using hypersingular boundary integral equation

    SciTech Connect

    Daeva, S.G.; Setukha, A.V.

    2015-03-10

    A numerical method for solving a problem of diffraction of acoustic waves by system of solid and thin objects based on the reduction the problem to a boundary integral equation in which the integral is understood in the sense of finite Hadamard value is proposed. To solve this equation we applied piecewise constant approximations and collocation methods numerical scheme. The difference between the constructed scheme and earlier known is in obtaining approximate analytical expressions to appearing system of linear equations coefficients by separating the main part of the kernel integral operator. The proposed numerical scheme is tested on the solution of the model problem of diffraction of an acoustic wave by inelastic sphere.

  5. Integral Deferred Correction methods for scientific computing

    NASA Astrophysics Data System (ADS)

    Morton, Maureen Marilla

    Since high order numerical methods frequently can attain accurate solutions more efficiently than low order methods, we develop and analyze new high order numerical integrators for the time discretization of ordinary and partial differential equations. Our novel methods address some of the issues surrounding high order numerical time integration, such as the difficulty of many popular methods' construction and handling the effects of disparate behaviors produce by different terms in the equations to be solved. We are motivated by the simplicity of how Deferred Correction (DC) methods achieve high order accuracy [72, 27]. DC methods are numerical time integrators that, rather than calculating tedious coefficients for order conditions, instead construct high order accurate solutions by iteratively improving a low order preliminary numerical solution. With each iteration, an error equation is solved, the error decreases, and the order of accuracy increases. Later, DC methods were adjusted to include an integral formulation of the residual, which stabilizes the method. These Spectral Deferred Correction (SDC) methods [25] motivated Integral Deferred Corrections (IDC) methods. Typically, SDC methods are limited to increasing the order of accuracy by one with each iteration due to smoothness properties imposed by the gridspacing. However, under mild assumptions, explicit IDC methods allow for any explicit rth order Runge-Kutta (RK) method to be used within each iteration, and then an order of accuracy increase of r is attained after each iteration [18]. We extend these results to the construction of implicit IDC methods that use implicit RK methods, and we prove analogous results for order of convergence. One means of solving equations with disparate parts is by semi-implicit integrators, handling a "fast" part implicitly and a "slow" part explicitly. We incorporate additive RK (ARK) integrators into the iterations of IDC methods in order to construct new arbitrary order

  6. 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.

  7. Numerical methods for supersonic astrophysical jets

    NASA Astrophysics Data System (ADS)

    Ha, Youngsoo

    2003-09-01

    The Euler equations of gas dynamics are used for the simulation of general astrophysical fluid flows including high Mach number astrophysical jets with radiative cooling. To accurately compute supersonic jet solutions with sharp resolution of shock waves, three modern numerical methods for gas dynamics were used: (1)a second-order Godunov method in LeVeque's software package CLAWPACK, (2)the Nessyahu-Tadmor-Kurganov (NTK) central hyperbolic scheme, and (3)the WENO-LF (Weighted Essentially Non-Oscillatory Lax-Friedrichs) scheme. Then simulations of supersonic astrophysical jets were compared, first without and then with radiative cooling. CLAWPACK consists of routines for solving time-dependent nonlinear hyperbolic conservation laws based on higher order Godunov methods and approximate Riemann problem solutions; the NTK scheme solves conservation laws using a modified Lax-Friedrichs central difference method without appealing to Riemann problem solutions; and the WENO-LF finite difference scheme is based on the Essentially Non-Oscillatory (ENO) idea by using Lax- Friedrichs flux splitting. The ENO method constructs a solution using the smoothness of the interpolating polynomial on given stencils; on the other hand, the WENO scheme uses a convex combination of the interpolate functions on all candidate stencils. The third-order and fifth-order WENO-LF methods were used to simulate the high Mach number jets. Appropriate numerical methods for incorporating radiative cooling in these numerical methods are also discussed. Interactions of supersonic jets with their environments (jet-“blob” interactions) are shown after modifying the codes to handle high Mach numbers and radiative cooling.

  8. Hyperbolic conservation laws and numerical methods

    NASA Technical Reports Server (NTRS)

    Leveque, Randall J.

    1990-01-01

    The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.

  9. Numerical methods for molecular dynamics. Progress report

    SciTech Connect

    Skeel, R.D.

    1991-12-31

    This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.

  10. Construction of the two-electron contribution to the Fock matrix by numerical integration

    NASA Astrophysics Data System (ADS)

    Losilla, Sergio A.; Mehine, Mooses M.; Sundholm, Dage

    2012-10-01

    A novel method to numerically calculate the Fock matrix is presented. The Coulomb operator is re-expressed as an integral identity, which is discretized. The discretization of the auxiliary t dimension separates the x, y, and z dependencies transforming the two-electron Coulomb integrals of Gaussian-type orbitals (GTO) to a linear sum of products of two-dimensional integrals. The s-type integrals are calculated analytically and integrals of the higher angular-momentum functions are obtained using recursion formulae. The contributions to the two-body Coulomb integrals obtained for each discrete t value can be evaluated independently. The two-body Fock matrix elements can be integrated numerically, using common sets of quadrature points and weights. The aim is to calculate Fock matrices of enough accuracy for electronic structure calculations. Preliminary calculations indicate that it is possible to achieve an overall accuracy of at least 10-12 E h using the numerical approach.

  11. Numerical analysis method for linear induction machines.

    NASA Technical Reports Server (NTRS)

    Elliott, D. G.

    1972-01-01

    A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.

  12. Numerical methods for finding stationary gravitational solutions

    NASA Astrophysics Data System (ADS)

    Dias, Óscar J. C.; Santos, Jorge E.; Way, Benson

    2016-07-01

    The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory–Laflamme zero modes of small rotating black holes in AdS{}5× {S}5. We also include several tools and tricks that have been useful throughout the literature.

  13. Numerical solution of a class of integral equations arising in two-dimensional aerodynamics

    NASA Technical Reports Server (NTRS)

    Fromme, J.; Golberg, M. A.

    1978-01-01

    We consider the numerical solution of a class of integral equations arising in the determination of the compressible flow about a thin airfoil in a ventilated wind tunnel. The integral equations are of the first kind with kernels having a Cauchy singularity. Using appropriately chosen Hilbert spaces, it is shown that the kernel gives rise to a mapping which is the sum of a unitary operator and a compact operator. This allows the problem to be studied in terms of an equivalent integral equation of the second kind. A convergent numerical algorithm for its solution is derived by using Galerkin's method. It is shown that this algorithm is numerically equivalent to Bland's collocation method, which is then used as the method of computation. Extensive numerical calculations are presented establishing the validity of the theory.

  14. Application of numerical methods to elasticity imaging.

    PubMed

    Castaneda, Benjamin; Ormachea, Juvenal; Rodríguez, Paul; Parker, Kevin J

    2013-03-01

    Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity. PMID:24010245

  15. Mathematica with a Numerical Methods Course

    NASA Astrophysics Data System (ADS)

    Varley, Rodney

    2003-04-01

    An interdisciplinary "Numerical Methods" course has been shared between physics, mathematics and computer science since 1992 at Hunter C. Recently, the lectures and workshops for this course have become formalized and placed on the internet at http://www.ph.hunter.cuny.edu (follow the links "Course Listings and Websites" >> "PHYS385 (Numerical Methods)". Mathematica notebooks for the lectures are available for automatic download (by "double clicking" the lecture icon) for student use in the classroom or at home. AOL (or Netscape/Explorer) can be used provided Mathematica (or the "free" MathReader) has been made a "helper application". Using Mathematica has the virtue that mathematical equations (no LaTex required) can easily be included with the text and Mathematica's graphing is easy to use. Computational cells can be included within the notebook and students may easily modify the calculation to see the result of "what if..." questions. Homework is sent as Mathematica notebooks to the instructor via the internet and the corrected workshops are returned in the same manner. Most exam questions require computational solutions.

  16. A numerical method for interface problems in elastodynamics

    NASA Technical Reports Server (NTRS)

    Mcghee, D. S.

    1984-01-01

    The numerical implementation of a formulation for a class of interface problems in elastodynamics is discussed. This formulation combines the use of the finite element and boundary integral methods to represent the interior and the exteriro regions, respectively. In particular, the response of a semicylindrical alluvial valley in a homogeneous halfspace to incident antiplane SH waves is considered to determine the accuracy and convergence of the numerical procedure. Numerical results are obtained from several combinations of the incidence angle, frequency of excitation, and relative stiffness between the inclusion and the surrounding halfspace. The results tend to confirm the theoretical estimates that the convergence is of the order H(2) for the piecewise linear elements used. It was also observed that the accuracy descreases as the frequency of excitation increases or as the relative stiffness of the inclusion decreases.

  17. Integrated product definition representation for agile numerical control applications

    SciTech Connect

    Simons, W.R. Jr.; Brooks, S.L.; Kirk, W.J. III; Brown, C.W.

    1994-11-01

    Realization of agile manufacturing capabilities for a virtual enterprise requires the integration of technology, management, and work force into a coordinated, interdependent system. This paper is focused on technology enabling tools for agile manufacturing within a virtual enterprise specifically relating to Numerical Control (N/C) manufacturing activities and product definition requirements for these activities.

  18. Monograph - The Numerical Integration of Ordinary Differential Equations.

    ERIC Educational Resources Information Center

    Hull, T. E.

    The materials presented in this monograph are intended to be included in a course on ordinary differential equations at the upper division level in a college mathematics program. These materials provide an introduction to the numerical integration of ordinary differential equations, and they can be used to supplement a regular text on this…

  19. Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems

    SciTech Connect

    Cai, Wei

    2014-05-15

    Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equations such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.

  20. Numerical methods for problems in computational aeroacoustics

    NASA Astrophysics Data System (ADS)

    Mead, Jodi Lorraine

    1998-12-01

    A goal of computational aeroacoustics is the accurate calculation of noise from a jet in the far field. This work concerns the numerical aspects of accurately calculating acoustic waves over large distances and long time. More specifically, the stability, efficiency, accuracy, dispersion and dissipation in spatial discretizations, time stepping schemes, and absorbing boundaries for the direct solution of wave propagation problems are determined. Efficient finite difference methods developed by Tam and Webb, which minimize dispersion and dissipation, are commonly used for the spatial and temporal discretization. Alternatively, high order pseudospectral methods can be made more efficient by using the grid transformation introduced by Kosloff and Tal-Ezer. Work in this dissertation confirms that the grid transformation introduced by Kosloff and Tal-Ezer is not spectrally accurate because, in the limit, the grid transformation forces zero derivatives at the boundaries. If a small number of grid points are used, it is shown that approximations with the Chebyshev pseudospectral method with the Kosloff and Tal-Ezer grid transformation are as accurate as with the Chebyshev pseudospectral method. This result is based on the analysis of the phase and amplitude errors of these methods, and their use for the solution of a benchmark problem in computational aeroacoustics. For the grid transformed Chebyshev method with a small number of grid points it is, however, more appropriate to compare its accuracy with that of high- order finite difference methods. This comparison, for an order of accuracy 10-3 for a benchmark problem in computational aeroacoustics, is performed for the grid transformed Chebyshev method and the fourth order finite difference method of Tam. Solutions with the finite difference method are as accurate. and the finite difference method is more efficient than, the Chebyshev pseudospectral method with the grid transformation. The efficiency of the Chebyshev

  1. Numerical methods for scattering from electrically large objects

    NASA Astrophysics Data System (ADS)

    Enguist, Bjorn; Murphy, W. D.; Rokhlin, Vladimir; Vassiliou, Marius S.

    1991-05-01

    A new and computationally very efficient integral equation numerical method for computing electromagnetic scattering and radar cross section (RCS) was developed. A theory of higher order impedance boundary conditions was derived to handle single and multiple dielectric coatings around conductors. The method was tested in two dimensions using a 14,000-line FORTRAN program and was found to be very promising for electrically large objects. Initial ideas for extensions to three dimensions were explored. Treatments of trailing edge and corner singularities were developed.

  2. Technical Report: Scalable Parallel Algorithms for High Dimensional Numerical Integration

    SciTech Connect

    Masalma, Yahya; Jiao, Yu

    2010-10-01

    We implemented a scalable parallel quasi-Monte Carlo numerical high-dimensional integration for tera-scale data points. The implemented algorithm uses the Sobol s quasi-sequences to generate random samples. Sobol s sequence was used to avoid clustering effects in the generated random samples and to produce low-discrepancy random samples which cover the entire integration domain. The performance of the algorithm was tested. Obtained results prove the scalability and accuracy of the implemented algorithms. The implemented algorithm could be used in different applications where a huge data volume is generated and numerical integration is required. We suggest using the hyprid MPI and OpenMP programming model to improve the performance of the algorithms. If the mixed model is used, attention should be paid to the scalability and accuracy.

  3. Controlled time integration for the numerical simulation of meteor radar reflections

    NASA Astrophysics Data System (ADS)

    Räbinä, Jukka; Mönkölä, Sanna; Rossi, Tuomo; Markkanen, Johannes; Gritsevich, Maria; Muinonen, Karri

    2016-07-01

    We model meteoroids entering the Earth's atmosphere as objects surrounded by non-magnetized plasma, and consider efficient numerical simulation of radar reflections from meteors in the time domain. Instead of the widely used finite difference time domain method (FDTD), we use more generalized finite differences by applying the discrete exterior calculus (DEC) and non-uniform leapfrog-style time discretization. The computational domain is presented by convex polyhedral elements. The convergence of the time integration is accelerated by the exact controllability method. The numerical experiments show that our code is efficiently parallelized. The DEC approach is compared to the volume integral equation (VIE) method by numerical experiments. The result is that both methods are competitive in modelling non-magnetized plasma scattering. For demonstrating the simulation capabilities of the DEC approach, we present numerical experiments of radar reflections and vary parameters in a wide range.

  4. Numerical Method for the Astronomical Almanac and Orbit Calculations

    NASA Astrophysics Data System (ADS)

    Kim, Kap-Sung

    1993-12-01

    We have calculated the astronomical almanac 1994 and simulated the trajectory of a satellite orbit considering all perturbative forces with various initial conditions. In this work, Gauss Jackson multistep integration method has been used to calculate our basic equation of motion with high numerical accuracy. It has been found that our results agree well with the Astronomical Almanac Data distributed by JPL of NASA and the orbit simulations have been carried out with fast speed, stability and excellent round-off error accumulation, comparing with other numerical methods. In order to be carried out our works on almanac and orbit calculations easily by anyone who uses a personal computer, we have made a computer program on graphical user interface to provide various menus for detail works selected by a mouse.

  5. Numerical evaluation of electron repulsion integrals for pseudoatomic orbitals and their derivatives.

    PubMed

    Toyoda, Masayuki; Ozaki, Taisuke

    2009-03-28

    A numerical method to calculate the four-center electron-repulsion integrals for strictly localized pseudoatomic orbital basis sets has been developed. Compared to the conventional Gaussian expansion method, this method has an advantage in the ease of combination with O(N) density functional calculations. Additional mathematical derivations are also presented including the analytic derivatives of the integrals with respect to atomic positions and spatial damping of the Coulomb interaction due to the screening effect. In the numerical test for a simple molecule, the convergence up to 10(-5) hartree in energy is successfully obtained with a feasible cost of computation. PMID:19334815

  6. Ensemble-type numerical uncertainty information from single model integrations

    SciTech Connect

    Rauser, Florian Marotzke, Jochem; Korn, Peter

    2015-07-01

    We suggest an algorithm that quantifies the discretization error of time-dependent physical quantities of interest (goals) for numerical models of geophysical fluid dynamics. The goal discretization error is estimated using a sum of weighted local discretization errors. The key feature of our algorithm is that these local discretization errors are interpreted as realizations of a random process. The random process is determined by the model and the flow state. From a class of local error random processes we select a suitable specific random process by integrating the model over a short time interval at different resolutions. The weights of the influences of the local discretization errors on the goal are modeled as goal sensitivities, which are calculated via automatic differentiation. The integration of the weighted realizations of local error random processes yields a posterior ensemble of goal approximations from a single run of the numerical model. From the posterior ensemble we derive the uncertainty information of the goal discretization error. This algorithm bypasses the requirement of detailed knowledge about the models discretization to generate numerical error estimates. The algorithm is evaluated for the spherical shallow-water equations. For two standard test cases we successfully estimate the error of regional potential energy, track its evolution, and compare it to standard ensemble techniques. The posterior ensemble shares linear-error-growth properties with ensembles of multiple model integrations when comparably perturbed. The posterior ensemble numerical error estimates are of comparable size as those of a stochastic physics ensemble.

  7. A Hybrid Numerical Analysis Method for Structural Health Monitoring

    NASA Technical Reports Server (NTRS)

    Forth, Scott C.; Staroselsky, Alexander

    2001-01-01

    A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

  8. COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE

    SciTech Connect

    Kritsuk, Alexei G.; Collins, David; Norman, Michael L.; Xu Hao E-mail: dccollins@lanl.gov

    2011-08-10

    Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the

  9. Fast integral methods for integrated optical systems simulations: a review

    NASA Astrophysics Data System (ADS)

    Kleemann, Bernd H.

    2015-09-01

    Boundary integral equation methods (BIM) or simply integral methods (IM) in the context of optical design and simulation are rigorous electromagnetic methods solving Helmholtz or Maxwell equations on the boundary (surface or interface of the structures between two materials) for scattering or/and diffraction purposes. This work is mainly restricted to integral methods for diffracting structures such as gratings, kinoforms, diffractive optical elements (DOEs), micro Fresnel lenses, computer generated holograms (CGHs), holographic or digital phase holograms, periodic lithographic structures, and the like. In most cases all of the mentioned structures have dimensions of thousands of wavelengths in diameter. Therefore, the basic methods necessary for the numerical treatment are locally applied electromagnetic grating diffraction algorithms. Interestingly, integral methods belong to the first electromagnetic methods investigated for grating diffraction. The development started in the mid 1960ies for gratings with infinite conductivity and it was mainly due to the good convergence of the integral methods especially for TM polarization. The first integral equation methods (IEM) for finite conductivity were the methods by D. Maystre at Fresnel Institute in Marseille: in 1972/74 for dielectric, and metallic gratings, and later for multiprofile, and other types of gratings and for photonic crystals. Other methods such as differential and modal methods suffered from unstable behaviour and slow convergence compared to BIMs for metallic gratings in TM polarization from the beginning to the mid 1990ies. The first BIM for gratings using a parametrization of the profile was developed at Karl-Weierstrass Institute in Berlin under a contract with Carl Zeiss Jena works in 1984-1986 by A. Pomp, J. Creutziger, and the author. Due to the parametrization, this method was able to deal with any kind of surface grating from the beginning: whether profiles with edges, overhanging non

  10. Numerical computation of 2D Sommerfeld integrals - Decomposition of the angular integral

    NASA Astrophysics Data System (ADS)

    Dvorak, Steven L.; Kuester, Edward F.

    1992-02-01

    The computational efficiency of the 2D Sommerfeld integrals is shown to undergo improvement through the discovery of novel ways to compute the inner angular integral in polar representations. It is shown that the angular integral can be decomposed into a finite number of incomplete Lipschitz-Hankel integrals; these can in turn be calculated through a series of expansions, so that the angular integral can be computed by summing a series rather than applying a standard numerical integration algorithm. The technique is most efficient and accurate when piecewise-sinusoidal basis functions are employed to analyze a printed strip-dipole antenna in a layered medium.

  11. On the stability of numerical integration routines for ordinary differential equations.

    NASA Technical Reports Server (NTRS)

    Glover, K.; Willems, J. C.

    1973-01-01

    Numerical integration methods for the solution of initial value problems for ordinary vector differential equations may be modelled as discrete time feedback systems. The stability criteria discovered in modern control theory are applied to these systems and criteria involving the routine, the step size and the differential equation are derived. Linear multistep, Runge-Kutta, and predictor-corrector methods are all investigated.

  12. Integrated numeric and symbolic signal processing using a heterogeneous design environment

    NASA Astrophysics Data System (ADS)

    Mani, Ramamurthy; Nawab, S. Hamid; Winograd, Joseph M.; Evans, Brian L.

    1996-10-01

    We present a solution to a complex multi-tone transient detection problem to illustrate the integrated use of symbolic and numeric processing techniques which are supported by well-established underlying models. Examples of such models include synchronous dataflow for numeric processing and the blackboard paradigm for symbolic heuristic search. Our transient detection solution serves to emphasize the importance of developing system design methods and tools which can support the integrated use of well- established symbolic and numerical models of computation. Recently, we incorporated a blackboard-based model of computation underlying the Integrated Processing and Understanding of Signals (IPUS) paradigm into a system-level design environment for numeric processing called Ptolemy. Using the IPUS/Ptolemy environment, we are implementing our solution to the multi-tone transient detection problem.

  13. Asymptotic and Numerical Methods for Rapidly Rotating Buoyant Flow

    NASA Astrophysics Data System (ADS)

    Grooms, Ian G.

    This thesis documents three investigations carried out in pursuance of a doctoral degree in applied mathematics at the University of Colorado (Boulder). The first investigation concerns the properties of rotating Rayleigh-Benard convection -- thermal convection in a rotating infinite plane layer between two constant-temperature boundaries. It is noted that in certain parameter regimes convective Taylor columns appear which dominate the dynamics, and a semi-analytical model of these is presented. Investigation of the columns and of various other properties of the flow is ongoing. The second investigation concerns the interactions between planetary-scale and mesoscale dynamics in the oceans. Using multiple-scale asymptotics the possible connections between planetary geostrophic and quasigeostrophic dynamics are investigated, and three different systems of coupled equations are derived. Possible use of these equations in conjunction with the method of superparameterization, and extension of the asymptotic methods to the interactions between mesoscale and submesoscale dynamics is ongoing. The third investigation concerns the linear stability properties of semi-implicit methods for the numerical integration of ordinary differential equations, focusing in particular on the linear stability of IMEX (Implicit-Explicit) methods and exponential integrators applied to systems of ordinary differential equations arising in the numerical solution of spatially discretized nonlinear partial differential equations containing both dispersive and dissipative linear terms. While these investigations may seem unrelated at first glance, some reflection shows that they are in fact closely linked. The investigation of rotating convection makes use of single-space, multiple-time-scale asymptotics to deal with dynamics strongly constrained by rotation. Although the context of thermal convection in an infinite layer seems somewhat removed from large-scale ocean dynamics, the asymptotic

  14. Efficient integration method for fictitious domain approaches

    NASA Astrophysics Data System (ADS)

    Duczek, Sascha; Gabbert, Ulrich

    2015-10-01

    In the current article, we present an efficient and accurate numerical method for the integration of the system matrices in fictitious domain approaches such as the finite cell method (FCM). In the framework of the FCM, the physical domain is embedded in a geometrically larger domain of simple shape which is discretized using a regular Cartesian grid of cells. Therefore, a spacetree-based adaptive quadrature technique is normally deployed to resolve the geometry of the structure. Depending on the complexity of the structure under investigation this method accounts for most of the computational effort. To reduce the computational costs for computing the system matrices an efficient quadrature scheme based on the divergence theorem (Gauß-Ostrogradsky theorem) is proposed. Using this theorem the dimension of the integral is reduced by one, i.e. instead of solving the integral for the whole domain only its contour needs to be considered. In the current paper, we present the general principles of the integration method and its implementation. The results to several two-dimensional benchmark problems highlight its properties. The efficiency of the proposed method is compared to conventional spacetree-based integration techniques.

  15. Numerical methods for analyzing electromagnetic scattering

    NASA Technical Reports Server (NTRS)

    Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.

    1985-01-01

    Numerical methods to analyze electromagnetic scattering are presented. The dispersions and attenuations of the normal modes in a circular waveguide coated with lossy material were completely analyzed. The radar cross section (RCS) from a circular waveguide coated with lossy material was calculated. The following is observed: (1) the interior irradiation contributes to the RCS much more than does the rim diffraction; (2) at low frequency, the RCS from the circular waveguide terminated by a perfect electric conductor (PEC) can be reduced more than 13 dB down with a coating thickness less than 1% of the radius using the best lossy material available in a 6 radius-long cylinder; (3) at high frequency, a modal separation between the highly attenuated and the lowly attenuated modes is evident if the coating material is too lossy, however, a large RCS reduction can be achieved for a small incident angle with a thin layer of coating. It is found that the waveguide coated with a lossy magnetic material can be used as a substitute for a corrugated waveguide to produce a circularly polarized radiation yield.

  16. A numerical method for cardiac mechanoelectric simulations.

    PubMed

    Pathmanathan, Pras; Whiteley, Jonathan P

    2009-05-01

    Much effort has been devoted to developing numerical techniques for solving the equations that describe cardiac electrophysiology, namely the monodomain equations and bidomain equations. Only a limited selection of publications, however, address the development of numerical techniques for mechanoelectric simulations where cardiac electrophysiology is coupled with deformation of cardiac tissue. One problem commonly encountered in mechanoelectric simulations is instability of the coupled numerical scheme. In this study, we develop a stable numerical scheme for mechanoelectric simulations. A number of convergence tests are carried out using this stable technique for simulations where deformations are of the magnitude typically observed in a beating heart. These convergence tests demonstrate that accurate computation of tissue deformation requires a nodal spacing of around 1 mm in the mesh used to calculate tissue deformation. This is a much finer computational grid than has previously been acknowledged, and has implications for the computational efficiency of the resulting numerical scheme. PMID:19263223

  17. Numerical integration of the stochastic Landau-Lifshitz-Gilbert equation in generic time-discretization schemes.

    PubMed

    Romá, Federico; Cugliandolo, Leticia F; Lozano, Gustavo S

    2014-08-01

    We introduce a numerical method to integrate the stochastic Landau-Lifshitz-Gilbert equation in spherical coordinates for generic discretization schemes. This method conserves the magnetization modulus and ensures the approach to equilibrium under the expected conditions. We test the algorithm on a benchmark problem: the dynamics of a uniformly magnetized ellipsoid. We investigate the influence of various parameters, and in particular, we analyze the efficiency of the numerical integration, in terms of the number of steps needed to reach a chosen long time with a given accuracy. PMID:25215839

  18. Integration methods for molecular dynamics

    SciTech Connect

    Leimkuhler, B.J.; Reich, S.; Skeel, R.D.

    1996-12-31

    Classical molecular dynamics simulation of a macromolecule requires the use of an efficient time-stepping scheme that can faithfully approximate the dynamics over many thousands of timesteps. Because these problems are highly nonlinear, accurate approximation of a particular solution trajectory on meaningful time intervals is neither obtainable nor desired, but some restrictions, such as symplecticness, can be imposed on the discretization which tend to imply good long term behavior. The presence of a variety of types and strengths of interatom potentials in standard molecular models places severe restrictions on the timestep for numerical integration used in explicit integration schemes, so much recent research has concentrated on the search for alternatives that possess (1) proper dynamical properties, and (2) a relative insensitivity to the fastest components of the dynamics. We survey several recent approaches. 48 refs., 2 figs.

  19. Time-dependent corona models - A numerical method

    NASA Astrophysics Data System (ADS)

    Korevaar, P.; van Leer, B.

    1988-07-01

    A time-dependent numerical method for calculating gas flows is described. The method is implicit and especially suitable for finding stationary flow solutions. Although the method is general in its application to ideal compressible fluids, this paper applies it to a stellar atmosphere, heated to coronal temperatures by dissipation of mechanical energy. The integration scheme is based on conservative upwind spatial differencing. The upwind switching is provided by Van Leer's method of differentiable flux-splitting. It is shown that the code can handle large differences in density: up to 14 orders of magnitude. Special attention is paid to the boundary conditions, which are made completely transparent to disturbances. Besides some test-results, converged solutions for various values of the initial mechanical flux are presented which are in good agreement with previous time-independent calculations.

  20. Numerical integration of discontinuities on arbitrary domains based on moment fitting

    NASA Astrophysics Data System (ADS)

    Joulaian, Meysam; Hubrich, Simeon; Düster, Alexander

    2016-03-01

    Discretization methods based on meshes that do not conform to the geometry of the problem under consideration require special treatment when it comes to the integration of finite elements that are broken by the boundary or internal interfaces. To this end, we propose a numerical approach suitable for integrating broken elements with a low number of integration points. In this method, which is based on the moment fitting approach, an individual quadrature rule is set up for each cut element. The approach requires a B-rep representation of the broken element, which can be either achieved by processing a triangulated surface obtained from a CAD software or by taking advantage of a voxel model resulting from computed tomography. The numerical examples presented in this paper reveal that the proposed method delivers for a wide variety of geometrical situations very accurate results and requires a rather low number of integration points.

  1. Numerical integration of discontinuities on arbitrary domains based on moment fitting

    NASA Astrophysics Data System (ADS)

    Joulaian, Meysam; Hubrich, Simeon; Düster, Alexander

    2016-06-01

    Discretization methods based on meshes that do not conform to the geometry of the problem under consideration require special treatment when it comes to the integration of finite elements that are broken by the boundary or internal interfaces. To this end, we propose a numerical approach suitable for integrating broken elements with a low number of integration points. In this method, which is based on the moment fitting approach, an individual quadrature rule is set up for each cut element. The approach requires a B-rep representation of the broken element, which can be either achieved by processing a triangulated surface obtained from a CAD software or by taking advantage of a voxel model resulting from computed tomography. The numerical examples presented in this paper reveal that the proposed method delivers for a wide variety of geometrical situations very accurate results and requires a rather low number of integration points.

  2. [Numerical methods for multi-fluid flows]. Final progress report

    SciTech Connect

    Pozrikidis, C.

    1998-07-21

    The central objective of this research has been to develop efficient numerical methods for computing multi-fluid flows with large interfacial deformations, and apply these methods to study the rheology of suspensions of deformable particles with viscous and non-Newtonian interfacial behavior. The mathematical formulation employs boundary-integral, immersed-boundary, and related numerical methods. Particles of interest include liquid drops with constant surface tension and capsules whose interfaces exhibit viscoelastic and incompressible characteristics. In one family of problems, the author has considered the shear-driven and pressure-driven flow of a suspension of two-dimensional liquid drops with ordered and random structure. In a second series of investigations, the author carried out dynamic simulations of two-dimensional, unbounded, doubly-periodic shear flows with random structure. Another family of problems addresses the deformation of three-dimensional capsules whose interfaces exhibit isotropic surface tension, viscous, elastic, or incompressible behavior, in simple shear flow. The numerical results extend previous asymptotic theories for small deformations and illuminate the mechanism of membrane rupture.

  3. The instanton method and its numerical implementation in fluid mechanics

    NASA Astrophysics Data System (ADS)

    Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

    2015-08-01

    A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.

  4. Integrating Numerical Groundwater Modeling Results With Geographic Information Systems

    NASA Astrophysics Data System (ADS)

    Witkowski, M. S.; Robinson, B. A.; Linger, S. P.

    2001-12-01

    Many different types of data are used to create numerical models of flow and transport of groundwater in the vadose zone. Results from water balance studies, infiltration models, hydrologic properties, and digital elevation models (DEMs) are examples of such data. Because input data comes in a variety of formats, for consistency the data need to be assembled in a coherent fashion on a single platform. Through the use of a geographic information system (GIS), all data sources can effectively be integrated on one platform to store, retrieve, query, and display data. In our vadoze zone modeling studies in support of Los Alamos National Laboratory's Environmental Restoration Project, we employ a GIS comprised of a Raid storage device, an Oracle database, ESRI's spatial database engine (SDE), ArcView GIS, and custom GIS tools for three-dimensional (3D) analysis. We store traditional GIS data, such as, contours, historical building footprints, and study area locations, as points, lines, and polygons with attributes. Numerical flow and transport model results from the Finite Element Heat and Mass Transfer Code (FEHM) are stored as points with attributes, such as fluid saturation, or pressure, or contaminant concentration at a given location. We overlay traditional types of GIS data with numerical model results, thereby allowing us to better build conceptual models and perform spatial analyses. We have also developed specialized analysis tools to assist in the data and model analysis process. This approach provides an integrated framework for performing tasks such as comparing the model to data and understanding the relationship of model predictions to existing contaminant source locations and water supply wells. Our process of integrating GIS and numerical modeling results allows us to answer a wide variety of questions about our conceptual model design: - Which set of locations should be identified as contaminant sources based on known historical building operations

  5. Comparison of integrated numerical experiments with accelerator and FEL experiments

    SciTech Connect

    Thode, L.E.; Carlsten, B.E.; Chan, K.C.D.; Cooper, R.K.; Elliott, J.C.; Gitomer, S.J.; Goldstein, J.C.; Jones, M.E.; McVey, B.D.; Schmitt, M.J.; Takeda, H.; Tokar, R.L.; Wang, T.S.; Young, L.M.

    1991-01-01

    Even at the conceptual level the strong coupling between the laser subsystem elements, such as the accelerator, wiggler, optics, and control, greatly complicates the understanding and design of an FEL. Given the requirements for a high-performance FEL, the coupling between the laser subsystems must be included in the design approach. To address the subsystem coupling the concept of an integrated numerical experiment (INEX) has been implemented. Unique features of the INEX approach are consistency and numerical equivalence of experimental diagnostic. The equivalent numerical diagnostics mitigates the major problem of misinterpretation that often occurs when theoretical and experimental data are compared. A complete INEX model has been applied to the 10{mu}m high-extraction-efficiency experiment at Los Alamos and the 0.6-{mu}m Burst Mode experiment at Boeing Aerospace. In addition, various subsets of the INEX model have been compared with a number of other experiments. Overall, the agreement between INEX and the experiments is very good. With the INEX approach, it now appears possible to design high-performance FELS for numerous applications. The first full-scale test of the INEX approach is the Los Alamos HIBAF experiment. The INEX concept, implementation, and validation with experiments are discussed. 28 refs., 13 figs., 1 tab.

  6. INEX (integrated numerical experiment) simulations of the Boeing FEL system

    SciTech Connect

    Tokar, R.L.; Young, L.M.; Lumpkin, A.H.; McVey, B.D.; Thode, L.E.; Bender, S.C.; Chan, K.C.D. ); Yeremian, A.D.; Dowell, D.H.; Lowrey, A.R. )

    1989-01-01

    The INEX (integrated numerical experiment) numerical model is applied to the 0.6 {mu}m FEL oscillator at Boeing Aerospace and Electronics Company in Seattle, WA. This system consists of a 110 MeV L-band rf linac, a beam transport line from the accelerator to the entrance of the wiggler, the 5.0 meter THUNDER variable taper wiggler, and a near concentric two mirror optical oscillator. Many aspects of the model for the electron beam accelerator and transport line agree with experimental measurements. Predictions for lasing performance are compared with data obtained in May and June 1989 using a mild tapered wiggler. We obtain good agreement with the achieved extraction efficiency, while 1D pulse simulations reproduce the observed sideband instability. 15 refs., 11 figs.

  7. Numerical methods for determining interstitial oxygen in silicon

    SciTech Connect

    Stevenson, J.O.; Medernach, J.W.

    1995-01-01

    The interstitial oxygen (O{sub i}) concentration in Czochralski silicon and the subsequent SiO{sub x} precipitation are important parameters for integrated circuit fabrication. Uncontrolled SiO{sub x} precipitation during processing can create detrimental mechanical and electrical effects that contribute to poor performance. An inability to consistently and accurately measure the initial O{sub i} concentration in heavily doped silicon has led to contradictory results regarding the effects of dopant type and concentration on SiO{sub x} precipitation. The authors have developed a software package for reliably determining and comparing O{sub i} in heavily doped silicon. The SiFTIR{copyright} code implements three independent oxygen analysis methods in a single integrated package. Routine oxygen measurements are desirable over a wide range of silicon resistivities, but there has been confusion concerning which of the three numerical methods is most suitable for the low resistivity portion of the continuum. A major strength of the software is an ability to rapidly produce results for all three methods using only a single Fourier Transform Infrared Spectroscopy (FTIR) spectrum as input. This ability to perform three analyses on a single data set allows a detailed comparison of the three methods across the entire range of resistivities in question. Integrated circuit manufacturers could use the enabling technology provided by SiFTIR{copyright} to monitor O{sub i} content. Early detection of O{sub i} using this diagnostic could be beneficial in controlling SiO{sub x} precipitation during integrated circuit processing.

