Sample records for method numerical examples

  1. Elimination of numerical diffusion in 1 - phase and 2 - phase flows

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

    Rajamaeki, M.

    1997-07-01

    The new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) is capable of avoiding the excessive errors, numerical diffusion and also numerical dispersion. The hydraulics solver CFDPLIM uses PLIM and solves the time-dependent one-dimensional flow equations in network geometry. An example is given for 1-phase flow in the case when thermal-hydraulics and reactor kinetics are strongly coupled. Another example concerns oscillations in 2-phase flow. Both the example computations are not possible with conventional methods.

  2. Computing the optimal path in stochastic dynamical systems

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

    Bauver, Martha; Forgoston, Eric, E-mail: eric.forgoston@montclair.edu; Billings, Lora

    2016-08-15

    In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensionalmore » system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.« less

  3. Parametric symplectic partitioned Runge-Kutta methods with energy-preserving properties for Hamiltonian systems

    NASA Astrophysics Data System (ADS)

    Wang, Dongling; Xiao, Aiguo; Li, Xueyang

    2013-02-01

    Based on W-transformation, some parametric symplectic partitioned Runge-Kutta (PRK) methods depending on a real parameter α are developed. For α=0, the corresponding methods become the usual PRK methods, including Radau IA-IA¯ and Lobatto IIIA-IIIB methods as examples. For any α≠0, the corresponding methods are symplectic and there exists a value α∗ such that energy is preserved in the numerical solution at each step. The existence of the parameter and the order of the numerical methods are discussed. Some numerical examples are presented to illustrate these results.

  4. Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

    NASA Astrophysics Data System (ADS)

    Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

    2013-10-01

    In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

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

    Xing, Yulong; Shu, Chi-wang; Noelle, Sebastian

    This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium. For such examples, still-water well-balanced methods are not capable of capturing the small perturbations of the moving-water equilibrium and may generate significant spurious oscillations, unless an extremely refined mesh is used. On the other hand, moving-water well-balanced methods perform well in these tests. The numerical examples in this note clearly demonstrate the importance of utilizing moving-water well-balanced methods for solutions near a moving-water equilibrium.

  6. A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations

    NASA Astrophysics Data System (ADS)

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

    2015-07-01

    In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.

  7. Self-Scheduling Parallel Methods for Multiple Serial Codes with Application to WOPWOP

    NASA Technical Reports Server (NTRS)

    Long, Lyle N.; Brentner, Kenneth S.

    2000-01-01

    This paper presents a scheme for efficiently running a large number of serial jobs on parallel computers. Two examples are given of computer programs that run relatively quickly, but often they must be run numerous times to obtain all the results needed. It is very common in science and engineering to have codes that are not massive computing challenges in themselves, but due to the number of instances that must be run, they do become large-scale computing problems. The two examples given here represent common problems in aerospace engineering: aerodynamic panel methods and aeroacoustic integral methods. The first example simply solves many systems of linear equations. This is representative of an aerodynamic panel code where someone would like to solve for numerous angles of attack. The complete code for this first example is included in the appendix so that it can be readily used by others as a template. The second example is an aeroacoustics code (WOPWOP) that solves the Ffowcs Williams Hawkings equation to predict the far-field sound due to rotating blades. In this example, one quite often needs to compute the sound at numerous observer locations, hence parallelization is utilized to automate the noise computation for a large number of observers.

  8. Quasi-generalized variables

    NASA Technical Reports Server (NTRS)

    Baumgarten, J.; Ostermeyer, G. P.

    1986-01-01

    The numerical solution of a system of differential and algebraic equations is difficult, due to the appearance of numerical instabilities. A method is presented here which permits numerical solutions of such a system to be obtained which satisfy the algebraic constraint equations exactly without reducing the order of the differential equations. The method is demonstrated using examples from mechanics.

  9. Aerodynamic design using numerical optimization

    NASA Technical Reports Server (NTRS)

    Murman, E. M.; Chapman, G. T.

    1983-01-01

    The procedure of using numerical optimization methods coupled with computational fluid dynamic (CFD) codes for the development of an aerodynamic design is examined. Several approaches that replace wind tunnel tests, develop pressure distributions and derive designs, or fulfill preset design criteria are presented. The method of Aerodynamic Design by Numerical Optimization (ADNO) is described and illustrated with examples.

  10. Factorization and reduction methods for optimal control of distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Burns, J. A.; Powers, R. K.

    1985-01-01

    A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.

  11. Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations: Theory and Implementation

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.

    2014-01-01

    Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.

  12. Finite element method formulation in polar coordinates for transient heat conduction problems

    NASA Astrophysics Data System (ADS)

    Duda, Piotr

    2016-04-01

    The aim of this paper is the formulation of the finite element method in polar coordinates to solve transient heat conduction problems. It is hard to find in the literature a formulation of the finite element method (FEM) in polar or cylindrical coordinates for the solution of heat transfer problems. This document shows how to apply the most often used boundary conditions. The global equation system is solved by the Crank-Nicolson method. The proposed algorithm is verified in three numerical tests. In the first example, the obtained transient temperature distribution is compared with the temperature obtained from the presented analytical solution. In the second numerical example, the variable boundary condition is assumed. In the last numerical example the component with the shape different than cylindrical is used. All examples show that the introduction of the polar coordinate system gives better results than in the Cartesian coordinate system. The finite element method formulation in polar coordinates is valuable since it provides a higher accuracy of the calculations without compacting the mesh in cylindrical or similar to tubular components. The proposed method can be applied for circular elements such as boiler drums, outlet headers, flux tubes. This algorithm can be useful during the solution of inverse problems, which do not allow for high density grid. This method can calculate the temperature distribution in the bodies of different properties in the circumferential and the radial direction. The presented algorithm can be developed for other coordinate systems. The examples demonstrate a good accuracy and stability of the proposed method.

  13. Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.

    PubMed

    Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo

    2016-05-01

    We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

  14. Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules

    PubMed Central

    Sun, Hui; Zhou, Shenggao; Moore, David K.; Cheng, Li-Tien; Li, Bo

    2015-01-01

    We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems. PMID:27365866

  15. Numerical analysis for distributed-order differential equations

    NASA Astrophysics Data System (ADS)

    Diethelm, Kai; Ford, Neville J.

    2009-03-01

    In this paper we present and analyse a numerical method for the solution of a distributed-order differential equation of the general form where m is a positive real number and where the derivative is taken to be a fractional derivative of Caputo type of order r. We give a convergence theory for our method and conclude with some numerical examples.

  16. Stable Numerical Approach for Fractional Delay Differential Equations

    NASA Astrophysics Data System (ADS)

    Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

    2017-12-01

    In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

  17. Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

    NASA Astrophysics Data System (ADS)

    Agarwal, P.; El-Sayed, A. A.

    2018-06-01

    In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

  18. Numerical solution of distributed order fractional differential equations

    NASA Astrophysics Data System (ADS)

    Katsikadelis, John T.

    2014-02-01

    In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

  19. Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

    PubMed Central

    Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.

    2013-01-01

    We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853

  20. On method of solving third-order ordinary differential equations directly using Bernstein polynomials

    NASA Astrophysics Data System (ADS)

    Khataybeh, S. N.; Hashim, I.

    2018-04-01

    In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

  1. An approach to achieve progress in spacecraft shielding

    NASA Astrophysics Data System (ADS)

    Thoma, K.; Schäfer, F.; Hiermaier, S.; Schneider, E.

    2004-01-01

    Progress in shield design against space debris can be achieved only when a combined approach based on several tools is used. This approach depends on the combined application of advanced numerical methods, specific material models and experimental determination of input parameters for these models. Examples of experimental methods for material characterization are given, covering the range from quasi static to very high strain rates for materials like Nextel and carbon fiber-reinforced materials. Mesh free numerical methods have extraordinary capabilities in the simulation of extreme material behaviour including complete failure with phase changes, combined with shock wave phenomena and the interaction with structural components. In this paper the benefits from combining numerical methods, material modelling and detailed experimental studies for shield design are demonstrated. The following examples are given: (1) Development of a material model for Nextel and Kevlar-Epoxy to enable numerical simulation of hypervelocity impacts on complex heavy protection shields for the International Space Station. (2) The influence of projectile shape on protection performance of Whipple Shields and how experimental problems in accelerating such shapes can be overcome by systematic numerical simulation. (3) The benefits of using metallic foams in "sandwich bumper shields" for spacecraft and how to approach systematic characterization of such materials.

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

    NASA Astrophysics Data System (ADS)

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

    2005-01-01

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

  3. 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.

  4. A practical introduction to tensor networks: Matrix product states and projected entangled pair states

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

    Orús, Román, E-mail: roman.orus@uni-mainz.de

    This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems aremore » also discussed. - Highlights: • A practical introduction to selected aspects of tensor network methods is presented. • We provide analytical examples of MPS and 2d PEPS. • We provide basic aspects on several numerical methods for MPS and 2d PEPS. • We discuss a number of applications of tensor network methods from a broad perspective.« less

  5. A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems

    NASA Astrophysics Data System (ADS)

    Liu, Hailiang; Wang, Zhongming

    2017-01-01

    We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivity of numerical solutions is enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states.

  6. The numerical solution of linear multi-term fractional differential equations: systems of equations

    NASA Astrophysics Data System (ADS)

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  7. Determination of stresses in gas-turbine disks subjected to plastic flow and creep

    NASA Technical Reports Server (NTRS)

    Millenson, M B; Manson, S S

    1948-01-01

    A finite-difference method previously presented for computing elastic stresses in rotating disks is extended to include the computation of the disk stresses when plastic flow and creep are considered. A finite-difference method is employed to eliminate numerical integration and to permit nontechnical personnel to make the calculations with a minimum of engineering supervision. Illustrative examples are included to facilitate explanation of the procedure by carrying out the computations on a typical gas-turbine disk through a complete running cycle. The results of the numerical examples presented indicate that plastic flow markedly alters the elastic-stress distribution.

  8. A Method of DTM Construction Based on Quadrangular Irregular Networks and Related Error Analysis

    PubMed Central

    Kang, Mengjun

    2015-01-01

    A new method of DTM construction based on quadrangular irregular networks (QINs) that considers all the original data points and has a topological matrix is presented. A numerical test and a real-world example are used to comparatively analyse the accuracy of QINs against classical interpolation methods and other DTM representation methods, including SPLINE, KRIGING and triangulated irregular networks (TINs). The numerical test finds that the QIN method is the second-most accurate of the four methods. In the real-world example, DTMs are constructed using QINs and the three classical interpolation methods. The results indicate that the QIN method is the most accurate method tested. The difference in accuracy rank seems to be caused by the locations of the data points sampled. Although the QIN method has drawbacks, it is an alternative method for DTM construction. PMID:25996691

  9. Application of singular value decomposition to structural dynamics systems with constraints

    NASA Technical Reports Server (NTRS)

    Juang, J.-N.; Pinson, L. D.

    1985-01-01

    Singular value decomposition is used to construct a coordinate transformation for a linear dynamic system subject to linear, homogeneous constraint equations. The method is compared with two commonly used methods, namely classical Gaussian elimination and Walton-Steeves approach. Although the classical method requires fewer numerical operations, the singular value decomposition method is more accurate and convenient in eliminating the dependent coordinates. Numerical examples are presented to demonstrate the application of the method.

  10. Effective numerical method of spectral analysis of quantum graphs

    NASA Astrophysics Data System (ADS)

    Barrera-Figueroa, Víctor; Rabinovich, Vladimir S.

    2017-05-01

    We present in the paper an effective numerical method for the determination of the spectra of periodic metric graphs equipped by Schrödinger operators with real-valued periodic electric potentials as Hamiltonians and with Kirchhoff and Neumann conditions at the vertices. Our method is based on the spectral parameter power series method, which leads to a series representation of the dispersion equation, which is suitable for both analytical and numerical calculations. Several important examples demonstrate the effectiveness of our method for some periodic graphs of interest that possess potentials usually found in quantum mechanics.

  11. Numerical Simulation of Selecting Model Scale of Cable in Wind Tunnel Test

    NASA Astrophysics Data System (ADS)

    Huang, Yifeng; Yang, Jixin

    The numerical simulation method based on computational Fluid Dynamics (CFD) provides a possible alternative means of physical wind tunnel test. Firstly, the correctness of the numerical simulation method is validated by one certain example. In order to select the minimum length of the cable as to a certain diameter in the numerical wind tunnel tests, the numerical wind tunnel tests based on CFD are carried out on the cables with several different length-diameter ratios (L/D). The results show that, when the L/D reaches to 18, the drag coefficient is stable essentially.

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

    Zhang, Ch.; Gao, X. W.; Sladek, J.

    This paper reports our recent research works on crack analysis in continuously non-homogeneous and linear elastic functionally graded materials. A meshless boundary element method is developed for this purpose. Numerical examples are presented and discussed to demonstrate the efficiency and the accuracy of the present numerical method, and to show the effects of the material gradation on the crack-opening-displacements and the stress intensity factors.

  13. Towards a wave-extraction method for numerical relativity. III. Analytical examples for the Beetle-Burko radiation scalar

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

    Burko, Lior M.; Department of Physics, University of Alabama in Huntsville, Huntsville, Alabama 35899; Baumgarte, Thomas W.

    2006-01-15

    Beetle and Burko recently introduced a background-independent scalar curvature invariant for general relativity that carries information about the gravitational radiation in generic spacetimes, in cases where such radiation is incontrovertibly defined. In this paper we adopt a formalism that only uses spatial data as they are used in numerical relativity and compute the Beetle-Burko radiation scalar for a number of analytical examples, specifically linearized Einstein-Rosen cylindrical waves, linearized quadrupole waves, the Kerr spacetime, Bowen-York initial data, and the Kasner spacetime. These examples illustrate how the Beetle-Burko radiation scalar can be used to examine the gravitational wave content of numerically generatedmore » spacetimes, and how it may provide a useful diagnostic for initial data sets.« less

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

    NASA Technical Reports Server (NTRS)

    Vezewski, D. J.

    1980-01-01

    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 scalar 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.

  15. 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.

  16. Numerical solution of the time fractional reaction-diffusion equation with a moving boundary

    NASA Astrophysics Data System (ADS)

    Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J.

    2017-06-01

    A fractional reaction-diffusion model with a moving boundary is presented in this paper. An efficient numerical method is constructed to solve this moving boundary problem. Our method makes use of a finite difference approximation for the temporal discretization, and spectral approximation for the spatial discretization. The stability and convergence of the method is studied, and the errors of both the semi-discrete and fully-discrete schemes are derived. Numerical examples, motivated by problems from developmental biology, show a good agreement with the theoretical analysis and illustrate the efficiency of our method.

  17. Tutorial examples for uncertainty quantification methods.

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

    De Bord, Sarah

    2015-08-01

    This report details the work accomplished during my 2015 SULI summer internship at Sandia National Laboratories in Livermore, CA. During this internship, I worked on multiple tasks with the common goal of making uncertainty quantification (UQ) methods more accessible to the general scientific community. As part of my work, I created a comprehensive numerical integration example to incorporate into the user manual of a UQ software package. Further, I developed examples involving heat transfer through a window to incorporate into tutorial lectures that serve as an introduction to UQ methods.

  18. Merits and limitations of optimality criteria method for structural optimization

    NASA Technical Reports Server (NTRS)

    Patnaik, Surya N.; Guptill, James D.; Berke, Laszlo

    1993-01-01

    The merits and limitations of the optimality criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement, and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the Optimality Criteria Design Code that was developed for this purpose at NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. Salient features of the code include multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analyzers, and analytical and numerical sensitivities. The performance of the OC method, on the basis of the examples solved, was found to be satisfactory for problems with few active constraints or with small numbers of design variables. For problems with large numbers of behavior constraints and design variables, the OC method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.

  19. Journal of Aeronautics.

    DTIC Science & Technology

    1982-07-21

    aerodynamic tool for design of elastic aircraft. Several numerical examples are given and some dynamical problems of elastic aircraft are also discussed...Qiangang, Wu Changlin, Jian Zheng Northwestern Polytechnical University Abstract: A numerical metbod,6* ted for predicting the aerodynamic characte- ristics... Numerical value calculation method is one important means of the present research on elastic aircraft pneumatic characteristics. Be- cause this

  20. Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

    NASA Astrophysics Data System (ADS)

    Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye

    2018-04-01

    The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

  1. Weierstrass method for quaternionic polynomial root-finding

    NASA Astrophysics Data System (ADS)

    Falcão, M. Irene; Miranda, Fernando; Severino, Ricardo; Soares, M. Joana

    2018-01-01

    Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas which motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper we propose a Weierstrass-like method for finding simultaneously {\\sl all} the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented.

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

    NASA Technical Reports Server (NTRS)

    Cockburn, Bernardo; Shu, Chi-Wang

    1991-01-01

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

  3. Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

    DOE PAGES

    Liang, Xiao; Khaliq, Abdul Q. M.; Xing, Yulong

    2015-01-23

    In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

  4. Multi-fidelity stochastic collocation method for computation of statistical moments

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

    Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu; Linebarger, Erin M., E-mail: aerinline@sci.utah.edu; Xiu, Dongbin, E-mail: xiu.16@osu.edu

    We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.

  5. Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling

    NASA Astrophysics Data System (ADS)

    Dobronets, B. S.; Popova, O. A.

    2018-05-01

    Data aggregation issues for numerical modeling are reviewed in the present study. The authors discuss data aggregation procedures as preprocessing for subsequent numerical modeling. To calculate the data aggregation, the authors propose using numerical probabilistic analysis (NPA). An important feature of this study is how the authors represent the aggregated data. The study shows that the offered approach to data aggregation can be interpreted as the frequency distribution of a variable. To study its properties, the density function is used. For this purpose, the authors propose using the piecewise polynomial models. A suitable example of such approach is the spline. The authors show that their approach to data aggregation allows reducing the level of data uncertainty and significantly increasing the efficiency of numerical calculations. To demonstrate the degree of the correspondence of the proposed methods to reality, the authors developed a theoretical framework and considered numerical examples devoted to time series aggregation.

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

    NASA Astrophysics Data System (ADS)

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

    2017-12-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2018-01-01

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

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

    NASA Technical Reports Server (NTRS)

    Gossard, Myron L

    1952-01-01

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

  9. Nonclassicality thresholds for multiqubit states: Numerical analysis

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

    Gruca, Jacek; Zukowski, Marek; Laskowski, Wieslaw

    2010-07-15

    States that strongly violate Bell's inequalities are required in many quantum-informational protocols as, for example, in cryptography, secret sharing, and the reduction of communication complexity. We investigate families of such states with a numerical method which allows us to reveal nonclassicality even without direct knowledge of Bell's inequalities for the given problem. An extensive set of numerical results is presented and discussed.

  10. High-Order Methods for Incompressible Fluid Flow

    NASA Astrophysics Data System (ADS)

    Deville, M. O.; Fischer, P. F.; Mund, E. H.

    2002-08-01

    High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular sttention given to enforcement of imcompressibility. Advanced discretizations. implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications.

  11. Numerical modeling method on the movement of water flow and suspended solids in two-dimensional sedimentation tanks in the wastewater treatment plant.

    PubMed

    Zeng, Guang-Ming; Jiang, Yi-Min; Qin, Xiao-Sheng; Huang, Guo-He; Li, Jian-Bing

    2003-01-01

    Taking the distributing calculation of velocity and concentration as an example, the paper established a series of governing equations by the vorticity-stream function method, and dispersed the equations by the finite differencing method. After figuring out the distribution field of velocity, the paper also calculated the concentration distribution in sedimentation tank by using the two-dimensional concentration transport equation. The validity and feasibility of the numerical method was verified through comparing with experimental data. Furthermore, the paper carried out a tentative exploration into the application of numerical simulation of sedimentation tanks.

  12. Purely numerical approach for analyzing flow to a well intercepting a vertical fracture

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

    Narasimhan, T.N.; Palen, W.A.

    1979-03-01

    A numerical method, based on an Integral Finite Difference approach, is presented to investigate wells intercepting fractures in general and vertical fractures in particular. Such features as finite conductivity, wellbore storage, damage, and fracture deformability and its influence as permeability are easily handled. The advantage of the numerical approach is that it is based on fewer assumptions than analytic solutions and hence has greater generality. Illustrative examples are given to validate the method against known solutions. New results are presenteed to demonstrate the applicability of the method to problems not apparently considered in the literature so far.

  13. A sensitivity equation approach to shape optimization in fluid flows

    NASA Technical Reports Server (NTRS)

    Borggaard, Jeff; Burns, John

    1994-01-01

    A sensitivity equation method to shape optimization problems is applied. An algorithm is developed and tested on a problem of designing optimal forebody simulators for a 2D, inviscid supersonic flow. The algorithm uses a BFGS/Trust Region optimization scheme with sensitivities computed by numerically approximating the linear partial differential equations that determine the flow sensitivities. Numerical examples are presented to illustrate the method.

  14. Instruments for Water Quality Monitoring

    ERIC Educational Resources Information Center

    Ballinger, Dwight G.

    1972-01-01

    Presents information regarding available instruments for industries and agencies who must monitor numerous aquatic parameters. Charts denote examples of parameters sampled, testing methods, range and accuracy of test methods, cost analysis, and reliability of instruments. (BL)

  15. Re-Computation of Numerical Results Contained in NACA Report No. 496

    NASA Technical Reports Server (NTRS)

    Perry, Boyd, III

    2015-01-01

    An extensive examination of NACA Report No. 496 (NACA 496), "General Theory of Aerodynamic Instability and the Mechanism of Flutter," by Theodore Theodorsen, is described. The examination included checking equations and solution methods and re-computing interim quantities and all numerical examples in NACA 496. The checks revealed that NACA 496 contains computational shortcuts (time- and effort-saving devices for engineers of the time) and clever artifices (employed in its solution methods), but, unfortunately, also contains numerous tripping points (aspects of NACA 496 that have the potential to cause confusion) and some errors. The re-computations were performed employing the methods and procedures described in NACA 496, but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in fair-to-very-good agreement with the re-computed results. The exceptions included what are speculated to be computational errors in the original in some instances and transcription errors in the original in others. Independent flutter calculations were performed and, in all cases, including those where the original and re-computed results differed significantly, were in excellent agreement with the re-computed results. Appendix A contains NACA 496; Appendix B contains a Matlab(Reistered) program that performs the re-computation of results; Appendix C presents three alternate solution methods, with examples, for the two-degree-of-freedom solution method of NACA 496; Appendix D contains the three-degree-of-freedom solution method (outlined in NACA 496 but never implemented), with examples.

  16. 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.

  17. The dimension split element-free Galerkin method for three-dimensional potential problems

    NASA Astrophysics Data System (ADS)

    Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M.

    2018-06-01

    This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

  18. A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Wu, Zedong; Alkhalifah, Tariq

    2018-07-01

    Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

  19. BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

    NASA Astrophysics Data System (ADS)

    Katsaounis, T. D.

    2005-02-01

    The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using Diffpack and MPI are also presented. Chapter 2 presents the overlapping domain decomposition method for solving PDEs. It is well known that these methods are suitable for parallel processing. The first part of the chapter covers the mathematical formulation of the method as well as algorithmic and implementational issues. The second part presents a serial and a parallel implementational framework within the programming environment of Diffpack. The chapter closes by showing how to solve two application examples with the overlapping domain decomposition method using Diffpack. Chapter 3 is a tutorial about how to incorporate the multigrid solver in Diffpack. The method is illustrated by examples such as a Poisson solver, a general elliptic problem with various types of boundary conditions and a nonlinear Poisson type problem. In chapter 4 the mixed finite element is introduced. Technical issues concerning the practical implementation of the method are also presented. The main difficulties of the efficient implementation of the method, especially in two and three space dimensions on unstructured grids, are presented and addressed in the framework of Diffpack. The implementational process is illustrated by two examples, namely the system formulation of the Poisson problem and the Stokes problem. Chapter 5 is closely related to chapter 4 and addresses the problem of how to solve efficiently the linear systems arising by the application of the mixed finite element method. The proposed method is block preconditioning. Efficient techniques for implementing the method within Diffpack are presented. Optimal block preconditioners are used to solve the system formulation of the Poisson problem, the Stokes problem and the bidomain model for the electrical activity in the heart. The subject of chapter 6 is systems of PDEs. Linear and nonlinear systems are discussed. Fully implicit and operator splitting methods are presented. Special attention is paid to how existing solvers for scalar equations in Diffpack can be used to derive fully implicit solvers for systems. The proposed techniques are illustrated in terms of two applications, namely a system of PDEs modelling pipeflow and a two-phase porous media flow. Stochastic PDEs is the topic of chapter 7. The first part of the chapter is a simple introduction to stochastic PDEs; basic analytical properties are presented for simple models like transport phenomena and viscous drag forces. The second part considers the numerical solution of stochastic PDEs. Two basic techniques are presented, namely Monte Carlo and perturbation methods. The last part explains how to implement and incorporate these solvers into Diffpack. Chapter 8 describes how to operate Diffpack from Python scripts. The main goal here is to provide all the programming and technical details in order to glue the programming environment of Diffpack with visualization packages through Python and in general take advantage of the Python interfaces. Chapter 9 attempts to show how to use numerical experiments to measure the performance of various PDE solvers. The authors gathered a rather impressive list, a total of 14 PDE solvers. Solvers for problems like Poisson, Navier--Stokes, elasticity, two-phase flows and methods such as finite difference, finite element, multigrid, and gradient type methods are presented. The authors provide a series of numerical results combining various solvers with various methods in order to gain insight into their computational performance and efficiency. In Chapter 10 the authors consider a computationally challenging problem, namely the computation of the electrical activity of the human heart. After a brief introduction on the biology of the problem the authors present the mathematical models involved and a numerical method for solving them within the framework of Diffpack. Chapter 11 and 12 are closely related; actually they could have been combined in a single chapter. Chapter 11 introduces several mathematical models used in finance, based on the Black--Scholes equation. Chapter 12 considers several numerical methods like Monte Carlo, lattice methods, finite difference and finite element methods. Implementation of these methods within Diffpack is presented in the last part of the chapter. Chapter 13 presents how the finite element method is used for the modelling and analysis of elastic structures. The authors describe the structural elements of Diffpack which include popular elements such as beams and plates and examples are presented on how to use them to simulate elastic structures. Chapter 14 describes an application problem, namely the extrusion of aluminum. This is a rather\\endcolumn complicated process which involves non-Newtonian flow, heat transfer and elasticity. The authors describe the systems of PDEs modelling the underlying process and use a finite element method to obtain a numerical solution. The implementation of the numerical method in Diffpack is presented along with some applications. The last chapter, chapter 15, focuses on mathematical and numerical models of systems of PDEs governing geological processes in sedimentary basins. The underlying mathematical model is solved using the finite element method within a fully implicit scheme. The authors discuss the implementational issues involved within Diffpack and they present results from several examples. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall the book is well written, the subject of each chapter is well presented and can serve as a reference for graduate students, researchers and engineers who are interested in the numerical solution of partial differential equations modelling various applications.