  8. The Use of Phase-Lag Derivatives in the Numerical Integration of ODEs with Oscillating Solutions

    SciTech Connect

    Anastassi, Z. A.; Vlachos, D. S.; Simos, T. E.

    2008-09-01

    In this paper we consider the fitting of the coefficients of a numerical method, not only due to the nullification of the phase-lag, but also to its derivatives. We show that the method gains efficiency with each derivative of the phase-lag nullified for various problems with oscillating solutions. The analysis of the local truncation error analysis and the stability of the methods show the importance of zero phase-lag derivatives when integrating oscillatory differential equations.

  9. Numerical solutions to ill-posed and well-posed impedance boundary condition integral equations

    NASA Astrophysics Data System (ADS)

    Rogers, J. R.

    1983-11-01

    Exterior scattering from a three-dimensional impedance body can be formulated in terms of various integral equations derived from the Leontovich impedance boundary condition (IBC). The electric and magnetic field integral equations are ill-posed because they theoretically admit spurious solutions at the frequencies of interior perfect conductor cavity resonances. A combined field formulation is well-posed because it does not allow the spurious solutions. This report outlines the derivation of IBC integral equations and describes a procedure for constructing moment-method solutions for bodies of revolution. Numerical results for scattering from impedance spheres are presented which contrast the stability and accuracy of solutions to the ill-posed equations with those of the well-posed equation. The results show that numerical solutions for exterior scattering to the electric and magnetic field integral equations can be severely contaminated by spurious resonant solutions regardless of whether the surface impedance of the body is lossy or lossless.

  10. NLOS UV channel modeling using numerical integration and an approximate closed-form path loss model

    NASA Astrophysics Data System (ADS)

    Gupta, Ankit; Noshad, Mohammad; Brandt-Pearce, Maïté

    2012-10-01

    In this paper we propose a simulation method using numerical integration, and develop a closed-form link loss model for physical layer channel characterization for non-line of sight (NLOS) ultraviolet (UV) communication systems. The impulse response of the channel is calculated by assuming both uniform and Gaussian profiles for transmitted beams and different geometries. The results are compared with previously published results. The accuracy of the integration approach is compared to the Monte Carlo simulation. Then the path loss using the simulation method and the suggested closed-form expression are presented for different link geometries. The accuracies are evaluated and compared to the results obtained using other methods.

  11. Numerical performance of projection methods in finite element consolidation models

    NASA Astrophysics Data System (ADS)

    Gambolati, Giuseppe; Pini, Giorgio; Ferronato, Massimiliano

    2001-12-01

    Projection, or conjugate gradient like, methods are becoming increasingly popular for the efficient solution of large sparse sets of unsymmetric indefinite equations arising from the numerical integration of (initial) boundary value problems. One such problem is soil consolidation coupling a flow and a structural model, typically solved by finite elements (FE) in space and a marching scheme in time (e.g. the Crank-Nicolson scheme). The attraction of a projection method stems from a number of factors, including the ease of implementation, the requirement of limited core memory and the low computational cost if a cheap and effective matrix preconditioner is available. In the present paper, biconjugate gradient stabilized (Bi- CGSTAB) is used to solve FE consolidation equations in 2-D and 3-D settings with variable time integration steps. Three different nodal orderings are selected along with the preconditioner ILUT based on incomplete triangular factorization and variable fill-in. The overall cost of the solver is made up of the preconditioning cost plus the cost to converge which is in turn related to the number of iterations and the elementary operations required by each iteration. The results show that nodal ordering affects the perfor mance of Bi-CGSTAB. For normally conditioned consolidation problems Bi-CGSTAB with the best ILUT preconditioner may converge in a number of iterations up to two order of magnitude smaller than the size of the FE model and proves an accurate, cost-effective and robust alternative to direct methods.

  12. Numerical implications of stabilization by the use of integrals

    NASA Technical Reports Server (NTRS)

    Beaudet, P. R.

    1975-01-01

    Liapunov or energy restraint methods for dynamic stabilization in two body motion perturbation problems are considered. Results of computerized orbital stabilization estimates show that the application of energy restraint prevents the occurrence of consistent timing errors in the stepwise integration of equations of motion for a nearly circular orbit.

  13. Finite element methods in numerical relativity.

    NASA Astrophysics Data System (ADS)

    Mann, P. J.

    The finite element method is very successful in Newtonian fluid simulations, and can be extended to relativitstic fluid flows. This paper describes the general method, and then outlines some preliminary results for spherically symmetric geometries. The mixed finite element - finite difference scheme is introduced, and used for the description of spherically symmetric collapse. Baker's (Newtonian) shock modelling method and Miller's moving finite element method are also mentioned. Collapse in double-null coordinates requires non-constant time slicing, so the full finite element method in space and time is described.

  14. Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer

    SciTech Connect

    D. S. Lucas

    2004-10-01

    A graduate level course for Thermal Hydraulics (T/H) was taught through Idaho State University in the spring of 2004. A numerical approach was taken for the content of this course since the students were employed at the Idaho National Laboratory and had been users of T/H codes. The majority of the students had expressed an interest in learning about the Courant Limit, mass error, semi-implicit and implicit numerical integration schemes in the context of a computer code. Since no introductory text was found the author developed notes taught from his own research and courses taught for Westinghouse on the subject. The course started with a primer on control volume methods and the construction of a Homogeneous Equilibrium Model (HEM) (T/H) code. The primer was valuable for giving the students the basics behind such codes and their evolution to more complex codes for Thermal Hydraulics and Computational Fluid Dynamics (CFD). The course covered additional material including the Finite Element Method and non-equilibrium (T/H). The control volume primer and the construction of a three-equation (mass, momentum and energy) HEM code are the subject of this paper . The Fortran version of the code covered in this paper is elementary compared to its descendants. The steam tables used are less accurate than the available commercial version written in C Coupled to a Graphical User Interface (GUI). The Fortran version and input files can be downloaded at www.microfusionlab.com.

  15. Numerical matrix method for quantum periodic potentials

    NASA Astrophysics Data System (ADS)

    Le Vot, Felipe; Meléndez, Juan J.; Yuste, Santos B.

    2016-06-01

    A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the wave functions as finite superpositions of eigenfunctions of the infinite well. A matrix eigenvalue equation then yields the energy levels of the periodic potential within an acceptable accuracy. The methodology has been successfully used to deal with problems based on the well-known Kronig-Penney (KP) model. Besides the original model, these problems are a dimerized KP solid, a KP solid containing a surface, and a KP solid under an external field. A short list of additional problems that can be solved with this procedure is presented.

  16. Method for numerical simulations of metastable states

    SciTech Connect

    Heller, U.M.; Seiberg, N.

    1983-06-15

    We present a numerical simulation of metastable states near a first-order phase transition in the example of a U(1) lattice gauge theory with a generalized action. In order to make measurements in these states possible their decay has to be prevented. We achieve this by using a microcanonical simulation for a finite system. We then obtain the coupling constant (inverse temperature) as a function of the action density. It turns out to be nonmonotonic and hence not uniquely invertible. From it we derive the effective potential for the action density. This effective potential is not always convex, a property that seems to be in contradiction with the standard lore about its convexity. This apparent ''paradox'' is resolved in a discussion about different definitions of the effective potential.

  17. Interpolation Method Needed for Numerical Uncertainty

    NASA Technical Reports Server (NTRS)

    Groves, Curtis E.; Ilie, Marcel; Schallhorn, Paul A.

    2014-01-01

    Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.

  18. Numerical methods in Markov chain modeling

    NASA Technical Reports Server (NTRS)

    Philippe, Bernard; Saad, Youcef; Stewart, William J.

    1989-01-01

    Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

  19. Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations

    SciTech Connect

    Weinstein, Marvin; /SLAC

    2009-02-12

    It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for the behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will

  20. A selective integrated tempering method.

    PubMed

    Yang, Lijiang; Qin Gao, Yi

    2009-12-01

    In this paper, based on the integrated tempering sampling we introduce a selective integrated tempering sampling (SITS) method for the efficient conformation sampling and thermodynamics calculations for a subsystem in a large one, such as biomolecules solvated in aqueous solutions. By introducing a potential surface scaled with temperature, the sampling over the configuration space of interest (e.g., the solvated biomolecule) is selectively enhanced but the rest of the system (e.g., the solvent) stays largely unperturbed. The applications of this method to biomolecular systems allow highly efficient sampling over both energy and configuration spaces of interest. Comparing to the popular and powerful replica exchange molecular dynamics (REMD), the method presented in this paper is significantly more efficient in yielding relevant thermodynamics quantities (such as the potential of mean force for biomolecular conformational changes in aqueous solutions). It is more important that SITS but not REMD yielded results that are consistent with the traditional umbrella sampling free energy calculations when explicit solvent model is used since SITS avoids the sampling of the irrelevant phase space (such as the boiling water at high temperatures). PMID:19968339

  1. A two-dimensional depth-integrated non-hydrostatic numerical model for nearshore wave propagation

    NASA Astrophysics Data System (ADS)

    Lu, Xinhua; Dong, Bingjiang; Mao, Bing; Zhang, Xiaofeng

    2015-12-01

    In this study, we develop a shallow-water depth-integrated non-hydrostatic numerical model (SNH model) using a hybrid finite-volume and finite-difference method. Numerical discretization is performed using the non-incremental pressure-correction method on a collocated grid. We demonstrate that an extension can easily be made from an existing finite-volume method and collocated-grid based hydrostatic shallow-water equations (SWE) model to a non-hydrostatic model. A series of benchmark tests are used to validate the proposed numerical model. Our results demonstrate that the proposed model is robust and well-balanced, and it captures the wet-dry fronts accurately. A comparison between the SNH and SWE models indicates the importance of considering the wave dispersion effect in simulations when the wave amplitude to water depth ratio is large.

  2. Space-time adaptive numerical methods for geophysical applications.

    PubMed

    Castro, C E; Käser, M; Toro, E F

    2009-11-28

    In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space-time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost. PMID:19840984

  3. Modelling asteroid brightness variations. I - Numerical methods

    NASA Technical Reports Server (NTRS)

    Karttunen, H.

    1989-01-01

    A method for generating lightcurves of asteroid models is presented. The effects of the shape of the asteroid and the scattering law of a surface element are distinctly separable, being described by chosen functions that can easily be changed. The shape is specified by means of two functions that yield the length of the radius vector and the normal vector of the surface at a given point. The general shape must be convex, but spherical concavities producing macroscopic shadowing can also be modeled.

  4. A numerical method for power plant simulations

    SciTech Connect

    Carcasci, C.; Facchini, B.

    1996-03-01

    This paper describes a highly flexible computerized method of calculating operating data in a power cycle. The computerized method presented here permits the study of steam, gas and combined plants. Its flexibility is not restricted by any defined cycle scheme. A power plant consists of simple elements (turbine, compressor, combustor chamber, pump, etc.). Each power plant component is represented by its typical equations relating to fundamental mechanical and thermodynamic laws, so a power plant system is represented by algebraic equations, which are the typical equations of components, continuity equations, and data concerning plant conditions. This equation system is not linear, but can be reduced to a linear equation system with variable coefficients. The solution is simultaneous for each component and it is determined by an iterative process. An example of a simple gas turbine cycle demonstrates the applied technique. This paper also presents the user interface based on MS-Windows. The input data, the results, and any characteristic parameters of a complex cycle scheme are also shown.

  5. Numerical evaluation of two-center integrals over Slater type orbitals

    NASA Astrophysics Data System (ADS)

    Kurt, S. A.; Yükçü, N.

    2016-03-01

    Slater Type Orbitals (STOs) which one of the types of exponential type orbitals (ETOs) are used usually as basis functions in the multicenter molecular integrals to better understand physical and chemical properties of matter. In this work, we develop algorithms for two-center overlap and two-center two-electron hybrid and Coulomb integrals which are calculated with help of translation method for STOs and some auxiliary functions by V. Magnasco's group. We use Mathematica programming language to produce algorithms for these calculations. Numerical results for some quantum numbers are presented in the tables. Consequently, we compare our obtained numerical results with the other known literature results and other details of evaluation method are discussed.

  6. Numerical methods for analyzing electromagnetic scattering

    NASA Technical Reports Server (NTRS)

    Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.

    1985-01-01

    Attenuation properties of the normal modes in an overmoded waveguide coated with a lossy material were analyzed. It is found that the low-order modes, can be significantly attenuated even with a thin layer of coating if the coating material is not too lossy. A thinner layer of coating is required for large attenuation of the low-order modes if the coating material is magnetic rather than dielectric. The Radar Cross Section (RCS) from an uncoated circular guide terminated by a perfect electric conductor was calculated and compared with available experimental data. It is confirmed that the interior irradiation contributes to the RCS. The equivalent-current method based on the geometrical theory of diffraction (GTD) was chosen for the calculation of the contribution from the rim diffraction. The RCS reduction from a coated circular guide terminated by a PEC are planned schemes for the experiments are included. The waveguide coated with a lossy magnetic material is suggested as a substitute for the corrugated waveguide.

  7. Hybrid Numerical Methods for Multiscale Simulations of Subsurface Biogeochemical Processes

    SciTech Connect

    Scheibe, Timothy D.; Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.; Redden, George D.; Meakin, Paul

    2007-08-01

    Many subsurface flow and transport problems of importance today involve coupled non-linear flow, transport, and reaction in media exhibiting complex heterogeneity. In particular, problems involving biological mediation of reactions fall into this class of problems. Recent experimental research has revealed important details about the physical, chemical, and biological mechanisms involved in these processes at a variety of scales ranging from molecular to laboratory scales. However, it has not been practical or possible to translate detailed knowledge at small scales into reliable predictions of field-scale phenomena important for environmental management applications. A large assortment of numerical simulation tools have been developed, each with its own characteristic scale including molecular (e.g., molecular dynamics), microbial (e.g., cellular automata or particle individual-based models), pore (e.g., lattice-Boltzmann, pore network models, and discrete particle methods such as smoothed particle hydrodynamics) and continuum scales (e.g., traditional partial differential equations solved by finite difference or finite element methods). While many problems can be effectively addressed by one of these models at a single scale, some problems may require explicit integration of models across multiple scales. We are developing a hybrid multi-scale subsurface reactive transport modeling framework that integrates models with diverse representations of physics, chemistry and biology at different scales (sub-pore, pore and continuum). The modeling framework is being designed to take advantage of advanced computational technologies including parallel code components using the Common Component Architecture, parallel solvers, gridding, data and workflow management, and visualization. This paper describes the specific methods/codes being used at each scale, techniques used to directly and adaptively couple across model scales, and preliminary results of application to a

  8. Development of numerical methods to problems of micromechanics

    NASA Astrophysics Data System (ADS)

    Garcia-Martinez, Jose Ramon

    In this dissertation we utilize the finite element method to investigate three micromechanical problems. In Chapter 2, we study the compliance contribution tensor H of multiple branched cracks. The cracks grow from a deltoid pore at their center into a triple crack. For plain strain conditions, two-dimensional models of the branched crack are modeled and solved in ABAQUS. The displacement field over the surface of the branched crack and the deltoid is curve fitted to carry out the integral surface of the compliance contribution tensor H. The predicted values are in good agreement with analytical solution. In Chapter 3 a three-dimensional finite element program using an unaligned mesh with an eight-node isoparametric element is developed to study the compliance contribution tensor H of cavities with superellipsoid shapes. A mesh clustering algorithm to increase the number of elements inside and near the superellipsoid surface to obtain a mesh independent solution is used. The numerical results are compared with the analytical solution of a sphere; the error of the numerical approximation varied from 8 to 11%. It is found that the number of elements inside the superellipsoid are insufficient. An algorithm to mesh independently the volumes inside and outside the cube is proposed to increase the accuracy in the calculation of H. As n1 and n2 increase, the numerical solutions show that, H1111 → 0 and H2211 → 0. Although, for these concave shapes no analytical solution exists a bound of 0 for the terms H 1111 and H2211 is suggested. Finally, in Chapter 4 a numerical verification of the cross-property connection between the effective fluid permeability and the effective electrical conductivity is study. A molecular dynamics algorithm is used to generate a set of different microstructural patterns. The volumetric average over a cubic volume is used to obtain the effective electrical conductivity and the effective fluid permeability. The tortuosity of the porous phase

  9. Exponential Methods for the Time Integration of Schroedinger Equation

    SciTech Connect

    Cano, B.; Gonzalez-Pachon, A.

    2010-09-30

    We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

  10. 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.

  11. Report of the Fifth Biennial Conference on Chemical Education. Birds-of-a-Feather Workshop Sessions: Numerical Methods Workshop.

    ERIC Educational Resources Information Center

    Johnson, K. J.

    1979-01-01

    This workshop was for participants who were interested in developing a numerical methods course. The contents of a numerical methods text were covered, with special emphasis on nonlinear least squares analysis, and the Runge-Kutta method of integrating systems of first-order differential equations. (BB)

  12. Elementary Techniques of Numerical Integration and Their Computer Implementation. Applications of Elementary Calculus to Computer Science. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 379.

    ERIC Educational Resources Information Center

    Motter, Wendell L.

    It is noted that there are some integrals which cannot be evaluated by determining an antiderivative, and these integrals must be subjected to other techniques. Numerical integration is one such method; it provides a sum that is an approximate value for some integral types. This module's purpose is to introduce methods of numerical integration and…

  13. Carbon Dioxide Dispersion in the Combustion Integrated Rack Simulated Numerically

    NASA Technical Reports Server (NTRS)

    Wu, Ming-Shin; Ruff, Gary A.

    2004-01-01

    When discharged into an International Space Station (ISS) payload rack, a carbon dioxide (CO2) portable fire extinguisher (PFE) must extinguish a fire by decreasing the oxygen in the rack by 50 percent within 60 sec. The length of time needed for this oxygen reduction throughout the rack and the length of time that the CO2 concentration remains high enough to prevent the fire from reigniting is important when determining the effectiveness of the response and postfire procedures. Furthermore, in the absence of gravity, the local flow velocity can make the difference between a fire that spreads rapidly and one that self-extinguishes after ignition. A numerical simulation of the discharge of CO2 from PFE into the Combustion Integrated Rack (CIR) in microgravity was performed to obtain the local velocity and CO2 concentration. The complicated flow field around the PFE nozzle exits was modeled by sources of equivalent mass and momentum flux at a location downstream of the nozzle. The time for the concentration of CO2 to reach a level that would extinguish a fire anywhere in the rack was determined using the Fire Dynamics Simulator (FDS), a computational fluid dynamics code developed by the National Institute of Standards and Technology specifically to evaluate the development of a fire and smoke transport. The simulation shows that CO2, as well as any smoke and combustion gases produced by a fire, would be discharged into the ISS cabin through the resource utility panel at the bottom of the rack. These simulations will be validated by comparing the results with velocity and CO2 concentration measurements obtained during the fire suppression system verification tests conducted on the CIR in March 2003. Once these numerical simulations are validated, portions of the ISS labs and living areas will be modeled to determine the local flow conditions before, during, and after a fire event. These simulations can yield specific information about how long it takes for smoke and

  14. Black shale weathering: An integrated field and numerical modeling study

    NASA Astrophysics Data System (ADS)

    Bolton, E. W.; Wildman, R. A., Jr.; Berner, R. A.; Eckert, J. O., Jr.; Petsch, S. T.; Mok, U.; Evans, B.

    2003-04-01

    We present an integrated study of black shale weathering in a near surface environment. Implications of this study contribute to our understanding of organic matter oxidation in uplifted sediments, along with erosion and reburial of ancient unoxidized organic matter, as major controls on atmospheric oxygen levels over geologic time. The field study used to launch the modeling effort is based on core samples from central-eastern Kentucky near Clay City (Late Devonian New Albany/Ohio Shale), where the strata are essentially horizontal. Samples from various depth intervals (up to 12 m depth) were analyzed for texture (SEM images), porosity fraction (0.02 to 0.1), and horizontal and vertical permeability (water and air permeabilities differ due to the fine-grained nature of the sediments, but are on the order of 0.01 to 1. millidarcies, respectively). Chemical analyses were also performed for per cent C, N, S, and basic mineralogy was determined (clays, quartz, pyrite, in addition to organic matter). The samples contained from 2 to 15 per cent ancient (non-modern soil) organic matter. These results were used in the creation of a numerical model for kinetically controlled oxidation of the organic matter within the shale (based on kinetics from Chang and Berner, 1999). The one-dimensional model includes erosion, oxygen diffusion in the partially saturated vadose zone as well as water percolation and solute transport. This study extends the studies of Petsch (2000) and the weathering component of Lasaga and Ohmoto (2002) to include more reactions (e.g., pyrite oxidation to sulfuric acid and weathering of silicates due to low pH) and to resolve the near-surface boundary layer. The model provides a convenient means of exploring the influence of variable rates of erosion, oxygen level, rainfall, as well as physical and chemical characteristics of the shale on organic matter oxidation.

  15. Integrated navigation method based on inertial navigation system and Lidar

    NASA Astrophysics Data System (ADS)

    Zhang, Xiaoyue; Shi, Haitao; Pan, Jianye; Zhang, Chunxi

    2016-04-01

    An integrated navigation method based on the inertial navigational system (INS) and Lidar was proposed for land navigation. Compared with the traditional integrated navigational method and dead reckoning (DR) method, the influence of the inertial measurement unit (IMU) scale factor and misalignment was considered in the new method. First, the influence of the IMU scale factor and misalignment on navigation accuracy was analyzed. Based on the analysis, the integrated system error model of INS and Lidar was established, in which the IMU scale factor and misalignment error states were included. Then the observability of IMU error states was analyzed. According to the results of the observability analysis, the integrated system was optimized. Finally, numerical simulation and a vehicle test were carried out to validate the availability and utility of the proposed INS/Lidar integrated navigational method. Compared with the test result of a traditional integrated navigation method and DR method, the proposed integrated navigational method could result in a higher navigation precision. Consequently, the IMU scale factor and misalignment error were effectively compensated by the proposed method and the new integrated navigational method is valid.

  16. Numerical integration for ab initio many-electron self energy calculations within the GW approximation

    SciTech Connect

    Liu, Fang; Lin, Lin; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F.; Sharifzadeh, Sahar; Jornada, Felipe H. da; Deslippe, Jack; Yang, Chao; and others

    2015-04-01

    We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.

  17. A numerical method for the time coarsening of transport processes at the atomistic scale

    NASA Astrophysics Data System (ADS)

    Gonzalez-Ferreiro, B.; Romero, I.; Ortiz, M.

    2016-05-01

    We propose a novel numerical scheme for the simulation of slow transport processes at the atomistic scale. The scheme is based on a model for non-equilibrium statistical thermodynamics recently proposed by the authors, and extends it by formulating a variational integrator, i.e. a discrete functional whose optimality conditions provide all the governing equations of the problem. The method is employed to study surface segregation of AuAg alloys and its convergence is confirmed numerically.

  18. Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

    NASA Astrophysics Data System (ADS)

    Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

    2013-09-01

    Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are

  19. Asymptotic-induced numerical methods for conservation laws

    NASA Technical Reports Server (NTRS)

    Garbey, Marc; Scroggs, Jeffrey S.

    1990-01-01

    Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.

  20. An iterative analytic—numerical method for scattering from a target buried beneath a rough surface

    NASA Astrophysics Data System (ADS)

    Xu, Run-Wen; Guo, Li-Xin; Wang, Rui

    2014-11-01

    An efficiently iterative analytical—numerical method is proposed for two-dimensional (2D) electromagnetic scattering from a perfectly electric conducting (PEC) target buried under a dielectric rough surface. The basic idea is to employ the Kirchhoff approximation (KA) to accelerate the boundary integral method (BIM). Below the rough surface, an iterative system is designed between the rough surface and the target. The KA is used to simulate the initial field on the rough surface based on the Fresnel theory, while the target is analyzed by the boundary integral method to obtain a precise result. The fields between the rough surface and the target can be linked by the boundary integral equations below the rough surface. The technique presented here is highly efficient in terms of computational memory, time, and versatility. Numerical simulations of two typical models are carried out to validate the method.

  1. A numerical method for approximating antenna surfaces defined by discrete surface points

    NASA Technical Reports Server (NTRS)

    Lee, R. Q.; Acosta, R.

    1985-01-01

    A simple numerical method for the quadratic approximation of a discretely defined reflector surface is described. The numerical method was applied to interpolate the surface normal of a parabolic reflector surface from a grid of nine closest surface points to the point of incidence. After computing the surface normals, the geometrical optics and the aperture integration method using the discrete Fast Fourier Transform (FFT) were applied to compute the radiaton patterns for a symmetric and an offset antenna configurations. The computed patterns are compared to that of the analytic case and to the patterns generated from another numerical technique using the spline function approximation. In the paper, examples of computations are given. The accuracy of the numerical method is discussed.

  2. Integrating Numerical Computation into the Modeling Instruction Curriculum

    ERIC Educational Resources Information Center

    Caballero, Marcos D.; Burk, John B.; Aiken, John M.; Thoms, Brian D.; Douglas, Scott S.; Scanlon, Erin M.; Schatz, Michael F.

    2014-01-01

    Numerical computation (the use of a computer to solve, simulate, or visualize a physical problem) has fundamentally changed the way scientific research is done. Systems that are too difficult to solve in closed form are probed using computation. Experiments that are impossible to perform in the laboratory are studied numerically. Consequently, in…

  3. Numerical Integration with GeoGebra in High School

    ERIC Educational Resources Information Center

    Herceg, Dorde; Herceg, Dragoslav

    2010-01-01

    The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

  4. Parallel processing numerical method for confined vortex dynamics and applications

    NASA Astrophysics Data System (ADS)

    Bistrian, Diana Alina

    2013-10-01

    This paper explores a combined analytical and numerical technique to investigate the hydrodynamic instability of confined swirling flows, with application to vortex rope dynamics in a Francis turbine diffuser, in condition of sophisticated boundary constraints. We present a new approach based on the method of orthogonal decomposition in the Hilbert space, implemented with a spectral descriptor scheme in discrete space. A parallel implementation of the numerical scheme is conducted reducing the computational time compared to other techniques.

  5. Numerical Asymptotic Solutions Of Differential Equations

    NASA Technical Reports Server (NTRS)

    Thurston, Gaylen A.

    1992-01-01

    Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

  6. Algorithms for the Fractional Calculus: A Selection of Numerical Methods

    NASA Technical Reports Server (NTRS)

    Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.

    2003-01-01

    Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.

  7. Collocation Method for Numerical Solution of Coupled Nonlinear Schroedinger Equation

    SciTech Connect

    Ismail, M. S.

    2010-09-30

    The coupled nonlinear Schroedinger equation models several interesting physical phenomena presents a model equation for optical fiber with linear birefringence. In this paper we use collocation method to solve this equation, we test this method for stability and accuracy. Numerical tests using single soliton and interaction of three solitons are used to test the resulting scheme.

  8. Investigating Convergence Patterns for Numerical Methods Using Data Analysis

    ERIC Educational Resources Information Center

    Gordon, Sheldon P.

    2013-01-01

    The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…

  9. A numerical method for solving singular De`s

    SciTech Connect

    Mahaver, W.T.

    1996-12-31

    A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

  10. A new numerical method of total solar eclipse photography processing

    NASA Astrophysics Data System (ADS)

    Druckmüller, M.; Rušin, V.; Minarovjech, M.

    2006-10-01

    A new numerical method of image processing suitable for visualization of corona images taken during total solar eclipses is presented. This method allows us to study both small- and large-scale coronal structures that remain invisible on original images because of their very high dynamic range of the coronal brightness. The method is based on the use of adaptive filters inspired by human vision and the sensitivity of resulting images is thus very close to that of the human eye during an eclipse. A high precision alignment method for white-light corona images is also discussed. The proposed method highly improves a widely used unsharp masking method employing a radially blurred mask. The results of these numerical image processing techniques are illustrated by a series of images taken during eclipses of the last decade. The method minimizes the risk of processing artifacts.

  11. Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

    PubMed

    Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K

    2007-07-01

    Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved

  12. Numerical solution of a diffusion problem by exponentially fitted finite difference methods.

    PubMed

    D'Ambrosio, Raffaele; Paternoster, Beatrice

    2014-01-01

    This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver. PMID:26034665

  13. 25 Years of Self-organized Criticality: Numerical Detection Methods

    NASA Astrophysics Data System (ADS)

    McAteer, R. T. James; Aschwanden, Markus J.; Dimitropoulou, Michaila; Georgoulis, Manolis K.; Pruessner, Gunnar; Morales, Laura; Ireland, Jack; Abramenko, Valentyna

    2016-01-01

    The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.

  14. Comparison of methods for numerical calculation of continuum damping

    SciTech Connect

    Bowden, G. W.; Hole, M. J.; Dennis, G. R.; Könies, A.; Gorelenkov, N. N.

    2014-05-15

    Continuum resonance damping is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this damping, particularly, in the case of the toroidicity-induced shear Alfvén eigenmode. This paper compares results obtained using an analytical perturbative approach with those found using resistive and complex contour numerical approaches. It is found that the perturbative method does not provide accurate agreement with reliable numerical methods for the range of parameters examined. This discrepancy exists even in the limit where damping approaches zero. When the perturbative technique is implemented using a standard finite element method, the damping estimate fails to converge with radial grid resolution. The finite elements used cannot accurately represent the eigenmode in the region of the continuum resonance, regardless of the number of radial grid points used.

  15. Implicit numerical integration for periodic solutions of autonomous nonlinear systems

    NASA Technical Reports Server (NTRS)

    Thurston, G. A.

    1982-01-01

    A change of variables that stabilizes numerical computations for periodic solutions of autonomous systems is derived. Computation of the period is decoupled from the rest of the problem for conservative systems of any order and for any second-order system. Numerical results are included for a second-order conservative system under a suddenly applied constant load. Near the critical load for the system, a small increment in load amplitude results in a large increase in amplitude of the response.

  16. SAMSAN- MODERN NUMERICAL METHODS FOR CLASSICAL SAMPLED SYSTEM ANALYSIS

    NASA Technical Reports Server (NTRS)

    Frisch, H. P.

    1994-01-01

    SAMSAN was developed to aid the control system analyst by providing a self consistent set of computer algorithms that support large order control system design and evaluation studies, with an emphasis placed on sampled system analysis. Control system analysts have access to a vast array of published algorithms to solve an equally large spectrum of controls related computational problems. The analyst usually spends considerable time and effort bringing these published algorithms to an integrated operational status and often finds them less general than desired. SAMSAN reduces the burden on the analyst by providing a set of algorithms that have been well tested and documented, and that can be readily integrated for solving control system problems. Algorithm selection for SAMSAN has been biased toward numerical accuracy for large order systems with computational speed and portability being considered important but not paramount. In addition to containing relevant subroutines from EISPAK for eigen-analysis and from LINPAK for the solution of linear systems and related problems, SAMSAN contains the following not so generally available capabilities: 1) Reduction of a real non-symmetric matrix to block diagonal form via a real similarity transformation matrix which is well conditioned with respect to inversion, 2) Solution of the generalized eigenvalue problem with balancing and grading, 3) Computation of all zeros of the determinant of a matrix of polynomials, 4) Matrix exponentiation and the evaluation of integrals involving the matrix exponential, with option to first block diagonalize, 5) Root locus and frequency response for single variable transfer functions in the S, Z, and W domains, 6) Several methods of computing zeros for linear systems, and 7) The ability to generate documentation "on demand". All matrix operations in the SAMSAN algorithms assume non-symmetric matrices with real double precision elements. There is no fixed size limit on any matrix in any

  17. Numerical Methods in Quantum Mechanics: Analysis of Numerical Schemes on One-Dimensional Schrodinger Wave Problems

    NASA Astrophysics Data System (ADS)

    Jones, Marvin Quenten, Jr.

    The motion and behavior of quantum processes can be described by the Schrodinger equation using the wave function, Psi(x,t). The use of the Schrodinger equation to study quantum phenomena is known as Quantum Mechanics, akin to classical mechanics being the tool to study classical physics. This research focuses on the emphasis of numerical techniques: Finite-Difference, Fast Fourier Transform (spectral method), finite difference schemes such as the Leapfrog method and the Crank-Nicolson scheme and second quantization to solve and analyze the Schrodinger equation for the infinite square well problem, the free particle with periodic boundary conditions, the barrier problem, tight-binding hamiltonians and a potential wall problem. We discuss these techniques and the problems created to test how these different techniques draw both physical and numerical conclusions in a tabular summary. We observed both numerical stability and quantum stability (conservation of energy, probability, momentum, etc.). We found in our results that the Crank-Nicolson scheme is an unconditionally stable scheme and conserves probability (unitary), and momentum, though dissipative with energy. The time-independent problems conserved energy, momentum and were unitary, which is of interest, but we found when time-dependence was introduced, quantum stability (i.e. conservation of mass, momentum, etc.) was not implied by numerical stability. Hence, we observed schemes that were numerically stable, but not quantum stable as well as schemes that were quantum stable, but not numerically stable for all of time, t. We also observed that second quantization removed the issues with stability as the problem was transformed into a discrete problem. Moreover, all quantum information is conserved in second quantization. This method, however, does not work universally for all problems.

  18. Method of descent for integrable lattices

    NASA Astrophysics Data System (ADS)

    Bogoyavlensky, Oleg

    2009-05-01

    A method of descent for constructing integrable Hamiltonian systems is introduced. The derived periodic and nonperiodic lattices possess Lax representations with spectral parameter and have plenty of first integrals. Examples of Liouville-integrable four-dimensional Hamiltonian Lotka-Volterra systems are presented.

  19. Evaluation of the Hubbell rectangular source integral using Haar wavelets method

    NASA Astrophysics Data System (ADS)

    Belkadhi, K.; Manai, K.

    2016-05-01

    Haar wavelets numerical integration method is exposed and used for evaluating the Hubbell rectangular source integral. The method convergence is studied to get the minimum iteration number for a desired precision. Haar wavelets results are finally compared to those obtained with other integration methods.

  20. Improving the numerical integration solution of satellite orbits in the presence of solar radiation pressure using modified back differences

    NASA Technical Reports Server (NTRS)

    Lundberg, J. B.; Feulner, M. R.; Abusali, P. A. M.; Ho, C. S.

    1991-01-01

    The method of modified back differences, a technique that significantly reduces the numerical integration errors associated with crossing shadow boundaries using a fixed-mesh multistep integrator without a significant increase in computer run time, is presented. While Hubbard's integral approach can produce significant improvements to the trajectory solution, the interpolation method provides the best overall results. It is demonstrated that iterating on the point mass term correction is also important for achieving the best overall results. It is also shown that the method of modified back differences can be implemented with only a small increase in execution time.

  1. Numerical modeling of magnetic induction tomography using the impedance method.

    PubMed

    Ramos, Airton; Wolff, Julia G B

    2011-02-01

    This article discusses the impedance method in the forward calculation in magnetic induction tomography (MIT). Magnetic field and eddy current distributions were obtained numerically for a sphere in the field of a coil and were compared with an analytical model. Additionally, numerical and experimental results for phase sensitivity in MIT were obtained and compared for a cylindrical object in a planar array of sensors. The results showed that the impedance method provides results that agree very well with reality in the frequency range from 100 kHz to 20 MHz and for low conductivity objects (10 S/m or less). This opens the possibility of using this numerical approach in image reconstruction in MIT. PMID:21229327

  2. Damping identification in frequency domain using integral method

    NASA Astrophysics Data System (ADS)

    Guo, Zhiwei; Sheng, Meiping; Ma, Jiangang; Zhang, Wulin

    2015-03-01

    A new method for damping identification of linear system in frequency domain is presented, by using frequency response function (FRF) with integral method. The FRF curve is firstly transformed to other type of frequency-related curve by changing the representations of horizontal and vertical axes. For the newly constructed frequency-related curve, integral is conducted and the area forming from the new curve is used to determine the damping. Three different methods based on integral are proposed in this paper, which are called FDI-1, FDI-2 and FDI-3 method, respectively. For a single degree of freedom (Sdof) system, the formulated relation of each method between integrated area and loss factor is derived theoretically. The numeral simulation and experiment results show that, the proposed integral methods have high precision, strong noise resistance and are very stable in repeated measurements. Among the three integral methods, FDI-3 method is the most recommended because of its higher accuracy and simpler algorithm. The new methods are limited to linear system in which modes are well separated, and for closely spaced mode system, mode decomposition process should be conducted firstly.