  20. Stable multi-domain spectral penalty methods for fractional partial differential equations

    NASA Astrophysics Data System (ADS)

    Xu, Qinwu; Hesthaven, Jan S.

    2014-01-01

    We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

  1. A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

    NASA Astrophysics Data System (ADS)

    Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

    2014-02-01

    This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

  2. A collocation-shooting method for solving fractional boundary value problems

    NASA Astrophysics Data System (ADS)

    Al-Mdallal, Qasem M.; Syam, Muhammed I.; Anwar, M. N.

    2010-12-01

    In this paper, we discuss the numerical solution of special class of fractional boundary value problems of order 2. The method of solution is based on a conjugating collocation and spline analysis combined with shooting method. A theoretical analysis about the existence and uniqueness of exact solution for the present class is proven. Two examples involving Bagley-Torvik equation subject to boundary conditions are also presented; numerical results illustrate the accuracy of the present scheme.

  3. Ratio-based vs. model-based methods to correct for urinary creatinine concentrations.

    PubMed

    Jain, Ram B

    2016-08-01

    Creatinine-corrected urinary analyte concentration is usually computed as the ratio of the observed level of analyte concentration divided by the observed level of the urinary creatinine concentration (UCR). This ratio-based method is flawed since it implicitly assumes that hydration is the only factor that affects urinary creatinine concentrations. On the contrary, it has been shown in the literature, that age, gender, race/ethnicity, and other factors also affect UCR. Consequently, an optimal method to correct for UCR should correct for hydration as well as other factors like age, gender, and race/ethnicity that affect UCR. Model-based creatinine correction in which observed UCRs are used as an independent variable in regression models has been proposed. This study was conducted to evaluate the performance of ratio-based and model-based creatinine correction methods when the effects of gender, age, and race/ethnicity are evaluated one factor at a time for selected urinary analytes and metabolites. It was observed that ratio-based method leads to statistically significant pairwise differences, for example, between males and females or between non-Hispanic whites (NHW) and non-Hispanic blacks (NHB), more often than the model-based method. However, depending upon the analyte of interest, the reverse is also possible. The estimated ratios of geometric means (GM), for example, male to female or NHW to NHB, were also compared for the two methods. When estimated UCRs were higher for the group (for example, males) in the numerator of this ratio, these ratios were higher for the model-based method, for example, male to female ratio of GMs. When estimated UCR were lower for the group (for example, NHW) in the numerator of this ratio, these ratios were higher for the ratio-based method, for example, NHW to NHB ratio of GMs. Model-based method is the method of choice if all factors that affect UCR are to be accounted for.

  4. Some observations on boundary conditions for numerical conservation laws

    NASA Technical Reports Server (NTRS)

    Kamowitz, David

    1988-01-01

    Four choices of outflow boundary conditions are considered for numerical conservation laws. All four methods are stable for linear problems, for which examples are presented where either a boundary layer forms or the numerical scheme, together with the boundary condition, is unstable due to the formation of a reflected shock. A simple heuristic argument is presented for determining the suitability of the boundary condition.

  5. Ordinary differential equations.

    PubMed

    Lebl, Jiří

    2013-01-01

    In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.

  6. Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

    NASA Technical Reports Server (NTRS)

    Yu, Sheng-Tao

    1992-01-01

    Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

  7. Adaptive multi-step Full Waveform Inversion based on Waveform Mode Decomposition

    NASA Astrophysics Data System (ADS)

    Hu, Yong; Han, Liguo; Xu, Zhuo; Zhang, Fengjiao; Zeng, Jingwen

    2017-04-01

    Full Waveform Inversion (FWI) can be used to build high resolution velocity models, but there are still many challenges in seismic field data processing. The most difficult problem is about how to recover long-wavelength components of subsurface velocity models when seismic data is lacking of low frequency information and without long-offsets. To solve this problem, we propose to use Waveform Mode Decomposition (WMD) method to reconstruct low frequency information for FWI to obtain a smooth model, so that the initial model dependence of FWI can be reduced. In this paper, we use adjoint-state method to calculate the gradient for Waveform Mode Decomposition Full Waveform Inversion (WMDFWI). Through the illustrative numerical examples, we proved that the low frequency which is reconstructed by WMD method is very reliable. WMDFWI in combination with the adaptive multi-step inversion strategy can obtain more faithful and accurate final inversion results. Numerical examples show that even if the initial velocity model is far from the true model and lacking of low frequency information, we still can obtain good inversion results with WMD method. From numerical examples of anti-noise test, we see that the adaptive multi-step inversion strategy for WMDFWI has strong ability to resist Gaussian noise. WMD method is promising to be able to implement for the land seismic FWI, because it can reconstruct the low frequency information, lower the dominant frequency in the adjoint source, and has a strong ability to resist noise.

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

    NASA Astrophysics Data System (ADS)

    Bao, Gang; Xu, Liwei; Yin, Tao

    2017-11-01

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

  9. APPLICATION OF FLOW SIMULATION FOR EVALUATION OF FILLING-ABILITY OF SELF-COMPACTING CONCRETE

    NASA Astrophysics Data System (ADS)

    Urano, Shinji; Nemoto, Hiroshi; Sakihara, Kohei

    In this paper, MPS method was applied to fluid an alysis of self-compacting concrete. MPS method is one of the particle method, and it is suitable for the simulation of moving boundary or free surface problems and large deformation problems. The constitutive equation of self-compacting concrete is assumed as bingham model. In order to investigate flow Stoppage and flow speed of self-compacting concrete, numerical analysis examples of slump flow and L-flow test were performed. In addition, to evaluate verification of compactability of self-compacting concrete, numerical analys is examples of compaction at the part of CFT diaphragm were performed. As a result, it was found that the MPS method was suitable for the simulation of compaction of self-compacting concrete, and a just appraisal was obtained by setting shear strain rate of flow-limit πc and limitation point of segregation.

  10. Design of two-dimensional channels with prescribed velocity distributions along the channel walls

    NASA Technical Reports Server (NTRS)

    Stanitz, John D

    1953-01-01

    A general method of design is developed for two-dimensional unbranched channels with prescribed velocities as a function of arc length along the channel walls. The method is developed for both compressible and incompressible, irrotational, nonviscous flow and applies to the design of elbows, diffusers, nozzles, and so forth. In part I solutions are obtained by relaxation methods; in part II solutions are obtained by a Green's function. Five numerical examples are given in part I including three elbow designs with the same prescribed velocity as a function of arc length along the channel walls but with incompressible, linearized compressible, and compressible flow. One numerical example is presented in part II for an accelerating elbow with linearized compressible flow, and the time required for the solution by a Green's function in part II was considerably less than the time required for the same solution by relaxation methods in part I.

  11. Scalar conservation and boundedness in simulations of compressible flow

    NASA Astrophysics Data System (ADS)

    Subbareddy, Pramod K.; Kartha, Anand; Candler, Graham V.

    2017-11-01

    With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g. passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variables are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. We present methods for passive and active scalars, and demonstrate their effectiveness with several examples.

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

    Subbareddy, Pramod K.; Kartha, Anand; Candler, Graham V.

    With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g.passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variablesmore » are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. As a result, we present methods for passive and active scalars, and demonstrate their effectiveness with several examples.« less

  13. Pareto Tracer: a predictor-corrector method for multi-objective optimization problems

    NASA Astrophysics Data System (ADS)

    Martín, Adanay; Schütze, Oliver

    2018-03-01

    This article proposes a novel predictor-corrector (PC) method for the numerical treatment of multi-objective optimization problems (MOPs). The algorithm, Pareto Tracer (PT), is capable of performing a continuation along the set of (local) solutions of a given MOP with k objectives, and can cope with equality and box constraints. Additionally, the first steps towards a method that manages general inequality constraints are also introduced. The properties of PT are first discussed theoretically and later numerically on several examples.

  14. Mountain bicycle frame testing as an example of practical implementation of hybrid simulation using RTFEM

    NASA Astrophysics Data System (ADS)

    Mucha, Waldemar; Kuś, Wacław

    2018-01-01

    The paper presents a practical implementation of hybrid simulation using Real Time Finite Element Method (RTFEM). Hybrid simulation is a technique for investigating dynamic material and structural properties of mechanical systems by performing numerical analysis and experiment at the same time. It applies to mechanical systems with elements too difficult or impossible to model numerically. These elements are tested experimentally, while the rest of the system is simulated numerically. Data between the experiment and numerical simulation are exchanged in real time. Authors use Finite Element Method to perform the numerical simulation. The following paper presents the general algorithm for hybrid simulation using RTFEM and possible improvements of the algorithm for computation time reduction developed by the authors. The paper focuses on practical implementation of presented methods, which involves testing of a mountain bicycle frame, where the shock absorber is tested experimentally while the rest of the frame is simulated numerically.

  15. Reconstruction of local perturbations in periodic surfaces

    NASA Astrophysics Data System (ADS)

    Lechleiter, Armin; Zhang, Ruming

    2018-03-01

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

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

    NASA Astrophysics Data System (ADS)

    Lin, Yingzhen; Lin, Jinnan

    2010-12-01

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

  17. Exponentially fitted symplectic Runge-Kutta-Nyström methods derived by partitioned Runge-Kutta methods

    NASA Astrophysics Data System (ADS)

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

    2013-10-01

    In this work we derive symplectic EF/TF RKN methods by symplectic EF/TF PRK methods. Also EF/TF symplectic RKN methods are constructed directly from classical symplectic RKN methods. Several numerical examples will be given in order to decide which is the most favourable implementation.

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

    NASA Astrophysics Data System (ADS)

    Husa, Sascha; Hinder, Ian; Lechner, Christiane

    2006-06-01

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

  19. A semantic framework to protect the privacy of electronic health records with non-numerical attributes.

    PubMed

    Martínez, Sergio; Sánchez, David; Valls, Aida

    2013-04-01

    Structured patient data like Electronic Health Records (EHRs) are a valuable source for clinical research. However, the sensitive nature of such information requires some anonymisation procedure to be applied before releasing the data to third parties. Several studies have shown that the removal of identifying attributes, like the Social Security Number, is not enough to obtain an anonymous data file, since unique combinations of other attributes as for example, rare diagnoses and personalised treatments, may lead to patient's identity disclosure. To tackle this problem, Statistical Disclosure Control (SDC) methods have been proposed to mask sensitive attributes while preserving, up to a certain degree, the utility of anonymised data. Most of these methods focus on continuous-scale numerical data. Considering that part of the clinical data found in EHRs is expressed with non-numerical attributes as for example, diagnoses, symptoms, procedures, etc., their application to EHRs produces far from optimal results. In this paper, we propose a general framework to enable the accurate application of SDC methods to non-numerical clinical data, with a focus on the preservation of semantics. To do so, we exploit structured medical knowledge bases like SNOMED CT to propose semantically-grounded operators to compare, aggregate and sort non-numerical terms. Our framework has been applied to several well-known SDC methods and evaluated using a real clinical dataset with non-numerical attributes. Results show that the exploitation of medical semantics produces anonymised datasets that better preserve the utility of EHRs. Copyright © 2012 Elsevier Inc. All rights reserved.

  20. A numerical study of the 3-periodic wave solutions to KdV-type equations

    NASA Astrophysics Data System (ADS)

    Zhang, Yingnan; Hu, Xingbiao; Sun, Jianqing

    2018-02-01

    In this paper, by using the direct method of calculating periodic wave solutions proposed by Akira Nakamura, we present a numerical process to calculate the 3-periodic wave solutions to several KdV-type equations: the Korteweg-de Vries equation, the Sawada-Koterra equation, the Boussinesq equation, the Ito equation, the Hietarinta equation and the (2 + 1)-dimensional Kadomtsev-Petviashvili equation. Some detailed numerical examples are given to show the existence of the three-periodic wave solutions numerically.

  1. Analytical approximation and numerical simulations for periodic travelling water waves

    NASA Astrophysics Data System (ADS)

    Kalimeris, Konstantinos

    2017-12-01

    We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity. This article is part of the theme issue 'Nonlinear water waves'.

  2. Least-squares finite element method for fluid dynamics

    NASA Technical Reports Server (NTRS)

    Jiang, Bo-Nan; Povinelli, Louis A.

    1989-01-01

    An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.

  3. Method for enhancing amidohydrolase activity of fatty acid amide hydrolase

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

    John, George; Nagarajan, Subbiah; Chapman, Kent

    A method for enhancing amidohydrolase activity of Fatty Acid Amide Hydrolase (FAAH) is disclosed. The method comprising administering a phenoxyacyl-ethanolamide that causes the enhanced activity. The enhanced activity can have numerous effects on biological organisms including, for example, enhancing the growth of certain seedlings.

  4. Fundamental solution of the problem of linear programming and method of its determination

    NASA Technical Reports Server (NTRS)

    Petrunin, S. V.

    1978-01-01

    The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.

  5. Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

    PubMed Central

    Song, Junqiang; Leng, Hongze; Lu, Fengshun

    2014-01-01

    We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. PMID:24511303

  6. Time-splitting combined with exponential wave integrator fourier pseudospectral method for Schrödinger-Boussinesq system

    NASA Astrophysics Data System (ADS)

    Liao, Feng; Zhang, Luming; Wang, Shanshan

    2018-02-01

    In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.

  7. The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

    PubMed

    Khader, M M

    2013-10-01

    In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

  8. Numerical Investigation on Detection of Prestress Losses in a Prestressed Concrete Slab by Modal Analysis

    NASA Astrophysics Data System (ADS)

    Kovalovs, A.; Rucevskis, S.; Akishin, P.; Kolupajevs, J.

    2017-10-01

    The paper presents numerical results of loss of prestress in the reinforced prestressed precast hollow core slabs by modal analysis. Loss of prestress is investigated by the 3D finite element method, using ANSYS software. In the numerical examples, variables initial stresses were introduced into seven-wire stress-relieved strands of the concrete slabs. The effects of span and material properties of concrete on the modal frequencies of the concrete structure under initial stress were studied. Modal parameters computed from the finite element models were compared. Applicability and effectiveness of the proposed method was investigated.

  9. Computing Evans functions numerically via boundary-value problems

    NASA Astrophysics Data System (ADS)

    Barker, Blake; Nguyen, Rose; Sandstede, Björn; Ventura, Nathaniel; Wahl, Colin

    2018-03-01

    The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been developed. In this paper, an alternative scheme for the numerical computation of Evans functions is presented that relies on an appropriate boundary-value problem formulation. Convergence of the algorithm is proved, and several examples, including the computation of eigenvalues for a multi-dimensional problem, are given. The main advantage of the scheme proposed here compared with earlier methods is that the scheme is linear and scalable to large problems.

  10. Fluid Stochastic Petri Nets: Theory, Applications, and Solution

    NASA Technical Reports Server (NTRS)

    Horton, Graham; Kulkarni, Vidyadhar G.; Nicol, David M.; Trivedi, Kishor S.

    1996-01-01

    In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.

  11. Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations

    NASA Astrophysics Data System (ADS)

    Kao, Chiu Yen; Osher, Stanley; Qian, Jianliang

    2004-05-01

    We propose a simple, fast sweeping method based on the Lax-Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton-Jacobi equations in any number of spatial dimensions. By using the Lax-Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss-Seidel type nonlinear iterative method can be utilized. Furthermore, by incorporating a group-wise causality principle into the Gauss-Seidel iteration by following a finite group of characteristics, we have an easy-to-implement, sweeping-type, and fast convergent numerical method. However, unlike other methods based on the Godunov numerical Hamiltonian, some computational boundary conditions are needed in the implementation. We give a simple recipe which enforces a version of discrete min-max principle. Some convergence analysis is done for the one-dimensional eikonal equation. Extensive 2-D and 3-D numerical examples illustrate the efficiency and accuracy of the new approach. To our knowledge, this is the first fast numerical method based on discretizing the Hamilton-Jacobi equation directly without assuming convexity and/or homogeneity of the Hamiltonian.

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

    NASA Astrophysics Data System (ADS)

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

    2018-06-01

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

  13. Some remarks on the numerical solution of parabolic partial differential equations

    NASA Astrophysics Data System (ADS)

    Campagna, R.; Cuomo, S.; Leveque, S.; Toraldo, G.; Giannino, F.; Severino, G.

    2017-11-01

    Numerous environmental/engineering applications relying upon the theory of diffusion phenomena into chaotic environments have recently stimulated the interest toward the numerical solution of parabolic partial differential equations (PDEs). In the present paper, we outline a formulation of the mathematical problem underlying a quite general diffusion mechanism in the natural environments, and we shortly emphasize some remarks concerning the applicability of the (straightforward) finite difference method. An illustration example is also presented.

  14. Dual domain material point method for multiphase flows

    NASA Astrophysics Data System (ADS)

    Zhang, Duan

    2017-11-01

    Although the particle-in-cell method was first invented in the 60's for fluid computations, one of its later versions, the material point method, is mostly used for solid calculations. Recent development of the multi-velocity formulations for multiphase flows and fluid-structure interactions requires the Lagrangian capability of the method be combined with Eulerian calculations for fluids. Because of different numerical representations of the materials, additional numerical schemes are needed to ensure continuity of the materials. New applications of the method to compute fluid motions have revealed numerical difficulties in various versions of the method. To resolve these difficulties, the dual domain material point method is introduced and improved. Unlike other particle based methods, the material point method uses both Lagrangian particles and Eulerian mesh, therefore it avoids direct communication between particles. With this unique property and the Lagrangian capability of the method, it is shown that a multiscale numerical scheme can be efficiently built based on the dual domain material point method. In this talk, the theoretical foundation of the method will be introduced. Numerical examples will be shown. Work sponsored by the next generation code project of LANL.

  15. 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.

  16. Using the Multilayer Free-Surface Flow Model to Solve Wave Problems

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

    Prokof’ev, V. A., E-mail: ProkofyevVA@vniig.ru

    2017-01-15

    A method is presented for changing over from a single-layer shallow-water model to a multilayer model with hydrostatic pressure profile and, then, to a multilayer model with nonhydrostatic pressure profile. The method does not require complex procedures for solving the discrete Poisson’s equation and features high computation efficiency. The results of validating the algorithm against experimental data critical for the numerical dissipation of the numerical scheme are presented. Examples are considered.

  17. Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

    NASA Astrophysics Data System (ADS)

    Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

    2017-11-01

    When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

  18. ULTRA-SHARP nonoscillatory convection schemes for high-speed steady multidimensional flow

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.; Mokhtari, Simin

    1990-01-01

    For convection-dominated flows, classical second-order methods are notoriously oscillatory and often unstable. For this reason, many computational fluid dynamicists have adopted various forms of (inherently stable) first-order upwinding over the past few decades. Although it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high convection conditions, these methods continue to enjoy widespread popularity for numerical heat transfer calculations, apparently due to a perceived lack of viable high accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as is shown, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high order accuracy, while requiring only a simple tridiagonal ADI line-solver, as used in the majority of general purpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high resolution nonoscillatory multidimensional steady state high speed convective modelling.

  19. Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites

    NASA Astrophysics Data System (ADS)

    Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.

    2018-04-01

    Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.

  20. The Harmonic Oscillator with a Gaussian Perturbation: Evaluation of the Integrals and Example Applications

    ERIC Educational Resources Information Center

    Earl, Boyd L.

    2008-01-01

    A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…

  1. On numerical solution of the Schrödinger equation: the shooting method revisited

    NASA Astrophysics Data System (ADS)

    Indjin, D.; Todorović, G.; Milanović, V.; Ikonić, Z.

    1995-09-01

    An alternative formulation of the "shooting" method for a numerical solution of the Schrödinger equation is described for cases of general asymmetric one-dimensional potential (planar geometry), and spherically symmetric potential. The method relies on matching the asymptotic wavefunctions and the potential core region wavefunctions, in course of finding bound states energies. It is demonstrated in the examples of Morse and Kratzer potentials, where a high accuracy of the calculated eigenvalues is found, together with a considerable saving of the computation time.

  2. 40 CFR 1042.230 - Engine families.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... example, raw-water vs. separate-circuit cooling). (3) Method of air aspiration. (4) Method of exhaust... (i.e., mechanical or electronic). (9) Application (commercial or recreational). (10) Numerical level... injection pressure. (17) The type of fuel injection system controls (i.e., mechanical or electronic). (18...

  3. A unified convergence theory of a numerical method, and applications to the replenishment policies.

    PubMed

    Mi, Xiang-jiang; Wang, Xing-hua

    2004-01-01

    In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But this approach requires calculation of the second derivative of the function. Avoiding this complex computation we use another iterative method presented by the second author. One of the goals of this paper is to present a unified convergence theory of this method. Then we give a numerical example to show the application of our theory.

  4. Monotonicity based imaging method for time-domain eddy current problems

    NASA Astrophysics Data System (ADS)

    Su, Z.; Ventre, S.; Udpa, L.; Tamburrino, A.

    2017-12-01

    Eddy current imaging is an example of inverse problem in nondestructive evaluation for detecting anomalies in conducting materials. This paper introduces the concept of time constants and associated natural modes in eddy current imaging. The monotonicity of time constants is then described and applied to develop a non-iterative imaging method. The proposed imaging method has a low computational cost which makes it suitable for real-time operations. Full 3D numerical examples prove the effectiveness of the method in realistic scenarios. This paper is dedicated to Professor Guglielmo Rubinacci on the occasion of his 65th Birthday.

  5. Scalar conservation and boundedness in simulations of compressible flow

    DOE PAGES

    Subbareddy, Pramod K.; Kartha, Anand; Candler, Graham V.

    2017-08-07

    With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g.passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variablesmore » are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. As a result, we present methods for passive and active scalars, and demonstrate their effectiveness with several examples.« less

  6. Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives

    NASA Astrophysics Data System (ADS)

    Antunes, Pedro R. S.; Ferreira, Rui A. C.

    2017-07-01

    In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented -RBF method. Several examples illustrate the good performance of the numerical method.

  7. S-matrix method for the numerical determination of bound states.

    NASA Technical Reports Server (NTRS)

    Bhatia, A. K.; Madan, R. N.

    1973-01-01

    A rapid numerical technique for the determination of bound states of a partial-wave-projected Schroedinger equation is presented. First, one needs to integrate the equation only outwards as in the scattering case, and second, the number of trials necessary to determine the eigenenergy and the corresponding eigenfunction is considerably less than in the usual method. As a nontrivial example of the technique, bound states are calculated in the exchange approximation for the e-/He+ system and l equals 1 partial wave.

  8. The use of rational functions in numerical quadrature

    NASA Astrophysics Data System (ADS)

    Gautschi, Walter

    2001-08-01

    Quadrature problems involving functions that have poles outside the interval of integration can profitably be solved by methods that are exact not only for polynomials of appropriate degree, but also for rational functions having the same (or the most important) poles as the function to be integrated. Constructive and computational tools for accomplishing this are described and illustrated in a number of quadrature contexts. The superiority of such rational/polynomial methods is shown by an analysis of the remainder term and documented by numerical examples.

  9. Recursive least squares method of regression coefficients estimation as a special case of Kalman filter

    NASA Astrophysics Data System (ADS)

    Borodachev, S. M.

    2016-06-01

    The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.

  10. Methods of making monolayers

    DOEpatents

    Alford, Kentin L [Pasco, WA; Simmons, Kevin L [Kennewick, WA; Samuels, William D [Richland, WA; Zemanian, Thomas S [Richland, WA; Liu, Jun [Albuquerque, NM; Shin, Yongsoon [Richland, WA; Fryxell, Glen E [Kennewick, WA

    2009-12-08

    The invention pertains to methods of forming monolayers on various surfaces. The surfaces can be selected from a wide array of materials, including, for example, aluminum dioxide, silicon dioxide, carbon and SiC. The substrates can be planar or porous. The monolayer is formed under enhanced pressure conditions. The monolayer contains functionalized molecules, and accordingly functionalizes a surface of the substrate. The properties of the functionalized substrate can enhance the substrate's applicability for numerous purposes including, for example, utilization in extracting contaminants, or incorporation into a polymeric matrix.

  11. Methods of making monolayers

    DOEpatents

    Alford, Kentin L [Pasco, WA; Simmons, Kevin L [Kennewick, WA; Samuels, William D [Richland, WA; Zemanian, Thomas S [Richland, WA; Liu, Jun [Albuquerque, NM; Shin, Yongsoon [Richland, WA; Fryxell, Glen E [Kennewick, WA

    2009-09-15

    The invention pertains to methods of forming monolayers on various surfaces. The surfaces can be selected from a wide array of materials, including, for example, aluminum dioxide, silicon dioxide, carbon and SiC. The substrates can be planar or porous. The monolayer is formed under enhanced pressure conditions. The monolayer contains functionalized molecules, and accordingly functionalizes a surface of the substrate. The properties of the functionalized substrate can enhance the substrate's applicability for numerous purposes including, for example, utilization in extracting contaminants, or incorporation into a polymeric matrix.

  12. A new Jacobi spectral collocation method for solving 1+1 fractional Schrödinger equations and fractional coupled Schrödinger systems

    NASA Astrophysics Data System (ADS)

    Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Van Gorder, Robert A.

    2014-12-01

    The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrödinger equation (T-FSE) and the space-fractional Schrödinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrödinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.

  13. The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method

    NASA Astrophysics Data System (ADS)

    Niki, Hiroshi; Harada, Kyouji; Morimoto, Munenori; Sakakihara, Michio

    2004-03-01

    Several preconditioned iterative methods reported in the literature have been used for improving the convergence rate of the Gauss-Seidel method. In this article, on the basis of nonnegative matrix, comparisons between some splittings for such preconditioned matrices are derived. Simple numerical examples are also given.

  14. Dual-mode nested search method for categorical uncertain multi-objective optimization

    NASA Astrophysics Data System (ADS)

    Tang, Long; Wang, Hu

    2016-10-01

    Categorical multi-objective optimization is an important issue involved in many matching design problems. Non-numerical variables and their uncertainty are the major challenges of such optimizations. Therefore, this article proposes a dual-mode nested search (DMNS) method. In the outer layer, kriging metamodels are established using standard regular simplex mapping (SRSM) from categorical candidates to numerical values. Assisted by the metamodels, a k-cluster-based intelligent sampling strategy is developed to search Pareto frontier points. The inner layer uses an interval number method to model the uncertainty of categorical candidates. To improve the efficiency, a multi-feature convergent optimization via most-promising-area stochastic search (MFCOMPASS) is proposed to determine the bounds of objectives. Finally, typical numerical examples are employed to demonstrate the effectiveness of the proposed DMNS method.

  15. Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

    NASA Astrophysics Data System (ADS)

    El-Kalla, I. L.; Al-Bugami, A. M.

    2010-11-01

    In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

  16. A moving mesh finite difference method for equilibrium radiation diffusion equations

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

    Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

    2015-10-01

    An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

  17. A progressive gradient moment nulling design technique.

    PubMed

    Pipe, J G; Chenevert, T L

    1991-05-01

    A method is presented for designing motion-compensated gradients in a progressive manner. The method is easily applicable to many types of waveforms, and can compensate for any order of motion. It can be implemented graphically or numerically. Underlying theory and examples of its application are provided.

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

    Sudiarta, I. Wayan; Angraini, Lily Maysari, E-mail: lilyangraini@unram.ac.id

    We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.

  19. A technique for increasing the accuracy of the numerical inversion of the Laplace transform with applications

    NASA Technical Reports Server (NTRS)

    Berger, B. S.; Duangudom, S.

    1973-01-01

    A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.

  20. 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.

  1. Two-Level Hierarchical FEM Method for Modeling Passive Microwave Devices

    NASA Astrophysics Data System (ADS)

    Polstyanko, Sergey V.; Lee, Jin-Fa

    1998-03-01

    In recent years multigrid methods have been proven to be very efficient for solving large systems of linear equations resulting from the discretization of positive definite differential equations by either the finite difference method or theh-version of the finite element method. In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which arise from thep-version of the finite element analysis applied to indefinite problems. A two-levelV-cycle algorithm has been implemented and studied with a Gauss-Seidel iterative scheme used as a smoother. The convergence of the method has been investigated, and numerical results for a number of numerical examples are presented.

  2. Fast algorithms for Quadrature by Expansion I: Globally valid expansions

    NASA Astrophysics Data System (ADS)

    Rachh, Manas; Klöckner, Andreas; O'Neil, Michael

    2017-09-01

    The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast algorithms for solving the resulting dense linear systems. Classically, these tools were developed separately. In this work, we present a unified numerical scheme based on coupling Quadrature by Expansion, a recent quadrature method, to a customized Fast Multipole Method (FMM) for the Helmholtz equation in two dimensions. The method allows the evaluation of layer potentials in linear-time complexity, anywhere in space, with a uniform, user-chosen level of accuracy as a black-box computational method. Providing this capability requires geometric and algorithmic considerations beyond the needs of standard FMMs as well as careful consideration of the accuracy of multipole translations. We illustrate the speed and accuracy of our method with various numerical examples.

  3. A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems

    NASA Astrophysics Data System (ADS)

    Dölz, Jürgen; Harbrecht, Helmut; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix

    2018-03-01

    We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract the problems arising due to the dense matrices produced by boundary element methods. By solving Laplace and Helmholtz problems via a single layer approach we show, through a series of numerical examples suitable for easy comparison with other numerical schemes, that one can indeed achieve extremely high rates of convergence of the pointwise potential through the utilisation of higher order B-spline-based ansatz functions.

  4. On a new iterative method for solving linear systems and comparison results

    NASA Astrophysics Data System (ADS)

    Jing, Yan-Fei; Huang, Ting-Zhu

    2008-10-01

    In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a different approach is established, which is both theoretically and numerically proven to be better than (at least the same as) Ujevic's. As the presented numerical examples show, in most cases, the convergence rate is more than one and a half that of Ujevic.

  5. Self-adjusting grid methods for one-dimensional hyperbolic conservation laws

    NASA Technical Reports Server (NTRS)

    Harten, A.; Hyman, J. M.

    1983-01-01

    The automatic adjustment of a grid which follows the dynamics of the numerical solution of hyperbolic conservation laws is given. The grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals. The resulting algorithm is a simple extension of many currently popular Godunov-type methods. Computer codes using one of these methods can be easily modified to add the moving mesh as an option. Numerical examples are given that illustrate the improved accuracy of Godunov's and Roe's methods on a self-adjusting mesh. Previously announced in STAR as N83-15008

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

    NASA Astrophysics Data System (ADS)

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

    2008-12-01

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

  7. Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter

    NASA Astrophysics Data System (ADS)

    Arnold, Andrea; Calvetti, Daniela; Somersalo, Erkki

    2014-10-01

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

  8. Dual Formulations of Mixed Finite Element Methods with Applications

    PubMed Central

    Gillette, Andrew; Bajaj, Chandrajit

    2011-01-01

    Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail. PMID:21984841

  9. 40 CFR 1054.230 - How do I select emission families?

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ...). (3) Valve configuration (for example, side-valve vs. overhead valve). (4) Method of air aspiration... configuration) and approximate total displacement. (7) Engine class, as defined in § 1054.801. (8) Method of control for engine operation, other than governing (mechanical or electronic). (9) The numerical level of...

  10. Data Acquisition Using Xbox Kinect Sensor

    ERIC Educational Resources Information Center

    Ballester, Jorge; Pheatt, Charles B.

    2012-01-01

    The study of motion is central in physics education and has taken many forms as technology has provided numerous methods to acquire data. For example, the analysis of still or moving images is particularly effective in discussions of two-dimensional motion. Introductory laboratory measurement methods have progressed through water clocks, spark…

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

    NASA Astrophysics Data System (ADS)

    Mamehrashi, K.; Yousefi, S. A.

    2017-02-01

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

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

    NASA Astrophysics Data System (ADS)

    Witte, J. H.; Reisinger, C.

    2010-09-01

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

  13. Spectral multigrid methods for elliptic equations 2

    NASA Technical Reports Server (NTRS)

    Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.

    1983-01-01

    A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

  14. Method for enhancing amidohydrolase activity of fatty acid amide hydrolase

    DOEpatents

    John, George; Nagarajan, Subbiah; Chapman, Kent; Faure, Lionel; Koulen, Peter

    2016-10-25

    A method for enhancing amidohydrolase activity of Fatty Acid Amide Hydrolase (FAAH) is disclosed. The method comprising administering a phenoxyacylethanolamide that causes the enhanced activity. The enhanced activity can have numerous effects on biological organisms including, for example, enhancing the growth of certain seedlings. The subject matter disclosed herein relates to enhancers of amidohydrolase activity.

  15. Spreadsheets in Science Teaching.

    ERIC Educational Resources Information Center

    Elliot, Chris

    1988-01-01

    Described is the use of a spreadsheet to model dynamic phenomena using numerical iterative methods. Uses the discharge of a capacitor, simple and damped harmonic motion, and the flow of heat along a bar as examples. (Author/CW)

  16. Numerical Characterization of Piezoceramics Using Resonance Curves

    PubMed Central

    Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar

    2016-01-01

    Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods. PMID:28787875

  17. Numerical Characterization of Piezoceramics Using Resonance Curves.

    PubMed

    Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar

    2016-01-27

    Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods.

  18. Time-dependent spectral renormalization method

    NASA Astrophysics Data System (ADS)

    Cole, Justin T.; Musslimani, Ziad H.

    2017-11-01

    The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

  19. Morphing continuum theory for turbulence: Theory, computation, and visualization.

    PubMed

    Chen, James

    2017-10-01

    A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance laws are deduced and presented from the Coleman-Noll procedure and Onsager's reciprocal relations. The governing equations are then arranged in conservation form and solved through the finite volume method with a second-order Lax-Friedrichs scheme for shock preservation. A numerical example of transonic flow over a three-dimensional bump is presented using MCT and the finite volume method. The comparison shows that MCT-based direct numerical simulation (DNS) provides a better prediction than Navier-Stokes (NS)-based DNS with less than 10% of the mesh number when compared with experiments. A MCT-based and frame-indifferent Q criterion is also derived to show the coherent eddy structure of the downstream turbulence in the numerical example. It should be emphasized that unlike the NS-based Q criterion, the MCT-based Q criterion is objective without the limitation of Galilean invariance.

  20. Numerical integration of discontinuous functions: moment fitting and smart octree

    NASA Astrophysics Data System (ADS)

    Hubrich, Simeon; Di Stolfo, Paolo; Kudela, László; Kollmannsberger, Stefan; Rank, Ernst; Schröder, Andreas; Düster, Alexander

    2017-11-01

    A fast and simple grid generation can be achieved by non-standard discretization methods where the mesh does not conform to the boundary or the internal interfaces of the problem. However, this simplification leads to discontinuous integrands for intersected elements and, therefore, standard quadrature rules do not perform well anymore. Consequently, special methods are required for the numerical integration. To this end, we present two approaches to obtain quadrature rules for arbitrary domains. The first approach is based on an extension of the moment fitting method combined with an optimization strategy for the position and weights of the quadrature points. In the second approach, we apply the smart octree, which generates curved sub-cells for the integration mesh. To demonstrate the performance of the proposed methods, we consider several numerical examples, showing that the methods lead to efficient quadrature rules, resulting in less integration points and in high accuracy.

  1. High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang

    2000-01-01

    This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

  2. Adaptive error covariances estimation methods for ensemble Kalman filters

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

    Zhen, Yicun, E-mail: zhen@math.psu.edu; Harlim, John, E-mail: jharlim@psu.edu

    2015-08-01

    This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of Belanger's recursive method, to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when the number of observations becomes large. When we use only product of innovation processes up to one-lag, the computational cost is indeed comparable to a recently proposed method by Berry–Sauer's. However, our method is more flexible since it allows for usingmore » information from product of innovation processes of more than one-lag. Extensive numerical comparisons between the proposed method and both the original Belanger's and Berry–Sauer's schemes are shown in various examples, ranging from low-dimensional linear and nonlinear systems of SDEs and 40-dimensional stochastically forced Lorenz-96 model. Our numerical results suggest that the proposed scheme is as accurate as the original Belanger's scheme on low-dimensional problems and has a wider range of more accurate estimates compared to Berry–Sauer's method on L-96 example.« less

  3. A NURBS-enhanced finite volume solver for steady Euler equations

    NASA Astrophysics Data System (ADS)

    Meng, Xucheng; Hu, Guanghui

    2018-04-01

    In Hu and Yi (2016) [20], a non-oscillatory k-exact reconstruction method was proposed towards the high-order finite volume methods for steady Euler equations, which successfully demonstrated the high-order behavior in the simulations. However, the degeneracy of the numerical accuracy of the approximate solutions to problems with curved boundary can be observed obviously. In this paper, the issue is resolved by introducing the Non-Uniform Rational B-splines (NURBS) method, i.e., with given discrete description of the computational domain, an approximate NURBS curve is reconstructed to provide quality quadrature information along the curved boundary. The advantages of using NURBS include i). both the numerical accuracy of the approximate solutions and convergence rate of the numerical methods are improved simultaneously, and ii). the NURBS curve generation is independent of other modules of the numerical framework, which makes its application very flexible. It is also shown in the paper that by introducing more elements along the normal direction for the reconstruction patch of the boundary element, significant improvement in the convergence to steady state can be achieved. The numerical examples confirm the above features very well.

  4. Lagrangian analysis of multiscale particulate flows with the particle finite element method

    NASA Astrophysics Data System (ADS)

    Oñate, Eugenio; Celigueta, Miguel Angel; Latorre, Salvador; Casas, Guillermo; Rossi, Riccardo; Rojek, Jerzy

    2014-05-01

    We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.

  5. New distributed activation energy model: numerical solution and application to pyrolysis kinetics of some types of biomass.

    PubMed

    Cai, Junmeng; Liu, Ronghou

    2008-05-01

    In the present paper, a new distributed activation energy model has been developed, considering the reaction order and the dependence of frequency factor on temperature. The proposed DAEM cannot be solved directly in a closed from, thus a method was used to obtain the numerical solution of the new DAEM equation. Two numerical examples to illustrate the proposed method were presented. The traditional DAEM and new DAEM have been used to simulate the pyrolytic process of some types of biomass. The new DAEM fitted the experimental data much better than the traditional DAEM as the dependence of the frequency factor on temperature was taken into account.

  6. Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

    NASA Technical Reports Server (NTRS)

    Sharma, A.; Cogley, A. C.

    1982-01-01

    The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

  7. Multiscale global identification of porous structures

    NASA Astrophysics Data System (ADS)

    Hatłas, Marcin; Beluch, Witold

    2018-01-01

    The paper is devoted to the evolutionary identification of the material constants of porous structures based on measurements conducted on a macro scale. Numerical homogenization with the RVE concept is used to determine the equivalent properties of a macroscopically homogeneous material. Finite element method software is applied to solve the boundary-value problem in both scales. Global optimization methods in form of evolutionary algorithm are employed to solve the identification task. Modal analysis is performed to collect the data necessary for the identification. A numerical example presenting the effectiveness of proposed attitude is attached.

  8. Legendre-tau approximations for functional differential equations

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1986-01-01

    The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

  9. Given a one-step numerical scheme, on which ordinary differential equations is it exact?

    NASA Astrophysics Data System (ADS)

    Villatoro, Francisco R.

    2009-01-01

    A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

  10. Legendre-Tau approximations for functional differential equations

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1983-01-01

    The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

  11. An Operator-Integration-Factor Splitting (OIFS) method for Incompressible Flows in Moving Domains

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

    Patel, Saumil S.; Fischer, Paul F.; Min, Misun

    In this paper, we present a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an effcient and stable numerical scheme. Using the spectral element method and an arbitrary Lagrangian-Eulerian formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of the scheme.

  12. Potential function of element measurement for form-finding of wide sense tensegrity

    NASA Astrophysics Data System (ADS)

    Soe, C. K.; Obiya, H.; Koga, D.; Nizam, Z. M.; Ijima, K.

    2018-04-01

    Tensegrity is a unique morphological structure in which disconnected compression members and connected tension members make the whole structure in self-equilibrium. Many researches have been done on tensegrity structure because of its mysteriousness in form-finding analysis. This study is proposed to investigate the trends and to group into some patterns of the shape that a tensegrity structure can have under the same connectivity and support condition. In this study, tangent stiffness method adopts two different functions, namely power function and logarithm function to element measurement. Numerical examples are based on a simplex initial shape with statically determinate support condition to examine the pure effectiveness of two proposed methods. The tangent stiffness method that can evaluate strict rigid body displacement of elements has a superiority to define various measure potentials and to allow the use of virtual element stiffness freely. From the results of numerical examples, the finding of the dominant trends and patterns of the equilibrium solutions is achieved although it has many related solutions under the same circumstances.

  13. An enriched finite element method to fractional advection-diffusion equation

    NASA Astrophysics Data System (ADS)

    Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

    2017-08-01

    In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

  14. Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

    NASA Astrophysics Data System (ADS)

    Gómez-Aguilar, J. F.

    2018-03-01

    In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

  15. The solitary wave solution of coupled Klein-Gordon-Zakharov equations via two different numerical methods

    NASA Astrophysics Data System (ADS)

    Dehghan, Mehdi; Nikpour, Ahmad

    2013-09-01

    In this research, we propose two different methods to solve the coupled Klein-Gordon-Zakharov (KGZ) equations: the Differential Quadrature (DQ) and Globally Radial Basis Functions (GRBFs) methods. In the DQ method, the derivative value of a function with respect to a point is directly approximated by a linear combination of all functional values in the global domain. The principal work in this method is the determination of weight coefficients. We use two ways for obtaining these coefficients: cosine expansion (CDQ) and radial basis functions (RBFs-DQ), the former is a mesh-based method and the latter categorizes in the set of meshless methods. Unlike the DQ method, the GRBF method directly substitutes the expression of the function approximation by RBFs into the partial differential equation. The main problem in the GRBFs method is ill-conditioning of the interpolation matrix. Avoiding this problem, we study the bases introduced in Pazouki and Schaback (2011) [44]. Some examples are presented to compare the accuracy and easy implementation of the proposed methods. In numerical examples, we concentrate on Inverse Multiquadric (IMQ) and second-order Thin Plate Spline (TPS) radial basis functions. The variable shape parameter (exponentially and random) strategies are applied in the IMQ function and the results are compared with the constant shape parameter.

  16. An Efficient Numerical Method for Computing Synthetic Seismograms for a Layered Half-space with Sources and Receivers at Close or Same Depths

    NASA Astrophysics Data System (ADS)

    Zhang, H.-m.; Chen, X.-f.; Chang, S.

    - It is difficult to compute synthetic seismograms for a layered half-space with sources and receivers at close to or the same depths using the generalized R/T coefficient method (Kennett, 1983; Luco and Apsel, 1983; Yao and Harkrider, 1983; Chen, 1993), because the wavenumber integration converges very slowly. A semi-analytic method for accelerating the convergence, in which part of the integration is implemented analytically, was adopted by some authors (Apsel and Luco, 1983; Hisada, 1994, 1995). In this study, based on the principle of the Repeated Averaging Method (Dahlquist and Björck, 1974; Chang, 1988), we propose an alternative, efficient, numerical method, the peak-trough averaging method (PTAM), to overcome the difficulty mentioned above. Compared with the semi-analytic method, PTAM is not only much simpler mathematically and easier to implement in practice, but also more efficient. Using numerical examples, we illustrate the validity, accuracy and efficiency of the new method.

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

    PubMed

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

    2016-01-01

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

  18. A simple finite element method for linear hyperbolic problems

    DOE PAGES

    Mu, Lin; Ye, Xiu

    2017-09-14

    Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

  19. A simple finite element method for linear hyperbolic problems

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

    Mu, Lin; Ye, Xiu

    Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

  20. Approximation and Numerical Analysis of Nonlinear Equations of Evolution.

    DTIC Science & Technology

    1980-01-31

    dominant convective terms, or Stefan type problems such as the flow of fluids through porous media or the melting and freezing of ice. Such problems...means of formulating time-dependent Stefan problems was initiated. Classes of problems considered here include the one-phase and two-phase Stefan ...some new numerical methods were 2 developed for two dimensional, two-phase Stefan problems with time dependent boundary conditions. A variety of example

  1. Solving PDEs with Intrepid

    DOE PAGES

    Bochev, P.; Edwards, H. C.; Kirby, R. C.; ...

    2012-01-01

    Intrepid is a Trilinos package for advanced discretizations of Partial Differential Equations (PDEs). The package provides a comprehensive set of tools for local, cell-based construction of a wide range of numerical methods for PDEs. This paper describes the mathematical ideas and software design principles incorporated in the package. We also provide representative examples showcasing the use of Intrepid both in the context of numerical PDEs and the more general context of data analysis.

  2. Solving rational matrix equations in the state space with applications to computer-aided control-system design

    NASA Technical Reports Server (NTRS)

    Packard, A. K.; Sastry, S. S.

    1986-01-01

    A method of solving a class of linear matrix equations over various rings is proposed, using results from linear geometric control theory. An algorithm, successfully implemented, is presented, along with non-trivial numerical examples. Applications of the method to the algebraic control system design methodology are discussed.

  3. A loop-counting method for covariate-corrected low-rank biclustering of gene-expression and genome-wide association study data.

    PubMed

    Rangan, Aaditya V; McGrouther, Caroline C; Kelsoe, John; Schork, Nicholas; Stahl, Eli; Zhu, Qian; Krishnan, Arjun; Yao, Vicky; Troyanskaya, Olga; Bilaloglu, Seda; Raghavan, Preeti; Bergen, Sarah; Jureus, Anders; Landen, Mikael

    2018-05-14

    A common goal in data-analysis is to sift through a large data-matrix and detect any significant submatrices (i.e., biclusters) that have a low numerical rank. We present a simple algorithm for tackling this biclustering problem. Our algorithm accumulates information about 2-by-2 submatrices (i.e., 'loops') within the data-matrix, and focuses on rows and columns of the data-matrix that participate in an abundance of low-rank loops. We demonstrate, through analysis and numerical-experiments, that this loop-counting method performs well in a variety of scenarios, outperforming simple spectral methods in many situations of interest. Another important feature of our method is that it can easily be modified to account for aspects of experimental design which commonly arise in practice. For example, our algorithm can be modified to correct for controls, categorical- and continuous-covariates, as well as sparsity within the data. We demonstrate these practical features with two examples; the first drawn from gene-expression analysis and the second drawn from a much larger genome-wide-association-study (GWAS).

  4. ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

    NASA Astrophysics Data System (ADS)

    Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

    2018-04-01

    In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

  5. Efficient Jacobi-Gauss collocation method for solving initial value problems of Bratu type

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.

    2013-09-01

    In this paper, we propose the shifted Jacobi-Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials J {/n (α,β)}( x) with α, β ∈ (-1, ∞), x ∈ [0, 1] and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.

  6. Gimbal-Angle Vectors of the Nonredundant CMG Cluster

    NASA Astrophysics Data System (ADS)

    Lee, Donghun; Bang, Hyochoong

    2018-05-01

    This paper deals with the method using the preferred gimbal angles of a control moment gyro (CMG) cluster for controlling spacecraft attitude. To apply the method to the nonredundant CMG cluster, analytical gimbal-angle solutions for the zero angular momentum state are derived, and the gimbal-angle vectors for the nonzero angular momentum states are studied by a numerical method. It will be shown that the number of the gimbal-angle vectors is determined from the given skew angle and the angular momentum state of the CMG cluster. Through numerical examples, it is shown that the method using the preferred gimbal-angle is an efficient approach to avoid internal singularities for the nonredundant CMG cluster.

  7. A study of delamination buckling of laminates

    NASA Technical Reports Server (NTRS)

    Mukherjee, Yu-Xie; Xie, Zhi-Cheng; Ingraffea, Anthony

    1990-01-01

    The subject of this paper is the buckling of laminated plates, with a preexisting delamination, subjected to in-plane loading. Each laminate is modelled as an orthotropic Mindlin plate. The analysis is carried out by a combination of the finite element and asymptotic expansion methods. By applying the finite element method, plates with general delamination regions can be studied. The asymptotic expansion method reduces the number of unknown variables of the eigenvalue equation to that of the equation for a single Kirchhoff plate. Numerical results are presented for several examples. The effects of the shape, size, and position of the delamination on the buckling load are studied through these examples.

  8. Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

    NASA Astrophysics Data System (ADS)

    Lai, Wencong; Khan, Abdul A.

    2018-04-01

    A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

  9. Quantum State Diffusion

    NASA Astrophysics Data System (ADS)

    Percival, Ian

    2005-10-01

    1. Introduction; 2. Brownian motion and Itô calculus; 3. Open quantum systems; 4. Quantum state diffusion; 5. Localisation; 6. Numerical methods and examples; 7. Quantum foundations; 8. Primary state diffusion; 9. Classical dynamics of quantum localisation; 10. Semiclassical theory and linear dynamics.

  10. A multi-domain spectral method for time-fractional differential equations

    NASA Astrophysics Data System (ADS)

    Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

    2015-07-01

    This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

  11. An adaptive gridless methodology in one dimension

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

    Snyder, N.T.; Hailey, C.E.

    1996-09-01

    Gridless numerical analysis offers great potential for accurately solving for flow about complex geometries or moving boundary problems. Because gridless methods do not require point connection, the mesh cannot twist or distort. The gridless method utilizes a Taylor series about each point to obtain the unknown derivative terms from the current field variable estimates. The governing equation is then numerically integrated to determine the field variables for the next iteration. Effects of point spacing and Taylor series order on accuracy are studied, and they follow similar trends of traditional numerical techniques. Introducing adaption by point movement using a spring analogymore » allows the solution method to track a moving boundary. The adaptive gridless method models linear, nonlinear, steady, and transient problems. Comparison with known analytic solutions is given for these examples. Although point movement adaption does not provide a significant increase in accuracy, it helps capture important features and provides an improved solution.« less

  12. A Semi-implicit Treatment of Porous Media in Steady-State CFD.

    PubMed

    Domaingo, Andreas; Langmayr, Daniel; Somogyi, Bence; Almbauer, Raimund

    There are many situations in computational fluid dynamics which require the definition of source terms in the Navier-Stokes equations. These source terms not only allow to model the physics of interest but also have a strong impact on the reliability, stability, and convergence of the numerics involved. Therefore, sophisticated numerical approaches exist for the description of such source terms. In this paper, we focus on the source terms present in the Navier-Stokes or Euler equations due to porous media-in particular the Darcy-Forchheimer equation. We introduce a method for the numerical treatment of the source term which is independent of the spatial discretization and based on linearization. In this description, the source term is treated in a fully implicit way whereas the other flow variables can be computed in an implicit or explicit manner. This leads to a more robust description in comparison with a fully explicit approach. The method is well suited to be combined with coarse-grid-CFD on Cartesian grids, which makes it especially favorable for accelerated solution of coupled 1D-3D problems. To demonstrate the applicability and robustness of the proposed method, a proof-of-concept example in 1D, as well as more complex examples in 2D and 3D, is presented.

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

    NASA Astrophysics Data System (ADS)

    Avitabile, Daniele; Bridges, Thomas J.

    2010-06-01

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

  14. Acceleration of convergence of vector sequences

    NASA Technical Reports Server (NTRS)

    Sidi, A.; Ford, W. F.; Smith, D. A.

    1983-01-01

    A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

  15. Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models

    NASA Astrophysics Data System (ADS)

    Gomez, Hector; Reali, Alessandro; Sangalli, Giancarlo

    2014-04-01

    We propose new collocation methods for phase-field models. Our algorithms are based on isogeometric analysis, a new technology that makes use of functions from computational geometry, such as, for example, Non-Uniform Rational B-Splines (NURBS). NURBS exhibit excellent approximability and controllable global smoothness, and can represent exactly most geometries encapsulated in Computer Aided Design (CAD) models. These attributes permitted us to derive accurate, efficient, and geometrically flexible collocation methods for phase-field models. The performance of our method is demonstrated by several numerical examples of phase separation modeled by the Cahn-Hilliard equation. We feel that our method successfully combines the geometrical flexibility of finite elements with the accuracy and simplicity of pseudo-spectral collocation methods, and is a viable alternative to classical collocation methods.

  16. A review of spectral methods

    NASA Technical Reports Server (NTRS)

    Lustman, L.

    1984-01-01

    An outline for spectral methods for partial differential equations is presented. The basic spectral algorithm is defined, collocation are emphasized and the main advantage of the method, the infinite order of accuracy in problems with smooth solutions are discussed. Examples of theoretical numerical analysis of spectral calculations are presented. An application of spectral methods to transonic flow is presented. The full potential transonic equation is among the best understood among nonlinear equations.

  17. Optimization of the Bridgman crystal growth process

    NASA Astrophysics Data System (ADS)

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

    2004-05-01

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

  18. A Fourier-based total-field/scattered-field technique for three-dimensional broadband simulations of elastic targets near a water-sand interface.