  3. A numerical adjoint parabolic equation (PE) method for tomography and geoacoustic inversion in shallow water

    NASA Astrophysics Data System (ADS)

    Hermand, Jean-Pierre; Berrada, Mohamed; Meyer, Matthias; Asch, Mark

    2005-09-01

    Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK '94 experimental conditions.

  4. TRANSPORT OF REACTING SOLUTES SUBJECT TO A MOVING DISSOLUTION BOUNDARY: NUMERICAL METHODS AND SOLUTIONS.

    USGS Publications Warehouse

    Willis, Catherine; Rubin, Jacob

    1987-01-01

    In this paper we consider examples of chemistry-affected transport processes in porous media. A moving boundary problem which arises during transport with precipitation-dissolution reactions is solved by three different numerical methods. Two of these methods (one explicit and one implicit) are based on an integral formulation of mass balance and lead to an approximation of a weak solution. These methods are compared to a front-tracking scheme. Although the two approaches are conceptually different, the numerical solutions showed good agreement. As the ratio of dispersion to convection decreases, the methods based on the integral formulation become computationally more efficient. Specific reactions were modeled to examine the dependence of the system on the physical and chemical parameters.

  5. A numerical method of tracing a vortical axis along local topological axis line

    NASA Astrophysics Data System (ADS)

    Nakayama, Katsuyuki; Hasegawa, Hideki

    2016-06-01

    A new numerical method is presented to trace or identify a vortical axis in flow, which is based on Galilean invariant flow topology. We focus on the local flow topology specified by the eigenvalues and eigenvectors of the velocity gradient tensor, and extract the axis component from its flow trajectory. Eigen-vortical-axis line is defined from the eigenvector of the real eigenvalue of the velocity gradient tensor where the tensor has the conjugate complex eigenvalues. This numerical method integrates the eigen-vortical-axis line and traces a vortical axis in terms of the invariant flow topology, which enables to investigate the feature of the topology-based vortical axis.

  6. Integrated control system and method

    SciTech Connect

    Wang, Paul Sai Keat; Baldwin, Darryl; Kim, Myoungjin

    2013-10-29

    An integrated control system for use with an engine connected to a generator providing electrical power to a switchgear is disclosed. The engine receives gas produced by a gasifier. The control system includes an electronic controller associated with the gasifier, engine, generator, and switchgear. A gas flow sensor monitors a gas flow from the gasifier to the engine through an engine gas control valve and provides a gas flow signal to the electronic controller. A gas oversupply sensor monitors a gas oversupply from the gasifier and provides an oversupply signal indicative of gas not provided to the engine. A power output sensor monitors a power output of the switchgear and provide a power output signal. The electronic controller changes gas production of the gasifier and the power output rating of the switchgear based on the gas flow signal, the oversupply signal, and the power output signal.

  7. An improvement in the numerical integration procedure used in the NASA Marshall engineering thermosphere model

    NASA Technical Reports Server (NTRS)

    Hickey, Michael Philip

    1988-01-01

    A proposed replacement scheme for the integration of the barometric and diffusion equations in the NASA Marshall Engineering Thermosphere (MET) model is presented. This proposed integration scheme is based on Gaussian Quadrature. Extensive numerical testing reveals it to be faster, more accurate and more reliable than the present integration scheme (a modified form of Simpson's Rule) used in the MET model. Numerous graphical examples are provided, along with a listing of a modified form of the MET model in which subroutine INTEGRATE (using Simpson's Rule) is replaced by subroutine GAUSS (which uses Gaussian Quadrature). It is recommended that the Gaussian Quadrature integration scheme, as used here, be used in the MET model.

  8. A novel gas-droplet numerical method for spray combustion

    NASA Technical Reports Server (NTRS)

    Chen, C. P.; Shang, H. M.; Jiang, Y.

    1991-01-01

    This paper presents a non-iterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully-interacting combination of Eulerian fluid and Lagrangian particle calculation. The interaction calculations between the two phases are formulated on a pressure-velocity coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell (PSIC) procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data, as well as efficiency assessments are given for some sprays typical of spray combustion applications.

  9. The TAB method for numerical calculation of spray droplet breakup

    NASA Astrophysics Data System (ADS)

    Orourke, P. J.; Amsden, A. A.

    A short history is given of the major milestones in the development of the stochastic particle method for calculating liquid fuel sprays. The most recent advance has been the discovery of the importance of drop breakup in engine sprays. A new method, called TAB, for calculating drop breakup is presented. Some theoretical properties of the method are derived; its numerical implementation in the computer program KIVA is described; and comparisons are presented between TAB-method calculations and experiments and calculations using another breakup model.

  10. Simple numerical method for predicting steady compressible flows

    NASA Technical Reports Server (NTRS)

    Vonlavante, Ernst; Nelson, N. Duane

    1986-01-01

    A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.

  11. Numerical simulation of dynamic processes in biomechanics using the grid-characteristic method

    NASA Astrophysics Data System (ADS)

    Beklemysheva, K. A.; Vasyukov, A. V.; Petrov, I. B.

    2015-08-01

    Results of the numerical simulation of mechanical processes occurring in biological tissues under dynamic actions are presented. The grid-characteristic method on unstructured grids is used to solve the system of equations of mechanics of deformable solids; this method takes into account the characteristic properties of the constitutive system of partial differential equations and produces adequate algorithms on interfaces between media and on the boundaries of integration domains.

  12. Super-Junction PIN Photodiode to Integrate Optoelectronic Integrated Circuits in Standard Technologies: A Numerical Study

    NASA Astrophysics Data System (ADS)

    Roig, Jaume; Stefanov, Evgueniy; Morancho, Frédéric

    2007-07-01

    The use of super-junction (SJ) techniques in PIN photodiodes is proposed in this letter for the first time with the objective to assist the optoelectronic integrated circuits (OEICs) implementation in complementary metal oxide semiconductor (CMOS), bipolar CMOS (BiCMOS) and bipolar-CMOS-double diffused MOS (BCD) technologies. Its technological viability is also discussed to make it credible as an alternative to other OEICs approaches. Numerical simulation of realistic SJ-PIN devices, widely used in high power electronics, demonstrates the possibility to integrate high-performance CMOS-based OEICs in epitaxial layers with doping concentrations above 1× 1015 cm-3. The induced lateral depletion at low reverse biased voltage, assisted by the alternated N and P-doped pillars, allows high-speed transient response in SJ-PIN detecting wavelengths between 400 and 800 nm. Moreover, other important parameters as the responsivity and the dark current are not degraded in respect to the conventional PIN (C-PIN) structures.

  13. On numerical integration with high-order quadratures: with application to the Rayleigh-Sommerfeld integral

    NASA Astrophysics Data System (ADS)

    Evans, W. A. B.; Torre, A.

    2012-11-01

    The paper focusses on the advantages of using high-order Gauss-Legendre quadratures for the precise evaluation of integrals with both smooth and rapidly changing integrands. Aspects of their precision are analysed in the light of Gauss' error formula. Some "test examples" are considered and evaluated in multiple precision to ≈ 200 significant decimal digits with David Bailey's multiprecision package to eliminate truncation/rounding errors. The increase of precision on doubling the number of subintervals is analysed, the relevant quadrature attribute being the precision increment. In order to exemplify the advantages that high-order quadrature afford, the technique is then used to evaluate several plots of the Rayleigh-Sommerfeld diffraction integral for axi-symmetric source fields defined on a planar aperture. A comparison of the high-order quadrature method against various FFT-based methods is finally given.

  14. Robust rotational-velocity-Verlet integration methods

    NASA Astrophysics Data System (ADS)

    Rozmanov, Dmitri; Kusalik, Peter G.

    2010-05-01

    Two rotational integration algorithms for rigid-body dynamics are proposed in velocity-Verlet formulation. The first method uses quaternion dynamics and was derived from the original rotational leap-frog method by Svanberg [Mol. Phys. 92, 1085 (1997)]; it produces time consistent positions and momenta. The second method is also formulated in terms of quaternions but it is not quaternion specific and can be easily adapted for any other orientational representation. Both the methods are tested extensively and compared to existing rotational integrators. The proposed integrators demonstrated performance at least at the level of previously reported rotational algorithms. The choice of simulation parameters is also discussed.

  15. Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

    NASA Technical Reports Server (NTRS)

    Radhakrishnan, K.

    1984-01-01

    The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency.

  16. Impact of numerical integration on gas curtain simulations

    SciTech Connect

    Rider, W.; Kamm, J.

    2000-11-01

    In recent years, we have presented a less than glowing experimental comparison of hydrodynamic codes with the gas curtain experiment (e.g., Kamm et al. 1999a). Here, we discuss the manner in which the details of the hydrodynamic integration techniques may conspire to produce poor results. This also includes some progress in improving the results and agreement with experimental results. Because our comparison was conducted on the details of the experimental images (i.e., their detailed structural information), our results do not conflict with previously published results of good agreement with Richtmyer-Meshkov instabilities based on the integral scale of mixing. New experimental and analysis techniques are also discussed.

  17. Numerical simulation methods for the Rouse model in flow

    NASA Astrophysics Data System (ADS)

    Howard, Michael P.; Milner, Scott T.

    2011-11-01

    Simulation of the Rouse model in flow underlies a great variety of numerical investigations of polymer dynamics, in both entangled melts and solutions and in dilute solution. Typically a simple explicit stochastic Euler method is used to evolve the Rouse model. Here we compare this approach to an operator splitting method, which splits the evolution operator into stochastic linear and deterministic nonlinear parts and takes advantage of an analytical solution for the linear Rouse model in terms of the noise history. We show that this splitting method has second-order weak convergence, whereas the Euler method has only first-order weak convergence. Furthermore, the splitting method is unconditionally stable, in contrast to the limited stability range of the Euler method. Similar splitting methods are applicable to a broad class of problems in stochastic dynamics in which noise competes with ordering and flow to determine steady-state order parameter structures.

  18. Numerical Polynomial Homotopy Continuation Method and String Vacua

    DOE PAGESBeta

    Mehta, Dhagash

    2011-01-01

    Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less

  19. On numerical methods in non-Newtonian flows

    NASA Astrophysics Data System (ADS)

    Fileas, G.

    1982-12-01

    The constitutive equations for non-Newtonian flows are presented and the various flow models derived from continuum mechanics and molecular theories are considered and evaluated. Detailed account is given of numerical simulation employing differential and integral models of different kinds of non-Newtonian flows using finite difference and finite element techniques. Procedures for computer set ups are described and references are given for finite difference, finite element and molecular theory based programs for several kinds of flow. Achievements and unreached goals in the field of numerical simulation of non-Newtonian flows are discussed and the lack of numerical work in the fields of suspension flows and heat transfer is pointed out. Finally, FFOCUS is presented as a newly built computer program which can simulate freezing flows of Newtonian fluids through various geometries and is aimed to be further developed to handle non-Newtonian freezing flows and certain types of suspension phenomena involved in corium flow after a hypothetical core melt down accident in a pressurized water reactor.

  20. Projected discrete ordinates methods for numerical transport problems

    SciTech Connect

    Larsen, E.W.

    1985-01-01

    A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.

  1. Computational methods for aerodynamic design using numerical optimization

    NASA Technical Reports Server (NTRS)

    Peeters, M. F.

    1983-01-01

    Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.

  2. Numerical methods for characterization of synchrotron radiation based on the Wigner function method

    NASA Astrophysics Data System (ADS)

    Tanaka, Takashi

    2014-06-01

    Numerical characterization of synchrotron radiation based on the Wigner function method is explored in order to accurately evaluate the light source performance. A number of numerical methods to compute the Wigner functions for typical synchrotron radiation sources such as bending magnets, undulators and wigglers, are presented, which significantly improve the computation efficiency and reduce the total computation time. As a practical example of the numerical characterization, optimization of betatron functions to maximize the brilliance of undulator radiation is discussed.

  3. Implementation of sinh method in integration space for boundary integrals with near singularity in potential problems

    NASA Astrophysics Data System (ADS)

    Xie, Guizhong; Zhang, Dehai; Zhang, Jianming; Meng, Fannian; Du, Wenliao; Wen, Xiaoyu

    2016-07-01

    As a widely used numerical method, boundary element method (BEM) is efficient for computer aided engineering (CAE). However, boundary integrals with near singularity need to be calculated accurately and efficiently to implement BEM for CAE analysis on thin bodies successfully. In this paper, the distance in the denominator of the fundamental solution is first designed as an equivalent form using approximate expansion and the original sinh method can be revised into a new form considering the minimum distance and the approximate expansion. Second, the acquisition of the projection point by Newton-Raphson method is introduced. We acquire the nearest point between the source point and element edge by solving a cubic equation if the location of the projection point is outside the element, where boundary integrals with near singularity appear. Finally, the subtriangles of the local coordinate space are mapped into the integration space and the sinh method is applied in the integration space. The revised sinh method can be directly performed in the integration element. Averification test of our method is proposed. Results demonstrate that our method is effective for regularizing the boundary integrals with near singularity.

  4. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

    PubMed

    Khoromskaia, Venera; Khoromskij, Boris N

    2015-12-21

    We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches. PMID:26016539

  5. Fast and stable numerical method for neuronal modelling

    NASA Astrophysics Data System (ADS)

    Hashemi, Soheil; Abdolali, Ali

    2016-11-01

    Excitable cell modelling is of a prime interest in predicting and targeting neural activity. Two main limits in solving related equations are speed and stability of numerical method. Since there is a tradeoff between accuracy and speed, most previously presented methods for solving partial differential equations (PDE) are focused on one side. More speed means more accurate simulations and therefore better device designing. By considering the variables in finite differenced equation in proper time and calculating the unknowns in the specific sequence, a fast, stable and accurate method is introduced in this paper for solving neural partial differential equations. Propagation of action potential in giant axon is studied by proposed method and traditional methods. Speed, consistency and stability of the methods are compared and discussed. The proposed method is as fast as forward methods and as stable as backward methods. Forward methods are known as fastest methods and backward methods are stable in any circumstances. Complex structures can be simulated by proposed method due to speed and stability of the method.

  6. Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime

    NASA Astrophysics Data System (ADS)

    Bao, WeiZhu; Cai, YongYong; Jia, XiaoWei; Yin, Jia

    2016-08-01

    We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation in the nonrelativistic limit regime, involving a small dimensionless parameter $0<\\varepsilon\\ll 1$ which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e. there are propagating waves with wavelength $O(\\varepsilon^2)$ and $O(1)$ in time and space, respectively. We begin with the conservative Crank-Nicolson finite difference (CNFD) method and establish rigorously its error estimate which depends explicitly on the mesh size $h$ and time step $\\tau$ as well as the small parameter $0<\\varepsilon\\le 1$. Based on the error bound, in order to obtain `correct' numerical solutions in the nonrelativistic limit regime, i.e. $0<\\varepsilon\\ll 1$, the CNFD method requests the $\\varepsilon$-scalability: $\\tau=O(\\varepsilon^3)$ and $h=O(\\sqrt{\\varepsilon})$. Then we propose and analyze two numerical methods for the discretization of the nonlinear Dirac equation by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and time-splitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their $\\varepsilon$-scalability is improved to $\\tau=O(\\varepsilon^2)$ and $h=O(1)$ when $0<\\varepsilon\\ll 1$ compared with the CNFD method. Extensive numerical results are reported to confirm our error estimates.

  7. Numerical method for shear bands in ductile metal with inclusions

    SciTech Connect

    Plohr, Jee Yeon N; Plohr, Bradley J

    2010-01-01

    A numerical method for mesoscale simulation of high strain-rate loading of ductile metal containing inclusions is described. Because of small-scale inhomogeneities, such a composite material is prone to localized shear deformation (adiabatic shear bands). The modeling framework is the Generalized Method of Cells of Paley and Aboudi [Mech. Materials, vol. 14, pp. /27-139, 1992], which ensures that the micromechanical response of the material is reflected in the behavior of the composite at the mesoscale. To calculate the effective plastic strain rate when shear bands are present, the analytic and numerical analysis of shear bands by Glimm, Plohr, and Sharp [Mech. Materials, vol. 24, pp. 31-41, 1996] is adapted and extended.

  8. Numerical method for wave forces acting on partially perforated caisson

    NASA Astrophysics Data System (ADS)

    Jiang, Feng; Tang, Xiao-cheng; Jin, Zhao; Zhang, Li; Chen, Hong-zhou

    2015-04-01

    The perforated caisson is widely applied to practical engineering because of its great advantages in effectively wave energy consumption and cost reduction. The attentions of many scientists were paid to the fluid-structure interaction between wave and perforated caisson studies, but until now, most concerns have been put on theoretical analysis and experimental model set up. In this paper, interaction between the wave and the partial perforated caisson in a 2D numerical wave flume is investigated by means of the renewed SPH algorithm, and the mathematical equations are in the form of SPH numerical approximation based on Navier-Stokes equations. The validity of the SPH mathematical method is examined and the simulated results are compared with the results of theoretical models, meanwhile the complex hydrodynamic characteristics when the water particles flow in or out of a wave absorbing chamber are analyzed and the wave pressure distribution of the perforated caisson is also addressed here. The relationship between the ratio of total horizontal force acting on caisson under regular waves and its influence factors is examined. The data show that the numerical calculation of the ratio of total horizontal force meets the empirical regression equation very well. The simulations of SPH about the wave nonlinearity and breaking are briefly depicted in the paper, suggesting that the advantages and great potentiality of the SPH method is significant compared with traditional methods.

  9. An alternative numerical method for the stationary pulsar magnetosphere

    NASA Astrophysics Data System (ADS)

    Takamori, Yohsuke; Okawa, Hirotada; Takamoto, Makoto; Suwa, Yudai

    2014-02-01

    Stationary pulsar magnetospheres in the force-free system are governed by the pulsar equation. In 1999, Contopoulos, Kazanas, and Fendt (hereafter CKF) numerically solved the pulsar equation and obtained a pulsar magnetosphere model called the CKF solution that has both closed and open magnetic field lines. The CKF solution is a successful solution, but it contains a poloidal current sheet that flows along the last open field line. This current sheet is artificially added to make the current system closed. In this paper, we suggest an alternative method to solve the pulsar equation and construct pulsar magnetosphere models without a current sheet. In our method, the pulsar equation is decomposed into Ampère's law and the force-free condition. We numerically solve these equations simultaneously with a fixed poloidal current. As a result, we obtain a pulsar magnetosphere model without a current sheet, which is similar to the CKF solution near the neutron star and has a jet-like structure at a distance along the pole. In addition, we discuss physical properties of the model and find that the force-free condition breaks down in a vicinity of the light cylinder due to dissipation that is included implicitly in the numerical method.

  10. EMERGY METHODS: VALUABLE INTEGRATED ASSESSMENT TOOLS

    EPA Science Inventory

    NHEERL's Atlantic Ecology Division is investigating emergy methods as tools for integrated assessment in several projects evaluating environmental impacts, policies, and alternatives for remediation and intervention. Emergy accounting is a methodology that provides a quantitative...

  11. A study of numerical methods of solution of the equations of motion of a controlled satellite under the influence of gravity gradient torque

    NASA Technical Reports Server (NTRS)

    Thompson, J. F.; Mcwhorter, J. C.; Siddiqi, S. A.; Shanks, S. P.

    1973-01-01

    Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.

  12. Dielectric Boundary Forces in Numerical Poisson-Boltzmann Methods: Theory and Numerical Strategies.

    PubMed

    Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

    2011-10-01

    Continuum modeling of electrostatic interactions based upon the numerical solutions of the Poisson-Boltzmann equation has been widely adopted in biomolecular applications. To extend their applications to molecular dynamics and energy minimization, robust and efficient methodologies to compute solvation forces must be developed. In this study, we have first reviewed the theory for the computation of dielectric boundary forces based on the definition of the Maxwell stress tensor. This is followed by a new formulation of the dielectric boundary force suitable for the finite-difference Poisson-Boltzmann methods. We have validated the new formulation with idealized analytical systems and realistic molecular systems. PMID:22125339

  13. Dielectric boundary force in numerical Poisson-Boltzmann methods: Theory and numerical strategies

    NASA Astrophysics Data System (ADS)

    Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

    2011-10-01

    Continuum modeling of electrostatic interactions based upon the numerical solutions of the Poisson-Boltzmann equation has been widely adopted in biomolecular applications. To extend their applications to molecular dynamics and energy minimization, robust and efficient methodologies to compute solvation forces must be developed. In this study, we have first reviewed the theory for the computation of dielectric boundary force based on the definition of the Maxwell stress tensor. This is followed by a new formulation of the dielectric boundary force suitable for the finite-difference Poisson-Boltzmann methods. We have validated the new formulation with idealized analytical systems and realistic molecular systems.

  14. 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.

  15. Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer

    SciTech Connect

    Lucas, D.S.

    2004-10-03

    This paper covers the basics of the implementation of the control volume method in the context of the Homogeneous Equilibrium Model (HEM)(T/H) code using the conservation equations of mass, momentum, and energy. This primer uses the advection equation as a template. The discussion will cover the basic equations of the control volume portion of the course in the primer, which includes the advection equation, numerical methods, along with the implementation of the various equations via FORTRAN into computer programs and the final result for a three equation HEM code and its validation.

  16. Explicit Integration of Extremely Stiff Reaction Networks: Partial Equilibrium Methods

    SciTech Connect

    Guidry, Mike W; Billings, J. J.; Hix, William Raphael

    2013-01-01

    In two preceding papers [1,2] we have shown that, when reaction networks are well removed from equilibrium, explicit asymptotic and quasi-steady-state approximations can give algebraically stabilized integration schemes that rival standard implicit methods in accuracy and speed for extremely stiff systems. However, we also showed that these explicit methods remain accurate but are no longer competitive in speed as the network approaches equilibrium. In this paper we analyze this failure and show that it is associated with the presence of fast equilibration timescales that neither asymptotic nor quasi-steady-state approximations are able to remove efficiently from the numerical integration. Based on this understanding, we develop a partial equilibrium method to deal effectively with the new partial equilibrium methods, give an integration scheme that plausibly can deal with the stiffest networks, even in the approach to equilibrium, with accuracy and speed competitive with that of implicit methods. Thus we demonstrate that algebraically stabilized explicit methods may offer alternatives to implicit integration of even extremely stiff systems, and that these methods may permit integration of much larger networks than have been feasible previously in a variety of fields.

  17. On the accuracy of numerical integration over the unit sphere applied to full network models

    NASA Astrophysics Data System (ADS)

    Itskov, Mikhail

    2016-05-01

    This paper is motivated by a recent study by Verron (Mecha Mater 89:216-228, 2015) which revealed huge errors of the numerical integration over the unit sphere in application to large strain problems. For the verification of numerical integration schemes we apply here other analytical integrals over the unit sphere which demonstrate much more accurate results. Relative errors of these integrals with respect to corresponding analytical solutions are evaluated also for a full network model of rubber elasticity based on a Padé approximation of the inverse Langevin function as the chain force. According to the results of our study, the numerical integration over the unit sphere can still be considered as a reliable and accurate tool for full network models.

  18. Numerical methods for the Poisson-Fermi equation in electrolytes

    NASA Astrophysics Data System (ADS)

    Liu, Jinn-Liang

    2013-08-01

    The Poisson-Fermi equation proposed by Bazant, Storey, and Kornyshev [Phys. Rev. Lett. 106 (2011) 046102] for ionic liquids is applied to and numerically studied for electrolytes and biological ion channels in three-dimensional space. This is a fourth-order nonlinear PDE that deals with both steric and correlation effects of all ions and solvent molecules involved in a model system. The Fermi distribution follows from classical lattice models of configurational entropy of finite size ions and solvent molecules and hence prevents the long and outstanding problem of unphysical divergence predicted by the Gouy-Chapman model at large potentials due to the Boltzmann distribution of point charges. The equation reduces to Poisson-Boltzmann if the correlation length vanishes. A simplified matched interface and boundary method exhibiting optimal convergence is first developed for this equation by using a gramicidin A channel model that illustrates challenging issues associated with the geometric singularities of molecular surfaces of channel proteins in realistic 3D simulations. Various numerical methods then follow to tackle a range of numerical problems concerning the fourth-order term, nonlinearity, stability, efficiency, and effectiveness. The most significant feature of the Poisson-Fermi equation, namely, its inclusion of steric and correlation effects, is demonstrated by showing good agreement with Monte Carlo simulation data for a charged wall model and an L type calcium channel model.

  19. Optimization methods and silicon solar cell numerical models

    NASA Technical Reports Server (NTRS)

    Girardini, K.; Jacobsen, S. E.

    1986-01-01

    An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.

  20. AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L2 OPTIMAL MASS TRANSFER PROBLEM*

    PubMed Central

    Haber, Eldad; Rehman, Tauseef; Tannenbaum, Allen

    2010-01-01

    In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L2 mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61–97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data. PMID:21278828

  1. Analysis of free turbulent shear flows by numerical methods

    NASA Technical Reports Server (NTRS)

    Korst, H. H.; Chow, W. L.; Hurt, R. F.; White, R. A.; Addy, A. L.

    1973-01-01

    Studies are described in which the effort was essentially directed to classes of problems where the phenomenologically interpreted effective transport coefficients could be absorbed by, and subsequently extracted from (by comparison with experimental data), appropriate coordinate transformations. The transformed system of differential equations could then be solved without further specifications or assumptions by numerical integration procedures. An attempt was made to delineate different regimes for which specific eddy viscosity models could be formulated. In particular, this would account for the carryover of turbulence from attached boundary layers, the transitory adjustment, and the asymptotic behavior of initially disturbed mixing regions. Such models were subsequently used in seeking solutions for the prescribed two-dimensional test cases, yielding a better insight into overall aspects of the exchange mechanisms.

  2. A Numerical Method for Solving Elasticity Equations with Interfaces

    PubMed Central

    Li, Zhilin; Wang, Liqun; Wang, Wei

    2012-01-01

    Solving elasticity equations with interfaces is a challenging problem for most existing methods. Nonetheless, it has wide applications in engineering and science. An accurate and efficient method is desired. In this paper, an efficient non-traditional finite element method with non-body-fitting grids is proposed to solve elasticity equations with interfaces. The main idea is to choose the test function basis to be the standard finite element basis independent of the interface and to choose the solution basis to be piecewise linear satisfying the jump conditions across the interface. The resulting linear system of equations is shown to be positive definite under certain assumptions. Numerical experiments show that this method is second order accurate in the L∞ norm for piecewise smooth solutions. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interface corner. PMID:22707984

  3. Advanced numerical methods in mesh generation and mesh adaptation

    SciTech Connect

    Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A

    2010-01-01

    Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge

  4. Novel Parallel Numerical Methods for Radiation& Neutron Transport

    SciTech Connect

    Brown, P N

    2001-03-06

    In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both.

  5. Mixed time integration methods for transient thermal analysis of structures

    NASA Technical Reports Server (NTRS)

    Liu, W. K.

    1983-01-01

    The computational methods used to predict and optimize the thermal-structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. The computer implementation aspects and numerical evaluation of these mixed time implicit-explicit algorithms in thermal analysis of structures are presented. A computationally-useful method of estimating the critical time step for linear quadrilateral element is also given. Numerical tests confirm the stability criterion and accuracy characteristics of the methods. The superiority of these mixed time methods to the fully implicit method or the fully explicit method is also demonstrated.

  6. A survey of payload integration methods

    NASA Technical Reports Server (NTRS)

    Engels, R. C.; Harcrow, H. W.

    1981-01-01

    The most prominent payload integration methods are presented and evaluated. The paper outlines the problem and some of the difficulties encountered when analyzing a coupled booster/payload system. Descriptions of both full-scale and short-cut methods are given together with an assessment of their strengths and weaknesses. Finally, an extensive list of references is included.

  7. Numerical Simulation of Parachute Inflation Process Using AN Overset Deforming Grids Method

    NASA Astrophysics Data System (ADS)

    Xia, Jian; Tian, Shuling; Wu, Yizhao

    A numerical method for the simulation of parachute inflation process is presented in this paper. The unsteady compressible N-S equations are fully coupled with MSD (Mass Spring Damper) structure model and integrated forward in time. The CFD solver is based on an unstructured finite volume algorithm and the preconditioning technique is applied to alleviate the stiffness caused by low Mach number. The Spalart-Allmaras one-equation turbulence model is implemented to evaluate the turbulent viscosity. The whole system (fluid equations and structural model equations) is marched implicitly in time using a dual time stepping method. An overset deforming grids method is adopted in this paper to deal with the very large domain deformation during the parachute inflation process. Finally numerical test is performed to validate the robustness of this method.

  8. Numerical Analysis of a Finite Element/Volume Penalty Method

    NASA Astrophysics Data System (ADS)

    Maury, Bertrand

    The penalty method makes it possible to incorporate a large class of constraints in general purpose Finite Element solvers like freeFEM++. We present here some contributions to the numerical analysis of this method. We propose an abstract framework for this approach, together with some general error estimates based on the discretization parameter ɛ and the space discretization parameter h. As this work is motivated by the possibility to handle constraints like rigid motion for fluid-particle flows, we shall pay a special attention to a model problem of this kind, where the constraint is prescribed over a subdomain. We show how the abstract estimate can be applied to this situation, in the case where a non-body-fitted mesh is used. In addition, we describe how this method provides an approximation of the Lagrange multiplier associated to the constraint.

  9. Numerical methods for high-dimensional probability density function equations

    NASA Astrophysics Data System (ADS)

    Cho, H.; Venturi, D.; Karniadakis, G. E.

    2016-01-01

    In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.

  10. Numerical analysis of composite STEEL-CONCRETE SECTIONS using integral equation of Volterra

    NASA Astrophysics Data System (ADS)

    Partov, Doncho; Kantchev, Vesselin

    2011-09-01

    The paper presents analysis of the stress and deflections changes due to creep in statically determinate composite steel-concrete beam. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann — Volterra for the concrete part. On the basis of the theory of the viscoelastic body of Arutyunian-Trost-Bažant for determining the redistribution of stresses in beam section between concrete plate and steel beam with respect to time "t", two independent Volterra integral equations of the second kind have been derived. Numerical method based on linear approximation of the singular kernal function in the integral equation is presented. Example with the model proposed is investigated. The creep functions is suggested by the model CEB MC90-99 and the "ACI 209R-92 model. The elastic modulus of concrete Ec(t) is assumed to be constant in time `t'. The obtained results from the both models are compared.

  11. Numerical analysis of composite STEEL-CONCRETE SECTIONS using integral equation of Volterra

    NASA Astrophysics Data System (ADS)

    Partov, Doncho; Kantchev, Vesselin

    2011-09-01

    The paper presents analysis of the stress and deflections changes due to creep in statically determinate composite steel-concrete beam. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann — Volterra for the concrete part. On the basis of the theory of the viscoelastic body of Arutyunian-Trost-Bažant for determining the redistribution of stresses in beam section between concrete plate and steel beam with respect to time "t", two independent Volterra integral equations of the second kind have been derived. Numerical method based on linear approximation of the singular kernal function in the integral equation is presented. Example with the model proposed is investigated. The creep functions is suggested by the model CEB MC90-99 and the "ACI 209R-92 model. The elastic modulus of concrete E c (t) is assumed to be constant in time `t'. The obtained results from the both models are compared.

  12. Improved numerical method for subchannel cross-flow calculations

    SciTech Connect

    Kaya, S.; Anghaie, S.

    1986-01-01

    COBRA-OSU is a fast running computer code for coupled kinetic and thermal-hydraulic analysis of nuclear reactor core subchannels, currently under development at Oregon State University. This code is a modified version of COBRA-IV with two major improved features. First, COBRA-OSU uses the Gaussian elimination method instead of Gauss-Seidel iteration for subchannel cross-flow calculation. Second, COBRA-OSU has an additional model for regionwise point reactor kinetics which includes all major feedback reactivity effects on calculation of the axial power profile during the course of a transient. This paper summarizes the improved numerical features of the COBRA-OSU code.

  13. A Fourier collocation time domain method for numerically solving Maxwell's equations

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    1991-01-01

    A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

  14. Numerical methods for the simulation of a coalescence-driven droplet size distribution

    NASA Astrophysics Data System (ADS)

    Bordás, Róbert; John, Volker; Schmeyer, Ellen; Thévenin, Dominique

    2013-06-01

    The droplet size distribution in a turbulent flow field is considered and modeled by means of a population balance system. This paper studies different numerical methods for the 4D population balance equation and their impact on an output of interest, the time-space-averaged droplet size distribution at the outlet, which is known from experiments. These methods include different interpolations of the experimental data at the inlet, various discretizations in time and space, and different schemes for computing the coalescence integrals. It will be shown that noticeable changes in the output of interest might occur. In addition, the computational efficiency of the studied methods is discussed.

  15. Numerical performance of half-sweep SOR method for solving second order composite closed Newton-Cotes system

    NASA Astrophysics Data System (ADS)

    Muthuvalu, Mohana Sundaram; Aruchunan, Elayaraja; Akhir, Mohd Kamalrulzaman Md; Sulaiman, Jumat; Karim, Samsul Ariffin Abdul

    2014-10-01

    In this paper, application of the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is extended by solving second order composite closed Newton-Cotes quadrature (2-CCNC) system. The performance of HSSOR method in solving 2-CCNC system is comparatively studied by their application on linear Fredholm integral equations of the second kind. The derivation and implementation of the method are discussed. In addition, numerical results by solving two test problems are included and compared with the standard Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) methods. Numerical results demonstrate that HSSOR method is an efficient method among the tested methods.

  16. A flexible importance sampling method for integrating subgrid processes

    NASA Astrophysics Data System (ADS)

    Raut, E. K.; Larson, V. E.

    2016-01-01

    Numerical models of weather and climate need to compute grid-box-averaged rates of physical processes such as microphysics. These averages are computed by integrating subgrid variability over a grid box. For this reason, an important aspect of atmospheric modeling is spatial integration over subgrid scales. The needed integrals can be estimated by Monte Carlo integration. Monte Carlo integration is simple and general but requires many evaluations of the physical process rate. To reduce the number of function evaluations, this paper describes a new, flexible method of importance sampling. It divides the domain of integration into eight categories, such as the portion that contains both precipitation and cloud, or the portion that contains precipitation but no cloud. It then allows the modeler to prescribe the density of sample points within each of the eight categories. The new method is incorporated into the Subgrid Importance Latin Hypercube Sampler (SILHS). The resulting method is tested on drizzling cumulus and stratocumulus cases. In the cumulus case, the sampling error can be considerably reduced by drawing more sample points from the region of rain evaporation.

  17. A flexible importance sampling method for integrating subgrid processes

    DOE PAGESBeta

    Raut, E. K.; Larson, V. E.

    2016-01-29

    Numerical models of weather and climate need to compute grid-box-averaged rates of physical processes such as microphysics. These averages are computed by integrating subgrid variability over a grid box. For this reason, an important aspect of atmospheric modeling is spatial integration over subgrid scales. The needed integrals can be estimated by Monte Carlo integration. Monte Carlo integration is simple and general but requires many evaluations of the physical process rate. To reduce the number of function evaluations, this paper describes a new, flexible method of importance sampling. It divides the domain of integration into eight categories, such as the portion that containsmore » both precipitation and cloud, or the portion that contains precipitation but no cloud. It then allows the modeler to prescribe the density of sample points within each of the eight categories. The new method is incorporated into the Subgrid Importance Latin Hypercube Sampler (SILHS). The resulting method is tested on drizzling cumulus and stratocumulus cases. In the cumulus case, the sampling error can be considerably reduced by drawing more sample points from the region of rain evaporation.« less

  18. A flexible importance sampling method for integrating subgrid processes

    SciTech Connect

    Raut, E. K.; Larson, V. E.

    2016-01-01

    Numerical models of weather and climate need to compute grid-box-averaged rates of physical processes such as microphysics. These averages are computed by integrating subgrid variability over a grid box. For this reason, an important aspect of atmospheric modeling is spatial integration over subgrid scales.

    The needed integrals can be estimated by Monte Carlo integration. Monte Carlo integration is simple and general but requires many evaluations of the physical process rate. To reduce the number of function evaluations, this paper describes a new, flexible method of importance sampling. It divides the domain of integration into eight categories, such as the portion that contains both precipitation and cloud, or the portion that contains precipitation but no cloud. It then allows the modeler to prescribe the density of sample points within each of the eight categories.

    The new method is incorporated into the Subgrid Importance Latin Hypercube Sampler (SILHS). The resulting method is tested on drizzling cumulus and stratocumulus cases. In the cumulus case, the sampling error can be considerably reduced by drawing more sample points from the region of rain evaporation.

  19. A flexible importance sampling method for integrating subgrid processes

    DOE PAGESBeta

    Raut, E. K.; Larson, V. E.

    2016-01-29

    Numerical models of weather and climate need to compute grid-box-averaged rates of physical processes such as microphysics. These averages are computed by integrating subgrid variability over a grid box. For this reason, an important aspect of atmospheric modeling is spatial integration over subgrid scales. The needed integrals can be estimated by Monte Carlo integration. Monte Carlo integration is simple and general but requires many evaluations of the physical process rate. To reduce the number of function evaluations, this paper describes a new, flexible method of importance sampling. It divides the domain of integration into eight categories, such as the portion that containsmore » both precipitation and cloud, or the portion that contains precipitation but no cloud. It then allows the modeler to prescribe the density of sample points within each of the eight categories. The new method is incorporated into the Subgrid Importance Latin Hypercube Sampler (SILHS). Here, the resulting method is tested on drizzling cumulus and stratocumulus cases. In the cumulus case, the sampling error can be considerably reduced by drawing more sample points from the region of rain evaporation.« less

  20. The determination of molecular structures by density functional theory. The evaluation of analytical energy gradients by numerical integration

    NASA Astrophysics Data System (ADS)

    Versluis, Louis; Ziegler, Tom

    1988-01-01

    An algorithm, based on numerical integration, has been proposed for the evaluation of analytical energy gradients within the Hartree-Fock-Slater (HFS) method. The utility of this algorithm in connection with molecular structure optimization is demonstrated by calculations on organics, main group molecules, and transition metal complexes. The structural parameters obtained from HFS calculations are in at least as good agreement with experiment as structures obtained from ab initio HF calculations. The time required to evaluate the energy gradient by numerical integration constitutes only a fraction (40%-25%) of the elapsed time in a full HFS-SCF calculation. The algorithm is also suitable for density functional methods with exchange-correlation potential different from that employed in the HFS method.

  1. Explicit Integration of Extremely Stiff Reaction Networks: Asymptotic Methods

    SciTech Connect

    Guidry, Mike W; Budiardja, R.; Feger, E.; Billings, J. J.; Hix, William Raphael; Messer, O.E.B.; Roche, K. J.; McMahon, E.; He, M.

    2013-01-01

    We show that, even for extremely stiff systems, explicit integration may compete in both accuracy and speed with implicit methods if algebraic methods are used to stabilize the numerical integration. The stabilizing algebra differs for systems well removed from equilibrium and those near equilibrium. This paper introduces a quantitative distinction between these two regimes and addresses the former case in depth, presenting explicit asymptotic methods appropriate when the system is extremely stiff but only weakly equilibrated. A second paper [1] examines quasi-steady-state methods as an alternative to asymptotic methods in systems well away from equilibrium and a third paper [2] extends these methods to equilibrium conditions in extremely stiff systems using partial equilibrium methods. All three papers present systematic evidence for timesteps competitive with implicit methods. Because explicit methods can execute a timestep faster than an implicit method, our results imply that algebraically stabilized explicit algorithms may offer a means to integration of larger networks than have been feasible previously in various disciplines.

  2. Optimization methods and silicon solar cell numerical models

    NASA Technical Reports Server (NTRS)

    Girardini, K.

    1986-01-01

    The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.

  3. Validation of a numerical method for unsteady flow calculations

    SciTech Connect

    Giles, M.; Haimes, R. . Dept. of Aeronautics and Astronautics)

    1993-01-01

    This paper describes and validates a numerical method for the calculation of unsteady inviscid and viscous flows. A companion paper compares experimental measurements of unsteady heat transfer on a transonic rotor with the corresponding computational results. The mathematical model is the Reynolds-averaged unsteady Navier-Stokes equations for a compressible ideal gas. Quasi-three-dimensionality is included through the use of a variable streamtube thickness. The numerical algorithm is unusual in two respects: (a) For reasons of efficiency and flexibility, it uses a hybrid Navier-Stokes/Euler method, and (b) to allow for the computation of stator/rotor combinations with arbitrary pitch ratio, a novel space-time coordinate transformation is used. Several test cases are presented to validate the performance of the computer program, UNSFLO. These include: (a) unsteady, inviscid flat plate cascade flows (b) steady and unsteady, viscous flat plate cascade flows, (c) steady turbine heat transfer and loss prediction. In the first two sets of cases comparisons are made with theory, and in the third the comparison is with experimental data.

  4. Poisson Green's function method for increased computational efficiency in numerical calculations of Coulomb coupling elements

    NASA Astrophysics Data System (ADS)

    Zimmermann, Anke; Kuhn, Sandra; Richter, Marten

    2016-01-01

    Often, the calculation of Coulomb coupling elements for quantum dynamical treatments, e.g., in cluster or correlation expansion schemes, requires the evaluation of a six dimensional spatial integral. Therefore, it represents a significant limiting factor in quantum mechanical calculations. If the size or the complexity of the investigated system increases, many coupling elements need to be determined. The resulting computational constraints require an efficient method for a fast numerical calculation of the Coulomb coupling. We present a computational method to reduce the numerical complexity by decreasing the number of spatial integrals for arbitrary geometries. We use a Green's function formulation of the Coulomb coupling and introduce a generalized scalar potential as solution of a generalized Poisson equation with a generalized charge density as the inhomogeneity. That enables a fast calculation of Coulomb coupling elements and, additionally, a straightforward inclusion of boundary conditions and arbitrarily spatially dependent dielectrics through the Coulomb Green's function. Particularly, if many coupling elements are included, the presented method, which is not restricted to specific symmetries of the model, presents a promising approach for increasing the efficiency of numerical calculations of the Coulomb interaction. To demonstrate the wide range of applications, we calculate internanostructure couplings, such as the Förster coupling, and illustrate the inclusion of symmetry considerations in the method for the Coulomb coupling between bound quantum dot states and unbound continuum states.

  5. 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.

  6. Differential temperature integrating diagnostic method and apparatus

    DOEpatents

    Doss, James D.; McCabe, Charles W.

    1976-01-01

    A method and device for detecting the presence of breast cancer in women by integrating the temperature difference between the temperature of a normal breast and that of a breast having a malignant tumor. The breast-receiving cups of a brassiere are each provided with thermally conductive material next to the skin, with a thermistor attached to the thermally conductive material in each cup. The thermistors are connected to adjacent arms of a Wheatstone bridge. Unbalance currents in the bridge are integrated with respect to time by means of an electrochemical integrator. In the absence of a tumor, both breasts maintain substantially the same temperature, and the bridge remains balanced. If the tumor is present in one breast, a higher temperature in that breast unbalances the bridge and the electrochemical cells integrate the temperature difference with respect to time.

  7. Asymmetric MRI magnet design using a hybrid numerical method.

    PubMed

    Zhao, H; Crozier, S; Doddrell, D M

    1999-12-01

    This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. PMID:10579958

  8. Integrated force method versus displacement method for finite element analysis

    NASA Technical Reports Server (NTRS)

    Patnaik, S. N.; Berke, L.; Gallagher, R. H.

    1991-01-01

    A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EEs) are integrated with the global compatibility conditions (CCs) to form the governing set of equations. In IFM the CCs are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

  9. Integrated force method versus displacement method for finite element analysis

    NASA Technical Reports Server (NTRS)

    Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.

    1990-01-01

    A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EE's) are integrated with the global compatibility conditions (CC's) to form the governing set of equations. In IFM the CC's are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

  10. Method to integrate full particle orbit in toroidal plasmas

    NASA Astrophysics Data System (ADS)

    Wei, X. S.; Xiao, Y.; Kuley, A.; Lin, Z.

    2015-09-01

    It is important to integrate full particle orbit accurately when studying charged particle dynamics in electromagnetic waves with frequency higher than cyclotron frequency. We have derived a form of the Boris scheme using magnetic coordinates, which can be used effectively to integrate the cyclotron orbit in toroidal geometry over a long period of time. The new method has been verified by a full particle orbit simulation in toroidal geometry without high frequency waves. The full particle orbit calculation recovers guiding center banana orbit. This method has better numeric properties than the conventional Runge-Kutta method for conserving particle energy and magnetic moment. The toroidal precession frequency is found to match that from guiding center simulation. Many other important phenomena in the presence of an electric field, such as E × B drift, Ware pinch effect and neoclassical polarization drift are also verified by the full orbit simulation.

  11. Advances in numerical solutions to integral equations in liquid state theory

    NASA Astrophysics Data System (ADS)

    Howard, Jesse J.

    Solvent effects play a vital role in the accurate description of the free energy profile for solution phase chemical and structural processes. The inclusion of solvent effects in any meaningful theoretical model however, has proven to be a formidable task. Generally, methods involving Poisson-Boltzmann (PB) theory and molecular dynamic (MD) simulations are used, but they either fail to accurately describe the solvent effects or require an exhaustive computation effort to overcome sampling problems. An alternative to these methods are the integral equations (IEs) of liquid state theory which have become more widely applicable due to recent advancements in the theory of interaction site fluids and the numerical methods to solve the equations. In this work a new numerical method is developed based on a Newton-type scheme coupled with Picard/MDIIS routines. To extend the range of these numerical methods to large-scale data systems, the size of the Jacobian is reduced using basis functions, and the Newton steps are calculated using a GMRes solver. The method is then applied to calculate solutions to the 3D reference interaction site model (RISM) IEs of statistical mechanics, which are derived from first principles, for a solute model of a pair of parallel graphene plates at various separations in pure water. The 3D IEs are then extended to electrostatic models using an exact treatment of the long-range Coulomb interactions for negatively charged walls and DNA duplexes in aqueous electrolyte solutions to calculate the density profiles and solution thermodynamics. It is found that the 3D-IEs provide a qualitative description of the density distributions of the solvent species when compared to MD results, but at a much reduced computational effort in comparison to MD simulations. The thermodynamics of the solvated systems are also qualitatively reproduced by the IE results. The findings of this work show the IEs to be a valuable tool for the study and prediction of

  12. A method for improving time-stepping numerics

    NASA Astrophysics Data System (ADS)

    Williams, P. D.

    2012-04-01

    In contemporary numerical simulations of the atmosphere, evidence suggests that time-stepping errors may be a significant component of total model error, on both weather and climate time-scales. This presentation will review the available evidence, and will then suggest a simple but effective method for substantially improving the time-stepping numerics at no extra computational expense. The most common time-stepping method is the leapfrog scheme combined with the Robert-Asselin (RA) filter. This method is used in the following atmospheric models (and many more): ECHAM, MAECHAM, MM5, CAM, MESO-NH, HIRLAM, KMCM, LIMA, SPEEDY, IGCM, PUMA, COSMO, FSU-GSM, FSU-NRSM, NCEP-GFS, NCEP-RSM, NSEAM, NOGAPS, RAMS, and CCSR/NIES-AGCM. Although the RA filter controls the time-splitting instability in these models, it also introduces non-physical damping and reduces the accuracy. This presentation proposes a simple modification to the RA filter. The modification has become known as the RAW filter (Williams 2011). When used in conjunction with the leapfrog scheme, the RAW filter eliminates the non-physical damping and increases the amplitude accuracy by two orders, yielding third-order accuracy. (The phase accuracy remains second-order.) The RAW filter can easily be incorporated into existing models, typically via the insertion of just a single line of code. Better simulations are obtained at no extra computational expense. Results will be shown from recent implementations of the RAW filter in various atmospheric models, including SPEEDY and COSMO. For example, in SPEEDY, the skill of weather forecasts is found to be significantly improved. In particular, in tropical surface pressure predictions, five-day forecasts made using the RAW filter have approximately the same skill as four-day forecasts made using the RA filter (Amezcua, Kalnay & Williams 2011). These improvements are encouraging for the use of the RAW filter in other models.

  13. Experimental analysis and numerical modeling of mollusk shells as a three dimensional integrated volume.

    PubMed

    Faghih Shojaei, M; Mohammadi, V; Rajabi, H; Darvizeh, A

    2012-12-01

    In this paper, a new numerical technique is presented to accurately model the geometrical and mechanical features of mollusk shells as a three dimensional (3D) integrated volume. For this purpose, the Newton method is used to solve the nonlinear equations of shell surfaces. The points of intersection on the shell surface are identified and the extra interior parts are removed. Meshing process is accomplished with respect to the coordinate of each point of intersection. The final 3D generated mesh models perfectly describe the spatial configuration of the mollusk shells. Moreover, the computational model perfectly matches with the actual interior geometry of the shells as well as their exterior architecture. The direct generation technique is employed to generate a 3D finite element (FE) model in ANSYS 11. X-ray images are taken to show the close similarity of the interior geometry of the models and the actual samples. A scanning electron microscope (SEM) is used to provide information on the microstructure of the shells. In addition, a set of compression tests were performed on gastropod shell specimens to obtain their ultimate compressive strength. A close agreement between experimental data and the relevant numerical results is demonstrated. PMID:23137621

  14. Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods

    NASA Technical Reports Server (NTRS)

    Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark

    2002-01-01

    Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.

  15. Unsaturated Shear Strength and Numerical Analysis Methods for Unsaturated Soils

    NASA Astrophysics Data System (ADS)

    Kim, D.; Kim, G.; Kim, D.; Baek, H.; Kang, S.

    2011-12-01

    The angles of shearing resistance(φb) and internal friction(φ') appear to be identical in low suction range, but the angle of shearing resistance shows non-linearity as suction increases. In most numerical analysis however, a fixed value for the angle of shearing resistance is applied even in low suction range for practical reasons, often leading to a false conclusion. In this study, a numerical analysis has been undertaken employing the estimated shear strength curve of unsaturated soils from the residual water content of SWCC proposed by Vanapalli et al.(1996). The result was also compared with that from a fixed value of φb. It is suggested that, in case it is difficult to measure the unsaturated shear strength curve through the triaxial soil tests, the estimated shear strength curve using the residual water content can be a useful alternative. This result was applied for analyzing the slope stablity of unsaturated soils. The effects of a continuous rainfall on slope stability were analyzed using a commercial program "SLOPE/W", with the coupled infiltration analysis program "SEEP/W" from the GEO-SLOPE International Ltd. The results show that, prior to the infiltration by the intensive rainfall, the safety factors using the estimated shear strength curve were substantially higher than that from the fixed value of φb at all time points. After the intensive infiltration, both methods showed a similar behavior.

  16. Implicit integration methods for dislocation dynamics

    SciTech Connect

    Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; Hommes, G.; Aubry, S.; Arsenlis, A.

    2015-01-20

    In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a way of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.

  17. Implicit integration methods for dislocation dynamics

    DOE PAGESBeta

    Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; Hommes, G.; Aubry, S.; Arsenlis, A.

    2015-01-20

    In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a waymore » of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.« less

  18. Bioluminescent bioreporter integrated circuit detection methods

    DOEpatents

    Simpson, Michael L.; Paulus, Michael J.; Sayler, Gary S.; Applegate, Bruce M.; Ripp, Steven A.

    2005-06-14

    Disclosed are monolithic bioelectronic devices comprising a bioreporter and an OASIC. These bioluminescent bioreporter integrated circuit are useful in detecting substances such as pollutants, explosives, and heavy-metals residing in inhospitable areas such as groundwater, industrial process vessels, and battlefields. Also disclosed are methods and apparatus for detection of particular analytes, including ammonia and estrogen compounds.

  19. Implicit integration methods for dislocation dynamics

    NASA Astrophysics Data System (ADS)

    Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; Hommes, G.; Aubry, S.; Arsenlis, A.

    2015-03-01

    In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. This paper investigates the viability of high-order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a way of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.

  20. Numerical method of characteristics for one-dimensional blood flow

    NASA Astrophysics Data System (ADS)

    Acosta, Sebastian; Puelz, Charles; Rivière, Béatrice; Penny, Daniel J.; Rusin, Craig G.

    2015-08-01

    Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.

  1. Fidelity of the Integrated Force Method Solution

    NASA Technical Reports Server (NTRS)

    Hopkins, Dale; Halford, Gary; Coroneos, Rula; Patnaik, Surya

    2002-01-01

    The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

  2. Application of variational principles and adjoint integrating factors for constructing numerical GFD models

    NASA Astrophysics Data System (ADS)

    Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

    2015-04-01

    The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each

  3. A multiple hypotheses uncertainty analysis in hydrological modelling: about model structure, landscape parameterization, and numerical integration

    NASA Astrophysics Data System (ADS)

    Pilz, Tobias; Francke, Till; Bronstert, Axel

    2016-04-01

    Until today a large number of competing computer models has been developed to understand hydrological processes and to simulate and predict streamflow dynamics of rivers. This is primarily the result of a lack of a unified theory in catchment hydrology due to insufficient process understanding and uncertainties related to model development and application. Therefore, the goal of this study is to analyze the uncertainty structure of a process-based hydrological catchment model employing a multiple hypotheses approach. The study focuses on three major problems that have received only little attention in previous investigations. First, to estimate the impact of model structural uncertainty by employing several alternative representations for each simulated process. Second, explore the influence of landscape discretization and parameterization from multiple datasets and user decisions. Third, employ several numerical solvers for the integration of the governing ordinary differential equations to study the effect on simulation results. The generated ensemble of model hypotheses is then analyzed and the three sources of uncertainty compared against each other. To ensure consistency and comparability all model structures and numerical solvers are implemented within a single simulation environment. First results suggest that the selection of a sophisticated numerical solver for the differential equations positively affects simulation outcomes. However, already some simple and easy to implement explicit methods perform surprisingly well and need less computational efforts than more advanced but time consuming implicit techniques. There is general evidence that ambiguous and subjective user decisions form a major source of uncertainty and can greatly influence model development and application at all stages.

  4. Simultaneous source-mask optimization: a numerical combining method

    NASA Astrophysics Data System (ADS)

    Mülders, Thomas; Domnenko, Vitaliy; Küchler, Bernd; Klimpel, Thomas; Stock, Hans-Jürgen; Poonawala, Amyn A.; Taravade, Kunal N.; Stanton, William A.

    2010-09-01

    A new method for simultaneous Source-Mask Optimization (SMO) is presented. In order to produce optimum imaging fidelity with respect to exposure lattitude, depth of focus (DoF) and mask error enhancement factor (MEEF) the presented method aims to leverage both, the available degrees of freedom of a pixelated source and those available for the mask layout. The approach described in this paper is designed as to work with dissected mask polygons. The dissection of the mask patterns is to be performed in advance (before SMO) with the Synopsys Proteus OPC engine, providing the available degrees of freedom for mask pattern optimization. This is similar to mask optimization done for optical proximity correction (OPC). Additionally, however, the illumination source will be simultaneously optimized. The SMO approach borrows many of the performance enhancement methods of OPC software for mask correction, but is especially designed as to simultaneously optimize a pixelated source shape as nowadays available in production environments. Designed as a numerical optimization approach the method is able to assess in acceptable times several hundreds of thousands source-mask combinations for small, critical layout snippets. This allows a global optimization scheme to be applied to the SMO problem which is expected to better explore the optimization space and thus to yield an improved solution quality compared to local optimizations methods. The method is applied to an example system for investigating the impact of source constraints on the SMO results. Also, it is investigated how well possibly conflicting goals of low MEEF and large DoF can be balanced.

  5. COMPARISON OF NUMERICAL METHODS FOR SOLVING THE SECOND-ORDER DIFFERENTIAL EQUATIONS OF MOLECULAR SCATTERING THEORY

    SciTech Connect

    Thomas, L.D.; Alexander, M.H.; Johnson, B.R.; Lester Jr., W. A.; Light, J.C.; McLenithan, K.D.; Parker, G.A.; Redmon, M.J.; Schmalz, T.G.; Secrest, D.; Walker, R.B.

    1980-07-01

    The numerical solution of coupled, second-order differential equations is a fundamental problem in theoretical physics and chemistry. There are presently over 20 commonly used methods. Unbiased comparisons of the methods are difficult to make and few have been attempted. Here we report a comparison of 11 different methods applied to 3 different test problems. The test problems have been constructed to approximate chemical systems of current research interest and to be representative of the state of the art in inelastic molecular collisions. All calculations were done on the same computer and the attempt was made to do all calculations to the same level of accuracy. The results of the initial tests indicated that an improved method might be obtained by using different methods in different integration regions. Such a hybrid program was developed and found to be at least 1.5 to 2.0 times faster than any individual method.

  6. Introduction to finite-difference methods for numerical fluid dynamics

    SciTech Connect

    Scannapieco, E.; Harlow, F.H.

    1995-09-01

    This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.

  7. Advanced numerical methods and software approaches for semiconductor device simulation

    SciTech Connect

    CAREY,GRAHAM F.; PARDHANANI,A.L.; BOVA,STEVEN W.

    2000-03-23

    In this article the authors concisely present several modern strategies that are applicable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of upwind and artificial dissipation schemes, generalization of the traditional Scharfetter-Gummel approach, Petrov-Galerkin and streamline-upwind Petrov Galerkin (SUPG), entropy variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. They have included numerical examples from the recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and they emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, they briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.

  8. a Numerical Method for Stability Analysis of Pinned Flexible Mechanisms

    NASA Astrophysics Data System (ADS)

    Beale, D. G.; Lee, S. W.

    1996-05-01

    A technique is presented to investigate the stability of mechanisms with pin-jointed flexible members. The method relies on a special floating frame from which elastic link co-ordinates are defined. Energies are easily developed for use in a Lagrange equation formulation, leading to a set of non-linear and mixed ordinary differential-algebraic equations of motion with constraints. Stability and bifurcation analysis is handled using a numerical procedure (generalized co-ordinate partitioning) that avoids the tedious and difficult task of analytically reducing the system of equations to a number equalling the system degrees of freedom. The proposed method was then applied to (1) a slider-crank mechanism with a flexible connecting rod and crank of constant rotational speed, and (2) a four-bar linkage with a flexible coupler with a constant speed crank. In both cases, a single pinned-pinned beam bending mode is employed to develop resonance curves and stability boundaries in the crank length-crank speed parameter plane. Flip and fold bifurcations are common occurrences in both mechanisms. The accuracy of the proposed method was also verified by comparison with previous experimental results [1].

  9. Numerical Simulations of Granular Dynamics: Method and Tests

    NASA Astrophysics Data System (ADS)

    Richardson, Derek C.; Walsh, K. J.; Murdoch, N.; Michel, P.; Schwartz, S. R.

    2010-10-01

    We present a new particle-based numerical method for the simulation of granular dynamics, with application to motions of particles (regolith) on small solar system bodies and planetary surfaces [1]. The method employs the parallel N-body tree code pkdgrav [2] to search for collisions and compute particle trajectories. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. Several tests of the method are presented, including a model granular "atmosphere” that achieves correct energy equipartition, and a series of tumbler simulations that compare favorably with actual laboratory experiments [3]. DCR and SRS acknowledge NASA Grant No. NNX08AM39G and NSF Grant No. AST0524875; KJW, the Poincaré Fellowship at OCA; NM, Thales Alenia Space and The Open University; and PM and NM, the French Programme National de Planétologie. References: [1] Richardson et al. (2010), Icarus, submitted; [2] Cf. Richardson et al. (2009), P&SS 57, 183 and references therein; [3] Brucks et al. (2007), PRE 75, 032301-1-032301-4.

  10. Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation

    DOE PAGESBeta

    Carey, Graham F.; Pardhanani, A. L.; Bova, S. W.

    2000-01-01

    In this article we concisely present several modern strategies that are applicable to driftdominated carrier transport in higher-order deterministic models such as the driftdiffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of “upwind” and artificial dissipation schemes, generalization of the traditional Scharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind Petrov Galerkin (SUPG), “entropy” variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of themore » methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.« less

  11. Effects of numerical methods on comparisons between experiments and simulations of shock-accelerated mixing.

    SciTech Connect

    Rider, William; Kamm, J. R.; Tomkins, C. D.; Zoldi, C. A.; Prestridge, K. P.; Marr-Lyon, M.; Rightley, P. M.; Benjamin, R. F.

    2002-01-01

    We consider the detailed structures of mixing flows for Richtmyer-Meshkov experiments of Prestridge et al. [PRE 00] and Tomkins et al. [TOM 01] and examine the most recent measurements from the experimental apparatus. Numerical simulations of these experiments are performed with three different versions of high resolution finite volume Godunov methods. We compare experimental data with simulations for configurations of one and two diffuse cylinders of SF{sub 6} in air using integral measures as well as fractal analysis and continuous wavelet transforms. The details of the initial conditions have a significant effect on the computed results, especially in the case of the double cylinder. Additionally, these comparisons reveal sensitive dependence of the computed solution on the numerical method.

  12. Numerical Comparison of Periodic MoM (Method of Moments) and BMIA (Banded Matrix Iteration Method)

    NASA Technical Reports Server (NTRS)

    Kim, Y.; Rodriguez, E.; Michel, T.

    1995-01-01

    The most popular numerical technique in rough surface scattering is the Method of Moments (MoM). Since the scattering patch size is finite, the edge current must be suppressed to obtain accurate scattering cross sections. Two standard ways to minimize the edge current are periodic boundary conditions and incident wave tapering. We compare the accuracy & computational requirements of these methods.

  13. 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

  14. Package for integrated optic circuit and method

    DOEpatents

    Kravitz, S.H.; Hadley, G.R.; Warren, M.E.; Carson, R.F.; Armendariz, M.G.

    1998-08-04

    A structure and method are disclosed for packaging an integrated optic circuit. The package comprises a first wall having a plurality of microlenses formed therein to establish channels of optical communication with an integrated optic circuit within the package. A first registration pattern is provided on an inside surface of one of the walls of the package for alignment and attachment of the integrated optic circuit. The package in one embodiment may further comprise a fiber holder for aligning and attaching a plurality of optical fibers to the package and extending the channels of optical communication to the fibers outside the package. In another embodiment, a fiber holder may be used to hold the fibers and align the fibers to the package. The fiber holder may be detachably connected to the package. 6 figs.

  15. Package for integrated optic circuit and method

    DOEpatents

    Kravitz, Stanley H.; Hadley, G. Ronald; Warren, Mial E.; Carson, Richard F.; Armendariz, Marcelino G.

    1998-01-01

    A structure and method for packaging an integrated optic circuit. The package comprises a first wall having a plurality of microlenses formed therein to establish channels of optical communication with an integrated optic circuit within the package. A first registration pattern is provided on an inside surface of one of the walls of the package for alignment and attachment of the integrated optic circuit. The package in one embodiment may further comprise a fiber holder for aligning and attaching a plurality of optical fibers to the package and extending the channels of optical communication to the fibers outside the package. In another embodiment, a fiber holder may be used to hold the fibers and align the fibers to the package. The fiber holder may be detachably connected to the package.

  16. Efficiency and Accuracy Verification of the Explicit Numerical Manifold Method for Dynamic Problems

    NASA Astrophysics Data System (ADS)

    Qu, X. L.; Wang, Y.; Fu, G. Y.; Ma, G. W.

    2015-05-01

    The original numerical manifold method (NMM) employs an implicit time integration scheme to achieve higher computational accuracy, but its efficiency is relatively low, especially when the open-close iterations of contact are involved. To improve its computational efficiency, a modified version of the NMM based on an explicit time integration algorithm is proposed in this study. The lumped mass matrix, internal force and damping vectors are derived for the proposed explicit scheme. A calibration study on P-wave propagation along a rock bar is conducted to investigate the efficiency and accuracy of the developed explicit numerical manifold method (ENMM) for wave propagation problems. Various considerations in the numerical simulations are discussed, and parametric studies are carried out to obtain an insight into the influencing factors on the efficiency and accuracy of wave propagation. To further verify the capability of the proposed ENMM, dynamic stability assessment for a fractured rock slope under seismic effect is analysed. It is shown that, compared to the original NMM, the computational efficiency of the proposed ENMM can be significantly improved.

  17. An equivalent domain integral method in the two-dimensional analysis of mixed mode crack problems

    NASA Technical Reports Server (NTRS)

    Raju, I. S.; Shivakumar, K. N.

    1990-01-01

    An equivalent domain integral (EDI) method for calculating J-integrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented.

  18. Numerical Methods for Forward and Inverse Problems in Discontinuous Media

    SciTech Connect

    Chartier, Timothy P.

    2011-03-08

    The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.

  19. Numerical Methods for Two-Dimensional Stem Cell Tissue Growth.

    PubMed

    Ovadia, Jeremy; Nie, Qing

    2014-01-01

    Growth of developing and regenerative biological tissues of different cell types is usually driven by stem cells and their local environment. Here, we present a computational framework for continuum tissue growth models consisting of stem cells, cell lineages, and diffusive molecules that regulate proliferation and differentiation through feedback. To deal with the moving boundaries of the models in both open geometries and closed geometries (through polar coordinates) in two dimensions, we transform the dynamic domains and governing equations to fixed domains, followed by solving for the transformation functions to track the interface explicitly. Clustering grid points in local regions for better efficiency and accuracy can be achieved by appropriate choices of the transformation. The equations resulting from the incompressibility of the tissue is approximated by high-order finite difference schemes and is solved using the multigrid algorithms. The numerical tests demonstrate an overall spatiotemporal second-order accuracy of the methods and their capability in capturing large deformations of the tissue boundaries. The methods are applied to two biological systems: stratified epithelia for studying the effects of two different types of stem cell niches and the scaling of a morphogen gradient with the size of the Drosophila imaginal wing disc during growth. Direct simulations of both systems suggest that that the computational framework is robust and accurate, and it can incorporate various biological processes critical to stem cell dynamics and tissue growth. PMID:24415847

  20. The numerical solution of ordinary differential equations by the Taylor series method

    NASA Technical Reports Server (NTRS)

    Silver, A. H.; Sullivan, E.

    1973-01-01

    A programming implementation of the Taylor series method is presented for solving ordinary differential equations. The compiler is written in PL/1, and the target language is FORTRAN IV. The reduction of a differential system to rational form is described along with the procedures required for automatic numerical integration. The Taylor method is compared with two other methods for a number of differential equations. Algorithms using the Taylor method to find the zeroes of a given differential equation and to evaluate partial derivatives are presented. An annotated listing of the PL/1 program which performs the reduction and code generation is given. Listings of the FORTRAN routines used by the Taylor series method are included along with a compilation of all the recurrence formulas used to generate the Taylor coefficients for non-rational functions.

  1. NUMERICAL APPROXIMATION OF SEMI-INTEGRALS AND SEMIDERIVATIVES BY PRODUCT QUADRATURE RULES

    EPA Science Inventory

    This paper is concerned with the numerical calculation of the semi-integral and semiderivative of a function f, whose values f (xj) are known on a discrete set of abscissas 0 = x(1) < x(2) < ... < x(n). A family of product quadrature rules is developed to approximate the semi-int...

  2. The Study of Gay-Berne Fluid:. Integral Equations Method

    NASA Astrophysics Data System (ADS)

    Khordad, Reza; Mohebbi, Mehran; Keshavarzi, Abolla; Poostforush, Ahmad; Ghajari Haghighi, Farnaz

    We study a classical fluid of nonspherical molecules. The components of the fluid are the ellipsoidal molecules interacting through the Gay-Berne potential model. A method is described, which allows the Percus-Yevick (PY) and hypernetted-chain (HNC) integral equation theories to be solved numerically for this fluid. Explicit results are given and comparisons are made with recent Monte Carlo (MC) simulations. It is found that, at lower cutoff lmax, the HNC and the PY closures give significantly different results. The HNC and PY (approximately) theories, at higher cutoff lmax, are superior in predicting the existence of the phase transition in a qualitative agreement with computer simulation.

  3. Extremal polynomials and methods of optimization of numerical algorithms

    SciTech Connect

    Lebedev, V I

    2004-10-31

    Chebyshev-Markov-Bernstein-Szegoe polynomials C{sub n}(x) extremal on [-1,1] with weight functions w(x)=(1+x){sup {alpha}}(1- x){sup {beta}}/{radical}(S{sub l}(x)) where {alpha},{beta}=0,1/2 and S{sub l}(x)={pi}{sub k=1}{sup m}(1-c{sub k}T{sub l{sub k}}(x))>0 are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight p(x)=w{sup 2}(x)(1-x{sup 2}){sup -1/2}. The parameters of optimal Chebyshev iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko-Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshev filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.

  4. Extremal polynomials and methods of optimization of numerical algorithms

    NASA Astrophysics Data System (ADS)

    Lebedev, V. I.

    2004-10-01

    Chebyshëv-Markov-Bernstein-Szegö polynomials C_n(x) extremal on \\lbrack -1,1 \\rbrack with weight functions w(x)=(1+x)^\\alpha(1- x)^\\beta/\\sqrt{S_l(x)} where \\alpha,\\beta=0,\\frac12 and S_l(x)=\\prod_{k=1}^m(1-c_kT_{l_k}(x))>0 are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight p(x)=w^2(x)(1-x^2)^{-1/2}. The parameters of optimal Chebyshëv iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko-Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshëv filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.

  5. Numerical Weather Predictions Evaluation Using Spatial Verification Methods

    NASA Astrophysics Data System (ADS)

    Tegoulias, I.; Pytharoulis, I.; Kotsopoulos, S.; Kartsios, S.; Bampzelis, D.; Karacostas, T.

    2014-12-01

    During the last years high-resolution numerical weather prediction simulations have been used to examine meteorological events with increased convective activity. Traditional verification methods do not provide the desired level of information to evaluate those high-resolution simulations. To assess those limitations new spatial verification methods have been proposed. In the present study an attempt is made to estimate the ability of the WRF model (WRF -ARW ver3.5.1) to reproduce selected days with high convective activity during the year 2010 using those feature-based verification methods. Three model domains, covering Europe, the Mediterranean Sea and northern Africa (d01), the wider area of Greece (d02) and central Greece - Thessaly region (d03) are used at horizontal grid-spacings of 15km, 5km and 1km respectively. By alternating microphysics (Ferrier, WSM6, Goddard), boundary layer (YSU, MYJ) and cumulus convection (Kain-­-Fritsch, BMJ) schemes, a set of twelve model setups is obtained. The results of those simulations are evaluated against data obtained using a C-Band (5cm) radar located at the centre of the innermost domain. Spatial characteristics are well captured but with a variable time lag between simulation results and radar data. Acknowledgements: This research is co­financed by the European Union (European Regional Development Fund) and Greek national funds, through the action "COOPERATION 2011: Partnerships of Production and Research Institutions in Focused Research and Technology Sectors" (contract number 11SYN_8_1088 - DAPHNE) in the framework of the operational programme "Competitiveness and Entrepreneurship" and Regions in Transition (OPC II, NSRF 2007-­-2013).

  6. Theoretical study of the partial derivatives produced by numerical integration of satellite orbits.

    NASA Astrophysics Data System (ADS)

    Hadjifotinou, K. G.; Ichtiaroglou, S.

    1997-06-01

    For the two-body system Saturn-Mimas and the theoretical three-body non-resonant system Saturn-Mimas-Tethys we present a theoretical analysis of the behaviour of the partial derivatives of the satellites' coordinates with respect to the parameters of the system, namely the satellites' initial conditions and their mass-ratios over Saturn. With the use of Floquet theory for the stability of periodic orbits we prove that all the partial derivatives have amplitudes that increase linearly with time. Their motion is a combination of periodic motions the periods of which can also be accurately predicted by the theory. This theoretical model can be used for checking the accuracy of the results of the different numerical integration methods used on satellite systems with the purpose of fitting the results to observations or analytical theories. On this basis, in the last part of the paper we extend the investigation of Hadjifotinou & Harper (1995A&A...303..940H) on the stability and efficience of the 10^th^-order Gauss-Jackson backward difference and the Runge-Kutta-Nystroem RKN12(10)17M methods by now applying them to the above mentioned three-body system.