    PubMed

    Shao, Yu; Wang, Shumin

    2016-12-01

    The numerical simulation of acoustic scattering from elastic objects near a water-sand interface is critical to underwater target identification. Frequency-domain methods are computationally expensive, especially for large-scale broadband problems. A numerical technique is proposed to enable the efficient use of finite-difference time-domain method for broadband simulations. By incorporating a total-field/scattered-field boundary, the simulation domain is restricted inside a tightly bounded region. The incident field is further synthesized by the Fourier transform for both subcritical and supercritical incidences. Finally, the scattered far field is computed using a half-space Green's function. Numerical examples are further provided to demonstrate the accuracy and efficiency of the proposed technique.

  19. Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

    NASA Astrophysics Data System (ADS)

    Želi, Velibor; Zorica, Dušan

    2018-02-01

    Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

  20. Efficient C1-continuous phase-potential upwind (C1-PPU) schemes for coupled multiphase flow and transport with gravity

    NASA Astrophysics Data System (ADS)

    Jiang, Jiamin; Younis, Rami M.

    2017-10-01

    In the presence of counter-current flow, nonlinear convergence problems may arise in implicit time-stepping when the popular phase-potential upwinding (PPU) scheme is used. The PPU numerical flux is non-differentiable across the co-current/counter-current flow regimes. This may lead to cycles or divergence in the Newton iterations. Recently proposed methods address improved smoothness of the numerical flux. The objective of this work is to devise and analyze an alternative numerical flux scheme called C1-PPU that, in addition to improving smoothness with respect to saturations and phase potentials, also improves the level of scalar nonlinearity and accuracy. C1-PPU involves a novel use of the flux limiter concept from the context of high-resolution methods, and allows a smooth variation between the co-current/counter-current flow regimes. The scheme is general and applies to fully coupled flow and transport formulations with an arbitrary number of phases. We analyze the consistency property of the C1-PPU scheme, and derive saturation and pressure estimates, which are used to prove the solution existence. Several numerical examples for two- and three-phase flows in heterogeneous and multi-dimensional reservoirs are presented. The proposed scheme is compared to the conventional PPU and the recently proposed Hybrid Upwinding schemes. We investigate three properties of these numerical fluxes: smoothness, nonlinearity, and accuracy. The results indicate that in addition to smoothness, nonlinearity may also be critical for convergence behavior and thus needs to be considered in the design of an efficient numerical flux scheme. Moreover, the numerical examples show that the C1-PPU scheme exhibits superior convergence properties for large time steps compared to the other alternatives.

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

    PubMed

    Bardhan, Jaydeep P

    2009-03-07

    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.

  2. The Reduced Basis Method in Geosciences: Practical examples for numerical forward simulations

    NASA Astrophysics Data System (ADS)

    Degen, D.; Veroy, K.; Wellmann, F.

    2017-12-01

    Due to the highly heterogeneous character of the earth's subsurface, the complex coupling of thermal, hydrological, mechanical, and chemical processes, and the limited accessibility we have to face high-dimensional problems associated with high uncertainties in geosciences. Performing the obviously necessary uncertainty quantifications with a reasonable number of parameters is often not possible due to the high-dimensional character of the problem. Therefore, we are presenting the reduced basis (RB) method, being a model order reduction (MOR) technique, that constructs low-order approximations to, for instance, the finite element (FE) space. We use the RB method to address this computationally challenging simulations because this method significantly reduces the degrees of freedom. The RB method is decomposed into an offline and online stage, allowing to make the expensive pre-computations beforehand to get real-time results during field campaigns. Generally, the RB approach is most beneficial in the many-query and real-time context.We will illustrate the advantages of the RB method for the field of geosciences through two examples of numerical forward simulations.The first example is a geothermal conduction problem demonstrating the implementation of the RB method for a steady-state case. The second examples, a Darcy flow problem, shows the benefits for transient scenarios. In both cases, a quality evaluation of the approximations is given. Additionally, the runtimes for both the FE and the RB simulations are compared. We will emphasize the advantages of this method for repetitive simulations by showing the speed-up for the RB solution in contrast to the FE solution. Finally, we will demonstrate how the used implementation is usable in high-performance computing (HPC) infrastructures and evaluate its performance for such infrastructures. Hence, we will especially point out its scalability, yielding in an optimal usage on HPC infrastructures and normal working stations.

  3. Use of a variational moment method in calculating propagation constants for waveguides with an arbitrary index profile.

    PubMed

    Hardy, A; Itzkowitz, M; Griffel, G

    1989-05-15

    A variational moment method is used to calculate propagation constants of 1-D optical waveguides with an arbitrary index profile. The method is applicable to 2-D waveguides as well, and the index profiles need not be symmetric. Examples are given for the lowest-order and the next higher-order modes and are compared with exact numerical solutions.

  4. Extension of rezoned Eulerian-Lagrangian method to astrophysical plasma applications

    NASA Technical Reports Server (NTRS)

    Song, M. T.; Wu, S. T.; Dryer, Murray

    1993-01-01

    The rezoned Eulerian-Lagrangian procedure developed by Brackbill and Pracht (1973), which is limited to simple configurations of the magnetic fields, is modified in order to make it applicable to astrophysical plasma. For this purpose, two specific methods are introduced, which make it possible to determine the initial field topology for which no analytical expressions are available. Numerical examples illustrating these methods are presented.

  5. Modeling and simulation of dynamics of a planar-motion rigid body with friction and surface contact

    NASA Astrophysics Data System (ADS)

    Wang, Xiaojun; Lv, Jing

    2017-07-01

    The modeling and numerical method for the dynamics of a planar-motion rigid body with frictional contact between plane surfaces were presented based on the theory of contact mechanics and the algorithm of linear complementarity problem (LCP). The Coulomb’s dry friction model is adopted as the friction law, and the normal contact forces are expressed as functions of the local deformations and their speeds in contact bodies. The dynamic equations of the rigid body are obtained by the Lagrange equation. The transition problem of stick-slip motions between contact surfaces is formulated and solved as LCP through establishing the complementary conditions of the friction law. Finally, a numerical example is presented as an example to show the application.

  6. Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains

    PubMed Central

    Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph

    2014-01-01

    The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to “lift” this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging -discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the “basis” of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage savings over direct approaches. PMID:24626049

  7. Accurate calculation of the geometric measure of entanglement for multipartite quantum states

    NASA Astrophysics Data System (ADS)

    Teng, Peiyuan

    2017-07-01

    This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction. Numerical examples are benchmarked and compared. Furthermore, we search for highly entangled qubit states to show the applicability of this method.

  8. Highly Accurate Beam Torsion Solutions Using the p-Version Finite Element Method

    NASA Technical Reports Server (NTRS)

    Smith, James P.

    1996-01-01

    A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.

  9. Méthode du second membre modifié pour la gestion de rapports de viscosité importants dans le problème de Stokes bifluide

    NASA Astrophysics Data System (ADS)

    Bui, Thi Thu Cuc; Frey, Pascal; Maury, Bertrand

    2008-06-01

    In this Note, we present a method to solve numerically the Stokes equation for the incompressible flow between two immiscible fluids presenting very different viscosities. The resolution of the finite element systems of equations is performed using Uzawa's method. The stiffness matrix conditioning problems related to the very important viscosity ratios are circumvented using an new iterative scheme. A numerical example is proposed to show the efficiency of this approach. To cite this article: T.T.C. Bui et al., C. R. Mecanique 336 (2008).

  10. Parametrically excited non-linear multidegree-of-freedom systems with repeated natural frequencies

    NASA Astrophysics Data System (ADS)

    Tezak, E. G.; Nayfeh, A. H.; Mook, D. T.

    1982-12-01

    A method for analyzing multidegree-of-freedom systems having a repeated natural frequency subjected to a parametric excitation is presented. Attention is given to the ordering of the various terms (linear and non-linear) in the governing equations. The analysis is based on the method of multiple scales. As a numerical example involving a parametric resonance, panel flutter is discussed in detail in order to illustrate the type of results one can expect to obtain with this analysis. Some of the analytical results are verified by a numerical integration of the governing equations.

  11. Grid refinement in Cartesian coordinates for groundwater flow models using the divergence theorem and Taylor's series.

    PubMed

    Mansour, M M; Spink, A E F

    2013-01-01

    Grid refinement is introduced in a numerical groundwater model to increase the accuracy of the solution over local areas without compromising the run time of the model. Numerical methods developed for grid refinement suffered certain drawbacks, for example, deficiencies in the implemented interpolation technique; the non-reciprocity in head calculations or flow calculations; lack of accuracy resulting from high truncation errors, and numerical problems resulting from the construction of elongated meshes. A refinement scheme based on the divergence theorem and Taylor's expansions is presented in this article. This scheme is based on the work of De Marsily (1986) but includes more terms of the Taylor's series to improve the numerical solution. In this scheme, flow reciprocity is maintained and high order of refinement was achievable. The new numerical method is applied to simulate groundwater flows in homogeneous and heterogeneous confined aquifers. It produced results with acceptable degrees of accuracy. This method shows the potential for its application to solving groundwater heads over nested meshes with irregular shapes. © 2012, British Geological Survey © NERC 2012. Ground Water © 2012, National GroundWater Association.

  12. The modeling of an automotive electronic control system and the application of optimizing methods

    NASA Astrophysics Data System (ADS)

    Zhang, Yansheng; Yang, Zhigang; Zhang, Xiang

    2005-12-01

    Now, MATLAB/SIMULINK software is popularly used by automotive electronic control designers to develop automotive electronic control systems and perform numerical simulations. But they will face problems, such as value initialization in the "integrator" block, conversion among different data types, selection of "if" block and "switch" block, realization of the "if-clause" under multiple options and the auto-switching control, etc. Taking as an example the designing of an Automated Mechanical Transmission (AMT) system, this paper discusses some techniques and methods for modeling the automotive electronic control system with MATLAB/SIMULINK, offering designers some successful examples.

  13. Boundary acquisition for setup of numerical simulation

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

    Diegert, C.

    1997-12-31

    The author presents a work flow diagram that includes a path that begins with taking experimental measurements, and ends with obtaining insight from results produced by numerical simulation. Two examples illustrate this path: (1) Three-dimensional imaging measurement at micron scale, using X-ray tomography, provides information on the boundaries of irregularly-shaped alumina oxide particles held in an epoxy matrix. A subsequent numerical simulation predicts the electrical field concentrations that would occur in the observed particle configurations. (2) Three-dimensional imaging measurement at meter scale, again using X-ray tomography, provides information on the boundaries fossilized bone fragments in a Parasaurolophus crest recently discoveredmore » in New Mexico. A subsequent numerical simulation predicts acoustic response of the elaborate internal structure of nasal passageways defined by the fossil record. The author must both add value, and must change the format of the three-dimensional imaging measurements before the define the geometric boundary initial conditions for the automatic mesh generation, and subsequent numerical simulation. The author applies a variety of filters and statistical classification algorithms to estimate the extents of the structures relevant to the subsequent numerical simulation, and capture these extents as faceted geometries. The author will describe the particular combination of manual and automatic methods used in the above two examples.« less

  14. PFEM-based modeling of industrial granular flows

    NASA Astrophysics Data System (ADS)

    Cante, J.; Dávalos, C.; Hernández, J. A.; Oliver, J.; Jonsén, P.; Gustafsson, G.; Häggblad, H.-Å.

    2014-05-01

    The potential of numerical methods for the solution and optimization of industrial granular flows problems is widely accepted by the industries of this field, the challenge being to promote effectively their industrial practice. In this paper, we attempt to make an exploratory step in this regard by using a numerical model based on continuous mechanics and on the so-called Particle Finite Element Method (PFEM). This goal is achieved by focusing two specific industrial applications in mining industry and pellet manufacturing: silo discharge and calculation of power draw in tumbling mills. Both examples are representative of variations on the granular material mechanical response—varying from a stagnant configuration to a flow condition. The silo discharge is validated using the experimental data, collected on a full-scale flat bottomed cylindrical silo. The simulation is conducted with the aim of characterizing and understanding the correlation between flow patterns and pressures for concentric discharges. In the second example, the potential of PFEM as a numerical tool to track the positions of the particles inside the drum is analyzed. Pressures and wall pressures distribution are also studied. The power draw is also computed and validated against experiments in which the power is plotted in terms of the rotational speed of the drum.

  15. An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Han, Jianqiang; Tang, Huazhong

    2007-01-01

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

  16. A New Model for Simulating Gas Metal Arc Welding based on Phase Field Model

    NASA Astrophysics Data System (ADS)

    Jiang, Yongyue; Li, Li; Zhao, Zhijiang

    2017-11-01

    Lots of physical process, such as metal melting, multiphase fluids flow, heat and mass transfer and thermocapillary effect (Marangoni) and so on, will occur in gas metal arc welding (GMAW) which should be considered as a mixture system. In this paper, based on the previous work, we propose a new model to simulate GMAW including Navier-Stokes equation, the phase field model and energy equation. Unlike most previous work, we take the thermocapillary effect into the phase field model considering mixture energy which is different of volume of fluid method (VOF) widely used in GMAW before. We also consider gravity, electromagnetic force, surface tension, buoyancy effect and arc pressure in momentum equation. The spray transfer especially the projected transfer in GMAW is computed as numerical examples with a continuous finite element method and a modified midpoint scheme. Pulse current is set as welding current as the numerical example to show the numerical simulation of metal transfer which fits the theory of GMAW well. From the result compared with the data of high-speed photography and VOF model, the accuracy and stability of the model and scheme are easily validated and also the new model has the higher precieion.

  17. On the probability of exceeding allowable leak rates through degraded steam generator tubes

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

    Cizelj, L.; Sorsek, I.; Riesch-Oppermann, H.

    1997-02-01

    This paper discusses some possible ways of predicting the behavior of the total leak rate through the damaged steam generator tubes. This failure mode is of special concern in cases where most through-wall defects may remain In operation. A particular example is the application of alternate (bobbin coil voltage) plugging criterion to Outside Diameter Stress Corrosion Cracking at the tube support plate intersections. It is the authors aim to discuss some possible modeling options that could be applied to solve the problem formulated as: Estimate the probability that the sum of all individual leak rates through degraded tubes exceeds themore » predefined acceptable value. The probabilistic approach is of course aiming at reliable and computationaly bearable estimate of the failure probability. A closed form solution is given for a special case of exponentially distributed individual leak rates. Also, some possibilities for the use of computationaly efficient First and Second Order Reliability Methods (FORM and SORM) are discussed. The first numerical example compares the results of approximate methods with closed form results. SORM in particular shows acceptable agreement. The second numerical example considers a realistic case of NPP in Krsko, Slovenia.« less

  18. The method of complex characteristics for design of transonic blade sections

    NASA Technical Reports Server (NTRS)

    Bledsoe, M. R.

    1986-01-01

    A variety of computational methods were developed to obtain shockless or near shockless flow past two-dimensional airfoils. The approach used was the method of complex characteristics, which determines smooth solutions to the transonic flow equations based on an input speed distribution. General results from fluid mechanics are presented. An account of the method of complex characteristics is given including a description of the particular spaces and coordinates, conformal transformations, and numerical procedures that are used. The operation of the computer program COMPRES is presented along with examples of blade sections designed with the code. A user manual is included with a glossary to provide additional information which may be helpful. The computer program in Fortran, including numerous comment cards is listed.

  19. A new procedure for calculating contact stresses in gear teeth

    NASA Technical Reports Server (NTRS)

    Somprakit, Paisan; Huston, Ronald L.

    1991-01-01

    A numerical procedure for evaluating and monitoring contact stresses in meshing gear teeth is discussed. The procedure is intended to extend the range of applicability and to improve the accuracy of gear contact stress analysis. The procedure is based upon fundamental solution from the theory of elasticity. It is an iterative numerical procedure. The method is believed to have distinct advantages over the classical Hertz method, the finite-element method, and over existing approaches with the boundary element method. Unlike many classical contact stress analyses, friction effects and sliding are included. Slipping and sticking in the contact region are studied. Several examples are discussed. The results are in agreement with classical results. Applications are presented for spur gears.

  20. Self-learning Monte Carlo method and cumulative update in fermion systems

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

    Liu, Junwei; Shen, Huitao; Qi, Yang

    2017-06-07

    In this study, we develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub “cumulative update”, to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far lessmore » than the conventional algorithm with local updates.« less

  1. A volume-of-fluid method for simulation of compressible axisymmetric multi-material flow

    NASA Astrophysics Data System (ADS)

    de Niem, D.; Kührt, E.; Motschmann, U.

    2007-02-01

    A two-dimensional Eulerian hydrodynamic method for the numerical simulation of inviscid compressible axisymmetric multi-material flow in external force fields for the situation of pure fluids separated by macroscopic interfaces is presented. The method combines an implicit Lagrangian step with an explicit Eulerian advection step. Individual materials obey separate energy equations, fulfill general equations of state, and may possess different temperatures. Material volume is tracked using a piecewise linear volume-of-fluid method. An overshoot-free logically simple and economic material advection algorithm for cylinder coordinates is derived, in an algebraic formulation. New aspects arising in the case of more than two materials such as the material ordering strategy during transport are presented. One- and two-dimensional numerical examples are given.

  2. Deming on Education: A View from the Seminar.

    ERIC Educational Resources Information Center

    Holt, Maurice

    1993-01-01

    W. Edwards Deming rejects school-improvement proposals based on formulating higher standards and enforcing them with performance assessments. To Deming, the Bush Administration's America 2000 education strategy is "a horrible example of numerical goals, tests, rewards, but no method." Emphasizing rationalist performance measures…

  3. Preliminary orbit determination for lunar satellites.

    NASA Technical Reports Server (NTRS)

    Lancaster, E. R.

    1973-01-01

    Methods for the determination of orbits of artificial lunar satellites from earth-based range rate measurements developed by Koskela (1964) and Bateman et al. (1966) are simplified and extended to include range measurements along with range rate measurements. For illustration, a numerical example is presented.

  4. Computer programs of information processing of nuclear physical methods as a demonstration material in studying nuclear physics and numerical methods

    NASA Astrophysics Data System (ADS)

    Bateev, A. B.; Filippov, V. P.

    2017-01-01

    The principle possibility of using computer program Univem MS for Mössbauer spectra fitting as a demonstration material at studying such disciplines as atomic and nuclear physics and numerical methods by students is shown in the article. This program is associated with nuclear-physical parameters such as isomer (or chemical) shift of nuclear energy level, interaction of nuclear quadrupole moment with electric field and of magnetic moment with surrounded magnetic field. The basic processing algorithm in such programs is the Least Square Method. The deviation of values of experimental points on spectra from the value of theoretical dependence is defined on concrete examples. This value is characterized in numerical methods as mean square deviation. The shape of theoretical lines in the program is defined by Gaussian and Lorentzian distributions. The visualization of the studied material on atomic and nuclear physics can be improved by similar programs of the Mössbauer spectroscopy, X-ray Fluorescence Analyzer or X-ray diffraction analysis.

  5. Comparing Methods for Assessing Reliability Uncertainty Based on Pass/Fail Data Collected Over Time

    DOE PAGES

    Abes, Jeff I.; Hamada, Michael S.; Hills, Charles R.

    2017-12-20

    In this paper, we compare statistical methods for analyzing pass/fail data collected over time; some methods are traditional and one (the RADAR or Rationale for Assessing Degradation Arriving at Random) was recently developed. These methods are used to provide uncertainty bounds on reliability. We make observations about the methods' assumptions and properties. Finally, we illustrate the differences between two traditional methods, logistic regression and Weibull failure time analysis, and the RADAR method using a numerical example.

  6. Comparing Methods for Assessing Reliability Uncertainty Based on Pass/Fail Data Collected Over Time

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

    Abes, Jeff I.; Hamada, Michael S.; Hills, Charles R.

    In this paper, we compare statistical methods for analyzing pass/fail data collected over time; some methods are traditional and one (the RADAR or Rationale for Assessing Degradation Arriving at Random) was recently developed. These methods are used to provide uncertainty bounds on reliability. We make observations about the methods' assumptions and properties. Finally, we illustrate the differences between two traditional methods, logistic regression and Weibull failure time analysis, and the RADAR method using a numerical example.

  7. A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry

    NASA Astrophysics Data System (ADS)

    Al-Marouf, M.; Samtaney, R.

    2017-05-01

    We present an embedded ghost fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The CNS equations are numerically solved by the second order multidimensional upwind method. Block-structured adaptive mesh refinement, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the embedded boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible flows to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

  8. Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates

    USGS Publications Warehouse

    Cheng, Ralph T.; Casulli, Vincenzo; Milford, S. Nevil

    1984-01-01

    The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order Lagrangian polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.

  9. Model and Data Reduction for Control, Identification and Compressed Sensing

    NASA Astrophysics Data System (ADS)

    Kramer, Boris

    This dissertation focuses on problems in design, optimization and control of complex, large-scale dynamical systems from different viewpoints. The goal is to develop new algorithms and methods, that solve real problems more efficiently, together with providing mathematical insight into the success of those methods. There are three main contributions in this dissertation. In Chapter 3, we provide a new method to solve large-scale algebraic Riccati equations, which arise in optimal control, filtering and model reduction. We present a projection based algorithm utilizing proper orthogonal decomposition, which is demonstrated to produce highly accurate solutions at low rank. The method is parallelizable, easy to implement for practitioners, and is a first step towards a matrix free approach to solve AREs. Numerical examples for n ≥ 106 unknowns are presented. In Chapter 4, we develop a system identification method which is motivated by tangential interpolation. This addresses the challenge of fitting linear time invariant systems to input-output responses of complex dynamics, where the number of inputs and outputs is relatively large. The method reduces the computational burden imposed by a full singular value decomposition, by carefully choosing directions on which to project the impulse response prior to assembly of the Hankel matrix. The identification and model reduction step follows from the eigensystem realization algorithm. We present three numerical examples, a mass spring damper system, a heat transfer problem, and a fluid dynamics system. We obtain error bounds and stability results for this method. Chapter 5 deals with control and observation design for parameter dependent dynamical systems. We address this by using local parametric reduced order models, which can be used online. Data available from simulations of the system at various configurations (parameters, boundary conditions) is used to extract a sparse basis to represent the dynamics (via dynamic mode decomposition). Subsequently, a new, compressed sensing based classification algorithm is developed which incorporates the extracted dynamic information into the sensing basis. We show that this augmented classification basis makes the method more robust to noise, and results in superior identification of the correct parameter. Numerical examples consist of a Navier-Stokes, as well as a Boussinesq flow application.

  10. Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

    NASA Astrophysics Data System (ADS)

    Beck, Joakim; Dia, Ben Mansour; Espath, Luis F. R.; Long, Quan; Tempone, Raúl

    2018-06-01

    In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

  11. A weak Galerkin least-squares finite element method for div-curl systems

    NASA Astrophysics Data System (ADS)

    Li, Jichun; Ye, Xiu; Zhang, Shangyou

    2018-06-01

    In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

  12. Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

    NASA Technical Reports Server (NTRS)

    Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

  13. On the critical forcing amplitude of forced nonlinear oscillators

    NASA Astrophysics Data System (ADS)

    Febbo, Mariano; Ji, Jinchen C.

    2013-12-01

    The steady-state response of forced single degree-of-freedom weakly nonlinear oscillators under primary resonance conditions can exhibit saddle-node bifurcations, jump and hysteresis phenomena, if the amplitude of the excitation exceeds a certain value. This critical value of excitation amplitude or critical forcing amplitude plays an important role in determining the occurrence of saddle-node bifurcations in the frequency-response curve. This work develops an alternative method to determine the critical forcing amplitude for single degree-of-freedom nonlinear oscillators. Based on Lagrange multipliers approach, the proposed method considers the calculation of the critical forcing amplitude as an optimization problem with constraints that are imposed by the existence of locations of vertical tangency. In comparison with the Gröbner basis method, the proposed approach is more straightforward and thus easy to apply for finding the critical forcing amplitude both analytically and numerically. Three examples are given to confirm the validity of the theoretical predictions. The first two present the analytical form for the critical forcing amplitude and the third one is an example of a numerically computed solution.

  14. Probabilistic methods for rotordynamics analysis

    NASA Technical Reports Server (NTRS)

    Wu, Y.-T.; Torng, T. Y.; Millwater, H. R.; Fossum, A. F.; Rheinfurth, M. H.

    1991-01-01

    This paper summarizes the development of the methods and a computer program to compute the probability of instability of dynamic systems that can be represented by a system of second-order ordinary linear differential equations. Two instability criteria based upon the eigenvalues or Routh-Hurwitz test functions are investigated. Computational methods based on a fast probability integration concept and an efficient adaptive importance sampling method are proposed to perform efficient probabilistic analysis. A numerical example is provided to demonstrate the methods.

  15. Backward-in-time methods to simulate large-scale transport and mixing in the ocean

    NASA Astrophysics Data System (ADS)

    Prants, S. V.

    2015-06-01

    In oceanography and meteorology, it is important to know not only where water or air masses are headed for, but also where they came from as well. For example, it is important to find unknown sources of oil spills in the ocean and of dangerous substance plumes in the atmosphere. It is impossible with the help of conventional ocean and atmospheric numerical circulation models to extrapolate backward from the observed plumes to find the source because those models cannot be reversed in time. We review here recently elaborated backward-in-time numerical methods to identify and study mesoscale eddies in the ocean and to compute where those waters came from to a given area. The area under study is populated with a large number of artificial tracers that are advected backward in time in a given velocity field that is supposed to be known analytically or numerically, or from satellite and radar measurements. After integrating advection equations, one gets positions of each tracer on a fixed day in the past and can identify from known destinations a particle positions at earlier times. The results provided show that the method is efficient, for example, in estimating probabilities to find increased concentrations of radionuclides and other pollutants in oceanic mesoscale eddies. The backward-in-time methods are illustrated in this paper with a few examples. Backward-in-time Lagrangian maps are applied to identify eddies in satellite-derived and numerically generated velocity fields and to document the pathways by which they exchange water with their surroundings. Backward-in-time trapping maps are used to identify mesoscale eddies in the altimetric velocity field with a risk to be contaminated by Fukushima-derived radionuclides. The results of simulations are compared with in situ mesurement of caesium concentration in sea water samples collected in a recent research vessel cruise in the area to the east of Japan. Backward-in-time latitudinal maps and the corresponding material-line techniques are applied to document transport of water masses across strong currents. Backward-in-time drift maps are shown to be useful in identifying the Lagrangian fronts favorable for fishery.

  16. Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction

    NASA Astrophysics Data System (ADS)

    Yu, Jie; Liu, Yikan; Yamamoto, Masahiro

    2018-04-01

    In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.

  17. Eigenvalue assignment by minimal state-feedback gain in LTI multivariable systems

    NASA Astrophysics Data System (ADS)

    Ataei, Mohammad; Enshaee, Ali

    2011-12-01

    In this article, an improved method for eigenvalue assignment via state feedback in the linear time-invariant multivariable systems is proposed. This method is based on elementary similarity operations, and involves mainly utilisation of vector companion forms, and thus is very simple and easy to implement on a digital computer. In addition to the controllable systems, the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs. Moreover, two types of state-feedback gain matrices can be achieved by this method: (1) the numerical one, which is unique, and (2) the parametric one, in which its parameters are determined in order to achieve a gain matrix with minimum Frobenius norm. The numerical examples are presented to demonstrate the advantages of the proposed method.