  7. Orbit determination based on meteor observations using numerical integration of equations of motion

    NASA Astrophysics Data System (ADS)

    Dmitriev, Vasily; Lupovka, Valery; Gritsevich, Maria

    2015-11-01

    Recently, there has been a worldwide proliferation of instruments and networks dedicated to observing meteors, including airborne and future space-based monitoring systems . There has been a corresponding rapid rise in high quality data accumulating annually. In this paper, we present a method embodied in the open-source software program "Meteor Toolkit", which can effectively and accurately process these data in an automated mode and discover the pre-impact orbit and possibly the origin or parent body of a meteoroid or asteroid. The required input parameters are the topocentric pre-atmospheric velocity vector and the coordinates of the atmospheric entry point of the meteoroid, i.e. the beginning point of visual path of a meteor, in an Earth centered-Earth fixed coordinate system, the International Terrestrial Reference Frame (ITRF). Our method is based on strict coordinate transformation from the ITRF to an inertial reference frame and on numerical integration of the equations of motion for a perturbed two-body problem. Basic accelerations perturbing a meteoroid's orbit and their influence on the orbital elements are also studied and demonstrated. Our method is then compared with several published studies that utilized variations of a traditional analytical technique, the zenith attraction method, which corrects for the direction of the meteor's trajectory and its apparent velocity due to Earth's gravity. We then demonstrate the proposed technique on new observational data obtained from the Finnish Fireball Network (FFN) as well as on simulated data. In addition, we propose a method of analysis of error propagation, based on general rule of covariance transformation.

  8. MOLECULAR LINE EMISSION FROM MULTIFLUID SHOCK WAVES. I. NUMERICAL METHODS AND BENCHMARK TESTS

    SciTech Connect

    Ciolek, Glenn E.; Roberge, Wayne G. E-mail: roberw@rpi.edu

    2013-05-01

    We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part, independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other, equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are << magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (1) MHD wave packets ranging over orders of magnitude in length- and timescales, (2) early evolution of multifluid shocks caused by two colliding clouds, and (3) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to an MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.

  9. Molecular Line Emission from Multifluid Shock Waves. I. Numerical Methods and Benchmark Tests

    NASA Astrophysics Data System (ADS)

    Ciolek, Glenn E.; Roberge, Wayne G.

    2013-05-01

    We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part, independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other, equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are Lt magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (1) MHD wave packets ranging over orders of magnitude in length- and timescales, (2) early evolution of multifluid shocks caused by two colliding clouds, and (3) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to an MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.

  10. The finite element method: Is weighted volume integration essential?

    NASA Astrophysics Data System (ADS)

    Narasimhan, T. N.

    In developing finite element equations for steady state and transient diffusion-type processes, weighted volume integration is generally assumed to be an intrinsic requirement. It is shown that such finite element equations can be developed directly and with ease on the basis of the elementary notion of a surface integral. Although weighted volume integration is mathematically correct, the algebraic equations stemming from it are no more informative than those derived directly on the basis of a surface integral. An interesting upshot is that the derivation based on surface integration does not require knowledge of a partial differential equation but yet is logically rigorous. It is commonly stated that weighted volume integration of the differential equation helps one carry out analyses of errors, convergence and existence, and therefore, weighted volume integration is preferable. It is suggested that because the direct derivation is logically consistent, numerical solutions emanating from it must be testable for accuracy and internal consistency in ways that the style of which may differ from the classical procedures of error- and convergence-analysis. In addition to simplifying the teaching of the finite element method, the thoughts presented in this paper may lead to establishing the finite element method independently in its own right, rather than it being a surrogate of the differential equation. The purpose of this paper is not to espouse any one particular way of formulating the finite element equations. Rather, it is one of introspection. The desire is to critically examine our traditional way of doing things and inquire whether alternate approaches may reveal to us new and interesting insights.

  11. On testing a subroutine for the numerical integration of ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.

    1973-01-01

    This paper discusses how to numerically test a subroutine for the solution of ordinary differential equations. Results obtained with a variable order Adams method are given for eleven simple test cases.-

  12. A Numerical Method for Determining Diffusivity from Annealing Experiments

    NASA Astrophysics Data System (ADS)

    Harris-Kuhlman, K. R.; Kulcinski, G. L.

    1998-12-01

    Terrestrial analogs of lunar ilmenite (FeTiO3) have been implanted with solar-wind energy 4He at 4 keV and 3He at 3 keV using Plasma Source Ion Implantation (PSII). Isochronal annealing of the samples revealed thermally induced 4He evolution similar to the helium release of the Apollo 11 regoliths reported by Pepin, et. al., [1970]. These annealing experiments are analyzed with a three dimensional numerical method based on Fick's law for diffusion. An iterative method is used to calculate the diffusivity. The code uses an assumed diffusivity to calculate the amount of gas released during a temperature step. The initial depth profile of the implanted species is generated using the TRIM electronic stopping code [Ziegler, 1996]. The calculated value is compared to the measured value and a linear regression is used to calculate a new diffusivity until there is convergence within a specified tolerance level. The diffusivity as a function of temperature is then fitted to an Arrhenius equation. Analysis of results for 4 keV 4He on ilmenite shows two distinct regions of Arrehnius behavior with activation energies of 0.5 +/- 0.1 eV at emperatures below 800 deg C and 1.5 +/- 0.2 eV at temperatures from 800 deg C to 1100 deg C. Pepin, R. O., L. E. Nyquist, D. Phinney, and D. C. Black (1970) "Rare Gases in Apollo 11 Lunar Material," Proceedings of the Apollo 11 Lunar Science Conference, 2, pp. 1435-1454. Ziegler, J. P. (1996) SRIM Instruction Manual: The Stopping and Range of Ions in Matter, (Yorktown, New York: IBM - Research); based on Ziegler, J. P., J. P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids, (New York: Pergamon Press, 1985).

  13. Integrated Compartment Method appication to the transient heat transfer in gas-cooled reactor

    SciTech Connect

    Chen, N.C.J.; Yeh, G.T.

    1983-01-01

    Integrated Compartment Method (ICM), an effective numerical integration algorithm, was developed to solve the transient heat conduction coupled with convection. Application of the ICM to the mathematical model simulating a graphite test structure heated in an annular flow stream of hot helium has been successfully demonstrated. However, the model validation can not be performed until experimental data become available.

  14. A Numerical Method for Obtaining Monoenergetic Neutron Flux Distributions and Transmissions in Multiple-Region Slabs

    NASA Technical Reports Server (NTRS)

    Schneider, Harold

    1959-01-01

    This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.

  15. Spectrophotometric methods for the evaluation of acidity constants-I Numerical methods for single equilibria.

    PubMed

    Asuero, A G; Navas, M J; Jiminez-Trillo, J L

    1986-02-01

    The spectrophotometric methods applicable to the numerical evaluation of acidity constants of monobasic acids are briefly reviewed. The equations are presented in a form suitable for easy calculation with a programmable pocket calculator. The aim of this paper is to cover a gap in the education analytical literature. PMID:18964064

  16. 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…

  17. Approximation method to compute domain related integrals in structural studies

    NASA Astrophysics Data System (ADS)

    Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.

    2015-11-01

    Various engineering calculi use integral calculus in theoretical models, i.e. analytical and numerical models. For usual problems, integrals have mathematical exact solutions. If the domain of integration is complicated, there may be used several methods to calculate the integral. The first idea is to divide the domain in smaller sub-domains for which there are direct calculus relations, i.e. in strength of materials the bending moment may be computed in some discrete points using the graphical integration of the shear force diagram, which usually has a simple shape. Another example is in mathematics, where the surface of a subgraph may be approximated by a set of rectangles or trapezoids used to calculate the definite integral. The goal of the work is to introduce our studies about the calculus of the integrals in the transverse section domains, computer aided solutions and a generalizing method. The aim of our research is to create general computer based methods to execute the calculi in structural studies. Thus, we define a Boolean algebra which operates with ‘simple’ shape domains. This algebraic standpoint uses addition and subtraction, conditioned by the sign of every ‘simple’ shape (-1 for the shapes to be subtracted). By ‘simple’ shape or ‘basic’ shape we define either shapes for which there are direct calculus relations, or domains for which their frontiers are approximated by known functions and the according calculus is carried out using an algorithm. The ‘basic’ shapes are linked to the calculus of the most significant stresses in the section, refined aspect which needs special attention. Starting from this idea, in the libraries of ‘basic’ shapes, there were included rectangles, ellipses and domains whose frontiers are approximated by spline functions. The domain triangularization methods suggested that another ‘basic’ shape to be considered is the triangle. The subsequent phase was to deduce the exact relations for the

  18. Integrated Force Method for Indeterminate Structures

    NASA Technical Reports Server (NTRS)

    Hopkins, Dale A.; Halford, Gary R.; Patnaik, Surya N.

    2008-01-01

    Two methods of solving indeterminate structural-mechanics problems have been developed as products of research on the theory of strain compatibility. In these methods, stresses are considered to be the primary unknowns (in contrast to strains and displacements being considered as the primary unknowns in some prior methods). One of these methods, denoted the integrated force method (IFM), makes it possible to compute stresses, strains, and displacements with high fidelity by use of modest finite-element models that entail relatively small amounts of computation. The other method, denoted the completed Beltrami Mitchell formulation (CBMF), enables direct determination of stresses in an elastic continuum with general boundary conditions, without the need to first calculate displacements as in traditional methods. The equilibrium equation, the compatibility condition, and the material law are the three fundamental concepts of the theory of structures. For almost 150 years, it has been commonly supposed that the theory is complete. However, until now, the understanding of the compatibility condition remained incomplete, and the compatibility condition was confused with the continuity condition. Furthermore, the compatibility condition as applied to structures in its previous incomplete form was inconsistent with the strain formulation in elasticity.

  19. NUMERICAL METHODS FOR THE SIMULATION OF HIGH INTENSITY HADRON SYNCHROTRONS.

    SciTech Connect

    LUCCIO, A.; D'IMPERIO, N.; MALITSKY, N.

    2005-09-12

    Numerical algorithms for PIC simulation of beam dynamics in a high intensity synchrotron on a parallel computer are presented. We introduce numerical solvers of the Laplace-Poisson equation in the presence of walls, and algorithms to compute tunes and twiss functions in the presence of space charge forces. The working code for the simulation here presented is SIMBAD, that can be run as stand alone or as part of the UAL (Unified Accelerator Libraries) package.

  20. A method to determine integrated steroid levels in wildlife claws.

    PubMed

    Matas, Devorah; Keren-Rotem, Tammy; Koren, Lee

    2016-05-01

    Glucocorticoids act throughout life to regulate numerous physiological and behavioral processes. Their levels are therefore highly labile, reacting to varying conditions and stressors. Hence, measuring glucocorticoids (and other steroids) in wildlife is challenging, and devising methods that are unaffected by the stress of capture and handling should be explored. Here we use the tip of free-ranging chameleons' claws that were cut to allow individual identification, and report a steroids extraction and quantification method. Claw steroids present an integrated level representing the period of claw growth. We found that we could measure corticosterone in small amounts of chameleon claw matrix using commercial EIA kits. Using this method, we learned that in wild male chameleons, claw corticosterone levels were associated with body size. We suggest that claw-testing can potentially provide an ideal matrix for wildlife biomonitoring. PMID:26993343

  1. Science-Based Approach for Advancing Marine and Hydrokinetic Energy: Integrating Numerical Simulations with Experiments

    NASA Astrophysics Data System (ADS)

    Sotiropoulos, F.; Kang, S.; Chamorro, L. P.; Hill, C.

    2011-12-01

    The field of MHK energy is still in its infancy lagging approximately a decade or more behind the technology and development progress made in wind energy engineering. Marine environments are characterized by complex topography and three-dimensional (3D) turbulent flows, which can greatly affect the performance and structural integrity of MHK devices and impact the Levelized Cost of Energy (LCoE). Since the deployment of multi-turbine arrays is envisioned for field applications, turbine-to-turbine interactions and turbine-bathymetry interactions need to be understood and properly modeled so that MHK arrays can be optimized on a site specific basis. Furthermore, turbulence induced by MHK turbines alters and interacts with the nearby ecosystem and could potentially impact aquatic habitats. Increased turbulence in the wake of MHK devices can also change the shear stress imposed on the bed ultimately affecting the sediment transport and suspension processes in the wake of these structures. Such effects, however, remain today largely unexplored. In this work a science-based approach integrating state-of-the-art experimentation with high-resolution computational fluid dynamics is proposed as a powerful strategy for optimizing the performance of MHK devices and assessing environmental impacts. A novel numerical framework is developed for carrying out Large-Eddy Simulation (LES) in arbitrarily complex domains with embedded MHK devices. The model is able to resolve the geometrical complexity of real-life MHK devices using the Curvilinear Immersed Boundary (CURVIB) method along with a wall model for handling the flow near solid surfaces. Calculations are carried out for an axial flow hydrokinetic turbine mounted on the bed of rectangular open channel on a grid with nearly 200 million grid nodes. The approach flow corresponds to fully developed turbulent open channel flow and is obtained from a separate LES calculation. The specific case corresponds to that studied

  2. An Integrated Numerical Hydrodynamic Shallow Flow-Solute Transport Model for Urban Area

    NASA Astrophysics Data System (ADS)

    Alias, N. A.; Mohd Sidek, L.

    2016-03-01

    The rapidly changing on land profiles in the some urban areas in Malaysia led to the increasing of flood risk. Extensive developments on densely populated area and urbanization worsen the flood scenario. An early warning system is really important and the popular method is by numerically simulating the river and flood flows. There are lots of two-dimensional (2D) flood model predicting the flood level but in some circumstances, still it is difficult to resolve the river reach in a 2D manner. A systematic early warning system requires a precisely prediction of flow depth. Hence a reliable one-dimensional (1D) model that provides accurate description of the flow is essential. Research also aims to resolve some of raised issues such as the fate of pollutant in river reach by developing the integrated hydrodynamic shallow flow-solute transport model. Presented in this paper are results on flow prediction for Sungai Penchala and the convection-diffusion of solute transports simulated by the developed model.

  3. Methods of Genomic Competency Integration in Practice

    PubMed Central

    Jenkins, Jean; Calzone, Kathleen A.; Caskey, Sarah; Culp, Stacey; Weiner, Marsha; Badzek, Laurie

    2015-01-01

    Purpose Genomics is increasingly relevant to health care, necessitating support for nurses to incorporate genomic competencies into practice. The primary aim of this project was to develop, implement, and evaluate a year-long genomic education intervention that trained, supported, and supervised institutional administrator and educator champion dyads to increase nursing capacity to integrate genomics through assessments of program satisfaction and institutional achieved outcomes. Design Longitudinal study of 23 Magnet Recognition Program® Hospitals (21 intervention, 2 controls) participating in a 1-year new competency integration effort aimed at increasing genomic nursing competency and overcoming barriers to genomics integration in practice. Methods Champion dyads underwent genomic training consisting of one in-person kick-off training meeting followed by monthly education webinars. Champion dyads designed institution-specific action plans detailing objectives, methods or strategies used to engage and educate nursing staff, timeline for implementation, and outcomes achieved. Action plans focused on a minimum of seven genomic priority areas: champion dyad personal development; practice assessment; policy content assessment; staff knowledge needs assessment; staff development; plans for integration; and anticipated obstacles and challenges. Action plans were updated quarterly, outlining progress made as well as inclusion of new methods or strategies. Progress was validated through virtual site visits with the champion dyads and chief nursing officers. Descriptive data were collected on all strategies or methods utilized, and timeline for achievement. Descriptive data were analyzed using content analysis. Findings The complexity of the competency content and the uniqueness of social systems and infrastructure resulted in a significant variation of champion dyad interventions. Conclusions Nursing champions can facilitate change in genomic nursing capacity through

  4. Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

    NASA Astrophysics Data System (ADS)

    Rangan, Aaditya V.; Cai, David; Tao, Louis

    2007-02-01

    Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of

  5. A Novel Method of Line Detection using Image Integration Method

    NASA Astrophysics Data System (ADS)

    Lin, Daniel; Sun, Bo

    2015-03-01

    We developed a novel line detection algorithm based on image integration method. Hough Transformation uses spatial image gradient method to detect lines on an image. This is problematic because if the image has a region of high noise intensity, the gradient would point towards the noisy region . Denoising the noisy image requires an application of sophisticated noise reduction algorithm which increases computation complexity. Our algorithm can remedy this problem by averaging the pixels around the image region of interest. We were able to detect collagen fiber lines on an image produced by confocal microscope.

  6. A Fast Numerical Method for a Nonlinear Black-Scholes Equation

    NASA Astrophysics Data System (ADS)

    Koleva, Miglena N.; Vulkov, Lubin G.

    2009-11-01

    In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed.

  7. A numerical method for computing unsteady 2-D boundary layer flows

    NASA Technical Reports Server (NTRS)

    Krainer, Andreas

    1988-01-01

    A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.

  8. Solution methods for very highly integrated circuits.

    SciTech Connect

    Nong, Ryan; Thornquist, Heidi K.; Chen, Yao; Mei, Ting; Santarelli, Keith R.; Tuminaro, Raymond Stephen

    2010-12-01

    While advances in manufacturing enable the fabrication of integrated circuits containing tens-to-hundreds of millions of devices, the time-sensitive modeling and simulation necessary to design these circuits poses a significant computational challenge. This is especially true for mixed-signal integrated circuits where detailed performance analyses are necessary for the individual analog/digital circuit components as well as the full system. When the integrated circuit has millions of devices, performing a full system simulation is practically infeasible using currently available Electrical Design Automation (EDA) tools. The principal reason for this is the time required for the nonlinear solver to compute the solutions of large linearized systems during the simulation of these circuits. The research presented in this report aims to address the computational difficulties introduced by these large linearized systems by using Model Order Reduction (MOR) to (i) generate specialized preconditioners that accelerate the computation of the linear system solution and (ii) reduce the overall dynamical system size. MOR techniques attempt to produce macromodels that capture the desired input-output behavior of larger dynamical systems and enable substantial speedups in simulation time. Several MOR techniques that have been developed under the LDRD on 'Solution Methods for Very Highly Integrated Circuits' will be presented in this report. Among those presented are techniques for linear time-invariant dynamical systems that either extend current approaches or improve the time-domain performance of the reduced model using novel error bounds and a new approach for linear time-varying dynamical systems that guarantees dimension reduction, which has not been proven before. Progress on preconditioning power grid systems using multi-grid techniques will be presented as well as a framework for delivering MOR techniques to the user community using Trilinos and the Xyce circuit simulator

  9. Numerical Analysis on the Vortex Pattern and Flux Particle Dispersion in KR Method Using MPS Method

    NASA Astrophysics Data System (ADS)

    Hirata, N.; Xu, Y.; Anzai, K.

    2015-06-01

    The mechanically-stirring vessel is widely used in many fields, such as chemical reactor, bioreactor, and metallurgy, etc. The type of vortex mode that formed during impeller stirring has great effect on stirring efficiency, chemical reacting rate and air entrapment. Many efforts have been made to numerically simulate the fluid flow in the stirring vessel with classical Eulerian method. However, it is difficult to directly investigate the vortex mode and flux particle dispersion. Therefore, moving particle semi-implicit (MPS) method, which is based on Lagrangian method, is applied to simulate the fluid flow in a KR method in this practice. Top height and bottom heights of vortex surface in a steady state under several rotation speed was taken as key parameters to compare the results of numerical and published results. Flux particle dispersion behaviour under a rotation speed range from 80 to 480 rpm was also compared with the past study. The result shows that the numerical calculation has high consistency with experimental results. It is confirmed that the calculation using MPS method well reflected the vortex mode and flux particle dispersion in a mechanically-stirring vessel.

  10. Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles, theory

    NASA Technical Reports Server (NTRS)

    Thomas, P. D.

    1979-01-01

    The theoretical foundation and formulation of a numerical method for predicting the viscous flowfield in and about isolated three dimensional nozzles of geometrically complex configuration are presented. High Reynolds number turbulent flows are of primary interest for any combination of subsonic, transonic, and supersonic flow conditions inside or outside the nozzle. An alternating-direction implicit (ADI) numerical technique is employed to integrate the unsteady Navier-Stokes equations until an asymptotic steady-state solution is reached. Boundary conditions are computed with an implicit technique compatible with the ADI technique employed at interior points of the flow region. The equations are formulated and solved in a boundary-conforming curvilinear coordinate system. The curvilinear coordinate system and computational grid is generated numerically as the solution to an elliptic boundary value problem. A method is developed that automatically adjusts the elliptic system so that the interior grid spacing is controlled directly by the a priori selection of the grid spacing on the boundaries of the flow region.

  11. Transient 3d contact problems—NTS method: mixed methods and conserving integration

    NASA Astrophysics Data System (ADS)

    Hesch, Christian; Betsch, Peter

    2011-10-01

    The present work deals with a new formulation for transient large deformation contact problems. It is well known, that one-step implicit time integration schemes for highly non-linear systems fail to conserve the total energy of the system. To deal with this drawback, a mixed method is newly proposed in conjunction with the concept of a discrete gradient. In particular, we reformulate the well known and widely-used node-to-segment methods and establish an energy-momentum scheme. The advocated approach ensures robustness and enhanced numerical stability, demonstrated in several three-dimensional applications of the proposed algorithm.

  12. Some remarks on the numerical computation of integrals on an unbounded interval

    NASA Astrophysics Data System (ADS)

    Capobianco, M.; Criscuolo, G.

    2007-08-01

    An account of the error and the convergence theory is given for Gauss?Laguerre and Gauss?Radau?Laguerre quadrature formulae. We develop also truncated models of the original Gauss rules to compute integrals extended over the positive real axis. Numerical examples confirming the theoretical results are given comparing these rules among themselves and with different quadrature formulae proposed by other authors (Evans, Int. J. Comput. Math. 82:721?730, 2005; Gautschi, BIT 31:438?446, 1991).

  13. Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame

    NASA Astrophysics Data System (ADS)

    Azarnykh, Dmitrii; Litvinov, Sergey; Adams, Nikolaus A.

    2016-06-01

    A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker-Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solved by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau-Lifshitz Navier-Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge-Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.

  14. Numerical simulation of quantum systems using the Particle-In-Cell method

    NASA Astrophysics Data System (ADS)

    Dirkmann, Sven; Youssef, Ziad; Hemke, Torben; Mussenbrock, Thomas

    2014-10-01

    The Particle-In-Cell (PIC) method is a very powerful method for studying the dynamics of plasmas. It has been primarily developed for tracking the charged particle trajectories subject to selfconsistent and external electromagnetic fields. Exploiting the power of modern computers, one is able to track the classical paths of tens of millions of particles at the same time. In the late 1980th, it was Dawson (and later Dauger) who had the idea to apply the PIC method to the classical part in the semiclassical approach to quantum systems via path integral methods. One could estimate that if a thousands of classical paths are sufficient to describe the dynamics of one quantum particle, then millions classical paths could describe the dynamics of a quantum particle system. A PIC code in the frame of a semiclassical approach would therefore enable the investigation of a number of quantum phenomena, e.g., optical properties, electrical properties, and, ultimately, chemical reactions. In this contribution we explain the use of the PIC code yapic (developed by the authors) in the frame of the path integral method and discuss the numerical results for simple quantum phenomena, i.e., the quantum harmonic oscillator and quantum tunneling. This work is supported by the German Research Foundation in the frame of FOR 2093.

  15. A simple numerical method for snowmelt simulation based on the equation of heat energy.

    PubMed

    Stojković, Milan; Jaćimović, Nenad

    2016-01-01

    This paper presents one-dimensional numerical model for snowmelt/accumulation simulations, based on the equation of heat energy. It is assumed that the snow column is homogeneous at the current time step; however, its characteristics such as snow density and thermal conductivity are treated as functions of time. The equation of heat energy for snow column is solved using the implicit finite difference method. The incoming energy at the snow surface includes the following parts: conduction, convection, radiation and the raindrop energy. Along with the snow melting process, the model includes a model for snow accumulation. The Euler method for the numerical integration of the balance equation is utilized in the proposed model. The model applicability is demonstrated at the meteorological station Zlatibor, located in the western region of Serbia at 1,028 meters above sea level (m.a.s.l.) Simulation results of snowmelt/accumulation suggest that the proposed model achieved better agreement with observed data in comparison with the temperature index method. The proposed method may be utilized as part of a deterministic hydrological model in order to improve short and long term predictions of possible flood events. PMID:27054726

  16. J-integral evaluation for 2D mixed-mode crack problems employing a meshfree stabilized conforming nodal integration method

    NASA Astrophysics Data System (ADS)

    Tanaka, Satoyuki; Suzuki, Hirotaka; Sadamoto, Shota; Sannomaru, Shogo; Yu, Tiantang; Bui, Tinh Quoc

    2016-08-01

    Two-dimensional (2D) in-plane mixed-mode fracture mechanics problems are analyzed employing an efficient meshfree Galerkin method based on stabilized conforming nodal integration (SCNI). In this setting, the reproducing kernel function as meshfree interpolant is taken, while employing the SCNI for numerical integration of stiffness matrix in the Galerkin formulation. The strain components are smoothed and stabilized employing Gauss divergence theorem. The path-independent integral ( J-integral) is solved based on the nodal integration by summing the smoothed physical quantities and the segments of the contour integrals. In addition, mixed-mode stress intensity factors (SIFs) are extracted from the J-integral by decomposing the displacement and stress fields into symmetric and antisymmetric parts. The advantages and features of the present formulation and discretization in evaluation of the J-integral of in-plane 2D fracture problems are demonstrated through several representative numerical examples. The mixed-mode SIFs are evaluated and compared with reference solutions. The obtained results reveal high accuracy and good performance of the proposed meshfree method in the analysis of 2D fracture problems.

  17. A fast method of numerical quadrature for p-version finite element matrices

    NASA Technical Reports Server (NTRS)

    Hinnant, Howard E.

    1993-01-01

    A new technique of numerical quadrature especially suited for p-version finite element matrices is presented. This new technique separates the integrand into two parts, and numerically operates on each part separately. The objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function. The efficiency of the new technique is compared with Gaussian quadrature and found to take a small fraction of the computational effort.

  18. Analytical Solutions Using Integral Formulations and Their Coupling with Numerical Approaches.

    PubMed

    Morel-Seytoux, Hubert J

    2015-01-01

    Analytical and numerical approaches have their own distinct domains of merit and application. Unfortunately there has been a tendency to use either one or the other even when their domains overlap. Yet there is definite advantage in combining the two approaches. Being relatively new this emerging technique of combining the approaches is, at this stage, more of an art than a science. In this article we suggest approaches for the combination through simple examples. We also suggest that the integral formulation of the analytical problems may have some advantages over the differential formulation. The differential formulation limits somewhat the range of linear system descriptions that can be applied to a variety of practical problems. On the other hand the integral approach tends to focus attention to overall integrated behavior and properties of the system rather than on minute details. This is particularly useful in the coupling with a numerical model as in practice it generally deals also with only the integrated behavior of the system. The thesis of this article is illustrated with some simple stream-aquifer flow exchange examples. PMID:25213772

  19. Computation of inflationary cosmological perturbations in chaotic inflationary scenarios using the phase-integral method

    SciTech Connect

    Rojas, Clara

    2009-05-15

    The phase-integral approximation devised by Froeman and Froeman is used for computing cosmological perturbations in the quadratic chaotic inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to fifth order of the phase-integral approximation. We show that the phase integral gives a very good approximation for the shape of the power spectra associated with scalar and tensor perturbations as well as the spectral indices. We find that the accuracy of the phase-integral approximation compares favorably with the numerical results and those obtained using the slow-roll and uniform-approximation methods.

  20. Numerical modeling of undersea acoustics using a partition of unity method with plane waves enrichment

    NASA Astrophysics Data System (ADS)

    Hospital-Bravo, Raúl; Sarrate, Josep; Díez, Pedro

    2016-05-01

    A new 2D numerical model to predict the underwater acoustic propagation is obtained by exploring the potential of the Partition of Unity Method (PUM) enriched with plane waves. The aim of the work is to obtain sound pressure level distributions when multiple operational noise sources are present, in order to assess the acoustic impact over the marine fauna. The model takes advantage of the suitability of the PUM for solving the Helmholtz equation, especially for the practical case of large domains and medium frequencies. The seawater acoustic absorption and the acoustic reflectance of the sea surface and sea bottom are explicitly considered, and perfectly matched layers (PML) are placed at the lateral artificial boundaries to avoid spurious reflexions. The model includes semi-analytical integration rules which are adapted to highly oscillatory integrands with the aim of reducing the computational cost of the integration step. In addition, we develop a novel strategy to mitigate the ill-conditioning of the elemental and global system matrices. Specifically, we compute a low-rank approximation of the local space of solutions, which in turn reduces the number of degrees of freedom, the CPU time and the memory footprint. Numerical examples are presented to illustrate the capabilities of the model and to assess its accuracy.

  1. Method of adiabatic modes in research of smoothly irregular integrated optical waveguides: zero approximation

    SciTech Connect

    Egorov, A A; Sevast'yanov, L A; Sevast'yanov, A L

    2014-02-28

    We consider the application of the method of adiabatic waveguide modes for calculating the propagation of electromagnetic radiation in three-dimensional (3D) irregular integrated optical waveguides. The method of adiabatic modes takes into account a three-dimensional distribution of quasi-waveguide modes and explicit ('inclined') tangential boundary conditions. The possibilities of the method are demonstrated on the example of numerical research of two major elements of integrated optics: a waveguide of 'horn' type and a thin-film generalised waveguide Luneburg lens by the methods of adiabatic modes and comparative waveguides. (integral optical waveguides)

  2. Potential flow around two-dimensional airfoils using a singular integral method

    NASA Technical Reports Server (NTRS)

    Nguyen, Yves; Wilson, Dennis

    1987-01-01

    The problem of potential flow around two-dimensional airfoils is solved by using a new singular integral method. The potential flow equations for incompressible potential flow are written in a singular integral equation. The equation is solved at N collocation points on the airfoil surface. A unique feature of this method is that the airfoil geometry is specified as an independent variable in the exact integral equation. Compared to other numerical methods, the present calculation procedure is much simpler and gives remarkable accuracy for many body shapes. An advantage of the present method is that it allows the inverse design calculation and the results are extremely accurate.

  3. DE 102 - A numerically integrated ephemeris of the moon and planets spanning forty-four centuries

    NASA Technical Reports Server (NTRS)

    Newhall, X. X.; Standish, E. M.; Willams, J. G.

    1983-01-01

    It is pointed out that the 1960's were the turning point for the generation of lunar and planetary ephemerides. All previous measurements of the positions of solar system bodies were optical angular measurements. New technological improvements leading to immense changes in observational accuracy are related to developments concerning radar, Viking landers on Mars, and laser ranges to lunar corner cube retroreflectors. Suitable numerical integration techniques and more comprehensive physical models were developed to match the accuracy of the modern data types. The present investigation is concerned with the first integrated ephemeris, DE 102, which covers the entire span of the historical astronomical observations of usable accuracy which are known. The fit is made to modern data. The integration spans the time period from 1411 BC to 3002 AD.

  4. Path Integral Monte Carlo Methods for Fermions

    NASA Astrophysics Data System (ADS)

    Ethan, Ethan; Dubois, Jonathan; Ceperley, David

    2014-03-01

    In general, Quantum Monte Carlo methods suffer from a sign problem when simulating fermionic systems. This causes the efficiency of a simulation to decrease exponentially with the number of particles and inverse temperature. To circumvent this issue, a nodal constraint is often implemented, restricting the Monte Carlo procedure from sampling paths that cause the many-body density matrix to change sign. Unfortunately, this high-dimensional nodal surface is not a priori known unless the system is exactly solvable, resulting in uncontrolled errors. We will discuss two possible routes to extend the applicability of finite-temperatue path integral Monte Carlo. First we extend the regime where signful simulations are possible through a novel permutation sampling scheme. Afterwards, we discuss a method to variationally improve the nodal surface by minimizing a free energy during simulation. Applications of these methods will include both free and interacting electron gases, concluding with discussion concerning extension to inhomogeneous systems. Support from DOE DE-FG52-09NA29456, DE-AC52-07NA27344, LLNL LDRD 10- ERD-058, and the Lawrence Scholar program.

  5. Some variance reduction methods for numerical stochastic homogenization.

    PubMed

    Blanc, X; Le Bris, C; Legoll, F

    2016-04-28

    We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here. PMID:27002065

  6. On the collocation methods for singular integral equations with Hilbert kernel

    NASA Astrophysics Data System (ADS)

    Du, Jinyuan

    2009-06-01

    In the present paper, we introduce some singular integral operators, singular quadrature operators and discretization matrices of singular integral equations with Hilbert kernel. These results both improve the classical theory of singular integral equations and develop the theory of singular quadrature with Hilbert kernel. Then by using them a unified framework for various collocation methods of numerical solutions of singular integral equations with Hilbert kernel is given. Under the framework, it is very simple and obvious to obtain the coincidence theorem of collocation methods, then the existence and convergence for constructing approximate solutions are also given based on the coincidence theorem.

  7. Application of boundary integral method to elastic analysis of V-notched beams

    NASA Technical Reports Server (NTRS)

    Rzasnicki, W.; Mendelson, A.; Albers, L. U.

    1973-01-01

    A semidirect boundary integral method, using Airy's stress function and its derivatives in Green's boundary integral formula, is used to obtain an accurate numerical solution for elastic stress and strain fields in V-notched beams in pure bending. The proper choice of nodal spacing on the boundary is shown to be necessary to achieve an accurate stress field in the vicinity of the tip of the notch. Excellent agreement is obtained with the results of the collocation method of solution.

  8. Quantitative evaluation of numerical integration schemes for Lagrangian particle dispersion models

    NASA Astrophysics Data System (ADS)

    Ramli, Huda Mohd.; Esler, J. Gavin

    2016-07-01

    A rigorous methodology for the evaluation of integration schemes for Lagrangian particle dispersion models (LPDMs) is presented. A series of one-dimensional test problems are introduced, for which the Fokker-Planck equation is solved numerically using a finite-difference discretisation in physical space and a Hermite function expansion in velocity space. Numerical convergence errors in the Fokker-Planck equation solutions are shown to be much less than the statistical error associated with a practical-sized ensemble (N = 106) of LPDM solutions; hence, the former can be used to validate the latter. The test problems are then used to evaluate commonly used LPDM integration schemes. The results allow for optimal time-step selection for each scheme, given a required level of accuracy. The following recommendations are made for use in operational models. First, if computational constraints require the use of moderate to long time steps, it is more accurate to solve the random displacement model approximation to the LPDM rather than use existing schemes designed for long time steps. Second, useful gains in numerical accuracy can be obtained, at moderate additional computational cost, by using the relatively simple "small-noise" scheme of Honeycutt.

  9. Achieving better cooling of turbine blades using numerical simulation methods

    NASA Astrophysics Data System (ADS)

    Inozemtsev, A. A.; Tikhonov, A. S.; Sendyurev, C. I.; Samokhvalov, N. Yu.

    2013-02-01

    A new design of the first-stage nozzle vane for the turbine of a prospective gas-turbine engine is considered. The blade's thermal state is numerically simulated in conjugate statement using the ANSYS CFX 13.0 software package. Critical locations in the blade design are determined from the distribution of heat fluxes, and measures aimed at achieving more efficient cooling are analyzed. Essentially lower (by 50-100°C) maximal temperature of metal has been achieved owing to the results of the performed work.

  10. Magnetohydrodynamic (MHD) modelling of solar active phenomena via numerical methods

    NASA Technical Reports Server (NTRS)

    Wu, S. T.

    1988-01-01

    Numerical ideal MHD models for the study of solar active phenomena are summarized. Particular attention is given to the following physical phenomena: (1) local heating of a coronal loop in an isothermal and stratified atmosphere, and (2) the coronal dynamic responses due to magnetic field movement. The results suggest that local heating of a magnetic loop will lead to the enhancement of the density of the neighboring loops through MHD wave compression. It is noted that field lines can be pinched off and may form a self-contained magnetized plasma blob that may move outward into interplanetary space.

  11. Numerical methods for a general class of porous medium equations

    SciTech Connect

    Rose, M. E.

    1980-03-01

    The partial differential equation par. deltau/par. deltat + par. delta(f(u))/par. deltax = par. delta(g(u)par. deltau/par. deltax)/par. deltax, where g(u) is a non-negative diffusion coefficient that may vanish for one or more values of u, was used to model fluid flow through a porous medium. Error estimates for a numerical procedure to approximate the solution are derived. A revised version of this report will appear in Computers and Mathematics with Applications.

  12. Sensitivity method for integrated structure/active control law design

    NASA Technical Reports Server (NTRS)

    Gilbert, Michael G.