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

    Shadid, John Nicolas; Fish, Jacob; Waisman, Haim

    Two heuristic strategies intended to enhance the performance of the generalized global basis (GGB) method [H. Waisman, J. Fish, R.S. Tuminaro, J. Shadid, The Generalized Global Basis (GGB) method, International Journal for Numerical Methods in Engineering 61(8), 1243-1269] applied to nonlinear systems are presented. The standard GGB accelerates a multigrid scheme by an additional coarse grid correction that filters out slowly converging modes. This correction requires a potentially costly eigen calculation. This paper considers reusing previously computed eigenspace information. The GGB? scheme enriches the prolongation operator with new eigenvectors while the modified method (MGGB) selectively reuses the same prolongation. Bothmore » methods use the criteria of principal angles between subspaces spanned between the previous and current prolongation operators. Numerical examples clearly indicate significant time savings in particular for the MGGB scheme.« less

  19. Overset meshing coupled with hybridizable discontinuous Galerkin finite elements

    DOE PAGES

    Kauffman, Justin A.; Sheldon, Jason P.; Miller, Scott T.

    2017-03-01

    We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusionmore » and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.« less

  20. Multi-step-ahead Method for Wind Speed Prediction Correction Based on Numerical Weather Prediction and Historical Measurement Data

    NASA Astrophysics Data System (ADS)

    Wang, Han; Yan, Jie; Liu, Yongqian; Han, Shuang; Li, Li; Zhao, Jing

    2017-11-01

    Increasing the accuracy of wind speed prediction lays solid foundation to the reliability of wind power forecasting. Most traditional correction methods for wind speed prediction establish the mapping relationship between wind speed of the numerical weather prediction (NWP) and the historical measurement data (HMD) at the corresponding time slot, which is free of time-dependent impacts of wind speed time series. In this paper, a multi-step-ahead wind speed prediction correction method is proposed with consideration of the passing effects from wind speed at the previous time slot. To this end, the proposed method employs both NWP and HMD as model inputs and the training labels. First, the probabilistic analysis of the NWP deviation for different wind speed bins is calculated to illustrate the inadequacy of the traditional time-independent mapping strategy. Then, support vector machine (SVM) is utilized as example to implement the proposed mapping strategy and to establish the correction model for all the wind speed bins. One Chinese wind farm in northern part of China is taken as example to validate the proposed method. Three benchmark methods of wind speed prediction are used to compare the performance. The results show that the proposed model has the best performance under different time horizons.

  1. Use of CFD modelling for analysing air parameters in auditorium halls

    NASA Astrophysics Data System (ADS)

    Cichowicz, Robert

    2017-11-01

    Modelling with the use of numerical methods is currently the most popular method of solving scientific as well as engineering problems. Thanks to the use of computer methods it is possible for example to comprehensively describe the conditions in a given room and to determine thermal comfort, which is a complex issue including subjective sensations of the persons in a given room. The article presents the results of measurements and numerical computing that enabled carrying out the assessment of environment parameters, taking into consideration microclimate, temperature comfort, speeds in the zone of human presence and dustiness in auditory halls. For this purpose measurements of temperature, relative humidity and dustiness were made with the use of a digital microclimate meter and a laser dust particles counter. Thanks to the above by using the application DesignBuilder numerical computing was performed and the obtained results enabled determining PMV comfort indicator in selected rooms.

  2. A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Hu, Changqing; Shu, Chi-Wang

    1998-01-01

    In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.

  3. Iterative computation of generalized inverses, with an application to CMG steering laws

    NASA Technical Reports Server (NTRS)

    Steincamp, J. W.

    1971-01-01

    A cubically convergent iterative method for computing the generalized inverse of an arbitrary M X N matrix A is developed and a FORTRAN subroutine by which the method was implemented for real matrices on a CDC 3200 is given, with a numerical example to illustrate accuracy. Application to a redundant single-gimbal CMG assembly steering law is discussed.

  4. Performance-Based Seismic Design of Steel Frames Utilizing Colliding Bodies Algorithm

    PubMed Central

    Veladi, H.

    2014-01-01

    A pushover analysis method based on semirigid connection concept is developed and the colliding bodies optimization algorithm is employed to find optimum seismic design of frame structures. Two numerical examples from the literature are studied. The results of the new algorithm are compared to the conventional design methods to show the power or weakness of the algorithm. PMID:25202717

  5. Performance-based seismic design of steel frames utilizing colliding bodies algorithm.

    PubMed

    Veladi, H

    2014-01-01

    A pushover analysis method based on semirigid connection concept is developed and the colliding bodies optimization algorithm is employed to find optimum seismic design of frame structures. Two numerical examples from the literature are studied. The results of the new algorithm are compared to the conventional design methods to show the power or weakness of the algorithm.

  6. Technical Evaluation Report for Symposium AVT-147: Computational Uncertainty in Military Vehicle Design

    NASA Technical Reports Server (NTRS)

    Radespiel, Rolf; Hemsch, Michael J.

    2007-01-01

    The complexity of modern military systems, as well as the cost and difficulty associated with experimentally verifying system and subsystem design makes the use of high-fidelity based simulation a future alternative for design and development. The predictive ability of such simulations such as computational fluid dynamics (CFD) and computational structural mechanics (CSM) have matured significantly. However, for numerical simulations to be used with confidence in design and development, quantitative measures of uncertainty must be available. The AVT 147 Symposium has been established to compile state-of-the art methods of assessing computational uncertainty, to identify future research and development needs associated with these methods, and to present examples of how these needs are being addressed and how the methods are being applied. Papers were solicited that address uncertainty estimation associated with high fidelity, physics-based simulations. The solicitation included papers that identify sources of error and uncertainty in numerical simulation from either the industry perspective or from the disciplinary or cross-disciplinary research perspective. Examples of the industry perspective were to include how computational uncertainty methods are used to reduce system risk in various stages of design or development.

  7. Phase space methods in HMD systems

    NASA Astrophysics Data System (ADS)

    Babington, James

    2017-06-01

    We consider using phase space techniques and methods in analysing optical ray propagation in head mounted display systems. Two examples are considered that illustrate the concepts and methods. Firstly, a shark tooth freeform geometry, and secondly, a waveguide geometry that replicates a pupil in one dimension. Classical optics and imaging in particular provide a natural stage to employ phase space techniques, albeit as a constrained system. We consider how phase space provides a global picture of the physical ray trace data. As such, this gives a complete optical world history of all of the rays propagating through the system. Using this data one can look at, for example, how aberrations arise on a surface by surface basis. These can be extracted numerically from phase space diagrams in the example of a freeform imaging prism. For the waveguide geometry, phase space diagrams provide a way of illustrating how replicated pupils behave and what these imply for design considerations such as tolerances.

  8. A combined analytical and numerical analysis of the flow-acoustic coupling in a cavity-pipe system

    NASA Astrophysics Data System (ADS)

    Langthjem, Mikael A.; Nakano, Masami

    2018-05-01

    The generation of sound by flow through a closed, cylindrical cavity (expansion chamber) accommodated with a long tailpipe is investigated analytically and numerically. The sound generation is due to self-sustained flow oscillations in the cavity. These oscillations may, in turn, generate standing (resonant) acoustic waves in the tailpipe. The main interest of the paper is in the interaction between these two sound sources. An analytical, approximate solution of the acoustic part of the problem is obtained via the method of matched asymptotic expansions. The sound-generating flow is represented by a discrete vortex method, based on axisymmetric vortex rings. It is demonstrated through numerical examples that inclusion of acoustic feedback from the tailpipe is essential for a good representation of the sound characteristics.

  9. Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes

    DOE PAGES

    Chen, Zheng; Huang, Hongying; Yan, Jue

    2015-12-21

    We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β 0,β 1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried outmore » to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.« less

  10. Class and Home Problems. The Lambert W Function in Ultrafiltration and Diafiltration

    ERIC Educational Resources Information Center

    Foley, Greg

    2016-01-01

    Novel analytical solutions based on the Lambert W function for two problems in ultrafiltration and diafiltration are described. Example problems, suitable for incorporation into an introductory module in unit operations, membrane processing, or numerical methods are provided in each case.

  11. Automatic Error Analysis Using Intervals

    ERIC Educational Resources Information Center

    Rothwell, E. J.; Cloud, M. J.

    2012-01-01

    A technique for automatic error analysis using interval mathematics is introduced. A comparison to standard error propagation methods shows that in cases involving complicated formulas, the interval approach gives comparable error estimates with much less effort. Several examples are considered, and numerical errors are computed using the INTLAB…

  12. Interfacial gauge methods for incompressible fluid dynamics

    PubMed Central

    Saye, Robert

    2016-01-01

    Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of “gauge freedom” to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work, high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena. PMID:27386567

  13. Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

    PubMed

    Hasegawa, Chihiro; Duffull, Stephen B

    2018-02-01

    Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

  14. The vibroacoustic response and sound absorption performance of multilayer, microperforated rib-stiffened plates

    NASA Astrophysics Data System (ADS)

    Zhou, Haian; Wang, Xiaoming; Wu, Huayong; Meng, Jianbing

    2017-10-01

    The vibroacoustic response and sound absorption performance of a structure composed of multilayer plates and one rigid back wall are theoretically analyzed. In this structure, all plates are two-dimensional, microperforated, and periodically rib-stiffened. To investigate such a structural system, semianalytical models of one-layer and multilayer plate structures considering the vibration effects are first developed. Then approaches of the space harmonic method and Fourier transforms are applied to a one-layer plate, and finally the cascade connection method is utilized for a multilayer plate structure. Based on fundamental acoustic formulas, the vibroacoustic responses of microperforated stiffened plates are expressed as functions of a series of harmonic amplitudes of plate displacement, which are then solved by employing the numerical truncation method. Applying the inverse Fourier transform, wave propagation, and linear addition properties, the equations of the sound pressures and absorption coefficients for the one-layer and multilayer stiffened plates in physical space are finally derived. Using numerical examples, the effects of the most important physical parameters—for example, the perforation ratio of the plate, sound incident angles, and periodical rib spacing—on sound absorption performance are examined. Numerical results indicate that the sound absorption performance of the studied structure is effectively enhanced by the flexural vibration of the plate in water. Finally, the proposed approaches are validated by comparing the results of stiffened plates of the present work with solutions from previous studies.

  15. Computation of rare transitions in the barotropic quasi-geostrophic equations

    NASA Astrophysics Data System (ADS)

    Laurie, Jason; Bouchet, Freddy

    2015-01-01

    We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier-Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager-Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

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

    NASA Astrophysics Data System (ADS)

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

    2014-06-01

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

  17. Generalized query-based active learning to identify differentially methylated regions in DNA.

    PubMed

    Haque, Md Muksitul; Holder, Lawrence B; Skinner, Michael K; Cook, Diane J

    2013-01-01

    Active learning is a supervised learning technique that reduces the number of examples required for building a successful classifier, because it can choose the data it learns from. This technique holds promise for many biological domains in which classified examples are expensive and time-consuming to obtain. Most traditional active learning methods ask very specific queries to the Oracle (e.g., a human expert) to label an unlabeled example. The example may consist of numerous features, many of which are irrelevant. Removing such features will create a shorter query with only relevant features, and it will be easier for the Oracle to answer. We propose a generalized query-based active learning (GQAL) approach that constructs generalized queries based on multiple instances. By constructing appropriately generalized queries, we can achieve higher accuracy compared to traditional active learning methods. We apply our active learning method to find differentially DNA methylated regions (DMRs). DMRs are DNA locations in the genome that are known to be involved in tissue differentiation, epigenetic regulation, and disease. We also apply our method on 13 other data sets and show that our method is better than another popular active learning technique.

  18. Lattice Boltzmann model for simulation of magnetohydrodynamics

    NASA Technical Reports Server (NTRS)

    Chen, Shiyi; Chen, Hudong; Martinez, Daniel; Matthaeus, William

    1991-01-01

    A numerical method, based on a discrete Boltzmann equation, is presented for solving the equations of magnetohydrodynamics (MHD). The algorithm provides advantages similar to the cellular automaton method in that it is local and easily adapted to parallel computing environments. Because of much lower noise levels and less stringent requirements on lattice size, the method appears to be more competitive with traditional solution methods. Examples show that the model accurately reproduces both linear and nonlinear MHD phenomena.

  19. Method for determining the weight of functional objectives on manufacturing system.

    PubMed

    Zhang, Qingshan; Xu, Wei; Zhang, Jiekun

    2014-01-01

    We propose a three-dimensional integrated weight determination to solve manufacturing system functional objectives, where consumers are weighted by triangular fuzzy numbers to determine the enterprises. The weights, subjective parts are determined by the expert scoring method, the objective parts are determined by the entropy method with the competitive advantage of determining. Based on the integration of three methods and comprehensive weight, we provide some suggestions for the manufacturing system. This paper provides the numerical example analysis to illustrate the feasibility of this method.

  20. Alternating direction implicit methods for parabolic equations with a mixed derivative

    NASA Technical Reports Server (NTRS)

    Beam, R. M.; Warming, R. F.

    1980-01-01

    Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A(0)-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A(0)-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.

  1. Alternating direction implicit methods for parabolic equations with a mixed derivative

    NASA Technical Reports Server (NTRS)

    Beam, R. M.; Warming, R. F.

    1979-01-01

    Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.

  2. Solving the multi-frequency electromagnetic inverse source problem by the Fourier method

    NASA Astrophysics Data System (ADS)

    Wang, Guan; Ma, Fuming; Guo, Yukun; Li, Jingzhi

    2018-07-01

    This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and the polarization vector decomposition, we propose a novel method for determining the source function in the full vector Maxwell's system. Rigorous mathematical justifications of the method are given and numerical examples are provided to demonstrate the feasibility and effectiveness of the method.

  3. Studies in astronomical time series analysis. I - Modeling random processes in the time domain

    NASA Technical Reports Server (NTRS)

    Scargle, J. D.

    1981-01-01

    Several random process models in the time domain are defined and discussed. Attention is given to the moving average model, the autoregressive model, and relationships between and combinations of these models. Consideration is then given to methods for investigating pulse structure, procedures of model construction, computational methods, and numerical experiments. A FORTRAN algorithm of time series analysis has been developed which is relatively stable numerically. Results of test cases are given to study the effect of adding noise and of different distributions for the pulse amplitudes. A preliminary analysis of the light curve of the quasar 3C 272 is considered as an example.

  4. Stress evaluation in displacement-based 2D nonlocal finite element method

    NASA Astrophysics Data System (ADS)

    Pisano, Aurora Angela; Fuschi, Paolo

    2018-06-01

    The evaluation of the stress field within a nonlocal version of the displacement-based finite element method is addressed. With the aid of two numerical examples it is shown as some spurious oscillations of the computed nonlocal stresses arise at sections (or zones) of macroscopic inhomogeneity of the examined structures. It is also shown how the above drawback, which renders the stress numerical solution unreliable, can be viewed as the so-called locking in FEM, a subject debated in the early seventies. It is proved that a well known remedy for locking, i.e. the reduced integration technique, can be successfully applied also in the nonlocal elasticity context.

  5. Reconstructing gravitational wave source parameters via direct comparisons to numerical relativity II: Applications

    NASA Astrophysics Data System (ADS)

    O'Shaughnessy, Richard; Lange, Jacob; Healy, James; Carlos, Lousto; Shoemaker, Deirdre; Lovelace, Geoffrey; Scheel, Mark

    2016-03-01

    In this talk, we apply a procedure to reconstruct the parameters of sufficiently massive coalescing compact binaries via direct comparison with numerical relativity simulations. We illustrate how to use only comparisons between synthetic data and these simulations to reconstruct properties of a synthetic candidate source. We demonstrate using selected examples that we can reconstruct posterior distributions obtained by other Bayesian methods with our sparse grid. We describe how followup simulations can corroborate and improve our understanding of a candidate signal.

  6. Numerical Function Generators Using LUT Cascades

    DTIC Science & Technology

    2007-06-01

    either algebraically (for example, sinðxÞ) or as a table of input/ output values. The user defines the numerical function by using the syntax of Scilab ...defined function in Scilab or specify it directly. Note that, by changing the parser of our system, any format can be used for the design entry. First...Methods for Multiple-Valued Input Address Generators,” Proc. 36th IEEE Int’l Symp. Multiple-Valued Logic (ISMVL ’06), May 2006. [29] Scilab 3.0, INRIA-ENPC

  7. A Parallel Stochastic Framework for Reservoir Characterization and History Matching

    DOE PAGES

    Thomas, Sunil G.; Klie, Hector M.; Rodriguez, Adolfo A.; ...

    2011-01-01

    The spatial distribution of parameters that characterize the subsurface is never known to any reasonable level of accuracy required to solve the governing PDEs of multiphase flow or species transport through porous media. This paper presents a numerically cheap, yet efficient, accurate and parallel framework to estimate reservoir parameters, for example, medium permeability, using sensor information from measurements of the solution variables such as phase pressures, phase concentrations, fluxes, and seismic and well log data. Numerical results are presented to demonstrate the method.

  8. Neighboring extremal optimal control design including model mismatch errors

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

    Kim, T.J.; Hull, D.G.

    1994-11-01

    The mismatch control technique that is used to simplify model equations of motion in order to determine analytic optimal control laws is extended using neighboring extremal theory. The first variation optimal control equations are linearized about the extremal path to account for perturbations in the initial state and the final constraint manifold. A numerical example demonstrates that the tuning procedure inherent in the mismatch control method increases the performance of the controls to the level of a numerically-determined piecewise-linear controller.

  9. Propagation of diffuse light in a turbid medium with multiple spherical inhomogeneities.

    PubMed

    Pustovit, Vitaliy N; Markel, Vadim A

    2004-01-01

    We develop a fast and accurate solver for the forward problem of diffusion tomography in the case of several spherical inhomogeneities. The approach allows one to take into account multiple scattering of diffuse waves between different inhomogeneities. Theoretical results are illustrated with numerical examples; excellent numerical convergence and efficiency are demonstrated. The method is generalized for the case of additional planar diffuse-nondiffuse interfaces and is therefore applicable to the half-space and slab imaging geometries.

  10. Robust Fault Detection for Switched Fuzzy Systems With Unknown Input.

    PubMed

    Han, Jian; Zhang, Huaguang; Wang, Yingchun; Sun, Xun

    2017-10-03

    This paper investigates the fault detection problem for a class of switched nonlinear systems in the T-S fuzzy framework. The unknown input is considered in the systems. A novel fault detection unknown input observer design method is proposed. Based on the proposed observer, the unknown input can be removed from the fault detection residual. The weighted H∞ performance level is considered to ensure the robustness. In addition, the weighted H₋ performance level is introduced, which can increase the sensibility of the proposed detection method. To verify the proposed scheme, a numerical simulation example and an electromechanical system simulation example are provided at the end of this paper.

  11. On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems

    DOE PAGES

    Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan

    2015-05-19

    The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less

  12. Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

    NASA Astrophysics Data System (ADS)

    Rubin, M. B.; Cardiff, P.

    2017-11-01

    Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

  13. Mask Design for the Space Interferometry Mission Internal Metrology

    NASA Technical Reports Server (NTRS)

    Marx, David; Zhao, Feng; Korechoff, Robert

    2005-01-01

    This slide presentation reviews the mask design used for the internal metrology of the Space Interferometry Mission (SIM). Included is information about the project, the method of measurements with SIM, the internal metrology, numerical model of internal metrology, wavefront examples, performance metrics, and mask design

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

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

    Mu, Lin; Wang, Junping; Ye, Xiu

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

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

    DOE PAGES

    Mu, Lin; Wang, Junping; Ye, Xiu

    2017-08-17

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

  16. Comparison of Response Surface Construction Methods for Derivative Estimation Using Moving Least Squares, Kriging and Radial Basis Functions

    NASA Technical Reports Server (NTRS)

    Krishnamurthy, Thiagarajan

    2005-01-01

    Response construction methods using Moving Least Squares (MLS), Kriging and Radial Basis Functions (RBF) are compared with the Global Least Squares (GLS) method in three numerical examples for derivative generation capability. Also, a new Interpolating Moving Least Squares (IMLS) method adopted from the meshless method is presented. It is found that the response surface construction methods using the Kriging and RBF interpolation yields more accurate results compared with MLS and GLS methods. Several computational aspects of the response surface construction methods also discussed.

  17. Thermal protection system gap analysis using a loosely coupled fluid-structural thermal numerical method

    NASA Astrophysics Data System (ADS)

    Huang, Jie; Li, Piao; Yao, Weixing

    2018-05-01

    A loosely coupled fluid-structural thermal numerical method is introduced for the thermal protection system (TPS) gap thermal control analysis in this paper. The aerodynamic heating and structural thermal are analyzed by computational fluid dynamics (CFD) and numerical heat transfer (NHT) methods respectively. An interpolation algorithm based on the control surface is adopted for the data exchanges on the coupled surface. In order to verify the analysis precision of the loosely coupled method, a circular tube example was analyzed, and the wall temperature agrees well with the test result. TPS gap thermal control performance was studied by the loosely coupled method successfully. The gap heat flux is mainly distributed in the small region at the top of the gap which is the high temperature region. Besides, TPS gap temperature and the power of the active cooling system (CCS) calculated by the traditional uncoupled method are higher than that calculated by the coupled method obviously. The reason is that the uncoupled method doesn't consider the coupled effect between the aerodynamic heating and structural thermal, however the coupled method considers it, so TPS gap thermal control performance can be analyzed more accurately by the coupled method.

  18. Upwind and symmetric shock-capturing schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1987-01-01

    The development of numerical methods for hyperbolic conservation laws has been a rapidly growing area for the last ten years. Many of the fundamental concepts and state-of-the-art developments can only be found in meeting proceedings or internal reports. This review paper attempts to give an overview and a unified formulation of a class of shock-capturing methods. Special emphasis is on the construction of the basic nonlinear scalar second-order schemes and the methods of extending these nonlinear scalar schemes to nonlinear systems via the extact Riemann solver, approximate Riemann solvers, and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows is discussed. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas dynamics problems.

  19. Identifiability of Additive Actuator and Sensor Faults by State Augmentation

    NASA Technical Reports Server (NTRS)

    Joshi, Suresh; Gonzalez, Oscar R.; Upchurch, Jason M.

    2014-01-01

    A class of fault detection and identification (FDI) methods for bias-type actuator and sensor faults is explored in detail from the point of view of fault identifiability. The methods use state augmentation along with banks of Kalman-Bucy filters for fault detection, fault pattern determination, and fault value estimation. A complete characterization of conditions for identifiability of bias-type actuator faults, sensor faults, and simultaneous actuator and sensor faults is presented. It is shown that FDI of simultaneous actuator and sensor faults is not possible using these methods when all sensors have unknown biases. The fault identifiability conditions are demonstrated via numerical examples. The analytical and numerical results indicate that caution must be exercised to ensure fault identifiability for different fault patterns when using such methods.

  20. Neural network approach for the calculation of potential coefficients in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Ossandón, Sebastián; Reyes, Camilo; Cumsille, Patricio; Reyes, Carlos M.

    2017-05-01

    A numerical method based on artificial neural networks is used to solve the inverse Schrödinger equation for a multi-parameter class of potentials. First, the finite element method was used to solve repeatedly the direct problem for different parametrizations of the chosen potential function. Then, using the attainable eigenvalues as a training set of the direct radial basis neural network a map of new eigenvalues was obtained. This relationship was later inverted and refined by training an inverse radial basis neural network, allowing the calculation of the unknown parameters and therefore estimating the potential function. Three numerical examples are presented in order to prove the effectiveness of the method. The results show that the method proposed has the advantage to use less computational resources without a significant accuracy loss.

  1. Finite element implementation of state variable-based viscoplasticity models

    NASA Technical Reports Server (NTRS)

    Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.

    1991-01-01

    The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.

  2. Modelling of non-equilibrium flow in the branched pipeline systems

    NASA Astrophysics Data System (ADS)

    Sumskoi, S. I.; Sverchkov, A. M.; Lisanov, M. V.; Egorov, A. F.

    2016-09-01

    This article presents a mathematical model and a numerical method for solving the task of water hammer in the branched pipeline system. The task is considered in the onedimensional non-stationary formulation taking into account the realities such as the change in the diameter of the pipeline and its branches. By comparison with the existing analytic solution it has been shown that the proposed method possesses good accuracy. With the help of the developed model and numerical method the task has been solved concerning the transmission of the compression waves complex in the branching pipeline system when several shut down valves operate. It should be noted that the offered model and method may be easily introduced to a number of other tasks, for example, to describe the flow of blood in the vessels.

  3. Reentry trajectory optimization based on a multistage pseudospectral method.

    PubMed

    Zhao, Jiang; Zhou, Rui; Jin, Xuelian

    2014-01-01

    Of the many direct numerical methods, the pseudospectral method serves as an effective tool to solve the reentry trajectory optimization for hypersonic vehicles. However, the traditional pseudospectral method is time-consuming due to large number of discretization points. For the purpose of autonomous and adaptive reentry guidance, the research herein presents a multistage trajectory control strategy based on the pseudospectral method, capable of dealing with the unexpected situations in reentry flight. The strategy typically includes two subproblems: the trajectory estimation and trajectory refining. In each processing stage, the proposed method generates a specified range of trajectory with the transition of the flight state. The full glide trajectory consists of several optimal trajectory sequences. The newly focused geographic constraints in actual flight are discussed thereafter. Numerical examples of free-space flight, target transition flight, and threat avoidance flight are used to show the feasible application of multistage pseudospectral method in reentry trajectory optimization.

  4. Reentry Trajectory Optimization Based on a Multistage Pseudospectral Method

    PubMed Central

    Zhou, Rui; Jin, Xuelian

    2014-01-01

    Of the many direct numerical methods, the pseudospectral method serves as an effective tool to solve the reentry trajectory optimization for hypersonic vehicles. However, the traditional pseudospectral method is time-consuming due to large number of discretization points. For the purpose of autonomous and adaptive reentry guidance, the research herein presents a multistage trajectory control strategy based on the pseudospectral method, capable of dealing with the unexpected situations in reentry flight. The strategy typically includes two subproblems: the trajectory estimation and trajectory refining. In each processing stage, the proposed method generates a specified range of trajectory with the transition of the flight state. The full glide trajectory consists of several optimal trajectory sequences. The newly focused geographic constraints in actual flight are discussed thereafter. Numerical examples of free-space flight, target transition flight, and threat avoidance flight are used to show the feasible application of multistage pseudospectral method in reentry trajectory optimization. PMID:24574929

  5. Sampling the isothermal-isobaric ensemble by Langevin dynamics

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

    Gao, Xingyu; Institute of Applied Physics and Computational Mathematics, Fenghao East Road 2, Beijing 100094; CAEP Software Center for High Performance Numerical Simulation, Huayuan Road 6, Beijing 100088

    2016-03-28

    We present a new method of conducting fully flexible-cell molecular dynamics simulation in isothermal-isobaric ensemble based on Langevin equations of motion. The stochastic coupling to all particle and cell degrees of freedoms is introduced in a correct way, in the sense that the stationary configurational distribution is proved to be consistent with that of the isothermal-isobaric ensemble. In order to apply the proposed method in computer simulations, a second order symmetric numerical integration scheme is developed by Trotter’s splitting of the single-step propagator. Moreover, a practical guide of choosing working parameters is suggested for user specified thermo- and baro-coupling timemore » scales. The method and software implementation are carefully validated by a numerical example.« less

  6. Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water flows in open channels

    NASA Astrophysics Data System (ADS)

    Qian, Shouguo; Li, Gang; Shao, Fengjing; Xing, Yulong

    2018-05-01

    We construct and study efficient high order discontinuous Galerkin methods for the shallow water flows in open channels with irregular geometry and a non-flat bottom topography in this paper. The proposed methods are well-balanced for the still water steady state solution, and can preserve the non-negativity of wet cross section numerically. The well-balanced property is obtained via a novel source term separation and discretization. A simple positivity-preserving limiter is employed to provide efficient and robust simulations near the wetting and drying fronts. Numerical examples are performed to verify the well-balanced property, the non-negativity of the wet cross section, and good performance for both continuous and discontinuous solutions.

  7. Extension of transonic flow computational concepts in the analysis of cavitated bearings

    NASA Technical Reports Server (NTRS)

    Vijayaraghavan, D.; Keith, T. G., Jr.; Brewe, D. E.

    1990-01-01

    An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

  8. Numerical simulation of vessel dynamics in manoeuvrability and seakeeping problems

    NASA Astrophysics Data System (ADS)

    Blishchik, A. E.; Taranov, A. E.

    2018-05-01

    This paper deals with some examples of numerical modelling for ship's dynamics problems and data comparison with corresponding experimental results. It was considered two kinds of simulation: self-propelled turning motion of crude carrier KVLCC2 and changing position of container carrier S 175 due to wave loadings. Mesh generation and calculation were made in STAR-CCM+ package. URANS equations were used as system of equations closed by k-w SST turbulence model. The vessel had several degrees of freedom, which depend on task. Based on the results of this research, the conclusion was made concerning the applicability of used numerical methods.

  9. Time-dependent wave splitting and source separation

    NASA Astrophysics Data System (ADS)

    Grote, Marcus J.; Kray, Marie; Nataf, Frédéric; Assous, Franck

    2017-02-01

    Starting from classical absorbing boundary conditions, we propose a method for the separation of time-dependent scattered wave fields due to multiple sources or obstacles. In contrast to previous techniques, our method is local in space and time, deterministic, and avoids a priori assumptions on the frequency spectrum of the signal. Numerical examples in two space dimensions illustrate the usefulness of wave splitting for time-dependent scattering problems.

  10. The least-squares finite element method for low-mach-number compressible viscous flows

    NASA Technical Reports Server (NTRS)

    Yu, Sheng-Tao

    1994-01-01

    The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

  11. Summary of tracking and identification methods

    NASA Astrophysics Data System (ADS)

    Blasch, Erik; Yang, Chun; Kadar, Ivan

    2014-06-01

    Over the last two decades, many solutions have arisen to combine target tracking estimation with classification methods. Target tracking includes developments from linear to non-linear and Gaussian to non-Gaussian processing. Pattern recognition includes detection, classification, recognition, and identification methods. Integrating tracking and pattern recognition has resulted in numerous approaches and this paper seeks to organize the various approaches. We discuss the terminology so as to have a common framework for various standards such as the NATO STANAG 4162 - Identification Data Combining Process. In a use case, we provide a comparative example highlighting that location information (as an example) with additional mission objectives from geographical, human, social, cultural, and behavioral modeling is needed to determine identification as classification alone does not allow determining identification or intent.

  12. Direct numerical solution of the Ornstein-Zernike integral equation and spatial distribution of water around hydrophobic molecules

    NASA Astrophysics Data System (ADS)

    Ikeguchi, Mitsunori; Doi, Junta

    1995-09-01

    The Ornstein-Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid-spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso-value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α-cholest-2-ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.

  13. An ultra-accurate numerical method in the design of liquid phononic crystals with hard inclusion

    NASA Astrophysics Data System (ADS)

    Li, Eric; He, Z. C.; Wang, G.; Liu, G. R.

    2017-12-01

    The phononics crystals (PCs) are periodic man-made composite materials. In this paper, a mass-redistributed finite element method (MR-FEM) is formulated to study the wave propagation within liquid PCs with hard inclusion. With a perfect balance between stiffness and mass in the MR-FEM model, the dispersion error of longitudinal wave is minimized by redistribution of mass. Such tuning can be easily achieved by adjusting the parameter r that controls the location of integration points of mass matrix. More importantly, the property of mass conservation in the MR-FEM model indicates that the locations of integration points inside or outside the element are immaterial. Four numerical examples are studied in this work, including liquid PCs with cross and circle hard inclusions, different size of inclusion and defect. Compared with standard finite element method, the numerical results have verified the accuracy and effectiveness of MR-FEM. The proposed MR-FEM is a unique and innovative numerical approach with its outstanding features, which has strong potentials to study the stress wave within multi-physics PCs.

  14. In vitro Alternative Methodologies for Central Nervous System Assessment: A Critique using Nanoscale Materials as an Example.

    EPA Science Inventory

    Identifying the potential health hazards to the central nervous system of a new family of materials presents many challenges. Whole-animal toxicity testing has been the tradition, but in vitro methods have been steadily gaining popularity. There are numerous challenges in testing...

  15. A calculation procedure for viscous flow in turbomachines, volume 3. [computer programs

    NASA Technical Reports Server (NTRS)

    Khalil, I.; Sheoran, Y.; Tabakoff, W.

    1980-01-01

    A method for analyzing the nonadiabatic viscous flow through turbomachine blade passages was developed. The field analysis is based upon the numerical integration of the full incompressible Navier-Stokes equations, together with the energy equation on the blade-to-blade surface. A FORTRAN IV computer program was written based on this method. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system. The flow may be axial, radial or mixed and there may be a change in stream channel thickness in the through-flow direction. The inputs required for two FORTRAN IV programs are presented. The first program considers laminar flows and the second can handle turbulent flows. Numerical examples are included to illustrate the use of the program, and to show the results that are obtained.

  16. Numerical modeling for the retrofit of the hydraulic cooling subsystems in operating power plant

    NASA Astrophysics Data System (ADS)

    AlSaqoor, S.; Alahmer, A.; Al Quran, F.; Andruszkiewicz, A.; Kubas, K.; Regucki, P.; Wędrychowicz, W.

    2017-08-01

    This paper presents the possibility of using the numerical methods to analyze the work of hydraulic systems on the example of a cooling system of a power boiler auxiliary devices. The variety of conditions at which hydraulic system that operated in specific engineering subsystems requires an individualized approach to the model solutions that have been developed for these systems modernizing. A mathematical model of a series-parallel propagation for the cooling water was derived and iterative methods were used to solve the system of nonlinear equations. The results of numerical calculations made it possible to analyze different variants of a modernization of the studied system and to indicate its critical elements. An economic analysis of different options allows an investor to choose an optimal variant of a reconstruction of the installation.

  17. On finite element implementation and computational techniques for constitutive modeling of high temperature composites

    NASA Technical Reports Server (NTRS)

    Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.

    1989-01-01

    The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

  18. Batch mode grid generation: An endangered species

    NASA Technical Reports Server (NTRS)

    Schuster, David M.

    1992-01-01

    Non-interactive grid generation schemes should thrive as emphasis shifts from development of numerical analysis and design methods to application of these tools to real engineering problems. A strong case is presented for the continued development and application of non-interactive geometry modeling methods. Guidelines, strategies, and techniques for developing and implementing these tools are presented using current non-interactive grid generation methods as examples. These schemes play an important role in the development of multidisciplinary analysis methods and some of these applications are also discussed.

  19. Large deformation frictional contact analysis with immersed boundary method

    NASA Astrophysics Data System (ADS)

    Navarro-Jiménez, José Manuel; Tur, Manuel; Albelda, José; Ródenas, Juan José

    2018-01-01

    This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method.

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

    Tuo, Rui; Wu, C. F. Jeff

    Many computer models contain unknown parameters which need to be estimated using physical observations. Furthermore, the calibration method based on Gaussian process models may lead to unreasonable estimate for imperfect computer models. In this work, we extend their study to calibration problems with stochastic physical data. We propose a novel method, called the L 2 calibration, and show its semiparametric efficiency. The conventional method of the ordinary least squares is also studied. Theoretical analysis shows that it is consistent but not efficient. Here, numerical examples show that the proposed method outperforms the existing ones.

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

    NASA Astrophysics Data System (ADS)

    Roul, Pradip; Warbhe, Ujwal

    2017-08-01

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

  2. Symplectic discretization for spectral element solution of Maxwell's equations

    NASA Astrophysics Data System (ADS)

    Zhao, Yanmin; Dai, Guidong; Tang, Yifa; Liu, Qinghuo

    2009-08-01

    Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.

  3. A Two-Dimensional Helmholtz Equation Solution for the Multiple Cavity Scattering Problem

    DTIC Science & Technology

    2013-02-01

    obtained by using the block Gauss – Seidel iterative meth- od. To show the convergence of the iterative method, we define the error between two...models to the general multiple cavity setting. Numerical examples indicate that the convergence of the Gauss – Seidel iterative method depends on the...variational approach. A block Gauss – Seidel iterative method is introduced to solve the cou- pled system of the multiple cavity scattering problem, where

  4. REVIEWS OF TOPICAL PROBLEMS: Population synthesis in astrophysics

    NASA Astrophysics Data System (ADS)

    Popov, S. B.; Prokhorov, M. E.

    2007-11-01

    Population synthesis is a method for numerical simulation of the population of objects with a complex evolution. This method is widely used in astrophysics. We consider its main applications to studying astronomical objects. Examples of modeling evolution are given for populations of close binaries and isolated neutron stars. The application of the method to studying active galactic nuclei and the integral spectral characteristics of galaxies is briefly discussed. An extensive bibliography on all the topics covered is provided.

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

    NASA Technical Reports Server (NTRS)

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

    1993-01-01

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

  6. Lotka-Volterra systems in environments with randomly disordered temporal periodicity

    NASA Astrophysics Data System (ADS)

    Naess, Arvid; Dimentberg, Michael F.; Gaidai, Oleg

    2008-08-01

    A generalized Lotka-Volterra model for a pair of interacting populations of predators and prey is studied. The model accounts for the prey’s interspecies competition and therefore is asymptotically stable, whereas its oscillatory behavior is induced by temporal variations in environmental conditions simulated by those in the prey’s reproduction rate. Two models of the variations are considered, each of them combining randomness with “hidden” periodicity. The stationary joint probability density function (PDF) of the number of predators and prey is calculated numerically by the path integration (PI) method based on the use of characteristic functions and the fast Fourier transform. The numerical results match those for the asymptotic case of white-noise variations for which an analytical solution is available. Several examples are studied, with calculations of important characteristics of oscillations, for example the expected rate of up-crossings given the level of the predator number. The calculated PDFs may be of predominantly random (unimodal) or predominantly periodic nature (bimodal). Thus, the PI method has been demonstrated to be a powerful tool for studies of the dynamics of predator-prey pairs. The method captures the random oscillations as observed in nature, taking into account potential periodicity in the environmental conditions.

  7. Lotka-Volterra systems in environments with randomly disordered temporal periodicity.

    PubMed

    Naess, Arvid; Dimentberg, Michael F; Gaidai, Oleg

    2008-08-01

    A generalized Lotka-Volterra model for a pair of interacting populations of predators and prey is studied. The model accounts for the prey's interspecies competition and therefore is asymptotically stable, whereas its oscillatory behavior is induced by temporal variations in environmental conditions simulated by those in the prey's reproduction rate. Two models of the variations are considered, each of them combining randomness with "hidden" periodicity. The stationary joint probability density function (PDF) of the number of predators and prey is calculated numerically by the path integration (PI) method based on the use of characteristic functions and the fast Fourier transform. The numerical results match those for the asymptotic case of white-noise variations for which an analytical solution is available. Several examples are studied, with calculations of important characteristics of oscillations, for example the expected rate of up-crossings given the level of the predator number. The calculated PDFs may be of predominantly random (unimodal) or predominantly periodic nature (bimodal). Thus, the PI method has been demonstrated to be a powerful tool for studies of the dynamics of predator-prey pairs. The method captures the random oscillations as observed in nature, taking into account potential periodicity in the environmental conditions.

  8. Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

    NASA Astrophysics Data System (ADS)

    Chew, J. V. L.; Sulaiman, J.

    2017-09-01

    Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

  9. On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron

    2004-01-01

    We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge-Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.

  10. Bounded Error Schemes for the Wave Equation on Complex Domains

    NASA Technical Reports Server (NTRS)

    Abarbanel, Saul; Ditkowski, Adi; Yefet, Amir

    1998-01-01

    This paper considers the application of the method of boundary penalty terms ("SAT") to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g. the staggered Yee scheme) - we achieve a decrease of two orders of magnitude in the level of the L2-error.

  11. LQR Control of Thin Shell Dynamics: Formulation and Numerical Implementation

    NASA Technical Reports Server (NTRS)

    delRosario, R. C. H.; Smith, R. C.

    1997-01-01

    A PDE-based feedback control method for thin cylindrical shells with surface-mounted piezoceramic actuators is presented. Donnell-Mushtari equations modified to incorporate both passive and active piezoceramic patch contributions are used to model the system dynamics. The well-posedness of this model and the associated LQR problem with an unbounded input operator are established through analytic semigroup theory. The model is discretized using a Galerkin expansion with basis functions constructed from Fourier polynomials tensored with cubic splines, and convergence criteria for the associated approximate LQR problem are established. The effectiveness of the method for attenuating the coupled longitudinal, circumferential and transverse shell displacements is illustrated through a set of numerical examples.

  12. Efficient optimization of the quantum relative entropy

    NASA Astrophysics Data System (ADS)

    Fawzi, Hamza; Fawzi, Omar

    2018-04-01

    Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable states. The various capacities of quantum channels can also be written in this way. We propose a unified framework to numerically compute these quantities using off-the-shelf semidefinite programming solvers, exploiting the approximation method proposed in Fawzi, Saunderson and Parrilo (2017 arXiv: 1705.00812). As a notable application, this method allows us to provide numerical counterexamples for a proposed lower bound on the quantum conditional mutual information in terms of the relative entropy of recovery.

  13. A Gauss-Newton full-waveform inversion in PML-truncated domains using scalar probing waves

    NASA Astrophysics Data System (ADS)

    Pakravan, Alireza; Kang, Jun Won; Newtson, Craig M.

    2017-12-01

    This study considers the characterization of subsurface shear wave velocity profiles in semi-infinite media using scalar waves. Using surficial responses caused by probing waves, a reconstruction of the material profile is sought using a Gauss-Newton full-waveform inversion method in a two-dimensional domain truncated by perfectly matched layer (PML) wave-absorbing boundaries. The PML is introduced to limit the semi-infinite extent of the half-space and to prevent reflections from the truncated boundaries. A hybrid unsplit-field PML is formulated in the inversion framework to enable more efficient wave simulations than with a fully mixed PML. The full-waveform inversion method is based on a constrained optimization framework that is implemented using Karush-Kuhn-Tucker (KKT) optimality conditions to minimize the objective functional augmented by PML-endowed wave equations via Lagrange multipliers. The KKT conditions consist of state, adjoint, and control problems, and are solved iteratively to update the shear wave velocity profile of the PML-truncated domain. Numerical examples show that the developed Gauss-Newton inversion method is accurate enough and more efficient than another inversion method. The algorithm's performance is demonstrated by the numerical examples including the case of noisy measurement responses and the case of reduced number of sources and receivers.

  14. Interfacial gauge methods for incompressible fluid dynamics

    DOE PAGES

    Saye, R.

    2016-06-10

    Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of "gauge freedom" to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work,more » high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena.« less

  15. A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions

    NASA Astrophysics Data System (ADS)

    Ma, Lin

    2017-11-01

    This paper develops a method for precisely determining the tension of an inclined cable with unknown boundary conditions. First, the nonlinear motion equation of an inclined cable is derived, and a numerical model of the motion of the cable is proposed using the finite difference method. The proposed numerical model includes the sag-extensibility, flexural stiffness, inclination angle and rotational stiffness at two ends of the cable. Second, the influence of the dynamic parameters of the cable on its frequencies is discussed in detail, and a method for precisely determining the tension of an inclined cable is proposed based on the derivatives of the eigenvalues of the matrices. Finally, a multiparameter identification method is developed that can simultaneously identify multiple parameters, including the rotational stiffness at two ends. This scheme is applicable to inclined cables with varying sag, varying flexural stiffness and unknown boundary conditions. Numerical examples indicate that the method provides good precision. Because the parameters of cables other than tension (e.g., the flexural stiffness and rotational stiffness at the ends) are not accurately known in practical engineering, the multiparameter identification method could further improve the accuracy of cable tension measurements.

  16. Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

    PubMed

    Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing

    2016-10-01

    The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.

  17. Vortex loops and Majoranas

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

    Chesi, Stefano; CEMS, RIKEN, Wako, Saitama 351-0198; Jaffe, Arthur

    2013-11-15

    We investigate the role that vortex loops play in characterizing eigenstates of interacting Majoranas. We give some general results and then focus on ladder Hamiltonian examples as a test of further ideas. Two methods yield exact results: (i) A mapping of certain spin Hamiltonians to quartic interactions of Majoranas shows that the spectra of these two examples coincide. (ii) In cases with reflection-symmetric Hamiltonians, we use reflection positivity for Majoranas to characterize vortices in the ground states. Two additional methods suggest wider applicability of these results: (iii) Numerical evidence suggests similar behavior for certain systems without reflection symmetry. (iv) Amore » perturbative analysis also suggests similar behavior without the assumption of reflection symmetry.« less

  18. Variable Step-Size Selection Methods for Implicit Integration Schemes

    DTIC Science & Technology

    2005-10-01

    for ρk numerically. 23 4 Examples In this section we explore this variable step-size selection method for two problems, the Lotka - Volterra model and...the Kepler problem. 4.1 The Lotka - Volterra Model For this example we consider the Lotka - Volterra model of a simple predator- prey system from...problems. Consider this variation to the Lotka - Volterra problem:   u̇ v̇   =   u2v(v − 2) v2u(1− u)   = f(u, v); t ∈ [0, 50

  19. A modified precise integration method for transient dynamic analysis in structural systems with multiple damping models

    NASA Astrophysics Data System (ADS)

    Ding, Zhe; Li, Li; Hu, Yujin

    2018-01-01

    Sophisticated engineering systems are usually assembled by subcomponents with significantly different levels of energy dissipation. Therefore, these damping systems often contain multiple damping models and lead to great difficulties in analyzing. This paper aims at developing a time integration method for structural systems with multiple damping models. The dynamical system is first represented by a generally damped model. Based on this, a new extended state-space method for the damped system is derived. A modified precise integration method with Gauss-Legendre quadrature is then proposed. The numerical stability and accuracy of the proposed integration method are discussed in detail. It is verified that the method is conditionally stable and has inherent algorithmic damping, period error and amplitude decay. Numerical examples are provided to assess the performance of the proposed method compared with other methods. It is demonstrated that the method is more accurate than other methods with rather good efficiency and the stable condition is easy to be satisfied in practice.

  20. Representing ductile damage with the dual domain material point method

    DOE PAGES

    Long, C. C.; Zhang, D. Z.; Bronkhorst, C. A.; ...

    2015-12-14

    In this study, we incorporate a ductile damage material model into a computational framework based on the Dual Domain Material Point (DDMP) method. As an example, simulations of a flyer plate experiment involving ductile void growth and material failure are performed. The results are compared with experiments performed on high purity tantalum. We also compare the numerical results obtained from the DDMP method with those obtained from the traditional Material Point Method (MPM). Effects of an overstress model, artificial viscosity, and physical viscosity are investigated. Our results show that a physical bulk viscosity and overstress model are important in thismore » impact and failure problem, while physical shear viscosity and artificial shock viscosity have negligible effects. A simple numerical procedure with guaranteed convergence is introduced to solve for the equilibrium plastic state from the ductile damage model.« less

  1. Long-Term Dynamics of Autonomous Fractional Differential Equations

    NASA Astrophysics Data System (ADS)

    Liu, Tao; Xu, Wei; Xu, Yong; Han, Qun

    This paper aims to investigate long-term dynamic behaviors of autonomous fractional differential equations with effective numerical method. The long-term dynamic behaviors predict where systems are heading after long-term evolution. We make some modification and transplant cell mapping methods to autonomous fractional differential equations. The mapping time duration of cell mapping is enlarged to deal with the long memory effect. Three illustrative examples, i.e. fractional Lotka-Volterra equation, fractional van der Pol oscillator and fractional Duffing equation, are studied with our revised generalized cell mapping method. We obtain long-term dynamics, such as attractors, basins of attraction, and saddles. Compared with some existing stability and numerical results, the validity of our method is verified. Furthermore, we find that the fractional order has its effect on the long-term dynamics of autonomous fractional differential equations.

  2. A numerical fragment basis approach to SCF calculations.

    NASA Astrophysics Data System (ADS)

    Hinde, Robert J.

    1997-11-01

    The counterpoise method is often used to correct for basis set superposition error in calculations of the electronic structure of bimolecular systems. One drawback of this approach is the need to specify a ``reference state'' for the system; for reactive systems, the choice of an unambiguous reference state may be difficult. An example is the reaction F^- + HCl arrow HF + Cl^-. Two obvious reference states for this reaction are F^- + HCl and HF + Cl^-; however, different counterpoise-corrected interaction energies are obtained using these two reference states. We outline a method for performing SCF calculations which employs numerical basis functions; this method attempts to eliminate basis set superposition errors in an a priori fashion. We test the proposed method on two one-dimensional, three-center systems and discuss the possibility of extending our approach to include electron correlation effects.

  3. A fast numerical scheme for causal relativistic hydrodynamics with dissipation

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

    Takamoto, Makoto, E-mail: takamoto@tap.scphys.kyoto-u.ac.jp; Inutsuka, Shu-ichiro

    2011-08-01

    Highlights: {yields} We have developed a new multi-dimensional numerical scheme for causal relativistic hydrodynamics with dissipation. {yields} Our new scheme can calculate the evolution of dissipative relativistic hydrodynamics faster and more effectively than existing schemes. {yields} Since we use the Riemann solver for solving the advection steps, our method can capture shocks very accurately. - Abstract: In this paper, we develop a stable and fast numerical scheme for relativistic dissipative hydrodynamics based on Israel-Stewart theory. Israel-Stewart theory is a stable and causal description of dissipation in relativistic hydrodynamics although it includes relaxation process with the timescale for collision of constituentmore » particles, which introduces stiff equations and makes practical numerical calculation difficult. In our new scheme, we use Strang's splitting method, and use the piecewise exact solutions for solving the extremely short timescale problem. In addition, since we split the calculations into inviscid step and dissipative step, Riemann solver can be used for obtaining numerical flux for the inviscid step. The use of Riemann solver enables us to capture shocks very accurately. Simple numerical examples are shown. The present scheme can be applied to various high energy phenomena of astrophysics and nuclear physics.« less

  4. Numerical Modelling of Foundation Slabs with use of Schur Complement Method

    NASA Astrophysics Data System (ADS)

    Koktan, Jiří; Brožovský, Jiří

    2017-10-01

    The paper discusses numerical modelling of foundation slabs with use of advanced numerical approaches, which are suitable for parallel processing. The solution is based on the Finite Element Method with the slab-type elements. The subsoil is modelled with use of Winklertype contact model (as an alternative a multi-parameter model can be used). The proposed modelling approach uses the Schur Complement method to speed-up the computations of the problem. The method is based on a special division of the analyzed model to several substructures. It adds some complexity to the numerical procedures, especially when subsoil models are used inside the finite element method solution. In other hand, this method makes possible a fast solution of large models but it introduces further problems to the process. Thus, the main aim of this paper is to verify that such method can be successfully used for this type of problem. The most suitable finite elements will be discussed, there will be also discussion related to finite element mesh and limitations of its construction for such problem. The core approaches of the implementation of the Schur Complement Method for this type of the problem will be also presented. The proposed approach was implemented in the form of a computer program, which will be also briefly introduced. There will be also presented results of example computations, which prove the speed-up of the solution - there will be shown important speed-up of solution even in the case of on-parallel processing and the ability of bypass size limitations of numerical models with use of the discussed approach.

  5. Evaluation of methods for measuring relative permeability of anhydride from the Salado Formation: Sensitivity analysis and data reduction

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

    Christiansen, R.L.; Kalbus, J.S.; Howarth, S.M.