    1987-01-01

    The development is described of an integrated structure/active control law design methodology for aeroelastic aircraft applications. A short motivating introduction to aeroservoelasticity is given along with the need for integrated structures/controls design algorithms. Three alternative approaches to development of an integrated design method are briefly discussed with regards to complexity, coordination and tradeoff strategies, and the nature of the resulting solutions. This leads to the formulation of the proposed approach which is based on the concepts of sensitivity of optimum solutions and multi-level decompositions. The concept of sensitivity of optimum is explained in more detail and compared with traditional sensitivity concepts of classical control theory. The analytical sensitivity expressions for the solution of the linear, quadratic cost, Gaussian (LQG) control problem are summarized in terms of the linear regulator solution and the Kalman Filter solution. Numerical results for a state space aeroelastic model of the DAST ARW-II vehicle are given, showing the changes in aircraft responses to variations of a structural parameter, in this case first wing bending natural frequency.

  13. Non-isotropic solution of an OZ equation: matrix methods for integral equations

    NASA Astrophysics Data System (ADS)

    Chen, Zhuo-Min; Pettitt, B. Montgomery

    1995-02-01

    Integral equations of the Ornstein-Zernike (OZ) type have been useful constructs in the theory of liquids for nearly a century. Only a limited number of model systems yield an analytic solution; the rest must be solved numerically. For anisotropic systems the numerical problems are heightened by the coupling of more unknowns and equations. A matrix method for solving the full anisotropic OZ integral equation is presented. The method is compared in the isotropic limit with traditional approaches. Examples are given for a 1-D fluid with a corrugated (periodic) external potential. The full two point correlation functions for both isotropic and anisotropic systems are given and discussed.

  14. Projection methods for the numerical solution of Markov chain models

    NASA Technical Reports Server (NTRS)

    Saad, Youcef

    1989-01-01

    Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

  15. CALL FOR PAPERS: Special Issue on `Geometric Numerical Integration of Differential Equations'

    NASA Astrophysics Data System (ADS)

    Quispel, G. R. W.; McLachlan, R. I.

    2005-02-01

    This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Geometric Numerical Integration of Differential Equations'. This issue should be a repository for high quality original work. We are interested in having the topic interpreted broadly, that is, to include contributions dealing with symplectic or multisymplectic integration; volume-preserving integration; symmetry-preserving integration; integrators that preserve first integrals, Lyapunov functions, or dissipation; exponential integrators; integrators for highly oscillatory systems; Lie-group integrators, etc. Papers on geometric integration of both ODEs and PDEs will be considered, as well as application to molecular-scale integration, celestial mechanics, particle accelerators, fluid flows, population models, epidemiological models and/or any other areas of science. We believe that this issue is timely, and hope that it will stimulate further development of this new and exciting field. The Editorial Board has invited G R W Quispel and R I McLachlan to serve as Guest Editors for the special issue. Their criteria for acceptance of contributions are the following: • The subject of the paper should relate to geometric numerical integration in the sense described above. • Contributions will be refereed and processed according to the usual procedure of the journal. • Papers should be original; reviews of a work published elsewhere will not be accepted. The guidelines for the preparation of contributions are as follows: • The DEADLINE for submission of contributions is 1 September 2005. This deadline will allow the special issue to appear in late 2005 or early 2006. • There is a strict page limit of 16 printed pages (approximately 9600 words) per contribution. For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and General

  16. Numerical conformal mapping methods for exterior and doubly connected regions

    SciTech Connect

    DeLillo, T.K.; Pfaltzgraff, J.A.

    1996-12-31

    Methods are presented and analyzed for approximating the conformal map from the exterior of the disk to the exterior a smooth, simple closed curve and from an annulus to a bounded, doubly connected region with smooth boundaries. The methods are Newton-like methods for computing the boundary correspondences and conformal moduli similar to Fornberg`s method for the interior of the disk. We show that the linear systems are discretizations of the identity plus a compact operator and, hence, that the conjugate gradient method converges superlinearly.

  17. Sensitivity of inelastic response to numerical integration of strain energy. [for cantilever beam

    NASA Technical Reports Server (NTRS)

    Kamat, M. P.

    1976-01-01

    The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the nonlinear transient responses of a beam with solid cross section and that of a thin-walled beam on elastic supports under impulsive loads are examined.

  18. Method for numerical simulation of two-term exponentially correlated colored noise

    SciTech Connect

    Yilmaz, B.; Ayik, S.; Abe, Y.; Gokalp, A.; Yilmaz, O.

    2006-04-15

    A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications.

  19. Exponential Methods for the Time Integration of Schrödinger Equation

    NASA Astrophysics Data System (ADS)

    Cano, B.; González-Pachón, A.

    2010-09-01

    We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schrödinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

  20. VINE-A NUMERICAL CODE FOR SIMULATING ASTROPHYSICAL SYSTEMS USING PARTICLES. I. DESCRIPTION OF THE PHYSICS AND THE NUMERICAL METHODS

    SciTech Connect

    Wetzstein, M.; Nelson, Andrew F.; Naab, T.; Burkert, A.

    2009-10-01

    We present a numerical code for simulating the evolution of astrophysical systems using particles to represent the underlying fluid flow. The code is written in Fortran 95 and is designed to be versatile, flexible, and extensible, with modular options that can be selected either at the time the code is compiled or at run time through a text input file. We include a number of general purpose modules describing a variety of physical processes commonly required in the astrophysical community and we expect that the effort required to integrate additional or alternate modules into the code will be small. In its simplest form the code can evolve the dynamical trajectories of a set of particles in two or three dimensions using a module which implements either a Leapfrog or Runge-Kutta-Fehlberg integrator, selected by the user at compile time. The user may choose to allow the integrator to evolve the system using individual time steps for each particle or with a single, global time step for all. Particles may interact gravitationally as N-body particles, and all or any subset may also interact hydrodynamically, using the smoothed particle hydrodynamic (SPH) method by selecting the SPH module. A third particle species can be included with a module to model massive point particles which may accrete nearby SPH or N-body particles. Such particles may be used to model, e.g., stars in a molecular cloud. Free boundary conditions are implemented by default, and a module may be selected to include periodic boundary conditions. We use a binary 'Press' tree to organize particles for rapid access in gravity and SPH calculations. Modules implementing an interface with special purpose 'GRAPE' hardware may also be selected to accelerate the gravity calculations. If available, forces obtained from the GRAPE coprocessors may be transparently substituted for those obtained from the tree, or both tree and GRAPE may be used as a combination GRAPE/tree code. The code may be run without

  1. Transient three-dimensional contact problems: mortar method. Mixed methods and conserving integration

    NASA Astrophysics Data System (ADS)

    Hesch, Christian; Betsch, Peter

    2011-10-01

    The present work deals with the development of an energy-momentum conserving method to unilateral contact constraints and is a direct continuation of a previous work (Hesch and Betsch in Comput Mech 2011, doi: 10.1007/s00466-011-0597-2) dealing with the NTS method. In this work, we introduce the mortar method and a newly developed segmentation process for the consistent integration of the contact interface. For the application of the energy-momentum approach to mortar constraints, we extend an approach based on a mixed formulation to the segment definition of the mortar constraints. The enhanced numerical stability of the newly proposed discretization method will be shown in several examples.

  2. Numerical method to digital photoelasticity using plane polariscope.

    PubMed

    Júnior, P A A Magalhães; Vieira, F G; Magalhães, C A; Ribeiro, J S; Rios, I G

    2016-06-13

    This research aims to find a new way to get the intensity equations for the phase-shifting model in digital photoelasticity. The procedure is based on the rotation of the analyzer itself. From the intensity equations, the isoclinic and isochromatic equations parameters are deduced by applying a new numerical technique. This approach can be done to calculate how many images allow the resolution of the polariscope. Each image indicates the stress forces in the object. In this study the plane polariscope was used. The amount of images will determinate the number of errors and uncertainties of the study, due to the observation that the veracity of the equations increases considerably with a large amout of images. Several analyses are performed with different amounts of photographic images. The results showed the possibility to measure stress forces with high precision using plane polariscopes. PMID:27410283

  3. MODELING COLLISIONAL CASCADES IN DEBRIS DISKS: THE NUMERICAL METHOD

    SciTech Connect

    Gaspar, Andras; Psaltis, Dimitrios; Oezel, Feryal; Rieke, George H.; Cooney, Alan E-mail: dpsaltis@as.arizona.edu E-mail: grieke@as.arizona.edu

    2012-04-10

    We develop a new numerical algorithm to model collisional cascades in debris disks. Because of the large dynamical range in particle masses, we solve the integro-differential equations describing erosive and catastrophic collisions in a particle-in-a-box approach, while treating the orbital dynamics of the particles in an approximate fashion. We employ a new scheme for describing erosive (cratering) collisions that yields a continuous set of outcomes as a function of colliding masses. We demonstrate the stability and convergence characteristics of our algorithm and compare it with other treatments. We show that incorporating the effects of erosive collisions results in a decay of the particle distribution that is significantly faster than with purely catastrophic collisions.

  4. Numerical and analytical tests of quasi-integrability in modified sine-Gordon models

    NASA Astrophysics Data System (ADS)

    Ferreira, L. A.; Zakrzewski, Wojtek J.

    2014-01-01

    Following our attempts to define quasi-integrability in which we related this concept to a particular symmetry of the two-soliton function we check this condition in three classes of modified sine-Gordon models in (1 + 1) dimensions. We find that the numerical results seen in various scatterings of two solitons and in the time evolution of breather-like structures support our ideas about the symmetry of the field configurations and its effects on the anomalies of the conservation laws of the charges.

  5. Computational flow development for unsteady viscous flows: Foundation of the numerical method

    NASA Technical Reports Server (NTRS)

    Bratanow, T.; Spehert, T.

    1978-01-01

    A procedure is presented for effective consideration of viscous effects in computational development of high Reynolds number flows. The procedure is based on the interpretation of the Navier-Stokes equations as vorticity transport equations. The physics of the flow was represented in a form suitable for numerical analysis. Lighthill's concept for flow development for computational purposes was adapted. The vorticity transport equations were cast in a form convenient for computation. A statement for these equations was written using the method of weighted residuals and applying the Galerkin criterion. An integral representation of the induced velocity was applied on the basis of the Biot-Savart law. Distribution of new vorticity, produced at wing surfaces over small computational time intervals, was assumed to be confined to a thin region around the wing surfaces.

  6. Path integral method for DNA denaturation

    NASA Astrophysics Data System (ADS)

    Zoli, Marco

    2009-04-01

    The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillment of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature Tc∗ , whereas the fraction of unbound base pairs grows continuously around and above Tc∗ . The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus T . The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuously versus T while the specific heat displays a remarkable peak at Tc∗ . The location of the peak versus T varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second-order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.

  7. Numerical Modeling of Pressurization of Cryogenic Propellant Tank for Integrated Vehicle Fluid System

    NASA Technical Reports Server (NTRS)

    Majumdar, Alok K.; LeClair, Andre C.; Hedayat, Ali

    2016-01-01

    This paper presents a numerical model of pressurization of a cryogenic propellant tank for the Integrated Vehicle Fluid (IVF) system using the Generalized Fluid System Simulation Program (GFSSP). The IVF propulsion system, being developed by United Launch Alliance, uses boiloff propellants to drive thrusters for the reaction control system as well as to run internal combustion engines to develop power and drive compressors to pressurize propellant tanks. NASA Marshall Space Flight Center (MSFC) has been running tests to verify the functioning of the IVF system using a flight tank. GFSSP, a finite volume based flow network analysis software developed at MSFC, has been used to develop an integrated model of the tank and the pressurization system. This paper presents an iterative algorithm for converging the interface boundary conditions between different component models of a large system model. The model results have been compared with test data.

  8. Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides

    NASA Astrophysics Data System (ADS)

    Krasavin, A. V.; Zayats, A. V.

    2008-07-01

    Using full three-dimensional numerical modeling, we demonstrate highly efficient passive and active photonic circuit elements based on dielectric-loaded surface plasmon polariton waveguides (DLSPPWs). Highly confined surface plasmon polariton (SPP) mode having subwavelength cross section allows high level of integration of DLSPPW circuitry. We demonstrate very efficient guiding and routing of SPP signals with the passive waveguide elements such as bends, splitters, and Bragg reflectors, having a functional size of just a few microns at telecommunication wavelengths. Introducing a gain in the dielectric, we have found the requirement for lossless waveguiding and estimated the performance of DLSPPW lossless and active elements. DLSPPW based components have prospective implementation in photonic integrated chips, hybrid optical-electronic circuits, and lab-on-a-chip applications.

  9. AI/OR computational model for integrating qualitative and quantitative design methods

    NASA Technical Reports Server (NTRS)

    Agogino, Alice M.; Bradley, Stephen R.; Cagan, Jonathan; Jain, Pramod; Michelena, Nestor

    1990-01-01

    A theoretical framework for integrating qualitative and numerical computational methods for optimally-directed design is described. The theory is presented as a computational model and features of implementations are summarized where appropriate. To demonstrate the versatility of the methodology we focus on four seemingly disparate aspects of the design process and their interaction: (1) conceptual design, (2) qualitative optimal design, (3) design innovation, and (4) numerical global optimization.

  10. On a New Numerical Method for Solving General Variational Inequalities

    NASA Astrophysics Data System (ADS)

    Bnouhachem, Abdellah; Noor, Muhammad Aslam; Khalfaoui, Mohamed; Sheng, Zhaohan

    In this paper, we suggest and analyze a new extragradient method for solving the general variational inequalities involving two operators. We also prove the global convergence of the proposed modified method under certain mild conditions. We used a self-adaptive technique to adjust parameter ρ at each iteration. It is proved theoretically that the lower-bound of the progress obtained by the proposed method is greater than that by the extragradient method. An example is given to illustrate the efficiency and its comparison with the extragradient method. Since the general variational inequalities include the classical variational inequalities and complementarity problems as special cases, our results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as an improvement and refinement of the previously known results in this field.

  11. Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau IIA method

    NASA Astrophysics Data System (ADS)

    Ying, Teh Yuan; Yaacob, Nazeeruddin

    2013-04-01

    In this paper, a new implicit Runge-Kutta method which based on a 4-point Gauss-Kronrod-Radau II quadrature formula is developed. The resulting implicit method is a 4-stage sixth order Gauss-Kronrod-Radau IIA method, or in brief as GKRM(4,6)-IIA. GKRM(4,6)-IIA requires four function of evaluations at each integration step and it gives accuracy of order six. In addition, GKRM(4,6)-IIA has stage order four and being L-stable. Numerical experiments compare the accuracy between GKRM(4,6)-IIA and the classical 3-stage sixth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKRM(4,6)-IIA is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-IIA has higher stage order.

  12. Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method

    NASA Astrophysics Data System (ADS)

    Ying, Teh Yuan; Yaacob, Nazeeruddin

    2013-04-01

    In this paper, a new implicit Runge-Kutta method which based on a 7-point Gauss-Kronrod-Lobatto quadrature formula is developed. The resulting implicit method is a 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method, or in brief as GKLM(7,10)-IIIA. GKLM(7,10)-IIIA requires seven function of evaluations at each integration step and it gives accuracy of order ten. In addition, GKLM(7,10)-IIIA has stage order seven and being A-stable. Numerical experiments compare the accuracy between GKLM(7,10)-IIIA and the classical 5-stage tenth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKLM(7,10)-IIIA is more accurate than the 5-stage tenth order Gauss-Legendre method because GKLM(7,10)-IIIA has higher stage order.

  13. Exploring the Use of Discontinuous Galerkin Methods for Numerical Relativity

    NASA Astrophysics Data System (ADS)

    Hebert, Francois; Kidder, Lawrence; Teukolsky, Saul; SXS Collaboration

    2015-04-01

    The limited accuracy of relativistic hydrodynamic simulations constrains our insight into several important research problems, including among others our ability to generate accurate template waveforms for black hole-neutron star mergers, or our understanding of supernova explosion mechanisms. In many codes the algorithms used to evolve the matter, based on the finite volume method, struggle to reach the desired accuracy. We aim to show improved accuracy by using a discontinuous Galerkin method. This method's attractiveness comes from its combination of spectral convergence properties for smooth solutions and robust stability properties for shocks. We present the status of our work implementing a testbed GR-hydro code using discontinuous Galerkin.

  14. SINDA'85/FLUINT - SYSTEMS IMPROVED NUMERICAL DIFFERENCING ANALYZER AND FLUID INTEGRATOR (CONVEX VERSION)

    NASA Technical Reports Server (NTRS)

    Cullimore, B.

    1994-01-01

    SINDA, the Systems Improved Numerical Differencing Analyzer, is a software system for solving lumped parameter representations of physical problems governed by diffusion-type equations. SINDA was originally designed for analyzing thermal systems represented in electrical analog, lumped parameter form, although its use may be extended to include other classes of physical systems which can be modeled in this form. As a thermal analyzer, SINDA can handle such interrelated phenomena as sublimation, diffuse radiation within enclosures, transport delay effects, and sensitivity analysis. FLUINT, the FLUid INTegrator, is an advanced one-dimensional fluid analysis program that solves arbitrary fluid flow networks. The working fluids can be single phase vapor, single phase liquid, or two phase. The SINDA'85/FLUINT system permits the mutual influences of thermal and fluid problems to be analyzed. The SINDA system consists of a programming language, a preprocessor, and a subroutine library. The SINDA language is designed for working with lumped parameter representations and finite difference solution techniques. The preprocessor accepts programs written in the SINDA language and converts them into standard FORTRAN. The SINDA library consists of a large number of FORTRAN subroutines that perform a variety of commonly needed actions. The use of these subroutines can greatly reduce the programming effort required to solve many problems. A complete run of a SINDA'85/FLUINT model is a four step process. First, the user's desired model is run through the preprocessor which writes out data files for the processor to read and translates the user's program code. Second, the translated code is compiled. The third step requires linking the user's code with the processor library. Finally, the processor is executed. SINDA'85/FLUINT program features include 20,000 nodes, 100,000 conductors, 100 thermal submodels, and 10 fluid submodels. SINDA'85/FLUINT can also model two phase flow

  15. Implementation of equivalent domain integral method in the two-dimensional analysis of mixed mode problems

    NASA Technical Reports Server (NTRS)

    Raju, I. S.; Shivakumar, K. N.

    1989-01-01

    An equivalent domain integral (EDI) method for calculating J-intergrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The total and product integrals consist of the sum of an area of domain integral and line integrals on the crack faces. The line integrals vanish only when the crack faces are traction free and the loading is either pure mode 1 or pure mode 2 or a combination of both with only the square-root singular term in the stress field. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all problems analyzed. The EDI method when applied to a problem of an interface crack in two different materials showed that the mode 1 and mode 2 components are domain dependent while the total integral is not. This behavior is caused by the presence of the oscillatory part of the singularity in bimaterial crack problems. The EDI method, thus, shows behavior similar to the virtual crack closure method for bimaterial problems.

  16. A numerical method for eigenvalue problems in modeling liquid crystals

    SciTech Connect

    Baglama, J.; Farrell, P.A.; Reichel, L.; Ruttan, A.; Calvetti, D.

    1996-12-31

    Equilibrium configurations of liquid crystals in finite containments are minimizers of the thermodynamic free energy of the system. It is important to be able to track the equilibrium configurations as the temperature of the liquid crystals decreases. The path of the minimal energy configuration at bifurcation points can be computed from the null space of a large sparse symmetric matrix. We describe a new variant of the implicitly restarted Lanczos method that is well suited for the computation of extreme eigenvalues of a large sparse symmetric matrix, and we use this method to determine the desired null space. Our implicitly restarted Lanczos method determines adoptively a polynomial filter by using Leja shifts, and does not require factorization of the matrix. The storage requirement of the method is small, and this makes it attractive to use for the present application.

  17. Numerical Stability and Convergence of Approximate Methods for Conservation Laws

    NASA Astrophysics Data System (ADS)

    Galkin, V. A.

    We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.

  18. Finite element numerical integration for first order approximations on multi- and many-core architectures

    NASA Astrophysics Data System (ADS)

    Banaś, Krzysztof; Krużel, Filip; Bielański, Jan

    2016-06-01

    The paper presents investigations on the implementation and performance of the finite element numerical integration algorithm for first order approximations and three processor architectures, popular in scientific computing, classical CPU, Intel Xeon Phi and NVIDIA Kepler GPU. A unifying programming model and portable OpenCL implementation is considered for all architectures. Variations of the algorithm due to different problems solved and different element types are investigated and several optimizations aimed at proper optimization and mapping of the algorithm to computer architectures are demonstrated. Performance models of execution are developed for different processors and tested in practical experiments. The results show the varying levels of performance for different architectures, but indicate that the algorithm can be effectively ported to all of them. The general conclusion is that the finite element numerical integration can achieve sufficient performance on different multi- and many-core architectures and should not become a performance bottleneck for finite element simulation codes. Specific observations lead to practical advises on how to optimize the kernels and what performance can be expected for the tested architectures.

  19. Numerical simulation of installation process and uplift resistance for an integrated suction foundation in deep ocean

    NASA Astrophysics Data System (ADS)

    Li, Ying; Yang, Shu-geng; Yu, Shu-ming

    2016-03-01

    A concept design, named integrated suction foundation, is proposed for a tension leg platform (TLP) in deep ocean. The most important improvement in comparing with the traditional one is that a pressure-resistant storage module is designed. It utilizes the high hydrostatic pressure in deep ocean to drive water into the module to generate negative pressure for bucket suction. This work aims to further approve the feasibility of the concept design in the aspect of penetration installation and the uplift force in-place. Seepage is generated during suction penetration, and can have both positive and negative effects on penetration process. To study the effect of seepage on the penetration process of the integrated suction foundation, finite element analysis (FEA) is carried out in this work. In particular, an improved methodology to calculate the penetration resistance is proposed for the integrated suction foundation with respect to the reduction factor of penetration resistance. The maximum allowable negative pressure during suction penetration is calculated with the critical hydraulic gradient method through FEA. The simulation results of the penetration process show that the integrated suction foundation can be installed safely. Moreover, the uplift resistance of the integrated suction foundation is calculated and the feasibility of the integrated suction foundation working on-site is verified. In all, the analysis in this work further approves the feasibility of the integrated suction foundation for TLPs in deep ocean applications.

  20. Validation of a Numerical Method for Determining Liner Impedance

    NASA Technical Reports Server (NTRS)

    Watson, Willie R.; Jones, Michael G.; Tanner, Sharon E.; Parrott, Tony L.

    1996-01-01

    This paper reports the initial results of a test series to evaluate a method for determining the normal incidence impedance of a locally reacting acoustically absorbing liner, located on the lower wall of a duct in a grazing incidence, multi-modal, non-progressive acoustic wave environment without flow. This initial evaluation is accomplished by testing the methods' ability to converge to the known normal incidence impedance of a solid steel plate, and to the normal incidence impedance of an absorbing test specimen whose impedance was measured in a conventional normal incidence tube. The method is shown to converge to the normal incident impedance values and thus to be an adequate tool for determining the impedance of specimens in a grazing incidence, multi-modal, nonprogressive acoustic wave environment for a broad range of source frequencies.

  1. Integrated Numerical Experiments (INEX) and the Free-Electron Laser Physical Process Code (FELPPC)

    SciTech Connect

    Thode, L.E.; Chan, K.C.D.; Schmitt, M.J.; McKee, J.; Ostic, J.; Elliott, C.J.; McVey, B.D.

    1990-01-01

    The strong coupling of subsystem elements, such as the accelerator, wiggler, and optics, greatly complicates the understanding and design of a free electron laser (FEL), even at the conceptual level. Given the requirements for high-performance FELs, the strong coupling between the laser subsystems must be included to obtain a realistic picture of the potential operational capability. To address the strong coupling character of the FEL the concept of an Integrated Numerical Experiment (INEX) was proposed. Unique features of the INEX approach are consistency and numerical equivalence of experimental diagnostics. The equivalent numerical diagnostics mitigates the major problem of misinterpretation that often occurs when theoretical and experimental data are compared. The INEX approach has been applied to a large number of accelerator and FEL experiments. Overall, the agreement between INEX and the experiments is very good. Despite the success of INEX, the approach is difficult to apply to trade-off and initial design studies because of the significant manpower and computational requirements. On the other hand, INEX provides a base from which realistic accelerator, wiggler, and optics models can be developed. The Free Electron Laser Physical Process Code (FELPPC) includes models developed from INEX, provides coupling between the subsystems models and incorporates application models relevant to a specific trade-off or design study.

  2. Integrated Numerical Experiments (INEX) and the Free-Electron Laser Physical Process Code (FELPPC)

    NASA Astrophysics Data System (ADS)

    Thode, L. E.; Chan, K. C. D.; Schmitt, M. J.; McKee, J.; Ostic, J.; Elliott, C. J.; McVey, B. D.

    The strong coupling of subsystem elements, such as the accelerator, wiggler, and optics, greatly complicates the understanding and design of a free electron laser (FEL), even at the conceptual level. Given the requirements for high-performance FELs, the strong coupling between the laser subsystems must be included to obtain a realistic picture of the potential operational capability. To address the strong coupling character of the FEL the concept of an Integrated Numerical Experiment (INEX) was proposed. Unique features of the INEX approach are consistency and numerical equivalence of experimental diagnostics. The equivalent numerical diagnostics mitigates the major problem of misinterpretation that often occurs when theoretical and experimental data are compared. The INEX approach has been applied to a large number of accelerator and FEL experiments. Overall, the agreement between INEX and the experiments is very good. Despite the success of INEX, the approach is difficult to apply to trade-off and initial design studies because of the significant manpower and computational requirements. On the other hand, INEX provides a base from which realistic accelerator, wiggler, and optics models can be developed. The Free Electron Laser Physical Process Code (FELPPC) includes models developed from INEX, provides coupling between the subsystems models and incorporates application models relevant to a specific trade-off or design study.

  3. Improved numerical methods for turbulent viscous recirculating flows

    NASA Technical Reports Server (NTRS)

    Turan, A.; Vandoormaal, J. P.

    1988-01-01

    The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.

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

    NASA Astrophysics Data System (ADS)

    Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna

    2016-08-01

    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.

  5. Eulerian-Lagrangian numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods

    USGS Publications Warehouse

    Cox, T.J.; Runkel, R.L.

    2008-01-01

    Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.

  6. A finite volume method for numerical grid generation

    NASA Astrophysics Data System (ADS)

    Beale, S. B.

    1999-07-01

    A novel method to generate body-fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables , and is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re-zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid-correction procedure. The scalar variables are re-mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet-Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local-boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point-by-point and whole-field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright

  7. Evaluating numerical ODE/DAE methods, algorithms and software

    NASA Astrophysics Data System (ADS)

    Soderlind, Gustaf; Wang, Lina

    2006-01-01

    Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one method is better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris paribus conditions. Moreover, testing is an empirical science and as such requires a formal test protocol; without it conclusions are questionable, invalid or even false.We argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. The goals are computational stability, reproducibility, and improved software quality. We also focus on different error criteria and norms, and discuss modifications to DASPK and RADAU5. Finally, some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems.

  8. Calculation of transonic flows using an extended integral equation method

    NASA Technical Reports Server (NTRS)

    Nixon, D.

    1976-01-01

    An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

  9. Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers

    NASA Technical Reports Server (NTRS)

    Kennedy, Christopher A.; Carpenter, Mark H.

    1997-01-01

    An investigation is conducted on several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes use explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order variant of the schemes proposed by Rusanov and by Kutier, Lomax, and Warming (RKLW), and third- and fourth-order Runge-Kutta schemes. In each scheme, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(sub t) + aU(sub x) = alpha U(sub xx). Accuracy is also verified on the nonlinear problem, U(sub t) + F(sub x) = 0. Numerical treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for several sixth- and eighth-order central-difference schemes. Damping of high wave-number data is accomplished with explicit filters of arbitrary order. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients exist.

  10. Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

    NASA Technical Reports Server (NTRS)

    Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)

    2002-01-01

    Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

  11. A survey of numerical methods for shock physics applications

    SciTech Connect

    Hertel, E.S. Jr.

    1997-10-01

    Hydrocodes or more accurately, shock physics analysis packages, have been widely used in the US Department of Energy (DOE) laboratories and elsewhere around the world for over 30 years. Initial applications included weapons effects studies where the pressure levels were high enough to disregard the material strength, hence the term hydrocode. Over the last 30 years, Sandia has worked extensively to develop and apply advanced hydrocodes to armor/anti-armor interactions, warhead design, high explosive initiation, and nuclear weapon safety issues. The needs of the DOE have changed over the last 30 years, especially over the last decade. A much stronger emphasis is currently placed on the details of material deformation and high explosive initiation phenomena. The hydrocodes of 30 years ago have now evolved into sophisticated analysis tools that can replace testing in some situations and complement it in all situations. A brief history of the development of hydrocodes in the US will be given. The author also discusses and compares the four principal methods in use today for the solution of the conservation equations of mass, momentum, and energy for shock physics applications. The techniques discussed are the Eulerian methods currently employed by the Sandia multi-dimensional shock physics analysis package known as CTH; the element based Lagrangian method currently used by codes like DYNA; the element free Lagrangian method (also known as smooth particle hydrodynamics) used by codes like the Los Alamos code SPHINX; and the Arbitrary Lagrangian Eulerian methods used by codes like the Lawrence Livermore code CALE or the Sandia code ALEGRA.

  12. Applications of numerical methods to simulate the movement of contaminants in groundwater.

    PubMed Central

    Sun, N Z

    1989-01-01

    This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

  13. Numerical design method for thermally loaded plate-cylinder intersections

    SciTech Connect

    Baldur, R.; Laberge, C.A.; Lapointe, D. )

    1988-11-01

    This paper is an extension of work on stresses in corner radii described by the authors previously. Whereas the original study concerned itself with pressure effects only and the second reference gave the initial version of the work dealing with the thermal effects, this report gives more recent results concerning specifically thermal loads. As before, the results are limited to inside corner radii between cylinders and flat heat closures. Similarly, the analysis is based on a systematic series of finite element calculations with the significant parameters covering the field of useful design boundaries. The results are condensed into a rapid method for the determination of peak stresses needed for performing fatigue analysis in pressure vessels subjected to a significant, variable thermal load. The paper takes into account the influence of the film coefficient, temporal temperature variations, and material properties. A set of coefficients provides a convenient method of stress evaluation suitable for design purposes.

  14. Numerical optimization methods for critical currents in superconductors

    NASA Astrophysics Data System (ADS)

    Kimmel, Gregory; Sadovskyy, Ivan; Koshelev, Alex; Glatz, Andreas

    In this work, I present optimization methods for maximizing the critical current in high-temperature superconductors for energy applications. The critical current in the presence of an external magnetic field is mostly defined by the pinning landscape (pinscape) within the superconductor, which prevents magnetic vortices from moving and, therefore, increases its critical current. Our approach is to generate different pinscapes and obtain the resulting critical current by large-scale time-dependent Ginzburg-Landau equations. Pinning centers could be any combination of defects, including spherical and columnar defects. The parameters controlling the pinscape are adaptively adjusted in order to find the optimal parameter set, which maximizes the critical current. Here, we compare different optimization methods and discuss their performance. Work was supported by the Scientific Discovery through Advanced Computing (SciDAC) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences.

  15. The space-time solution element method: A new numerical approach for the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Scott, James R.; Chang, Sin-Chung

    1995-01-01

    This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

  16. Numerical modeling of surf zone dynamics under weakly plunging breakers with SPH method

    NASA Astrophysics Data System (ADS)

    Makris, Christos V.; Memos, Constantine D.; Krestenitis, Yannis N.

    2016-02-01

    The wave breaking of weak plungers over a relatively mild slope is investigated in this paper. Numerical modeling aspects are studied, concerning the propagation and breaking of shore-normal, nonlinear and regular waves. The two-dimensional (2-D) kinematics and dynamics (fluctuating flow features and large 2-D eddies) of the wave-induced flow on a vertical cross-section over the entire surf zone are simulated with the use of Smoothed Particle Hydrodynamics (SPH). The academic 'open source' code SPHysics v.2 is employed and the viscosity treatment is based on a Sub-Particle Scale (SPS) approach, similarly to the Large Eddy Simulations (LES) concept. Thorough analysis of the turbulent flow scales determines the necessary refinement of the spatial resolution. The initial particle discretization reaches down to the demarcation point between integral turbulence length scales and Taylor micro-scales. A convolution-type integration method is implemented for the transformation of scattered Lagrangian particle data to Eulerian values at fixed gauges. A heuristic technique of ensemble-averaging is used for the discrimination of the fluctuating flow components from coherent structures and ordered wave motion. Comparisons between numerical and experimental data give encouraging results for several wave features. The wave-induced mean flows are simulated plausibly, and even the 'streaming' effect near the bed is reproduced. The recurring vorticity patterns are derived, and coherent 2-D structures inside the surf zone are identified. Fourier spectral analysis of velocities reveals isotropy of 2-D fluctuating dynamics up to rather high frequencies in shear intensified regions. The simulated Reynolds stresses follow patterns that define the characteristic mechanism of wave breaking for weak plungers. Persisting discrepancies at the incipient breaking region confirm the need for fine, massively 'parallel' 3-D SPS-SPH simulations.

  17. Numerical simulation of fluid-structure interactions with stabilized finite element method

    NASA Astrophysics Data System (ADS)

    Sváček, Petr

    2016-03-01

    This paper is interested to the interactions of the incompressible flow with a flexibly supported airfoil. The bending and the torsion modes are considered. The problem is mathematically described. The numerical method is based on the finite element method. A combination of the streamline-upwind/Petrov-Galerkin and pressure stabilizing/Petrov-Galerkin method is used for the stabilization of the finite element method. The numerical results for a three-dimensional problem of flow over an airfoil are shown.

  18. A spectral boundary integral equation method for the 2-D Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Hu, Fang Q.

    1994-01-01

    In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

  19. Design of braided composite tubes by numerical analysis method

    SciTech Connect

    Hamada, Hiroyuki; Fujita, Akihiro; Maekawa, Zenichiro; Nakai, Asami; Yokoyama, Atsushi

    1995-11-01

    Conventional composite laminates have very poor strength through thickness and as a result are limited in their application for structural parts with complex shape. In this paper, the design for braided composite tube was proposed. The concept of analysis model which involved from micro model to macro model was presented. This method was applied to predict bending rigidity and initial fracture stress under bending load of the braided tube. The proposed analytical procedure can be included as a unit in CAE system for braided composites.

  20. The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle points

    NASA Technical Reports Server (NTRS)

    Connor, J. N. L.; Curtis, P. R.; Farrelly, D.

    1984-01-01

    Methods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.

  1. A boundary integral method for an inverse problem in thermal imaging

    NASA Technical Reports Server (NTRS)

    Bryan, Kurt

    1992-01-01

    An inverse problem in thermal imaging involving the recovery of a void in a material from its surface temperature response to external heating is examined. Uniqueness and continuous dependence results for the inverse problem are demonstrated, and a numerical method for its solution is developed. This method is based on an optimization approach, coupled with a boundary integral equation formulation of the forward heat conduction problem. Some convergence results for the method are proved, and several examples are presented using computationally generated data.

  2. Fast Numerical Methods for the Design of Layered Photonic Structures with Rough Interfaces

    NASA Technical Reports Server (NTRS)

    Komarevskiy, Nikolay; Braginsky, Leonid; Shklover, Valery; Hafner, Christian; Lawson, John

    2011-01-01

    Modified boundary conditions (MBC) and a multilayer approach (MA) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with arbitrary permittivity tensor. MBC and MA are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.

  3. Two Different Methods for Numerical Solution of the Modified Burgers' Equation

    PubMed Central

    Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi

    2014-01-01

    A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM. PMID:25162064

  4. Transforming Mean and Osculating Elements Using Numerical Methods

    NASA Technical Reports Server (NTRS)

    Ely, Todd A.

    2010-01-01

    Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order

  5. Transforming Mean and Osculating Elements Using Numerical Methods

    NASA Astrophysics Data System (ADS)

    Ely, Todd A.

    2015-03-01

    Mean element propagation of perturbed two body orbits has as its mathematical basis the averaging theory of nonlinear dynamical systems. Mean elements define an orbit's long-term evolution characteristics consisting of both secular and long-period effects. Using averaging theory, a near-identity transformation can be found that transforms between the mean elements and their osculating counterparts that augment the mean elements with short period effects. The ability to perform the conversion is necessary so that orbit design conducted in either mean elements or osculating can be effectively converted between each element type. In the present work, the near-identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the mean or osculating elements to first-order.