    This report documents, demonstrates, evaluates, and provides theoretical justification for methods used to convert experimental data into relative permeability relationships. The report facilities accurate determination of relative permeabilities of anhydride rock samples from the Salado Formation at the Waste Isolation Pilot Plant (WIPP). Relative permeability characteristic curves are necessary for WIPP Performance Assessment (PA) predictions of the potential for flow of waste-generated gas from the repository and brine flow into repository. This report follows Christiansen and Howarth (1995), a comprehensive literature review of methods for measuring relative permeability. It focuses on unsteady-state experiments and describes five methods for obtaining relativemore » permeability relationships from unsteady-state experiments. Unsteady-state experimental methods were recommended for relative permeability measurements of low-permeability anhydrite rock samples form the Salado Formation because these tests produce accurate relative permeability information and take significantly less time to complete than steady-state tests. Five methods for obtaining relative permeability relationships from unsteady-state experiments are described: the Welge method, the Johnson-Bossler-Naumann method, the Jones-Roszelle method, the Ramakrishnan-Cappiello method, and the Hagoort method. A summary, an example of the calculations, and a theoretical justification are provided for each of the five methods. Displacements in porous media are numerically simulated for the calculation examples. The simulated product data were processed using the methods, and the relative permeabilities obtained were compared with those input to the numerical model. A variety of operating conditions were simulated to show sensitivity of production behavior to rock-fluid properties.« less

  6. A simple finite element method for non-divergence form elliptic equation

    DOE PAGES

    Mu, Lin; Ye, Xiu

    2017-03-01

    Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

  7. A simple finite element method for non-divergence form elliptic equation

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

    Mu, Lin; Ye, Xiu

    Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

  8. Method for Determining the Weight of Functional Objectives on Manufacturing System

    PubMed Central

    Zhang, Qingshan; Xu, Wei; Zhang, Jiekun

    2014-01-01

    We propose a three-dimensional integrated weight determination to solve manufacturing system functional objectives, where consumers are weighted by triangular fuzzy numbers to determine the enterprises. The weights, subjective parts are determined by the expert scoring method, the objective parts are determined by the entropy method with the competitive advantage of determining. Based on the integration of three methods and comprehensive weight, we provide some suggestions for the manufacturing system. This paper provides the numerical example analysis to illustrate the feasibility of this method. PMID:25243203

  9. Assessment Methods of Groundwater Overdraft Area and Its Application

    NASA Astrophysics Data System (ADS)

    Dong, Yanan; Xing, Liting; Zhang, Xinhui; Cao, Qianqian; Lan, Xiaoxun

    2018-05-01

    Groundwater is an important source of water, and long-term large demand make groundwater over-exploited. Over-exploitation cause a lot of environmental and geological problems. This paper explores the concept of over-exploitation area, summarizes the natural and social attributes of over-exploitation area, as well as expounds its evaluation methods, including single factor evaluation, multi-factor system analysis and numerical method. At the same time, the different methods are compared and analyzed. And then taking Northern Weifang as an example, this paper introduces the practicality of appraisal method.

  10. An analytical-numerical method for determining the mechanical response of a condenser microphone

    PubMed Central

    Homentcovschi, Dorel; Miles, Ronald N.

    2011-01-01

    The paper is based on determining the reaction pressure on the diaphragm of a condenser microphone by integrating numerically the frequency domain Stokes system describing the velocity and the pressure in the air domain beneath the diaphragm. Afterwards, the membrane displacement can be obtained analytically or numerically. The method is general and can be applied to any geometry of the backplate holes, slits, and backchamber. As examples, the method is applied to the Bruel & Kjaer (B&K) 4134 1/2-inch microphone determining the mechanical sensitivity and the mechano-thermal noise for a domain of frequencies and also the displacement field of the membrane for two specified frequencies. These elements compare well with the measured values published in the literature. Also a new design, completely micromachined (including the backvolume) of the B&K micro-electro-mechanical systems (MEM) 1/4-inch measurement microphone is proposed. It is shown that its mechanical performances are very similar to those of the B&K MEMS measurement microphone. PMID:22225026

  11. An analytical-numerical method for determining the mechanical response of a condenser microphone.

    PubMed

    Homentcovschi, Dorel; Miles, Ronald N

    2011-12-01

    The paper is based on determining the reaction pressure on the diaphragm of a condenser microphone by integrating numerically the frequency domain Stokes system describing the velocity and the pressure in the air domain beneath the diaphragm. Afterwards, the membrane displacement can be obtained analytically or numerically. The method is general and can be applied to any geometry of the backplate holes, slits, and backchamber. As examples, the method is applied to the Bruel & Kjaer (B&K) 4134 1/2-inch microphone determining the mechanical sensitivity and the mechano-thermal noise for a domain of frequencies and also the displacement field of the membrane for two specified frequencies. These elements compare well with the measured values published in the literature. Also a new design, completely micromachined (including the backvolume) of the B&K micro-electro-mechanical systems (MEM) 1/4-inch measurement microphone is proposed. It is shown that its mechanical performances are very similar to those of the B&K MEMS measurement microphone. © 2011 Acoustical Society of America

  12. Fast sweeping method for the factored eikonal equation

    NASA Astrophysics Data System (ADS)

    Fomel, Sergey; Luo, Songting; Zhao, Hongkai

    2009-09-01

    We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

  13. Numerically evaluating the bispectrum in curved field-space— with PyTransport 2.0

    NASA Astrophysics Data System (ADS)

    Ronayne, John W.; Mulryne, David J.

    2018-01-01

    We extend the transport framework for numerically evaluating the power spectrum and bispectrum in multi-field inflation to the case of a curved field-space metric. This method naturally accounts for all sub- and super-horizon tree level effects, including those induced by the curvature of the field-space. We present an open source implementation of our equations in an extension of the publicly available PyTransport code. Finally we illustrate how our technique is applied to examples of inflationary models with a non-trivial field-space metric.

  14. Computer simulation of solutions of polyharmonic equations in plane domain

    NASA Astrophysics Data System (ADS)

    Kazakova, A. O.

    2018-05-01

    A systematic study of plane problems of the theory of polyharmonic functions is presented. A method of reducing boundary problems for polyharmonic functions to the system of integral equations on the boundary of the domain is given and a numerical algorithm for simulation of solutions of this system is suggested. Particular attention is paid to the numerical solution of the main tasks when the values of the function and its derivatives are given. Test examples are considered that confirm the effectiveness and accuracy of the suggested algorithm.

  15. Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion.

    PubMed

    Sun, Jiao-Jiao; Zhou, Shengwu; Zhang, Yan; Han, Miao; Wang, Fei

    2014-01-01

    The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed.

  16. Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion

    PubMed Central

    Sun, Jiao-Jiao; Zhou, Shengwu; Zhang, Yan; Han, Miao; Wang, Fei

    2014-01-01

    The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed. PMID:27433525

  17. High-order ENO schemes applied to two- and three-dimensional compressible flow

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang; Erlebacher, Gordon; Zang, Thomas A.; Whitaker, David; Osher, Stanley

    1991-01-01

    High order essentially non-oscillatory (ENO) finite difference schemes are applied to the 2-D and 3-D compressible Euler and Navier-Stokes equations. Practical issues, such as vectorization, efficiency of coding, cost comparison with other numerical methods, and accuracy degeneracy effects, are discussed. Numerical examples are provided which are representative of computational problems of current interest in transition and turbulence physics. These require both nonoscillatory shock capturing and high resolution for detailed structures in the smooth regions and demonstrate the advantage of ENO schemes.

  18. Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

    NASA Astrophysics Data System (ADS)

    Nestler, M.; Nitschke, I.; Praetorius, S.; Voigt, A.

    2018-02-01

    We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincaré-Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.

  19. The boundary element method applied to 3D magneto-electro-elastic dynamic problems

    NASA Astrophysics Data System (ADS)

    Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.

    2017-11-01

    Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.

  20. Numerical method for N electrons bound to a polar quantum dot with a Coulomb impurity

    NASA Astrophysics Data System (ADS)

    Yau, J. K.; Lee, C. M.

    2003-03-01

    A numerical method is proposed to calculate the Frohlich Hamiltonian containing N electrons bound to polar quantum dot with a Coulomb impurity without transformation to the coordination frame of the center of mass and by direct diagonalization. As an example to demonstrate the formalism of this method, the low-lying spectra of three interacting electrons bound to an on-center Coulomb impurity, both for accepter and donor, are calculated and analyzed in a polar quantum dot under a perpendicular magnetic field. Taking polaron effect into account, the physical meaning of the phonon-induced terms, both self-square terms and cross terms of the Hamiltonian are discussed. The calculation can also be applied to systems containing particles with opposite charges, such as excitons.

  1. Band-limited Green's Functions for Quantitative Evaluation of Acoustic Emission Using the Finite Element Method

    NASA Technical Reports Server (NTRS)

    Leser, William P.; Yuan, Fuh-Gwo; Leser, William P.

    2013-01-01

    A method of numerically estimating dynamic Green's functions using the finite element method is proposed. These Green's functions are accurate in a limited frequency range dependent on the mesh size used to generate them. This range can often match or exceed the frequency sensitivity of the traditional acoustic emission sensors. An algorithm is also developed to characterize an acoustic emission source by obtaining information about its strength and temporal dependence. This information can then be used to reproduce the source in a finite element model for further analysis. Numerical examples are presented that demonstrate the ability of the band-limited Green's functions approach to determine the moment tensor coefficients of several reference signals to within seven percent, as well as accurately reproduce the source-time function.

  2. Calculation of load distribution in stiffened cylindrical shells

    NASA Technical Reports Server (NTRS)

    Ebner, H; Koller, H

    1938-01-01

    Thin-walled shells with strong longitudinal and transverse stiffening (for example, stressed-skin fuselages and wings) may, under certain simplifying assumptions, be treated as static systems with finite redundancies. In this report the underlying basis for this method of treatment of the problem is presented and a computation procedure for stiffened cylindrical shells with curved sheet panels indicated. A detailed discussion of the force distribution due to applied concentrated forces is given, and the discussion illustrated by numerical examples which refer to an experimentally determined circular cylindrical shell.

  3. Ink-constrained halftoning with application to QR codes

    NASA Astrophysics Data System (ADS)

    Bayeh, Marzieh; Compaan, Erin; Lindsey, Theodore; Orlow, Nathan; Melczer, Stephen; Voller, Zachary

    2014-01-01

    This paper examines adding visually significant, human recognizable data into QR codes without affecting their machine readability by utilizing known methods in image processing. Each module of a given QR code is broken down into pixels, which are halftoned in such a way as to keep the QR code structure while revealing aspects of the secondary image to the human eye. The loss of information associated to this procedure is discussed, and entropy values are calculated for examples given in the paper. Numerous examples of QR codes with embedded images are included.

  4. Numerical solution of differential equations by artificial neural networks

    NASA Technical Reports Server (NTRS)

    Meade, Andrew J., Jr.

    1995-01-01

    Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks (ANN's) are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed by the author to mate the adaptability of the ANN with the speed and precision of the digital computer. This method has been successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

  5. Buckling analysis of SMA bonded sandwich structure – using FEM

    NASA Astrophysics Data System (ADS)

    Katariya, Pankaj V.; Das, Arijit; Panda, Subrata K.

    2018-03-01

    Thermal buckling strength of smart sandwich composite structure (bonded with shape memory alloy; SMA) examined numerically via a higher-order finite element model in association with marching technique. The excess geometrical distortion of the structure under the elevated environment modeled through Green’s strain function whereas the material nonlinearity counted with the help of marching method. The system responses are computed numerically by solving the generalized eigenvalue equations via a customized MATLAB code. The comprehensive behaviour of the current finite element solutions (minimum buckling load parameter) is established by solving the adequate number of numerical examples including the given input parameter. The current numerical model is extended further to check the influence of various structural parameter of the sandwich panel on the buckling temperature including the SMA effect and reported in details.

  6. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    NASA Astrophysics Data System (ADS)

    Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

    2017-07-01

    This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  7. Theoretical and numerical difficulties in 3-D vector potential methods in finite element magnetostatic computations

    NASA Technical Reports Server (NTRS)

    Demerdash, N. A.; Wang, R.

    1990-01-01

    This paper describes the results of application of three well known 3D magnetic vector potential (MVP) based finite element formulations for computation of magnetostatic fields in electrical devices. The three methods were identically applied to three practical examples, the first of which contains only one medium (free space), while the second and third examples contained a mix of free space and iron. The first of these methods is based on the unconstrained curl-curl of the MVP, while the second and third methods are predicated upon constraining the divergence of the MVP 10 zero (Coulomb's Gauge). It was found that the two latter methods cease to give useful and meaningful results when the global solution region contains a mix of media of high and low permeabilities. Furthermore, it was found that their results do not achieve the intended zero constraint on the divergence of the MVP.

  8. FORTRAN program for calculating total efficiency - specific speed characteristics of centrifugal compressors

    NASA Technical Reports Server (NTRS)

    Galvas, M. R.

    1972-01-01

    A computer program for predicting design point specific speed - efficiency characteristics of centrifugal compressors is presented with instructions for its use. The method permits rapid selection of compressor geometry that yields maximum total efficiency for a particular application. A numerical example is included to demonstrate the selection procedure.

  9. Determination of the Conservation Time of Periodicals for Optimal Shelf Maintenance of a Library.

    ERIC Educational Resources Information Center

    Miyamoto, Sadaaki; Nakayama, Kazuhiko

    1981-01-01

    Presents a method based on a constrained optimization technique that determines the time of removal of scientific periodicals from the shelf of a library. A geometrical interpretation of the theoretical result is given, and a numerical example illustrates how the technique is applicable to real bibliographic data. (FM)

  10. A Materials Index--Its Storage, Retrieval, and Display

    ERIC Educational Resources Information Center

    Rosen, Carol Z.

    1973-01-01

    An experimental procedure for indexing physical materials based on simple syntactical rules was tested by encoding the materials in the journal, Applied Physics Letters,'' to produce a materials index. The syntax and numerous examples together with an indication of the method by which retrieval can be effected are presented. (5 references)…

  11. Assessing Fit and Dimensionality in Least Squares Metric Multidimensional Scaling Using Akaike's Information Criterion

    ERIC Educational Resources Information Center

    Ding, Cody S.; Davison, Mark L.

    2010-01-01

    Akaike's information criterion is suggested as a tool for evaluating fit and dimensionality in metric multidimensional scaling that uses least squares methods of estimation. This criterion combines the least squares loss function with the number of estimated parameters. Numerical examples are presented. The results from analyses of both simulation…

  12. More on Systematic Error in a Boyle's Law Experiment

    ERIC Educational Resources Information Center

    McCall, Richard P.

    2012-01-01

    A recent article in "The Physics Teacher" describes a method for analyzing a systematic error in a Boyle's law laboratory activity. Systematic errors are important to consider in physics labs because they tend to bias the results of measurements. There are numerous laboratory examples and resources that discuss this common source of error.

  13. Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

    NASA Astrophysics Data System (ADS)

    Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

    2018-02-01

    In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

  14. Detection of symmetric homoclinic orbits to saddle-centres in reversible systems

    NASA Astrophysics Data System (ADS)

    Yagasaki, Kazuyuki; Wagenknecht, Thomas

    2006-02-01

    We present a perturbation technique for the detection of symmetric homoclinic orbits to saddle-centre equilibria in reversible systems of ordinary differential equations. We assume that the unperturbed system has primary, symmetric homoclinic orbits, which may be either isolated or appear in a family, and use an idea similar to that of Melnikov’s method to detect homoclinic orbits in their neighbourhood. This technique also allows us to identify bifurcations of unperturbed or perturbed, symmetric homoclinic orbits. Our technique is of importance in applications such as nonlinear optics and water waves since homoclinic orbits to saddle-centre equilibria describe embedded solitons (ESs) in systems of partial differential equations representing physical models, and except for special cases their existence has been previously studied only numerically using shooting methods and continuation techniques. We apply the general theory to two examples, a four-dimensional system describing ESs in nonlinear optical media and a six-dimensional system which can possess a one-parameter family of symmetric homoclinic orbits in the unperturbed case. For these examples, the analysis is compared with numerical computations and an excellent agreement between both results is found.

  15. A Review of Numerical Simulation and Analytical Modeling for Medical Devices Safety in MRI

    PubMed Central

    Kabil, J.; Belguerras, L.; Trattnig, S.; Pasquier, C.; Missoffe, A.

    2016-01-01

    Summary Objectives To review past and present challenges and ongoing trends in numerical simulation for MRI (Magnetic Resonance Imaging) safety evaluation of medical devices. Methods A wide literature review on numerical and analytical simulation on simple or complex medical devices in MRI electromagnetic fields shows the evolutions through time and a growing concern for MRI safety over the years. Major issues and achievements are described, as well as current trends and perspectives in this research field. Results Numerical simulation of medical devices is constantly evolving, supported by calculation methods now well-established. Implants with simple geometry can often be simulated in a computational human model, but one issue remaining today is the experimental validation of these human models. A great concern is to assess RF heating on implants too complex to be traditionally simulated, like pacemaker leads. Thus, ongoing researches focus on alternative hybrids methods, both numerical and experimental, with for example a transfer function method. For the static field and gradient fields, analytical models can be used for dimensioning simple implants shapes, but limited for complex geometries that cannot be studied with simplifying assumptions. Conclusions Numerical simulation is an essential tool for MRI safety testing of medical devices. The main issues remain the accuracy of simulations compared to real life and the studies of complex devices; but as the research field is constantly evolving, some promising ideas are now under investigation to take up the challenges. PMID:27830244

  16. On the numerical treatment of selected oscillatory evolutionary problems

    NASA Astrophysics Data System (ADS)

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

    2017-07-01

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

  17. Analytical treatment of gas flows through multilayer insulation, project 1

    NASA Technical Reports Server (NTRS)

    Lin, J. T.

    1972-01-01

    A theoretical investigation of gas flow inside a multilayer insulation system was made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was also investigated. It was shown that when the relaxation time is less than the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given and comparisons with experimental data were made.

  18. SToRM: A numerical model for environmental surface flows

    USGS Publications Warehouse

    Simoes, Francisco J.

    2009-01-01

    SToRM (System for Transport and River Modeling) is a numerical model developed to simulate free surface flows in complex environmental domains. It is based on the depth-averaged St. Venant equations, which are discretized using unstructured upwind finite volume methods, and contains both steady and unsteady solution techniques. This article provides a brief description of the numerical approach selected to discretize the governing equations in space and time, including important aspects of solving natural environmental flows, such as the wetting and drying algorithm. The presentation is illustrated with several application examples, covering both laboratory and natural river flow cases, which show the model’s ability to solve complex flow phenomena.

  19. Solution of quadratic matrix equations for free vibration analysis of structures.

    NASA Technical Reports Server (NTRS)

    Gupta, K. K.

    1973-01-01

    An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.

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

    Chen, Zheng; Huang, Hongying; Yan, Jue

    We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β 0,β 1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried outmore » to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.« less

  1. Mixed Arlequin method for multiscale poromechanics problems: Mixed Arlequin method for multiscale poromechanics problems

    DOE PAGES

    Sun, WaiChing; Cai, Zhijun; Choo, Jinhyun

    2016-11-18

    An Arlequin poromechanics model is introduced to simulate the hydro-mechanical coupling effects of fluid-infiltrated porous media across different spatial scales within a concurrent computational framework. A two-field poromechanics problem is first recast as the twofold saddle point of an incremental energy functional. We then introduce Lagrange multipliers and compatibility energy functionals to enforce the weak compatibility of hydro-mechanical responses in the overlapped domain. Here, to examine the numerical stability of this hydro-mechanical Arlequin model, we derive a necessary condition for stability, the twofold inf–sup condition for multi-field problems, and establish a modified inf–sup test formulated in the product space ofmore » the solution field. We verify the implementation of the Arlequin poromechanics model through benchmark problems covering the entire range of drainage conditions. Finally, through these numerical examples, we demonstrate the performance, robustness, and numerical stability of the Arlequin poromechanics model.« less

  2. Quadrature rules with multiple nodes for evaluating integrals with strong singularities

    NASA Astrophysics Data System (ADS)

    Milovanovic, Gradimir V.; Spalevic, Miodrag M.

    2006-05-01

    We present a method based on the Chakalov-Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turan quadrature rules, Numer. Algorithms 10 (1995), 27-39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhauser, Basel, 1999, pp. 109-119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.

  3. Dispersion analysis and measurement of circular cylindrical wedge-like acoustic waveguides.

    PubMed

    Yu, Tai-Ho

    2015-09-01

    This study investigated the propagation of flexural waves along the outer edge of a circular cylindrical wedge, the phase velocities, and the corresponding mode displacements. Thus far, only approximate solutions have been derived because the corresponding boundary-value problems are complex. In this study, dispersion curves were determined using the bi-dimensional finite element method and derived through the separation of variables and the Hamilton principle. Modal displacement calculations clarified that the maximal deformations appeared at the outer edge of the wedge tip. Numerical examples indicated how distinct thin-film materials deposited on the outer surface of the circular cylindrical wedge influenced the dispersion curves. Additionally, dispersion curves were measured using a laser-induced guided wave, a knife-edge measurement scheme, and a two-dimensional fast Fourier transform method. Both the numerical and experimental results correlated closely, thus validating the numerical solution. Copyright © 2015 Elsevier B.V. All rights reserved.

  4. A free energy-based surface tension force model for simulation of multiphase flows by level-set method

    NASA Astrophysics Data System (ADS)

    Yuan, H. Z.; Chen, Z.; Shu, C.; Wang, Y.; Niu, X. D.; Shu, S.

    2017-09-01

    In this paper, a free energy-based surface tension force (FESF) model is presented for accurately resolving the surface tension force in numerical simulation of multiphase flows by the level set method. By using the analytical form of order parameter along the normal direction to the interface in the phase-field method and the free energy principle, FESF model offers an explicit and analytical formulation for the surface tension force. The only variable in this formulation is the normal distance to the interface, which can be substituted by the distance function solved by the level set method. On one hand, as compared to conventional continuum surface force (CSF) model in the level set method, FESF model introduces no regularized delta function, due to which it suffers less from numerical diffusions and performs better in mass conservation. On the other hand, as compared to the phase field surface tension force (PFSF) model, the evaluation of surface tension force in FESF model is based on an analytical approach rather than numerical approximations of spatial derivatives. Therefore, better numerical stability and higher accuracy can be expected. Various numerical examples are tested to validate the robustness of the proposed FESF model. It turns out that FESF model performs better than CSF model and PFSF model in terms of accuracy, stability, convergence speed and mass conservation. It is also shown in numerical tests that FESF model can effectively simulate problems with high density/viscosity ratio, high Reynolds number and severe topological interfacial changes.

  5. Harmony search method: theory and applications.

    PubMed

    Gao, X Z; Govindasamy, V; Xu, H; Wang, X; Zenger, K

    2015-01-01

    The Harmony Search (HS) method is an emerging metaheuristic optimization algorithm, which has been employed to cope with numerous challenging tasks during the past decade. In this paper, the essential theory and applications of the HS algorithm are first described and reviewed. Several typical variants of the original HS are next briefly explained. As an example of case study, a modified HS method inspired by the idea of Pareto-dominance-based ranking is also presented. It is further applied to handle a practical wind generator optimal design problem.

  6. Engineering topological edge states in two dimensional magnetic photonic crystal

    NASA Astrophysics Data System (ADS)

    Yang, Bing; Wu, Tong; Zhang, Xiangdong

    2017-01-01

    Based on a perturbative approach, we propose a simple and efficient method to engineer the topological edge states in two dimensional magnetic photonic crystals. The topological edge states in the microstructures can be constructed and varied by altering the parameters of the microstructure according to the field-energy distributions of the Bloch states at the related Bloch wave vectors. The validity of the proposed method has been demonstrated by exact numerical calculations through three concrete examples. Our method makes the topological edge states "designable."

  7. Prediction of overall and blade-element performance for axial-flow pump configurations

    NASA Technical Reports Server (NTRS)

    Serovy, G. K.; Kavanagh, P.; Okiishi, T. H.; Miller, M. J.

    1973-01-01

    A method and a digital computer program for prediction of the distributions of fluid velocity and properties in axial flow pump configurations are described and evaluated. The method uses the blade-element flow model and an iterative numerical solution of the radial equilbrium and continuity conditions. Correlated experimental results are used to generate alternative methods for estimating blade-element turning and loss characteristics. Detailed descriptions of the computer program are included, with example input and typical computed results.

  8. MUSIC imaging method for electromagnetic inspection of composite multi-layers

    NASA Astrophysics Data System (ADS)

    Rodeghiero, Giacomo; Ding, Ping-Ping; Zhong, Yu; Lambert, Marc; Lesselier, Dominique

    2015-03-01

    A first-order asymptotic formulation of the electric field scattered by a small inclusion (with respect to the wavelength in dielectric regime or to the skin depth in conductive regime) embedded in composite material is given. It is validated by comparison with results obtained using a Method of Moments (MoM). A non-iterative MUltiple SIgnal Classification (MUSIC) imaging method is utilized in the same configuration to locate the position of small defects. The effectiveness of the imaging algorithm is illustrated through some numerical examples.

  9. UQTk Version 3.0.3 User Manual

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

    Sargsyan, Khachik; Safta, Cosmin; Chowdhary, Kamaljit Singh

    2017-05-01

    The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.0.3 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sen- sitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.

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

    NASA Technical Reports Server (NTRS)

    Noor, A. K.

    1981-01-01

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

  11. Method of locating related items in a geometric space for data mining

    DOEpatents

    Hendrickson, B.A.

    1999-07-27

    A method for locating related items in a geometric space transforms relationships among items to geometric locations. The method locates items in the geometric space so that the distance between items corresponds to the degree of relatedness. The method facilitates communication of the structure of the relationships among the items. The method is especially beneficial for communicating databases with many items, and with non-regular relationship patterns. Examples of such databases include databases containing items such as scientific papers or patents, related by citations or keywords. A computer system adapted for practice of the present invention can include a processor, a storage subsystem, a display device, and computer software to direct the location and display of the entities. The method comprises assigning numeric values as a measure of similarity between each pairing of items. A matrix is constructed, based on the numeric values. The eigenvectors and eigenvalues of the matrix are determined. Each item is located in the geometric space at coordinates determined from the eigenvectors and eigenvalues. Proper construction of the matrix and proper determination of coordinates from eigenvectors can ensure that distance between items in the geometric space is representative of the numeric value measure of the items' similarity. 12 figs.

  12. Method of locating related items in a geometric space for data mining

    DOEpatents

    Hendrickson, Bruce A.

    1999-01-01

    A method for locating related items in a geometric space transforms relationships among items to geometric locations. The method locates items in the geometric space so that the distance between items corresponds to the degree of relatedness. The method facilitates communication of the structure of the relationships among the items. The method is especially beneficial for communicating databases with many items, and with non-regular relationship patterns. Examples of such databases include databases containing items such as scientific papers or patents, related by citations or keywords. A computer system adapted for practice of the present invention can include a processor, a storage subsystem, a display device, and computer software to direct the location and display of the entities. The method comprises assigning numeric values as a measure of similarity between each pairing of items. A matrix is constructed, based on the numeric values. The eigenvectors and eigenvalues of the matrix are determined. Each item is located in the geometric space at coordinates determined from the eigenvectors and eigenvalues. Proper construction of the matrix and proper determination of coordinates from eigenvectors can ensure that distance between items in the geometric space is representative of the numeric value measure of the items' similarity.

  13. The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.

    PubMed

    Thamareerat, N; Luadsong, A; Aschariyaphotha, N

    2016-01-01

    In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.

  14. System equivalent model mixing

    NASA Astrophysics Data System (ADS)

    Klaassen, Steven W. B.; van der Seijs, Maarten V.; de Klerk, Dennis

    2018-05-01

    This paper introduces SEMM: a method based on Frequency Based Substructuring (FBS) techniques that enables the construction of hybrid dynamic models. With System Equivalent Model Mixing (SEMM) frequency based models, either of numerical or experimental nature, can be mixed to form a hybrid model. This model follows the dynamic behaviour of a predefined weighted master model. A large variety of applications can be thought of, such as the DoF-space expansion of relatively small experimental models using numerical models, or the blending of different models in the frequency spectrum. SEMM is outlined, both mathematically and conceptually, based on a notation commonly used in FBS. A critical physical interpretation of the theory is provided next, along with a comparison to similar techniques; namely DoF expansion techniques. SEMM's concept is further illustrated by means of a numerical example. It will become apparent that the basic method of SEMM has some shortcomings which warrant a few extensions to the method. One of the main applications is tested in a practical case, performed on a validated benchmark structure; it will emphasize the practicality of the method.