  6. On the numerical dispersion and the spectral fidelity of the Particle-In-Cell method

    NASA Astrophysics Data System (ADS)

    Huang, Chengkun; Meyers, M. D.; Zeng, Y.; Yi, S.; Albright, B. J.

    2015-11-01

    The Particle-In-Cell (PIC) method is widely used in plasma modeling. However, the PIC method exhibits grid type numerical instabilities, including the finite grid instability and the numerical Cherenkov instability that can render unphysical simulation results or disrupt the simulation. A faithful numerical dispersion of the electromagnetic PIC algorithm is obtained and analyzed to obtain the insight about the numerical instabilities inherent in such a computation model. Using this dispersion, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. Compared with the gridless model, we show that the lack of spectral fidelity relative to the real system due to the aliasing effect is a major cause of the numerical instabilities in the PIC model. Work supported by the U.S. Department of Energy through the LDRD program at Los Alamos National Laboratory.

  7. Solution of elastoplastic torsion problem by boundary integral method

    NASA Technical Reports Server (NTRS)

    Mendelson, A.

    1975-01-01

    The boundary integral method was applied to the elastoplastic analysis of the torsion of prismatic bars, and the results are compared with those obtained by the finite difference method. Although fewer unknowns were used, very good accuracy was obtained with the boundary integral method. Both simply and multiply connected bodies can be handled with equal ease.

  8. IMPROVED NUMERICAL METHODS FOR MODELING RIVER-AQUIFER INTERACTION.

    SciTech Connect

    Tidwell, Vincent C.; Sue Tillery; Phillip King

    2008-09-01

    A new option for Local Time-Stepping (LTS) was developed to use in conjunction with the multiple-refined-area grid capability of the U.S. Geological Survey's (USGS) groundwater modeling program, MODFLOW-LGR (MF-LGR). The LTS option allows each local, refined-area grid to simulate multiple stress periods within each stress period of a coarser, regional grid. This option is an alternative to the current method of MF-LGR whereby the refined grids are required to have the same stress period and time-step structure as the coarse grid. The MF-LGR method for simulating multiple-refined grids essentially defines each grid as a complete model, then for each coarse grid time-step, iteratively runs each model until the head and flux changes at the interfacing boundaries of the models are less than some specified tolerances. Use of the LTS option is illustrated in two hypothetical test cases consisting of a dual well pumping system and a hydraulically connected stream-aquifer system, and one field application. Each of the hypothetical test cases was simulated with multiple scenarios including an LTS scenario, which combined a monthly stress period for a coarse grid model with a daily stress period for a refined grid model. The other scenarios simulated various combinations of grid spacing and temporal refinement using standard MODFLOW model constructs. The field application simulated an irrigated corridor along the Lower Rio Grande River in New Mexico, with refinement of a small agricultural area in the irrigated corridor.The results from the LTS scenarios for the hypothetical test cases closely replicated the results from the true scenarios in the refined areas of interest. The head errors of the LTS scenarios were much smaller than from the other scenarios in relation to the true solution, and the run times for the LTS models were three to six times faster than the true models for the dual well and stream-aquifer test cases, respectively. The results of the field application

  9. Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

    NASA Technical Reports Server (NTRS)

    Pratt, D. T.; Radhakrishnan, K.

    1986-01-01

    The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

  10. golem95: A numerical program to calculate one-loop tensor integrals with up to six external legs

    NASA Astrophysics Data System (ADS)

    Binoth, T.; Guillet, J.-Ph.; Heinrich, G.; Pilon, E.; Reiter, T.

    2009-11-01

    We present a program for the numerical evaluation of form factors entering the calculation of one-loop amplitudes with up to six external legs. The program is written in Fortran95 and performs the reduction to a certain set of basis integrals numerically, using a formalism where inverse Gram determinants can be avoided. It can be used to calculate one-loop amplitudes with massless internal particles in a fast and numerically stable way. Catalogue identifier: AEEO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEO_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.: 50 105 No. of bytes in distributed program, including test data, etc.: 241 657 Distribution format: tar.gz Programming language: Fortran95 Computer: Any computer with a Fortran95 compiler Operating system: Linux, Unix RAM: RAM used per form factor is insignificant, even for a rank six six-point form factor Classification: 4.4, 11.1 External routines: Perl programming language (http://www.perl.com/) Nature of problem: Evaluation of one-loop multi-leg tensor integrals occurring in the calculation of next-to-leading order corrections to scattering amplitudes in elementary particle physics. Solution method: Tensor integrals are represented in terms of form factors and a set of basic building blocks ("basis integrals"). The reduction to the basis integrals is

  11. Third-order symplectic integration method with inverse time dispersion transform for long-term simulation

    NASA Astrophysics Data System (ADS)

    Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

    2016-06-01

    The symplectic integration method is popular in high-accuracy numerical simulations when discretizing temporal derivatives; however, it still suffers from time-dispersion error when the temporal interval is coarse, especially for long-term simulations and large-scale models. We employ the inverse time dispersion transform (ITDT) to the third-order symplectic integration method to reduce the time-dispersion error. First, we adopt the pseudospectral algorithm for the spatial discretization and the third-order symplectic integration method for the temporal discretization. Then, we apply the ITDT to eliminate time-dispersion error from the synthetic data. As a post-processing method, the ITDT can be easily cascaded in traditional numerical simulations. We implement the ITDT in one typical exiting third-order symplectic scheme and compare its performances with the performances of the conventional second-order scheme and the rapid expansion method. Theoretical analyses and numerical experiments show that the ITDT can significantly reduce the time-dispersion error, especially for long travel times. The implementation of the ITDT requires some additional computations on correcting the time-dispersion error, but it allows us to use the maximum temporal interval under stability conditions; thus, its final computational efficiency would be higher than that of the traditional symplectic integration method for long-term simulations. With the aid of the ITDT, we can obtain much more accurate simulation results but with a lower computational cost.

  12. A numerical method for the study of the circulation of the world ocean

    SciTech Connect

    Bryan, K.

    1997-08-01

    This paper describes a detail computational procedure involving a finite difference numerical schemes to study the circulation models of the world oceans. To obtain an efficient numerical method for low-frequency, large-scale current systems, surfaces gravity-inertial waves are filtered out by the rigid-lid approximation. Special features of the ocean circulation are resolved in the numerical model by allowing for a variable spacing in either the zonal or meridional direction. 20 refs., 5 figs., 1 tab.

  13. Integrative methods for studying cardiac energetics.

    PubMed

    Diolez, Philippe; Deschodt-Arsac, Véronique; Calmettes, Guillaume; Gouspillou, Gilles; Arsac, Laurent; Dos Santos, Pierre; Jais, Pierre; Haissaguerre, Michel

    2015-01-01

    The more recent studies of human pathologies have essentially revealed the complexity of the interactions involved at the different levels of integration in organ physiology. Integrated organ thus reveals functional properties not predictable by underlying molecular events. It is therefore obvious that current fine molecular analyses of pathologies should be fruitfully combined with integrative approaches of whole organ function. It follows an important issue in the comprehension of the link between molecular events in pathologies, and whole organ function/dysfunction is the development of new experimental strategies aimed at the study of the integrated organ physiology. Cardiovascular diseases are a good example as heart submitted to ischemic conditions has to cope both with a decreased supply of nutrients and oxygen, and the necessary increased activity required to sustain whole body-including the heart itself-oxygenation.By combining the principles of control analysis with noninvasive (31)P NMR measurement of the energetic intermediates and simultaneous measurement of heart contractile activity, we developed MoCA (for Modular Control and Regulation Analysis), an integrative approach designed to study in situ control and regulation of cardiac energetics during contraction in intact beating perfused isolated heart (Diolez et al., Am J Physiol Regul Integr Comp Physiol 293(1):R13-R19, 2007). Because it gives real access to integrated organ function, MoCA brings out a new type of information-the "elasticities," referring to internal responses to metabolic changes-that may be a key to the understanding of the processes involved in pathologies. MoCA can potentially be used not only to detect the origin of the defects associated with the pathology, but also to provide the quantitative description of the routes by which these defects-or also drugs-modulate global heart function, therefore opening therapeutic perspectives. This review presents selected examples of the

  14. Simulation of turbulent flows using nodal integral method

    NASA Astrophysics Data System (ADS)

    Singh, Suneet

    Nodal methods are the backbone of the production codes for neutron-diffusion and transport equations. Despite their high accuracy, use of these methods for simulation of fluid flow is relatively new. Recently, a modified nodal integral method (MNIM) has been developed for simulation of laminar flows. In view of its high accuracy and efficiency, extension of this method for the simulation of turbulent flows is a logical step forward. In this dissertation, MNIM is extended in two ways to simulate incompressible turbulent flows---a new MNIM is developed for the 2D k-epsilon equations; and 3D, parallel MNIM is developed for direct numerical simulations. Both developments are validated, and test problems are solved. In this dissertation, a new nodal numerical scheme is developed to solve the k-epsilon equations to simulate turbulent flows. The MNIM developed earlier for laminar flow equations is modified to incorporate eddy viscosity approximation and coupled with the above mentioned schemes for the k and epsilon equations, to complete the implementation of the numerical scheme for the k-epsilon model. The scheme developed is validated by comparing the results obtained by the developed method with the results available in the literature obtained using direct numerical simulations (DNS). The results of current simulations match reasonably well with the DNS results. The discrepancies in the results are mainly due to the limitations of the k-epsilon model rather than the deficiency in the developed MNIM. A parallel version of the MNIM is needed to enhance its capability, in order to carry out DNS of the turbulent flows. The parallelization of the scheme, however, presents some unique challenges as dependencies of the discrete variables are different from those that exist in other schemes (for example in finite volume based schemes). Hence, a parallel MNIM (PMNIM) is developed and implemented into a computer code with communication strategies based on the above mentioned

  15. A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations

    NASA Technical Reports Server (NTRS)

    Womble, M. E.; Potter, J. E.

    1975-01-01

    A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.

  16. Inelastic, nonlinear analysis of stiffened shells of revolution by numerical integration

    NASA Technical Reports Server (NTRS)

    Levine, H. S.; Svalbonas, V.

    1974-01-01

    This paper describes the latest addition to the STARS system of computer programs, STARS-2P, for the plastic, large deflection analysis of axisymmetrically loaded shells of revolution. The STARS system uses a numerical integration scheme to solve the governing differential equations. Several unique features for shell of revolution programs that are included in the STARS-2P program are described. These include orthotropic nonlinear kinematic hardening theory, a variety of shell wall cross sections and discrete ring stiffeners, cyclic and nonproportional mechanical and thermal loading capability, the coupled axisymmetric large deflection elasto-plastic torsion problem, an extensive restart option, arbitrary branching capability, and the provision for the inelastic treatment of smeared stiffeners, isogrid, and waffle wall constructions. To affirm the validity of the results, comparisons with available theoretical and experimental data are presented.

  17. Divergence preserving discrete surface integral methods for Maxwell's curl equations using non-orthogonal unstructured grids

    NASA Technical Reports Server (NTRS)

    Madsen, Niel K.

    1992-01-01

    Several new discrete surface integral (DSI) methods for solving Maxwell's equations in the time-domain are presented. These methods, which allow the use of general nonorthogonal mixed-polyhedral unstructured grids, are direct generalizations of the canonical staggered-grid finite difference method. These methods are conservative in that they locally preserve divergence or charge. Employing mixed polyhedral cells, (hexahedral, tetrahedral, etc.) these methods allow more accurate modeling of non-rectangular structures and objects because the traditional stair-stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided. Numerical results demonstrating the accuracy of these new methods are presented.

  18. A New High-Order Stable Numerical Method for Matrix Inversion

    PubMed Central

    Haghani, F. Khaksar; Soleymani, F.

    2014-01-01

    A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfth-order convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding Moore-Penrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples. PMID:24688436

  19. The numerical integration and 3-D finite element formulation of a viscoelastic model of glass

    SciTech Connect

    Chambers, R.S.

    1994-08-01

    The use of glasses is widespread in making hermetic, insulating seals for many electronic components. Flat panel displays and fiber optic connectors are other products utilizing glass as a structural element. When glass is cooled from sealing temperatures, residual stresses are generated due to mismatches in thermal shrinkage created by the dissimilar material properties of the adjoining materials. Because glass is such a brittle material at room temperature, tensile residual stresses must be kept small to ensure durability and avoid cracking. Although production designs and the required manufacturing process development can be deduced empirically, this is an expensive and time consuming process that does not necessarily lead to an optimal design. Agile manufacturing demands that analyses be used to reduce development costs and schedules by providing insight and guiding the design process through the development cycle. To make these gains, however, viscoelastic models of glass must be available along with the right tool to use them. A viscoelastic model of glass can be used to simulate the stress and volume relaxation that occurs at elevated temperatures as the molecular structure of the glass seeks to equilibrate to the state of the supercooled liquid. The substance of the numerical treatment needed to support the implementation of the model in a 3-D finite element program is presented herein. An accurate second-order, central difference integrator is proposed for the constitutive equations, and numerical solutions are compared to those obtained with other integrators. Inherent convergence problems are reviewed and fixes are described. The resulting algorithms are generally applicable to the broad class of viscoelastic material models. First-order error estimates are used as a basis for developing a scheme for automatic time step controls, and several demonstration problems are presented to illustrate the performance of the methodology.

  20. Multiple methods integration for structural mechanics analysis and design

    NASA Technical Reports Server (NTRS)

    Housner, J. M.; Aminpour, M. A.

    1991-01-01

    A new research area of multiple methods integration is proposed for joining diverse methods of structural mechanics analysis which interact with one another. Three categories of multiple methods are defined: those in which a physical interface are well defined; those in which a physical interface is not well-defined, but selected; and those in which the interface is a mathematical transformation. Two fundamental integration procedures are presented that can be extended to integrate various methods (e.g., finite elements, Rayleigh Ritz, Galerkin, and integral methods) with one another. Since the finite element method will likely be the major method to be integrated, its enhanced robustness under element distortion is also examined and a new robust shell element is demonstrated.

  1. Fully coupled simulation of cosmic reionization. I. numerical methods and tests

    SciTech Connect

    Norman, Michael L.; Reynolds, Daniel R.; So, Geoffrey C.; Harkness, Robert P.; Wise, John H.

    2015-01-09

    Here, we describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large similar to(100 Mpc)(3) cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. But, we employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. Finally, we illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200(3) Eulerian grid cells and dark matter particles.

  2. Fully Coupled Simulation of Cosmic Reionization. I. Numerical Methods and Tests

    NASA Astrophysics Data System (ADS)

    Norman, Michael L.; Reynolds, Daniel R.; So, Geoffrey C.; Harkness, Robert P.; Wise, John H.

    2015-01-01

    We describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large ~(100 Mpc)3 cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 32003 Eulerian grid cells and dark matter particles.

  3. FULLY COUPLED SIMULATION OF COSMIC REIONIZATION. I. NUMERICAL METHODS AND TESTS

    SciTech Connect

    Norman, Michael L.; So, Geoffrey C.; Reynolds, Daniel R.; Harkness, Robert P.; Wise, John H.

    2015-01-01

    We describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large ∼(100 Mpc){sup 3} cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use to advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200{sup 3} Eulerian grid cells and dark matter particles.

  4. Fully coupled simulation of cosmic reionization. I. numerical methods and tests

    DOE PAGESBeta

    Norman, Michael L.; Reynolds, Daniel R.; So, Geoffrey C.; Harkness, Robert P.; Wise, John H.

    2015-01-09

    Here, we describe an extension of the Enzo code to enable fully coupled radiation hydrodynamical simulation of inhomogeneous reionization in large similar to(100 Mpc)(3) cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. But, we employ a simple subgrid model for star formation which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. differing principally in the operator splitting algorithm we use tomore » advance the system of equations. Radiation transport is done in the gray flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. Finally, we illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with 3200(3) Eulerian grid cells and dark matter particles.« less

  5. A Numerical Investigation of CFRP-Steel Interfacial Failure with Material Point Method

    SciTech Connect

    Shen Luming; Faleh, Haydar; Al-Mahaidi, Riadh

    2010-05-21

    The success of retrofitting steel structures by using the Carbon Fibre Reinforced Polymers (CFRP) significantly depends on the performance and integrity of CFRP-steel joint and the effectiveness of the adhesive used. Many of the previous numerical studies focused on the design and structural performance of the CFRP-steel system and neglected the mechanical responses of adhesive layer, which results in the lack of understanding in how the adhesive layer between the CFRP and steel performs during the loading and failure stages. Based on the recent observation on the failure of CFRP-steel bond in the double lap shear tests, a numerical approach is proposed in this study to simulate the delamination process of CFRP sheet from steel plate using the Material Point Method (MPM). In the proposed approach, an elastoplasticity model with a linear hardening and softening law is used to model the epoxy layer. The MPM, which does not employ fixed mesh-connectivity, is employed as a robust spatial discretization method to accommodate the multi-scale discontinuities involved in the CFRP-steel bond failure process. To demonstrate the potential of the proposed approach, a parametric study is conducted to investigate the effects of bond length and loading rates on the capacity and failure modes of CFRP-steel system. The evolution of the CFRP-steel bond failure and the distribution of stress and strain along bond length direction will be presented. The simulation results not only well match the available experimental data but also provide a better understanding on the physics behind the CFRP sheet delamination process.

  6. An Evaluation of Solution Algorithms and Numerical Approximation Methods for Modeling an Ion Exchange Process

    PubMed Central

    Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.

    2010-01-01

    The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward-difference-formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications. PMID:20577570

  7. A Numerical Investigation of CFRP-Steel Interfacial Failure with Material Point Method

    NASA Astrophysics Data System (ADS)

    Shen, Luming; Faleh, Haydar; Al-Mahaidi, Riadh

    2010-05-01

    The success of retrofitting steel structures by using the Carbon Fibre Reinforced Polymers (CFRP) significantly depends on the performance and integrity of CFRP-steel joint and the effectiveness of the adhesive used. Many of the previous numerical studies focused on the design and structural performance of the CFRP-steel system and neglected the mechanical responses of adhesive layer, which results in the lack of understanding in how the adhesive layer between the CFRP and steel performs during the loading and failure stages. Based on the recent observation on the failure of CFRP-steel bond in the double lap shear tests [1], a numerical approach is proposed in this study to simulate the delamination process of CFRP sheet from steel plate using the Material Point Method (MPM). In the proposed approach, an elastoplasticity model with a linear hardening and softening law is used to model the epoxy layer. The MPM [2], which does not employ fixed mesh-connectivity, is employed as a robust spatial discretization method to accommodate the multi-scale discontinuities involved in the CFRP-steel bond failure process. To demonstrate the potential of the proposed approach, a parametric study is conducted to investigate the effects of bond length and loading rates on the capacity and failure modes of CFRP-steel system. The evolution of the CFRP-steel bond failure and the distribution of stress and strain along bond length direction will be presented. The simulation results not only well match the available experimental data but also provide a better understanding on the physics behind the CFRP sheet delamination process.

  8. An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

    NASA Astrophysics Data System (ADS)

    Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.

    2010-07-01

    The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.

  9. Numerical validation of MR-measurement-integrated simulation of blood flow in a cerebral aneurysm.

    PubMed

    Funamoto, Kenichi; Suzuki, Yoshitsugu; Hayase, Toshiyuki; Kosugi, Takashi; Isoda, Haruo

    2009-06-01

    This study proposes magnetic resonance (MR)-measurement-integrated (MR-MI) simulation, in which the difference between the computed velocity field and the phase-contrast MRI measurement data is fed back to the numerical simulation. The computational accuracy and the fundamental characteristics, such as steady characteristics and transient characteristics, of the MR-MI simulation were investigated by a numerical experiment. We dealt with reproduction of three-dimensional steady and unsteady blood flow fields in a realistic cerebral aneurysm developed at a bifurcation. The MR-MI simulation reduced the error derived from the incorrect boundary conditions in the blood flow in the cerebral aneurysm. For the reproduction of steady and unsteady standard solutions, the error of velocity decreased to 13% and to 22% in one cardiac cycle, respectively, compared with the ordinary simulation without feedback. Moreover, the application of feedback shortened the computational convergence, and thus the convergent solution and periodic solution were obtained within less computational time in the MR-MI simulation than that in the ordinary simulation. The dividing flow ratio toward the two outlets after bifurcation was well estimated owing to the improvement of computational accuracy. Furthermore, the MR-MI simulation yielded wall shear stress distribution on the cerebral aneurysm of the standard solution accurately and in detail. PMID:19350390

  10. Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction.

    PubMed

    Wu, Yumao; Lu, Ya Yan

    2011-06-01

    Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green's function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu, J. Opt. Soc. Am. A26, 2444 (2009)] is extended to conical diffraction problems. The method uses boundary integral equations to calculate the so-called Neumann-to-Dirichlet maps for homogeneous subdomains of the grating, so that the quasi-periodic Green's functions can be avoided. Since wave field components are coupled on material interfaces with the involvement of tangential derivatives, a least squares polynomial approximation technique is developed to evaluate tangential derivatives along these interfaces for conical diffraction problems. Numerical examples indicate that the method performs equally well for dielectric or metallic gratings. PMID:21643404

  11. Nearest neighbor interaction in the Path Integral Renormalization Group method

    NASA Astrophysics Data System (ADS)

    de Silva, Wasanthi; Clay, R. Torsten

    2014-03-01

    The Path Integral Renormalization Group (PIRG) method is an efficient numerical algorithm for studying ground state properties of strongly correlated electron systems. The many-body ground state wave function is approximated by an optimized linear combination of Slater determinants which satisfies the variational principle. A major advantage of PIRG is that is does not suffer the Fermion sign problem of quantum Monte Carlo. Results are exact in the noninteracting limit and can be enhanced using space and spin symmetries. Many observables can be calculated using Wick's theorem. PIRG has been used predominantly for the Hubbard model with a single on-site Coulomb interaction U. We describe an extension of PIRG to the extended Hubbard model (EHM) including U and a nearest-neighbor interaction V. The EHM is particularly important in models of charge-transfer solids (organic superconductors) and at 1/4-filling drives a charge-ordered state. The presence of lattice frustration also makes studying these systems difficult. We test the method with comparisons to small clusters and long one dimensional chains, and show preliminary results for a coupled-chain model for the (TMTTF)2X materials. This work was supported by DOE grant DE-FG02-06ER46315.

  12. Numerical methods for the design and analysis of wings at supersonic speeds

    NASA Technical Reports Server (NTRS)

    Carlson, H. W.; Miller, D. S.

    1974-01-01

    Numerical methods for the design and analysis of arbitrary-planform wings at supersonic speeds are reviewed. Certain deficiencies are revealed, particularly in application to wings with slightly subsonic leading edges. Recently devised numerical techniques which overcome the major part of these deficiencies are presented. The original development as well as the more recent revisions are subjected to a thorough review.

  13. A study of numerical methods for hyperbolic conservation laws with stiff source terms

    NASA Technical Reports Server (NTRS)

    Leveque, R. J.; Yee, H. C.

    1988-01-01

    The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.

  14. Improved accuracy for finite element structural analysis via a new integrated force method

    NASA Technical Reports Server (NTRS)

    Patnaik, Surya N.; Hopkins, Dale A.; Aiello, Robert A.; Berke, Laszlo

    1992-01-01

    A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

  15. Improved accuracy for finite element structural analysis via an integrated force method

    NASA Technical Reports Server (NTRS)

    Patnaik, S. N.; Hopkins, D. A.; Aiello, R. A.; Berke, L.

    1992-01-01

    A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

  16. Segment-based vs. element-based integration for mortar methods in computational contact mechanics

    NASA Astrophysics Data System (ADS)

    Farah, Philipp; Popp, Alexander; Wall, Wolfgang A.

    2015-01-01

    Mortar finite element methods provide a very convenient and powerful discretization framework for geometrically nonlinear applications in computational contact mechanics, because they allow for a variationally consistent treatment of contact conditions (mesh tying, non-penetration, frictionless or frictional sliding) despite the fact that the underlying contact surface meshes are non-matching and possibly also geometrically non-conforming. However, one of the major issues with regard to mortar methods is the design of adequate numerical integration schemes for the resulting interface coupling terms, i.e. curve integrals for 2D contact problems and surface integrals for 3D contact problems. The way how mortar integration is performed crucially influences the accuracy of the overall numerical procedure as well as the computational efficiency of contact evaluation. Basically, two different types of mortar integration schemes, which will be termed as segment-based integration and element-based integration here, can be found predominantly in the literature. While almost the entire existing literature focuses on either of the two mentioned mortar integration schemes without questioning this choice, the intention of this paper is to provide a comprehensive and unbiased comparison. The theoretical aspects covered here include the choice of integration rule, the treatment of boundaries of the contact zone, higher-order interpolation and frictional sliding. Moreover, a new hybrid scheme is proposed, which beneficially combines the advantages of segment-based and element-based mortar integration. Several numerical examples are presented for a detailed and critical evaluation of the overall performance of the different schemes within several well-known benchmark problems of computational contact mechanics.

  17. Numerical Stochastic Homogenization Method and Multiscale Stochastic Finite Element Method - A Paradigm for Multiscale Computation of Stochastic PDEs

    SciTech Connect

    X. Frank Xu

    2010-03-30

    Multiscale modeling of stochastic systems, or uncertainty quantization of multiscale modeling is becoming an emerging research frontier, with rapidly growing engineering applications in nanotechnology, biotechnology, advanced materials, and geo-systems, etc. While tremendous efforts have been devoted to either stochastic methods or multiscale methods, little combined work had been done on integration of multiscale and stochastic methods, and there was no method formally available to tackle multiscale problems involving uncertainties. By developing an innovative Multiscale Stochastic Finite Element Method (MSFEM), this research has made a ground-breaking contribution to the emerging field of Multiscale Stochastic Modeling (MSM) (Fig 1). The theory of MSFEM basically decomposes a boundary value problem of random microstructure into a slow scale deterministic problem and a fast scale stochastic one. The slow scale problem corresponds to common engineering modeling practices where fine-scale microstructure is approximated by certain effective constitutive constants, which can be solved by using standard numerical solvers. The fast scale problem evaluates fluctuations of local quantities due to random microstructure, which is important for scale-coupling systems and particularly those involving failure mechanisms. The Green-function-based fast-scale solver developed in this research overcomes the curse-of-dimensionality commonly met in conventional approaches, by proposing a random field-based orthogonal expansion approach. The MSFEM formulated in this project paves the way to deliver the first computational tool/software on uncertainty quantification of multiscale systems. The applications of MSFEM on engineering problems will directly enhance our modeling capability on materials science (composite materials, nanostructures), geophysics (porous media, earthquake), biological systems (biological tissues, bones, protein folding). Continuous development of MSFEM will

  18. New Techniques for Simulation of Ion Implantation by Numerical Integration of Boltzmann Transport Equation

    NASA Astrophysics Data System (ADS)

    Wang, Shyh-Wei; Guo, Shuang-Fa

    1998-01-01

    New techniques for more accurate and efficient simulation of ion implantations by a stepwise numerical integration of the Boltzmann transport equation (BTE) have been developed in this work. Instead of using uniform energy grid, a non-uniform grid is employed to construct the momentum distribution matrix. A more accurate simulation result is obtained for heavy ions implanted into silicon. In the same time, rather than utilizing the conventional Lindhard, Nielsen and Schoitt (LNS) approximation, an exact evaluation of the integrals involving the nuclear differential scattering cross-section (dσn=2πp dp) is proposed. The impact parameter p as a function of ion energy E and scattering angle φ is obtained by solving the magic formula iteratively and an interpolation techniques is devised during the simulation process. The simulation time using exact evaluation is about 3.5 times faster than that using the Littmark and Ziegler (LZ) spline fitted cross-section function for phosphorus implantation into silicon.

  19. An Energy-Efficient Cluster-Based Vehicle Detection on Road Network Using Intention Numeration Method

    PubMed Central

    Devasenapathy, Deepa; Kannan, Kathiravan

    2015-01-01

    The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN) is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate. PMID:25793221

  20. Optimization Algorithm for Kalman Filter Exploiting the Numerical Characteristics of SINS/GPS Integrated Navigation Systems

    PubMed Central

    Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu

    2015-01-01

    Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted “useful” data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency. PMID:26569247

  1. Optimization Algorithm for Kalman Filter Exploiting the Numerical Characteristics of SINS/GPS Integrated Navigation Systems.

    PubMed

    Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu

    2015-01-01

    Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency. PMID:26569247

  2. Numerical optimization of integrating cavities for diffraction-limited millimeter-wave bolometer arrays.

    PubMed

    Glenn, Jason; Chattopadhyay, Goutam; Edgington, Samantha F; Lange, Andrew E; Bock, James J; Mauskopf, Philip D; Lee, Adrian T

    2002-01-01

    Far-infrared to millimeter-wave bolometers designed to make astronomical observations are typically encased in integrating cavities at the termination of feedhorns or Winston cones. This photometer combination maximizes absorption of radiation, enables the absorber area to be minimized, and controls the directivity of absorption, thereby reducing susceptibility to stray light. In the next decade, arrays of hundreds of silicon nitride micromesh bolometers with planar architectures will be used in ground-based, suborbital, and orbital platforms for astronomy. The optimization of integrating cavity designs is required for achieving the highest possible sensitivity for these arrays. We report numerical simulations of the electromagnetic fields in integrating cavities with an infinite plane-parallel geometry formed by a solid reflecting backshort and the back surface of a feedhorn array block. Performance of this architecture for the bolometer array camera (Bolocam) for cosmology at a frequency of 214 GHz is investigated. We explore the sensitivity of absorption efficiency to absorber impedance and backshort location and the magnitude of leakage from cavities. The simulations are compared with experimental data from a room-temperature scale model and with the performance of Bolocam at a temperature of 300 mK. The main results of the simulations for Bolocam-type cavities are that (1) monochromatic absorptions as high as 95% are achievable with <1% cross talk between neighboring cavities, (2) the optimum absorber impedances are 400 ohms/sq, but with a broad maximum from approximately 150 to approximately 700 ohms/sq, and (3) maximum absorption is achieved with absorber diameters > or = 1.5 lambda. Good general agreement between the simulations and the experiments was found. PMID:11900429

  3. Numerical Modeling of the Chilldown of Cryogenic Transfer Lines Using a Sinda/GFSSP Integrated Solver

    NASA Technical Reports Server (NTRS)

    LeClair, Andre

    2011-01-01

    An important first step in cryogenic propellant loading is the chilldown of transfer lines. During the chilldown of the transfer line, the flow is two-phase and unsteady, with solid to fluid heat transfer and therefore a coupled thermo-fluid analysis is necessary to model the system. This paper describes a numerical model of pipe chilldown that utilizes the Sinda/GFSSP Conjugate Integrator (SGCI). SGCI is a new analysis tool developed at NASA's Marshall Space Flight Center (MSFC). SGCI facilitates the solution of thermofluid problems in interconnected solid-fluid systems. The solid component of the system is modeled in MSC Patran and translated into an MSC Sinda thermal network model. The fluid component is modeled in GFSSP, the Generalized Fluid System Simulation Program. GFSSP is a general network flow solver developed at NASA/MSFC. GFSSP uses a finite-volume approach to model fluid systems that can include phase change, multiple species, fluid transients, and heat transfer to simple solid networks. SGCI combines the GFSSP Fortran code with the Sinda input file and compiles the integrated model. Sinda solves for the temperatures of the solid network, while GFSSP simultaneously solves the fluid network for pressure, temperature, and flow rate. The two networks are coupled by convection heat transfer from the solid wall to the cryogenic fluid. The model presented here is based on a series of experiments conducted in 1966 by the National Bureau of Standards (NBS). A vacuum-jacketed, 200 ft copper transfer line was chilled by liquid nitrogen and liquid hydrogen. The predictions of transient temperature profiles and chilldown time of the integrated Sinda/GFSSP model will be compared to the experimental measurements.

  4. Advanced numerical methods for three dimensional two-phase flow calculations

    SciTech Connect

    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 an 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.

  5. Integrating Qualitative and Quantitative Evaluation Methods in Substance Abuse Research.

    ERIC Educational Resources Information Center

    Dennis, Michael L.; And Others

    1994-01-01

    Some specific opportunities and techniques are described for combining and integrating qualitative and quantitative methods from the design stage of a substance abuse program evaluation through implementation and reporting. The multiple problems and requirements of such an evaluation make integrated methods essential. (SLD)

  6. Solution of the WFNDEC 2015 eddy current benchmark with surface integral equation method

    NASA Astrophysics Data System (ADS)

    Demaldent, Edouard; Miorelli, Roberto; Reboud, Christophe; Theodoulidis, Theodoros

    2016-02-01

    In this paper, a numerical solution of WFNDEC 2015 eddy current benchmark is presented. In particular, the Surface Integral Equation (SIE) method has been employed for numerically solving the benchmark problem. The SIE method represent an effective and efficient alternative to standard numerical solver like Finite Element Method (FEM) when electromagnetic fields need to be calculated in problems involving homogeneous media. The formulation of SIE method allows to properly solve the electromagnetic problem by meshing the surface of the media instead to the complete media volume as done in FEM. The surface meshing enables to describe the problem with a smaller number of unknowns with respect to FEM. This property is directly translated in an obvious gain in terms of CPU time efficiency.

  7. Numerical methods for simulating blood flow at macro, micro, and multi scales.

    PubMed

    Imai, Yohsuke; Omori, Toshihiro; Shimogonya, Yuji; Yamaguchi, Takami; Ishikawa, Takuji

    2016-07-26

    In the past decade, numerical methods for the computational biomechanics of blood flow have progressed to overcome difficulties in diverse applications from cellular to organ scales. Such numerical methods may be classified by the type of computational mesh used for the fluid domain, into fixed mesh methods, moving mesh (boundary-fitted mesh) methods, and mesh-free methods. The type of computational mesh used is closely related to the characteristics of each method. We herein provide an overview of numerical methods recently used to simulate blood flow at macro and micro scales, with a focus on computational meshes. We also discuss recent progress in the multi-scale modeling of blood flow. PMID:26705108

  8. A Gas Dynamics Method Based on The Spectral Deferred Corrections (SDC) Time Integration Technique and The Piecewise Parabolic Method (PPM)

    SciTech Connect

    Samet Y. Kadioglu

    2011-12-01

    We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to define edge averaged quantities which are then used to evaluate numerical flux functions. The SDC technique is used to integrate solution in time. This kind of approach was first taken by Anita et al in [17]. However, [17] is problematic when it is implemented to certain shock problems. Here we propose significant improvements to [17]. The method is fourth order (both in space and time) for smooth flows, and provides highly resolved discontinuous solutions. We tested the method by solving variety of problems. Results indicate that the fourth order of accuracy in both space and time has been achieved when the flow is smooth. Results also demonstrate the shock capturing ability of the method.

  9. Numerical simulation of Stokes flow around particles via a hybrid Finite Difference-Boundary Integral scheme

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Amitabh

    2013-11-01

    An efficient algorithm for simulating Stokes flow around particles is presented here, in which a second order Finite Difference method (FDM) is coupled to a Boundary Integral method (BIM). This method utilizes the strong points of FDM (i.e. localized stencil) and BIM (i.e. accurate representation of particle surface). Specifically, in each iteration, the flow field away from the particles is solved on a Cartesian FDM grid, while the traction on the particle surface (given the the velocity of the particle) is solved using BIM. The two schemes are coupled by matching the solution in an intermediate region between the particle and surrounding fluid. We validate this method by solving for flow around an array of cylinders, and find good agreement with Hasimoto's (J. Fluid Mech. 1959) analytical results.

  10. A high-order fast method for computing convolution integral with smooth kernel

    SciTech Connect

    Qiang, Ji

    2009-09-28

    In this paper we report on a high-order fast method to numerically calculate convolution integral with smooth non-periodic kernel. This method is based on the Newton-Cotes quadrature rule for the integral approximation and an FFT method for discrete summation. The method can have an arbitrarily high-order accuracy in principle depending on the number of points used in the integral approximation and a computational cost of O(Nlog(N)), where N is the number of grid points. For a three-point Simpson rule approximation, the method has an accuracy of O(h{sup 4}), where h is the size of the computational grid. Applications of the Simpson rule based algorithm to the calculation of a one-dimensional continuous Gauss transform and to the calculation of a two-dimensional electric field from a charged beam are also presented.

  11. A numerical method for solving the 3D unsteady incompressible Navier Stokes equations in curvilinear domains with complex immersed boundaries

    NASA Astrophysics Data System (ADS)

    Ge, Liang; Sotiropoulos, Fotis

    2007-08-01

    A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow

  12. Numerical method for estimating the size of chaotic regions of phase space

    SciTech Connect

    Henyey, F.S.; Pomphrey, N.

    1987-10-01

    A numerical method for estimating irregular volumes of phase space is derived. The estimate weights the irregular area on a surface of section with the average return time to the section. We illustrate the method by application to the stadium and oval billiard systems and also apply the method to the continuous Henon-Heiles system. 15 refs., 10 figs. (LSP)

  13. Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration

    NASA Astrophysics Data System (ADS)

    Li, G. Q.; Zhu, Z. H.

    2015-12-01

    Dynamic modeling of tethered spacecraft with the consideration of elasticity of tether is prone to the numerical instability and error accumulation over long-term numerical integration. This paper addresses the challenges by proposing a globally stable numerical approach with the nodal position finite element method (NPFEM) and the implicit, symplectic, 2-stage and 4th order Gaussian-Legendre Runge-Kutta time integration. The NPFEM eliminates the numerical error accumulation by using the position instead of displacement of tether as the state variable, while the symplectic integration enforces the energy and momentum conservation of the discretized finite element model to ensure the global stability of numerical solution. The effectiveness and robustness of the proposed approach is assessed by an elastic pendulum problem, whose dynamic response resembles that of tethered spacecraft, in comparison with the commonly used time integrators such as the classical 4th order Runge-Kutta schemes and other families of non-symplectic Runge-Kutta schemes. Numerical results show that the proposed approach is accurate and the energy of the corresponding numerical model is conservative over the long-term numerical integration. Finally, the proposed approach is applied to the dynamic modeling of deorbiting process of tethered spacecraft over a long period.

  14. A survey of payload integration methods

    NASA Technical Reports Server (NTRS)

    Engels, R. C.; Craig, R. R., Jr.; Harcrow, H. W.

    1984-01-01

    Several full-scale and short-cut methods for analyzing a booster/payload system are presented. Two full-scale techniques are considered: (1) a technique that uses a restrained payload together with a free-booster model, the latter being augmented with residual mass and stiffness correction and (2) a technique that uses a restrained payload and booster model. Both techniques determine the 'modal modes', which require the solution of a system eigenvalue problem; the loads usually are then determined via an acceleration approach. A brief description is given of a number of short-cut methods which are of special interest to Shuttle payload design: structural modification, base drive, and interface impedance methods. Directions for further research and development are suggested.

  15. Treatment of domain integrals in boundary element methods

    SciTech Connect

    Nintcheu Fata, Sylvain

    2012-01-01

    A systematic and rigorous technique to calculate domain integrals without a volume-fitted mesh has been developed and validated in the context of a boundary element approximation. In the proposed approach, a domain integral involving a continuous or weakly-singular integrand is first converted into a surface integral by means of straight-path integrals that intersect the underlying domain. Then, the resulting surface integral is carried out either via analytic integration over boundary elements or by use of standard quadrature rules. This domain-to-boundary integral transformation is derived from an extension of the fundamental theorem of calculus to higher dimension, and the divergence theorem. In establishing the method, it is shown that the higher-dimensional version of the first fundamental theorem of calculus corresponds to the well-known Poincare lemma. The proposed technique can be employed to evaluate integrals defined over simply- or multiply-connected domains with Lipschitz boundaries which are embedded in an Euclidean space of arbitrary but finite dimension. Combined with the singular treatment of surface integrals that is widely available in the literature, this approach can also be utilized to effectively deal with boundary-value problems involving non-homogeneous source terms by way of a collocation or a Galerkin boundary integral equation method using only the prescribed surface discretization. Sample problems associated with the three-dimensional Poisson equation and featuring the Newton potential are successfully solved by a constant element collocation method to validate this study.

  16. The Validation of Complete Fourier Direct MR Method for Diffusion MRI via Biological and Numerical Phantoms

    PubMed Central

    Özcan, Alpay; Quirk, James D.; Wang, Yong; Wang, Qing; Sun, Peng; Spees, William M.; Song, Sheng–Kwei

    2012-01-01

    The equations of the Complete Fourier Direct (CFD) MR model are explicitly derived for diffusion weighted NMR experiments. The CFD–MR theory is validated by comparing a biological phantom constructed from nerve bundles and agar gel with its numerical implementation. The displacement integral distribution function estimated from the experimental data is in high agreement with the numerical phantom. CFD–MR’s ability to estimate accurately and fully spin diffusion properties demonstrated here, provides the experimental validation of the theoretical CFD–MR model. PMID:22255156

  17. A wavelet-based computational method for solving stochastic Itô–Volterra integral equations

    SciTech Connect

    Mohammadi, Fakhrodin

    2015-10-01

    This paper presents a computational method based on the Chebyshev wavelets for solving stochastic Itô–Volterra integral equations. First, a stochastic operational matrix for the Chebyshev wavelets is presented and a general procedure for forming this matrix is given. Then, the Chebyshev wavelets basis along with this stochastic operational matrix are applied for solving stochastic Itô–Volterra integral equations. Convergence and error analysis of the Chebyshev wavelets basis are investigated. To reveal the accuracy and efficiency of the proposed method some numerical examples are included.

  18. Integrated method for chaotic time series analysis

    DOEpatents

    Hively, L.M.; Ng, E.G.

    1998-09-29

    Methods and apparatus for automatically detecting differences between similar but different states in a nonlinear process monitor nonlinear data are disclosed. Steps include: acquiring the data; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; and determining by comparison whether differences between similar but different states are indicated. 8 figs.

  19. Integrated method for chaotic time series analysis

    DOEpatents

    Hively, Lee M.; Ng, Esmond G.

    1998-01-01

    Methods and apparatus for automatically detecting differences between similar but different states in a nonlinear process monitor nonlinear data. Steps include: acquiring the data; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; and determining by comparison whether differences between similar but different states are indicated.

  20. Integrating Formal Methods and Testing 2002

    NASA Technical Reports Server (NTRS)

    Cukic, Bojan

    2002-01-01

    Traditionally, qualitative program verification methodologies and program testing are studied in separate research communities. None of them alone is powerful and practical enough to provide sufficient confidence in ultra-high reliability assessment when used exclusively. Significant advances can be made by accounting not only tho formal verification and program testing. but also the impact of many other standard V&V techniques, in a unified software reliability assessment framework. The first year of this research resulted in the statistical framework that, given the assumptions on the success of the qualitative V&V and QA procedures, significantly reduces the amount of testing needed to confidently assess reliability at so-called high and ultra-high levels (10-4 or higher). The coming years shall address the methodologies to realistically estimate the impacts of various V&V techniques to system reliability and include the impact of operational risk to reliability assessment. Combine formal correctness verification, process and product metrics, and other standard qualitative software assurance methods with statistical testing with the aim of gaining higher confidence in software reliability assessment for high-assurance applications. B) Quantify the impact of these methods on software reliability. C) Demonstrate that accounting for the effectiveness of these methods reduces the number of tests needed to attain certain confidence level. D) Quantify and justify the reliability estimate for systems developed using various methods.

  1. Computational methods for inlet airframe integration

    NASA Technical Reports Server (NTRS)

    Towne, Charles E.

    1988-01-01

    Fundamental equations encountered in computational fluid dynamics (CFD), and analyses used for internal flow are introduced. Irrotational flow; Euler equations; boundary layers; parabolized Navier-Stokes equations; and time averaged Navier-Stokes equations are treated. Assumptions made and solution methods are outlined, with examples. The overall status of CFD in propulsion is indicated.

  2. Application of numerical methods for diffusion-based modeling of skin permeation.

    PubMed

    Frasch, H Frederick; Barbero, Ana M

    2013-02-01

    The application of numerical methods for mechanistic, diffusion-based modeling of skin permeation is reviewed. Methods considered here are finite difference, method of lines, finite element, finite volume, random walk, cellular automata, and smoothed particle hydrodynamics. First the methods are briefly explained with rudimentary mathematical underpinnings. Current state of the art numerical models are described, and then a chronological overview of published models is provided. Key findings and insights of reviewed models are highlighted. Model results support a primarily transcellular pathway with anisotropic lipid transport. Future endeavors would benefit from a fundamental analysis of drug/vehicle/skin interactions. PMID:22261307

  3. The lambda-scheme. [for numerical integration of Euler equation of compressible gas flow

    NASA Technical Reports Server (NTRS)

    Moretti, G.

    1979-01-01

    A method for integrating the Euler equations of gas dynamics for compressible flows in any hyperbolic case is presented. This method is applied to the Mach number distribution over a stretch of an infinite duct having a variable cross section, and to the distribution in a channel opening into a vacuum with the Mach number equalling 1.04. An example of the ability of this method to handle two-dimensional unsteady flows is shown using the steady shock-and-isobars pattern reached asymptotically about an ablated blunt body with a free stream Mach number equalling 12. A final example is presented where the technique is applied to a three-dimensional steady supersonic flow, with a Mach number of 2 and an angle of attack of 5 deg.

  4. Interactive statistical-distribution-analysis program utilizing numerical and graphical methods

    SciTech Connect

    Glandon, S. R.; Fields, D. E.

    1982-04-01

    The TERPED/P program is designed to facilitate the quantitative analysis of experimental data, determine the distribution function that best describes the data, and provide graphical representations of the data. This code differs from its predecessors, TEDPED and TERPED, in that a printer-plotter has been added for graphical output flexibility. The addition of the printer-plotter provides TERPED/P with a method of generating graphs that is not dependent on DISSPLA, Integrated Software Systems Corporation's confidential proprietary graphics package. This makes it possible to use TERPED/P on systems not equipped with DISSPLA. In addition, the printer plot is usually produced more rapidly than a high-resolution plot can be generated. Graphical and numerical tests are performed on the data in accordance with the user's assumption of normality or lognormality. Statistical analysis options include computation of the chi-squared statistic and its significance level and the Kolmogorov-Smirnov one-sample test confidence level for data sets of more than 80 points. Plots can be produced on a Calcomp paper plotter, a FR80 film plotter, or a graphics terminal using the high-resolution, DISSPLA-dependent plotter or on a character-type output device by the printer-plotter. The plots are of cumulative probability (abscissa) versus user-defined units (ordinate). The program was developed on a Digital Equipment Corporation (DEC) PDP-10 and consists of 1500 statements. The language used is FORTRAN-10, DEC's extended version of FORTRAN-IV.

  5. Shape integral method for magnetospheric shapes. [boundary layer calculations

    NASA Technical Reports Server (NTRS)

    Michel, F. C.

    1979-01-01

    A method is developed for calculating the shape of any magnetopause to arbitrarily high precision. The method uses an integral equation which is evaluated for a trial shape. The resulting values of the integral equation as a function of auxiliary variables indicate how close one is to the desired solution. A variational method can then be used to improve the trial shape. Some potential applications are briefly mentioned.

  6. Analytical solution based on the wavenumber integration method for the acoustic field in a Pekeris waveguide

    NASA Astrophysics Data System (ADS)

    Wen-Yu, Luo; Xiao-Lin, Yu; Xue-Feng, Yang; Ren-He, Zhang

    2016-04-01

    An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide. Project supported by the National Natural Science Foundation of China (Grant No. 11125420), the Knowledge Innovation Program of the Chinese Academy of Sciences, the China Postdoctoral Science Foundation (Grant No. 2014M561882), and the Doctoral Fund of Shandong Province, China (Grant No. BS2012HZ015).

  7. Numerical Modeling of Spray Combustion with an Unstructured-Grid Method

    NASA Technical Reports Server (NTRS)

    Shang, H. M.; Chen, Y. S.; Liaw, P.; Shih, M. H.; Wang, T. S.

    1996-01-01

    The present unstructured-grid method follows strictly the basic finite volume forms of the conservation laws of the governing equations for the entire flow domain. High-order spatially accurate formulation has been employed for the numerical solutions of the Navier-Stokes equations. A two-equation k-epsilon turbulence model is also incorporated in the unstructured-grid solver. The convergence of the resulted linear algebraic equation is accelerated with preconditioned Conjugate Gradient method. A statistical spray combustion model has been incorporated into the present unstructured-grid solver. In this model, spray is represented by discrete particles, rather than by continuous distributions. A finite number of computational particles are used to predict a sample of total population of particles. Particle trajectories are integrated using their momentum and motion equations and particles exchange mass, momentum and energy with the gas within the computational cell in which they are located. The interaction calculations are performed simultaneously and eliminate global iteration for the two-phase momentum exchange. A transient spray flame in a high pressure combustion chamber is predicted and then the solution of liquid-fuel combusting flow with a rotating cup atomizer is presented and compared with the experimental data. The major conclusion of this investigation is that the unstructured-grid method can be employed to study very complicated flow fields of turbulent spray combustion. Grid adaptation can be easily achieved in any flow domain such as droplet evaporation and combustion zone. Future applications of the present model can be found in the full three-dimensional study of flow fields of gas turbine and liquid propulsion engine combustion chambers with multi-injectors.

  8. Critical study of higher order numerical methods for solving the boundary-layer equations

    NASA Technical Reports Server (NTRS)

    Wornom, S. F.

    1978-01-01

    A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.

  9. Application of higher-order numerical methods to the boundary-layer equations

    NASA Technical Reports Server (NTRS)

    Wornom, S. F.

    1978-01-01

    A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

  10. An Efficient Boundary Integral Method for the Mullins Sekerka Problem

    NASA Astrophysics Data System (ADS)

    Zhu, Jingyi; Chen, Xinfu; Hou, Thomas Y.

    1996-09-01

    We use a boundary integral technique to study the two space dimensional Mullins-Sekerka free boundary problem which originates from a study of solidification and liquidation of materials of negligible specific heat. This is an area preserving and curve shortening motion. Evolution equations for the free boundaries are derived in terms of the tangent angle and total arclength, which makes a small scale decomposition possible and the Fourier transform a powerful tool in numerical calculations. With this formulation, implicit schemes can be implemented to avoid the difficult numerical stiffness associated with explicit schemes. We can compute solutions up to the time when there is a topological change, i.e., when particles touch or break up. Our numerical results for systems of a single particle or multi-particles provide some valuable information in the particle dynamics, such as the circularization of each individual particle, and the mass transfer between different particles during particle interactions.

  11. Gocad2OGS: Workflow to Integrate Geo-structural Information into Numerical Simulation Models

    NASA Astrophysics Data System (ADS)

    Fischer, Thomas; Walther, Marc; Naumov, Dmitri; Sattler, Sabine; Kolditz, Olaf

    2015-04-01

    The investigation of fluid circulation in the Thuringian syncline is one of the INFLUINS project's targets. A 3D geo-structural model including 12 stratigraphic layers and 54 fault zones is created by geologists in the first step using the Gocad software. Within the INFLUINS project a ground-water flow simulation is used to check existing hypotheses and to gain new ideas of the underground fluid flow behaviour. We used the scientific, platform independent, open source software OpenGeoSys that implements the finite element method to solve the governing equations describing fluid flow in porous media. The geo-structural Gocad model is not suitable for the FEM numerical analysis. Therefore it is converted into an unstructured grid satisfying all mesh quality criteria required for the ground-water flow simulation. The resulting grid is stored in an open data format given by the Visualization Toolkit (vtk). In this work we present a workflow to convert geological structural models, created using the Gocad software, into a simulation model that is easy to use from numerical simulation software. We tested our workflow with the 3D geo-structural model of the Thuringian syncline and were able to setup and to evaluate a hydrogeological simulation model successfully.

  12. Predicting geomorphic evolution through integration of numerical-model scenarios and topographic/bathymetric-survey updates

    NASA Astrophysics Data System (ADS)

    Plant, N. G.; Long, J.; Dalyander, S.; Thompson, D.; Miselis, J. L.

    2013-12-01

    Natural resource and hazard management of barrier islands requires an understanding of geomorphic changes associated with long-term processes and storms. Uncertainty exists in understanding how long-term processes interact with the geomorphic changes caused by storms and the resulting perturbations of the long-term evolution trajectories. We use high-resolution data sets to initialize and correct high-fidelity numerical simulations of oceanographic forcing and resulting barrier island evolution. We simulate two years of observed storms to determine the individual and cumulative impacts of these events. Results are separated into cross-shore and alongshore components of sediment transport and compared with observed topographic and bathymetric changes during these time periods. The discrete island change induced by these storms is integrated with previous knowledge of long-term net alongshore sediment transport to project island evolution. The approach has been developed and tested using data collected at the Chandeleur Island chain off the coast of Louisiana (USA). The simulation time period included impacts from tropical and winter storms, as well as a human-induced perturbation associated with construction of a sand berm along the island shoreline. The predictions and observations indicated that storm and long-term processes both contribute to the migration, lowering, and disintegration of the artificial berm and natural island. Further analysis will determine the relative importance of cross-shore and alongshore sediment transport processes and the dominant time scales that drive each of these processes and subsequent island morphologic response.

  13. Some self starting integrators for x Prime equals f (x, t). [Runge-Kutta method and orbital position estimation

    NASA Technical Reports Server (NTRS)

    Lear, W. M.

    1974-01-01

    The integration is discussed of the vector differential equation X = F(x, t) from time t sub i to t sub (i = 1) where only the values of x sub i are available for the the integration. No previous values of x or x prime are used. Using an orbit integration problem, comparisons are made between Taylor series integrators and various types and orders of Runge-Kutta integrators. A fourth order Runge-Kutta type integrator for orbital work is presented, and approximate (there may be no exact) fifth order Runge-Kutta integrators are discussed. Also discussed and compared is a self starting integrator ising delta f/delta x. A numerical method for controlling the accuracy of integration is given, and the special equations for accurately integrating accelerometer data are shown.

  14. A method for the direct numerical simulation of hypersonic boundary-layer instability with finite-rate chemistry

    SciTech Connect

    Marxen, Olaf; Magin, Thierry E.; Shaqfeh, Eric S.G.; Iaccarino, Gianluca

    2013-12-15

    A new numerical method is presented here that allows to consider chemically reacting gases during the direct numerical simulation of a hypersonic fluid flow. The method comprises the direct coupling of a solver for the fluid mechanical model and a library providing the physio-chemical model. The numerical method for the fluid mechanical model integrates the compressible Navier–Stokes equations using an explicit time advancement scheme and high-order finite differences. This Navier–Stokes code can be applied to the investigation of laminar-turbulent transition and boundary-layer instability. The numerical method for the physio-chemical model provides thermodynamic and transport properties for different gases as well as chemical production rates, while here we exclusively consider a five species air mixture. The new method is verified for a number of test cases at Mach 10, including the one-dimensional high-temperature flow downstream of a normal shock, a hypersonic chemical reacting boundary layer in local thermodynamic equilibrium and a hypersonic reacting boundary layer with finite-rate chemistry. We are able to confirm that the diffusion flux plays an important role for a high-temperature boundary layer in local thermodynamic equilibrium. Moreover, we demonstrate that the flow for a case previously considered as a benchmark for the investigation of non-equilibrium chemistry can be regarded as frozen. Finally, the new method is applied to investigate the effect of finite-rate chemistry on boundary layer instability by considering the downstream evolution of a small-amplitude wave and comparing results with those obtained for a frozen gas as well as a gas in local thermodynamic equilibrium.

  15. Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles. Part 2: Applications

    NASA Technical Reports Server (NTRS)

    Thomas, P. D.

    1980-01-01

    A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.

  16. Autonomous integrated navigation method based on the strapdown inertial navigation system and Lidar

    NASA Astrophysics Data System (ADS)

    Zhang, Xiaoyue; Lin, Zhili; Zhang, Chunxi

    2014-07-01

    An integrated navigation method based on the strapdown inertial navigation system (SINS) and Doppler Lidar was presented and its validity is demonstrated by practical experiments. A very effective and independent integrated navigation mode is realized that both an inertial navigation system (INS) and Lidar are not interfered with or screened by electromagnetic waves. In our work, the SINS error model was first introduced, and the velocity error model was transformed into body reference coordinates. Then the expression for measurement model of SINS/Lidar integrated navigation was deduced under Lidar reference coordinates. For application of land or vehicle navigation, the expression for the measurement model was simplified, and observation analysis was carried out. Finally, numerical simulation and vehicle test results were carried out to validate the availability and utility of the proposed SINS/Lidar integrated navigation method for land navigation.

  17. Morphology and dynamics of piercement structures: an integrated laboratory and numerical study

    NASA Astrophysics Data System (ADS)

    Galland, Olivier; Gisler, Galen R.; Haug, Øystein T.

    2013-04-01

    Piercement structures are numerous in many geological settings, including pockmarks, mud volcanoes, hydrothermal vents, maar-diatreme volcanoes, volcanic conduits in stratovolcanoes, and kimberlite volcanoes. These piercement structures exhibit various shapes, from sub-vertical pipes piercing through the country rock to open and wide conduits, such as volcanic craters resulting from volcanic explosions (e.g., Mount Pinatubo). In this contribution, we present an integrated laboratory/numerical study to constrain the dynamics of piercement structures and unravel the processes that control their morphology. The laboratory experiments consist of a Hele-Shaw cell filled with a pack of cohesive fine-grained granular material, at the bottom of which a volume V t of pressurized air is injected at high velocity. As a result of air injection, a piercement structure develops through the medium, and its morphology and evolution is monitored with an ultra-fast camera. We varied systematically the thickness of the model h and the injection pressure P , and show that two morphologies of piercement structures develop: vertical and V-shaped conduits. In a phase diagram with h and P as horizontal and vertical axes, respectively, the two morphologies group into two distinct domains separated by a transition line of critical slope P-h. This phase diagram shows that vertical conduits form for high P /low h, whereas V-shaped conduits form for low P /high h. 2D numerical simulations are performed using Sage, a finite volume hydrocode developed at the Los Alamos National Laboratory. We ran simulations and varied systematically the input pressure P and the strength of the country rock T . Our simulations produced three types of piercement structures: vertical, sub-horizontal and V-shaped conduits. In a phase diagram with T and P as horizontal and vertical axes, respectively, the three morphologies group into distinct domains separated by transition lines of critical slopes P-T . Vertical

  18. A critical study of higher-order numerical methods for solving the boundary-layer equations

    NASA Technical Reports Server (NTRS)

    Wornom, S. F.

    1977-01-01

    A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

  19. A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

    NASA Technical Reports Server (NTRS)

    Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.

    1992-01-01

    The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

  20. Development of mathematical models and numerical methods for aerodynamic design on multiprocessor computers

    NASA Astrophysics Data System (ADS)

    Maksimov, F. A.; Churakov, D. A.; Shevelev, Yu. D.

    2011-02-01

    Complex-geometry design and grid generation are addressed. The gasdynamic equations are solved, and the numerical results are compared with experimental data. For aerodynamic problems, a suite of mathematical and information technology tools is proposed for the support and management of geometric models of actual objects. Based on the mathematical modeling methods developed, numerical experiments can be performed for a wide class of geometric forms and the aerodynamic properties of aircraft can be predicted with allowance for the viscosity effects.

  1. A Rationale for Mixed Methods (Integrative) Research Programmes in Education

    ERIC Educational Resources Information Center

    Niaz, Mansoor

    2008-01-01

    Recent research shows that research programmes (quantitative, qualitative and mixed) in education are not displaced (as suggested by Kuhn) but rather lead to integration. The objective of this study is to present a rationale for mixed methods (integrative) research programs based on contemporary philosophy of science (Lakatos, Giere, Cartwright,…

  2. Steady and Unsteady Numerical Solution of Generalized Newtonian Fluids Flow by Runge-Kutta method

    NASA Astrophysics Data System (ADS)

    Keslerová, R.; Kozel, K.; Prokop, V.

    2010-09-01

    In this paper the laminar viscous incompressible flow for generalized Newtonian (Newtonian and non-Newtonian) fluids is considered. The governing system of equations is the system of Navier-Stokes equations and the continuity equation. The steady and unsteady numerical solution for this system is computed by finite volume method combined with an artificial compressibility method. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. The dual time-stepping method is considered for unsteady computation. The high artificial compressibility coefficient is used in the artificial compressibility method applied in the dual time τ. The steady and unsteady numerical results of Newtonian and non-Newtonian (shear thickening and shear thinning) fluids flow in the branching channel are presented.

  3. Numerical simulation of stratified shear flow using a higher order Taylor series expansion method

    SciTech Connect

    Iwashige, Kengo; Ikeda, Takashi

    1995-09-01

    A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.

  4. A study of numerical methods for hyperbolic conservation laws with stiff source terms

    NASA Technical Reports Server (NTRS)

    Leveque, R. J.; Yee, H. C.

    1990-01-01

    In the present study of the behavior of typical numerical methods in the case of a model advection equation having a parameter-dependent source term, two approaches to the incorporation of the source terms are used: MacCormack-type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. The latter are found to perform slightly better. The model scalar equation is used to show that the incorrectness of the propagation speeds of discontinuities observed in the stiff case is due to the introduction of nonequilibrium values through numerical dissipation in the advection step.

  5. Numerical implementation of the method of fictitious domains for elliptic equations

    NASA Astrophysics Data System (ADS)

    Temirbekov, Almas N.

    2016-08-01

    In the paper, we study the elliptical type equation with strongly changing coefficients. We are interested in studying such equation because the given type equations are yielded when we use the fictitious domain method. In this paper we suggest a special method for numerical solution of the elliptic equation with strongly changing coefficients. We have proved the theorem for the assessment of developed iteration process convergence rate. We have developed computational algorithm and numerical calculations have been done to illustrate the effectiveness of the suggested method.

  6. Numerical solution of seismic exploration problems in the Arctic region by applying the grid-characteristic method

    NASA Astrophysics Data System (ADS)

    Petrov, D. I.; Petrov, I. B.; Favorskaya, A. V.; Khokhlov, N. I.

    2016-06-01

    The goal of this paper is the numerical solution of direct problems concerning hydrocarbon seismic exploration on the Arctic shelf. The task is addressed by solving a complete system of linear elasticity equations and a system of acoustic field equations. Both systems are solved by applying the grid-characteristic method, which takes into account all wave processes in a detailed and physically correct manner and produces a solution near the boundaries and interfaces of the integration domain, including the interface between the acoustic and linear elastic media involved. The seismograms and wave patterns obtained by numerically solving these systems are compared. The effect of ice structures on the resulting wave patterns is examined.

  7. A Straightforward Method for Advance Estimation of User Charges for Information in Numeric Databases.

    ERIC Educational Resources Information Center

    Jarvelin, Kalervo

    1986-01-01

    Describes a method for advance estimation of user charges for queries in relational data model-based numeric databases when charges are based on data retrieved. Use of this approach is demonstrated by sample queries to an imaginary marketing database. The principles and methods of this approach and its relevance are discussed. (MBR)

  8. Integrated Research Methods for Applied Urban Hydrogeology of Karst Sites

    NASA Astrophysics Data System (ADS)

    Epting, J.; Romanov, D. K.; Kaufmann, G.; Huggenberger, P.

    2008-12-01

    measures. Theories describing the evolution of karst systems are mainly based on conceptual models. Although these models are based on fundamental and well established physical and chemical principles that allow studying important processes from initial small scale fracture networks to the mature karst, systems for monitoring the evolution of karst phenomena are rare. Integrated process-oriented investigation methods are presented, comprising the combination of multiple data sources (lithostratigraphic information of boreholes, extensive groundwater monitoring, dye tracer tests, geophysics) with high-resolution numerical groundwater modeling and model simulations of karstification below the dam. Subsequently, different scenarios evaluated the future development of the groundwater flow regime, the karstification processes as well as possible remediation measures. The approach presented assists in optimizing investigation methods, including measurement and monitoring technologies with predictive character for similar subsidence problems within karst environments in urban areas.

  9. Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems

    SciTech Connect

    Hykes, J. M.; Ferrer, R. M.

    2013-07-01

    The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is {sup 98}Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)

  10. Sull'Integrazione delle Strutture Numeriche nella Scuola dell'Obbligo (Integrating Numerical Structures in Mandatory School).

    ERIC Educational Resources Information Center

    Bonotto, C.

    1995-01-01

    Attempted to verify knowledge regarding decimal and rational numbers in children ages 10-14. Discusses how pupils can receive and assimilate extensions of the number system from natural numbers to decimals and fractions and later can integrate this extension into a single and coherent numerical structure. (Author/MKR)

  11. Splitting methods for time integration of trajectories in combined electric and magnetic fields.

    PubMed

    Knapp, Christian; Kendl, Alexander; Koskela, Antti; Ostermann, Alexander

    2015-12-01

    The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to commonly used algorithms, such as the Boris scheme. All the methods are represented in a general framework of splitting methods. We use the so-called ϕ functions, which give efficient ways for both analyzing and implementing the algorithms. Numerical experiments show an excellent long term stability for the method considered. PMID:26764856

  12. Vectorization on the star computer of several numerical methods for a fluid flow problem

    NASA Technical Reports Server (NTRS)

    Lambiotte, J. J., Jr.; Howser, L. M.

    1974-01-01

    A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.

  13. Comprehensive Numerical Analysis of Finite Difference Time Domain Methods for Improving Optical Waveguide Sensor Accuracy

    PubMed Central

    Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly

    2016-01-01

    This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.

  14. Numerical Evaluation of the "Dual-Kernel Counter-flow" Matric Convolution Integral that Arises in Discrete/Continuous (D/C) Control Theory

    NASA Technical Reports Server (NTRS)

    Nixon, Douglas D.

    2009-01-01

    Discrete/Continuous (D/C) control theory is a new generalized theory of discrete-time control that expands the concept of conventional (exact) discrete-time control to create a framework for design and implementation of discretetime control systems that include a continuous-time command function generator so that actuator commands need not be constant between control decisions, but can be more generally defined and implemented as functions that vary with time across sample period. Because the plant/control system construct contains two linear subsystems arranged in tandem, a novel dual-kernel counter-flow convolution integral appears in the formulation. As part of the D/C system design and implementation process, numerical evaluation of that integral over the sample period is required. Three fundamentally different evaluation methods and associated algorithms are derived for the constant-coefficient case. Numerical results are matched against three available examples that have closed-form solutions.

  15. An Imbricate Finite Element Method (I-FEM) using full, reduced, and smoothed integration

    NASA Astrophysics Data System (ADS)

    Cazes, Fabien; Meschke, Günther

    2013-11-01

    A method to design finite elements that imbricate with each other while being assembled, denoted as imbricate finite element method, is proposed to improve the smoothness and the accuracy of the approximation based upon low order elements. Although these imbricate elements rely on triangular meshes, the approximation stems from the shape functions of bilinear quadrilateral elements. These elements satisfy the standard requirements of the finite element method: continuity, delta function property, and partition of unity. The convergence of the proposed approximation is investigated by means of two numerical benchmark problems comparing three different schemes for the numerical integration including a cell-based smoothed FEM based on a quadratic shape of the elements edges. The method is compared to related existing methods.

  16. Integrability: mathematical methods for studying solitary waves theory

    NASA Astrophysics Data System (ADS)

    Wazwaz, Abdul-Majid

    2014-03-01

    In recent decades, substantial experimental research efforts have been devoted to linear and nonlinear physical phenomena. In particular, studies of integrable nonlinear equations in solitary waves theory have attracted intensive interest from mathematicians, with the principal goal of fostering the development of new methods, and physicists, who are seeking solutions that represent physical phenomena and to form a bridge between mathematical results and scientific structures. The aim for both groups is to build up our current understanding and facilitate future developments, develop more creative results and create new trends in the rapidly developing field of solitary waves. The notion of the integrability of certain partial differential equations occupies an important role in current and future trends, but a unified rigorous definition of the integrability of differential equations still does not exist. For example, an integrable model in the Painlevé sense may not be integrable in the Lax sense. The Painlevé sense indicates that the solution can be represented as a Laurent series in powers of some function that vanishes on an arbitrary surface with the possibility of truncating the Laurent series at finite powers of this function. The concept of Lax pairs introduces another meaning of the notion of integrability. The Lax pair formulates the integrability of nonlinear equation as the compatibility condition of two linear equations. However, it was shown by many researchers that the necessary integrability conditions are the existence of an infinite series of generalized symmetries or conservation laws for the given equation. The existence of multiple soliton solutions often indicates the integrability of the equation but other tests, such as the Painlevé test or the Lax pair, are necessary to confirm the integrability for any equation. In the context of completely integrable equations, studies are flourishing because these equations are able to describe the

  17. An unconditionally stable method for numerically solving solar sail spacecraft equations of motion

    NASA Astrophysics Data System (ADS)

    Karwas, Alex

    Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach

  18. Application of the method of integral relations to laminar boundary layers in three dimensions

    NASA Technical Reports Server (NTRS)

    Holt, M.; Modarress, D.

    1977-01-01

    The method of integral relations is extended to general three-dimensional compressible laminar boundary layer flows. The transformation employed to transform the basic three-dimensional compressible boundary layer equations into quasi-incompressible form is an extension of the Howarth transformation. The resulting system of differential equations is integrated numerically by the method of integral relations as proposed by Dorodnitsyn. To demonstrate the accuracy of the method, it is applied to calculation of the parabolic flow over a flat plate and the boundary flow over an infinite yawed cylinder, for which solutions are known. It is then applied to the flow over a flat plate disturbed by a cylinder normal to the plate, for which a finite-difference solution is available for comparison. It is finally applied to calculating the crossflow velocity variation for supersonic flow over a swept wedge.

  19. Building a Framework Earthquake Cycle Deformational Model for Subduction Megathrust Zones: Integrating Observations with Numerical Models

    NASA Astrophysics Data System (ADS)

    Furlong, Kevin P.; Govers, Rob; Herman, Matthew

    2016-04-01

    last for decades after a major event (e.g. Alaska 1964) We have integrated the observed patterns of upper-plate displacements (and deformation) with models of subduction zone evolution that allow us to incorporate both the transient behavior associated with post-earthquake viscous re-equilibration and the underlying long term, relatively constant elastic strain accumulation. Modeling the earthquake cycle through the use of a visco-elastic numerical model over numerous earthquake cycles, we have developed a framework model for the megathrust cycle that is constrained by observations made at a variety of plate boundary zones at different stages in their earthquake cycle (see paper by Govers et al., this meeting). Our results indicate that the observed patterns of co- and post- and inter-seismic deformation are largely controlled by interplay between elastic and viscous processes. Observed displacements represent the competition between steady elastic-strain accumulation driven by plate boundary coupling, and post-earthquake viscous behavior in response to the coseismic loading of the system by the rapid elastic rebound. The application of this framework model to observations from subduction zone observatories points up the dangers of simply extrapolating current deformation observations to the overall strain accumulation state of the subduction zoned allows us to develop improved assessments of the slip deficit accumulating within the seismogenic zone, and the near-future earthquake potential of different segments of the subduction plate boundary.

  20. A numerical method to study the dynamics of capillary fluid systems

    NASA Astrophysics Data System (ADS)

    Herrada, M. A.; Montanero, J. M.

    2016-02-01

    We propose a numerical approach to study both the nonlinear dynamics and linear stability of capillary fluid systems. In the nonlinear analysis, the time-dependent fluid region is mapped onto a fixed numerical domain through a coordinate transformation. The hydrodynamic equations are spatially discretized with the Chebyshev spectral collocation technique, while an implicit time advancement is performed using second-order backward finite differences. The resulting algebraic equations are solved with the iterative Newton-Raphson technique. The most novel aspect of the method is the fact that the elements of the Jacobian of the discretized system of equations are symbolic functions calculated before running the simulation. These functions are evaluated numerically in the Newton-Raphson iterations to find the solution at each time step, which reduces considerably the computing time. Besides, this numerical procedure can be easily adapted to solve the eigenvalue problem which determines the linear global modes of the capillary system. Therefore, both the nonlinear dynamics and the linear stability analysis can be conducted with essentially the same algorithm. We validate this numerical approach by studying the dynamics of a liquid bridge close to its minimum volume stability limit. The results are virtually the same as those obtained with other methods. The proposed approach proves to be much more computationally efficient than those other methods. Finally, we show the versatility of the method by calculating the linear global modes of a gravitational jet.