  15. Moving mesh finite element simulation for phase-field modeling of brittle fracture and convergence of Newton's iteration

    NASA Astrophysics Data System (ADS)

    Zhang, Fei; Huang, Weizhang; Li, Xianping; Zhang, Shicheng

    2018-03-01

    A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the decomposition of the strain tensor into tensile and compressive components is essential for the success of the phase-field modeling of brittle fracture but results in a non-smooth elastic energy and stronger nonlinearity in the governing equation. This makes the governing equation much more difficult to solve and, in particular, Newton's iteration often fails to converge. Three regularization methods are proposed to smooth out the decomposition of the strain tensor. Numerical examples of fracture propagation under quasi-static load demonstrate that all of the methods can effectively improve the convergence of Newton's iteration for relatively small values of the regularization parameter but without compromising the accuracy of the numerical solution. They also show that the moving mesh finite element method is able to adaptively concentrate the mesh elements around propagating cracks and handle multiple and complex crack systems.

  16. Essentially nonoscillatory postprocessing filtering methods

    NASA Technical Reports Server (NTRS)

    Lafon, F.; Osher, S.

    1992-01-01

    High order accurate centered flux approximations used in the computation of numerical solutions to nonlinear partial differential equations produce large oscillations in regions of sharp transitions. Here, we present a new class of filtering methods denoted by Essentially Nonoscillatory Least Squares (ENOLS), which constructs an upgraded filtered solution that is close to the physically correct weak solution of the original evolution equation. Our method relies on the evaluation of a least squares polynomial approximation to oscillatory data using a set of points which is determined via the ENO network. Numerical results are given in one and two space dimensions for both scalar and systems of hyperbolic conservation laws. Computational running time, efficiency, and robustness of method are illustrated in various examples such as Riemann initial data for both Burgers' and Euler's equations of gas dynamics. In all standard cases, the filtered solution appears to converge numerically to the correct solution of the original problem. Some interesting results based on nonstandard central difference schemes, which exactly preserve entropy, and have been recently shown generally not to be weakly convergent to a solution of the conservation law, are also obtained using our filters.

  17. 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 presented to compare the output from the MCPI library to current state-of-practice numerical integration methods. It is shown that MCPI is capable of out-performing the state-of-practice in terms of computational cost and accuracy.

  18. Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

    NASA Astrophysics Data System (ADS)

    Chen, Z.; Shu, C.; Tan, D.

    2018-05-01

    An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

  19. The L sub 1 finite element method for pure convection problems

    NASA Technical Reports Server (NTRS)

    Jiang, Bo-Nan

    1991-01-01

    The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.

  20. Fractional dynamics of charged particles in magnetic fields

    NASA Astrophysics Data System (ADS)

    Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Alvarado-Méndez, E.; Guerrero-Ramírez, G. V.; Escobar-Jiménez, R. F.

    2016-02-01

    In many physical applications the electrons play a relevant role. For example, when a beam of electrons accelerated to relativistic velocities is used as an active medium to generate Free Electron Lasers (FEL), the electrons are bound to atoms, but move freely in a magnetic field. The relaxation time, longitudinal effects and transverse variations of the optical field are parameters that play an important role in the efficiency of this laser. The electron dynamics in a magnetic field is a means of radiation source for coupling to the electric field. The transverse motion of the electrons leads to either gain or loss energy from or to the field, depending on the position of the particle regarding the phase of the external radiation field. Due to the importance to know with great certainty the displacement of charged particles in a magnetic field, in this work we study the fractional dynamics of charged particles in magnetic fields. Newton’s second law is considered and the order of the fractional differential equation is (0;1]. Based on the Grünwald-Letnikov (GL) definition, the discretization of fractional differential equations is reported to get numerical simulations. Comparison between the numerical solutions obtained on Euler’s numerical method for the classical case and the GL definition in the fractional approach proves the good performance of the numerical scheme applied. Three application examples are shown: constant magnetic field, ramp magnetic field and harmonic magnetic field. In the first example the results obtained show bistability. Dissipative effects are observed in the system and the standard dynamic is recovered when the order of the fractional derivative is 1.

  1. An asymptotic unsteady lifting-line theory with energetics and optimum motion of thrust-producing lifting surfaces. Thesis

    NASA Technical Reports Server (NTRS)

    Ahmadi, A. R.

    1981-01-01

    A low frequency unsteady lifting-line theory is developed for a harmonically oscillating wing of large aspect ratio. The wing is assumed to be chordwise rigid but completely flexible in the span direction. The theory is developed by use of the method of matched asymptotic expansions which reduces the problem from a singular integral equation to quadrature. The wing displacements are prescribed and the pressure field, airloads, and unsteady induced downwash are obtained in closed form. The influence of reduced frequency, aspect ratio, planform shape, and mode of oscillation on wing aerodynamics is demonstrated through numerical examples. Compared with lifting-surface theory, computation time is reduced significantly. Using the present theory, the energetic quantities associated with the propulsive performance of a finite wing oscillating in combined pitch and heave are obtained in closed form. Numerical examples are presented for an elliptic wing.

  2. Effects of Variable Inflationary Conditions on AN Inventory Model with Inflation-Proportional Demand Rate

    NASA Astrophysics Data System (ADS)

    Mirzazadeh, Abolfazl

    2009-08-01

    The inflation rate in the most of the previous researches has been considered constant and well-known over the time horizon, although the future rate of inflation is inherently uncertain and unstable, and is difficult to predict it accurately. Therefore, A time varying inventory model for deteriorating items with allowable shortages is developed in this paper. The inflation rates (internal and external) are time-dependent and demand rate is inflation-proportional. The inventory level is described by differential equations over the time horizon and present value method is used. The numerical example is given to explain the results. Some particular cases, which follow the main problem, will discuss and the results will compare with the main model by using the numerical examples. It has been achieved which shortages increases considerably in comparison with the case of without variable inflationary conditions.

  3. Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

    NASA Astrophysics Data System (ADS)

    Huang, Zhi-Xiang; Wu, Xian-Liang

    Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

  4. Efficient calibration for imperfect computer models

    DOE PAGES

    Tuo, Rui; Wu, C. F. Jeff

    2015-12-01

    Many computer models contain unknown parameters which need to be estimated using physical observations. Furthermore, the calibration method based on Gaussian process models may lead to unreasonable estimate for imperfect computer models. In this work, we extend their study to calibration problems with stochastic physical data. We propose a novel method, called the L 2 calibration, and show its semiparametric efficiency. The conventional method of the ordinary least squares is also studied. Theoretical analysis shows that it is consistent but not efficient. Here, numerical examples show that the proposed method outperforms the existing ones.

  5. Delay-slope-dependent stability results of recurrent neural networks.

    PubMed

    Li, Tao; Zheng, Wei Xing; Lin, Chong

    2011-12-01

    By using the fact that the neuron activation functions are sector bounded and nondecreasing, this brief presents a new method, named the delay-slope-dependent method, for stability analysis of a class of recurrent neural networks with time-varying delays. This method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed Lyapunov-Krasovskii functional. Then some improved delay-dependent stability criteria with less computational burden and conservatism are obtained. Numerical examples are given to illustrate the effectiveness and the benefits of the proposed method.

  6. Boundedness and convergence of online gradient method with penalty for feedforward neural networks.

    PubMed

    Zhang, Huisheng; Wu, Wei; Liu, Fei; Yao, Mingchen

    2009-06-01

    In this brief, we consider an online gradient method with penalty for training feedforward neural networks. Specifically, the penalty is a term proportional to the norm of the weights. Its roles in the method are to control the magnitude of the weights and to improve the generalization performance of the network. By proving that the weights are automatically bounded in the network training with penalty, we simplify the conditions that are required for convergence of online gradient method in literature. A numerical example is given to support the theoretical analysis.

  7. On Numerical Heating

    NASA Astrophysics Data System (ADS)

    Liou, Meng-Sing

    2013-11-01

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

  8. Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems.

    PubMed

    Wolf, Elizabeth Skubak; Anderson, David F

    2015-01-21

    Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations of model output quantities with respect to model parameters, are useful in this setting for a variety of applications. In this paper, we introduce a class of hybrid pathwise differentiation methods for the numerical estimation of parametric sensitivities. The new hybrid methods combine elements from the three main classes of procedures for sensitivity estimation and have a number of desirable qualities. First, the new methods are unbiased for a broad class of problems. Second, the methods are applicable to nearly any physically relevant biochemical CTMC model. Third, and as we demonstrate on several numerical examples, the new methods are quite efficient, particularly if one wishes to estimate the full gradient of parametric sensitivities. The methods are rather intuitive and utilize the multilevel Monte Carlo philosophy of splitting an expectation into separate parts and handling each in an efficient manner.

  9. Numerical Exposure Assessment Method for Low Frequency Range and Application to Wireless Power Transfer.

    PubMed

    Park, SangWook; Kim, Minhyuk

    2016-01-01

    In this paper, a numerical exposure assessment method is presented for a quasi-static analysis by the use of finite-difference time-domain (FDTD) algorithm. The proposed method is composed of scattered field FDTD method and quasi-static approximation for analyzing of the low frequency band electromagnetic problems. The proposed method provides an effective tool to compute induced electric fields in an anatomically realistic human voxel model exposed to an arbitrary non-uniform field source in the low frequency ranges. The method is verified, and excellent agreement with theoretical solutions is found for a dielectric sphere model exposed to a magnetic dipole source. The assessment method serves a practical example of the electric fields, current densities, and specific absorption rates induced in a human head and body in close proximity to a 150-kHz wireless power transfer system for cell phone charging. The results are compared to the limits recommended by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and the IEEE standard guidelines.

  10. Numerical Exposure Assessment Method for Low Frequency Range and Application to Wireless Power Transfer

    PubMed Central

    Kim, Minhyuk

    2016-01-01

    In this paper, a numerical exposure assessment method is presented for a quasi-static analysis by the use of finite-difference time-domain (FDTD) algorithm. The proposed method is composed of scattered field FDTD method and quasi-static approximation for analyzing of the low frequency band electromagnetic problems. The proposed method provides an effective tool to compute induced electric fields in an anatomically realistic human voxel model exposed to an arbitrary non-uniform field source in the low frequency ranges. The method is verified, and excellent agreement with theoretical solutions is found for a dielectric sphere model exposed to a magnetic dipole source. The assessment method serves a practical example of the electric fields, current densities, and specific absorption rates induced in a human head and body in close proximity to a 150-kHz wireless power transfer system for cell phone charging. The results are compared to the limits recommended by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and the IEEE standard guidelines. PMID:27898688

  11. Numerical solution of the exact cavity equations of motion for an unstable optical resonator.

    PubMed

    Bowers, M S; Moody, S E

    1990-09-20

    We solve numerically, we believe for the first time, the exact cavity equations of motion for a realistic unstable resonator with a simple gain saturation model. The cavity equations of motion, first formulated by Siegman ["Exact Cavity Equations for Lasers with Large Output Coupling," Appl. Phys. Lett. 36, 412-414 (1980)], and which we term the dynamic coupled modes (DCM) method of solution, solve for the full 3-D time dependent electric field inside the optical cavity by expanding the field in terms of the actual diffractive transverse eigenmodes of the bare (gain free) cavity with time varying coefficients. The spatially varying gain serves to couple the bare cavity transverse modes and to scatter power from mode to mode. We show that the DCM method numerically converges with respect to the number of eigenmodes in the basis set. The intracavity intensity in the numerical example shown reaches a steady state, and this steady state distribution is compared with that computed from the traditional Fox and Li approach using a fast Fourier transform propagation algorithm. The output wavefronts from both methods are quite similar, and the computed output powers agree to within 10%. The usefulness and advantages of using this method for predicting the output of a laser, especially pulsed lasers used for coherent detection, are discussed.

  12. Topology optimization of thermal fluid flows with an adjoint Lattice Boltzmann Method

    NASA Astrophysics Data System (ADS)

    Dugast, Florian; Favennec, Yann; Josset, Christophe; Fan, Yilin; Luo, Lingai

    2018-07-01

    This paper presents an adjoint Lattice Boltzmann Method (LBM) coupled with the Level-Set Method (LSM) for topology optimization of thermal fluid flows. The adjoint-state formulation implies discrete velocity directions in order to take into account the LBM boundary conditions. These boundary conditions are introduced at the beginning of the adjoint-state method as the LBM residuals, so that the adjoint-state boundary conditions can appear directly during the adjoint-state equation formulation. The proposed method is tested with 3 numerical examples concerning thermal fluid flows, but with different objectives: minimization of the mean temperature in the domain, maximization of the heat evacuated by the fluid, and maximization of the heat exchange with heated solid parts. This latter example, treated in several articles, is used to validate our method. In these optimization problems, a limitation of the maximal pressure drop and of the porosity (number of fluid elements) is also applied. The obtained results demonstrate that the method is robust and effective for solving topology optimization of thermal fluid flows.

  13. Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries

    NASA Astrophysics Data System (ADS)

    Xu, Ao; Shyy, Wei; Zhao, Tianshou

    2017-06-01

    Fuel cells and flow batteries are promising technologies to address climate change and air pollution problems. An understanding of the complex multiscale and multiphysics transport phenomena occurring in these electrochemical systems requires powerful numerical tools. Over the past decades, the lattice Boltzmann (LB) method has attracted broad interest in the computational fluid dynamics and the numerical heat transfer communities, primarily due to its kinetic nature making it appropriate for modeling complex multiphase transport phenomena. More importantly, the LB method fits well with parallel computing due to its locality feature, which is required for large-scale engineering applications. In this article, we review the LB method for gas-liquid two-phase flows, coupled fluid flow and mass transport in porous media, and particulate flows. Examples of applications are provided in fuel cells and flow batteries. Further developments of the LB method are also outlined.

  14. Practical Bayesian tomography

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

  15. Bridges for Pedestrians with Random Parameters using the Stochastic Finite Elements Analysis

    NASA Astrophysics Data System (ADS)

    Szafran, J.; Kamiński, M.

    2017-02-01

    The main aim of this paper is to present a Stochastic Finite Element Method analysis with reference to principal design parameters of bridges for pedestrians: eigenfrequency and deflection of bridge span. They are considered with respect to random thickness of plates in boxed-section bridge platform, Young modulus of structural steel and static load resulting from crowd of pedestrians. The influence of the quality of the numerical model in the context of traditional FEM is shown also on the example of a simple steel shield. Steel structures with random parameters are discretized in exactly the same way as for the needs of traditional Finite Element Method. Its probabilistic version is provided thanks to the Response Function Method, where several numerical tests with random parameter values varying around its mean value enable the determination of the structural response and, thanks to the Least Squares Method, its final probabilistic moments.

  16. A compensation controller based on a regional pole-assignment method for AMD control systems with a time-varying delay

    NASA Astrophysics Data System (ADS)

    Li, Zuohua; Chen, Chaojun; Teng, Jun; Wang, Ying

    2018-04-01

    Active mass damper/driver (AMD) control system has been proposed as an effective tool for high-rise buildings to resist strong dynamic loads. However, such disadvantage as time-varying delay in AMD control systems impedes their application in practices. Time-varying delay, which has an effect on the performance and stability of single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems, is considered in the paper. In addition, a new time-delay compensation controller based on regional pole-assignment method is presented. To verify its effectiveness, the proposed method is applied to a numerical example of a ten-storey frame and an experiment of a single span four-storey steel frame. Both numerical and experimental results demonstrate that the proposed method can enhance the performances of an AMD control system with time-varying delays.

  17. Introducing a new family of short-range potentials and their numerical solutions using the asymptotic iteration method

    NASA Astrophysics Data System (ADS)

    Assi, I. A.; Sous, A. J.

    2018-05-01

    The goal of this work is to derive a new class of short-range potentials that could have a wide range of physical applications, specially in molecular physics. The tridiagonal representation approach has been developed beyond its limitations to produce new potentials by requiring the representation of the Schrödinger wave operator to be multidiagonal and symmetric. This produces a family of Hulthén potentials that has a specific structure, as mentioned in the introduction. As an example, we have solved the nonrelativistic wave equation for the new four-parameter short-range screening potential numerically using the asymptotic iteration method, where we tabulated the eigenvalues for both s -wave and arbitrary l -wave cases in tables.

  18. Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

    NASA Technical Reports Server (NTRS)

    Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

    2011-01-01

    A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

  19. Development of Condensing Mesh Method for Corner Domain at Numerical Simulation Magnetic System

    NASA Astrophysics Data System (ADS)

    Perepelkin, E.; Tarelkin, A.; Polyakova, R.; Kovalenko, A.

    2018-05-01

    A magnetostatic problem arises in searching for the distribution of the magnetic field generated by magnet systems of many physics research facilities, e.g., accelerators. The domain in which the boundaryvalue problem is solved often has a piecewise smooth boundary. In this case, numerical calculations of the problem require the consideration of the solution behavior in the corner domain. In this work we obtained the upper estimation of the magnetic field growth and propose a method of condensing the differential grid near the corner domain of vacuum in case of 3-dimensional space based on this estimation. An example of calculating a real model problem for SDP NICA in the domain containing a corner point is given.

  20. A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

    NASA Technical Reports Server (NTRS)

    Xu, Kun

    1999-01-01

    A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.

  1. Effect of faulting on ground-water movement in the Death Valley Region, Nevada and California

    USGS Publications Warehouse

    Faunt, Claudia C.

    1997-01-01

    The current crustal stress field was combined with fault orientations to predict potential effects of faults on the regional groundwater flow regime. Numerous examples of faultcontrolled ground-water flow exist within the study area. Hydrologic data provided an independent method for checking some of the assumptions concerning preferential flow paths.

  2. Spin dynamics in storage rings and linear accelerators

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

    Irwin, J.

    1994-12-01

    The purpose of these lectures is to survey the subject of spin dynamics in accelerators: to give a sense of the underlying physics, the typical analytic and numeric methods used, and an overview of results achieved. Consideration will be limited to electrons and protons. Examples of experimental and theoretical results in both linear and circular machines are included.

  3. Classical and all-floating FETI methods for the simulation of arterial tissues

    PubMed Central

    Augustin, Christoph M.; Holzapfel, Gerhard A.; Steinbach, Olaf

    2015-01-01

    High-resolution and anatomically realistic computer models of biological soft tissues play a significant role in the understanding of the function of cardiovascular components in health and disease. However, the computational effort to handle fine grids to resolve the geometries as well as sophisticated tissue models is very challenging. One possibility to derive a strongly scalable parallel solution algorithm is to consider finite element tearing and interconnecting (FETI) methods. In this study we propose and investigate the application of FETI methods to simulate the elastic behavior of biological soft tissues. As one particular example we choose the artery which is – as most other biological tissues – characterized by anisotropic and nonlinear material properties. We compare two specific approaches of FETI methods, classical and all-floating, and investigate the numerical behavior of different preconditioning techniques. In comparison to classical FETI, the all-floating approach has not only advantages concerning the implementation but in many cases also concerning the convergence of the global iterative solution method. This behavior is illustrated with numerical examples. We present results of linear elastic simulations to show convergence rates, as expected from the theory, and results from the more sophisticated nonlinear case where we apply a well-known anisotropic model to the realistic geometry of an artery. Although the FETI methods have a great applicability on artery simulations we will also discuss some limitations concerning the dependence on material parameters. PMID:26751957

  4. Computer modeling of the mechanical behavior of composites -- Interfacial cracks in fiber-reinforced materials

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

    Schmauder, S.; Haake, S.; Mueller, W.H.

    Computer modeling of materials and especially modeling the mechanical behavior of composites became increasingly popular in the past few years. Among them are examples of micromechanical modeling of real structures as well as idealized model structures of linear elastic and elasto-plastic material response. In this paper, Erdogan`s Integral Equation Method (IEM) is chosen as an example for a powerful method providing principle insight into elastic fracture mechanical situations. IEM or, alternatively, complex function techniques sometimes even allow for deriving analytical solutions such as in the case of a circumferential crack along a fiber/matrix interface. The analytical formulae of this interfacemore » crack will be analyzed numerically and typical results will be presented graphically.« less

  5. Effects of viscosity on shock-induced damping of an initial sinusoidal disturbance

    NASA Astrophysics Data System (ADS)

    Ma, Xiaojuan; Liu, Fusheng; Jing, Fuqian

    2010-05-01

    A lack of reliable data treatment method has been for several decades the bottleneck of viscosity measurement by disturbance amplitude damping method of shock waves. In this work the finite difference method is firstly applied to obtain the numerical solutions for disturbance amplitude damping behavior of sinusoidal shock front in inviscid and viscous flow. When water shocked to 15 GPa is taken as an example, the main results are as follows: (1) For inviscid and lower viscous flows the numerical method gives results in good agreement with the analytic solutions under the condition of small disturbance ( a 0/ λ=0.02); (2) For the flow of viscosity beyond 200 Pa s ( η = κ) the analytic solution is found to overestimate obviously the effects of viscosity. It is attributed to the unreal pre-conditions of analytic solution by Miller and Ahrens; (3) The present numerical method provides an effective tool with more confidence to overcome the bottleneck of data treatment when the effects of higher viscosity in experiments of Sakharov and flyer impact are expected to be analyzed, because it can in principle simulate the development of shock waves in flows with larger disturbance amplitude, higher viscosity, and complicated initial flow.

  6. The origin of spurious solutions in computational electromagnetics

    NASA Technical Reports Server (NTRS)

    Jiang, Bo-Nan; Wu, Jie; Povinelli, L. A.

    1995-01-01

    The origin of spurious solutions in computational electromagnetics, which violate the divergence equations, is deeply rooted in a misconception about the first-order Maxwell's equations and in an incorrect derivation and use of the curl-curl equations. The divergence equations must be always included in the first-order Maxwell's equations to maintain the ellipticity of the system in the space domain and to guarantee the uniqueness of the solution and/or the accuracy of the numerical solutions. The div-curl method and the least-squares method provide rigorous derivation of the equivalent second-order Maxwell's equations and their boundary conditions. The node-based least-squares finite element method (LSFEM) is recommended for solving the first-order full Maxwell equations directly. Examples of the numerical solutions by LSFEM for time-harmonic problems are given to demonstrate that the LSFEM is free of spurious solutions.

  7. Numerical marching techniques for fluid flows with heat transfer

    NASA Technical Reports Server (NTRS)

    Hornbeck, R. W.

    1973-01-01

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

  8. A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics

    NASA Astrophysics Data System (ADS)

    Brovont, Aaron D.

    The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.

  9. Recent progress in inverse methods in France

    NASA Technical Reports Server (NTRS)

    Bry, Pierre-Francois; Jacquotte, Olivier-Pierre; Lepape, Marie-Claire

    1991-01-01

    Given the current level of jet engine performance, improvement of the various turbomachinery components requires the use of advanced methods in aerodynamics, heat transfer, and aeromechanics. In particular, successful blade design can only be achieved via numerical design methods which make it possible to reach optimized solutions in a much shorter time than ever before. Two design methods which are currently being used throughout the French turbomachinery industry to obtain optimized blade geometries are presented. Examples are presented for compressor and turbine applications. The status of these methods as far as improvement and extension to new fields of applications is also reported.

  10. Random learning units using WIRIS quizzes in Moodle

    NASA Astrophysics Data System (ADS)

    Mora, Ángel; Mérida, Enrique; Eixarch, Ramon

    2011-09-01

    Moodle is an extended learning management system for developing learning units, including mathematically-based subjects. A wide variety of material can be developed in Moodle which contains facilities for forums, questionnaires, lessons, tasks, wikis, glossaries and chats. Therefore, the Moodle platform provides a meeting point for those working in a mathematics course. Mathematics requires special materials and activities: The material must include mathematical objects and the activities included in the virtual course must be able to do mathematical computations. WIRIS is a powerful software for educational environments. It has libraries for calculus, algebra, geometry and much more. In this article, examples showing the use of WIRIS in numerical methods and examples of using a new tool, WIRIS quizzes, are illustrated. By enhancing Moodle with WIRIS, we can add random learning questions to modules. Moodle has a simpler version of this capability, but WIRIS extends the method in which the random material is presented to the students. Random objects can appear in a question, in a variable of a question, in a plot or in the definition of a mathematical object. This article illustrates material prepared for numerical methods using a WIRIS library integrated in WIRIS quizzes. As a result, WIRIS in Moodle can be considered as a global solution for mathematics education.

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

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1989-01-01

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

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

    Li, C.; Yu, G.; Wang, K.

    The physical designs of the new concept reactors which have complex structure, various materials and neutronic energy spectrum, have greatly improved the requirements to the calculation methods and the corresponding computing hardware. Along with the widely used parallel algorithm, heterogeneous platforms architecture has been introduced into numerical computations in reactor physics. Because of the natural parallel characteristics, the CPU-FPGA architecture is often used to accelerate numerical computation. This paper studies the application and features of this kind of heterogeneous platforms used in numerical calculation of reactor physics through practical examples. After the designed neutron diffusion module based on CPU-FPGA architecturemore » achieves a 11.2 speed up factor, it is proved to be feasible to apply this kind of heterogeneous platform into reactor physics. (authors)« less

  13. A tool for simulating collision probabilities of animals with marine renewable energy devices.

    PubMed

    Schmitt, Pál; Culloch, Ross; Lieber, Lilian; Molander, Sverker; Hammar, Linus; Kregting, Louise

    2017-01-01

    The mathematical problem of establishing a collision probability distribution is often not trivial. The shape and motion of the animal as well as of the the device must be evaluated in a four-dimensional space (3D motion over time). Earlier work on wind and tidal turbines was limited to a simplified two-dimensional representation, which cannot be applied to many new structures. We present a numerical algorithm to obtain such probability distributions using transient, three-dimensional numerical simulations. The method is demonstrated using a sub-surface tidal kite as an example. Necessary pre- and post-processing of the data created by the model is explained, numerical details and potential issues and limitations in the application of resulting probability distributions are highlighted.

  14. Numerical Investigation of the Performance of a Supersonic Combustion Chamber and Comparison with Experiments

    NASA Astrophysics Data System (ADS)

    Banica, M. C.; Chun, J.; Scheuermann, T.; Weigand, B.; Wolfersdorf, J. v.

    2009-01-01

    Scramjet powered vehicles can decrease costs for access to space but substantial obstacles still exist in their realization. For example, experiments in the relevant Mach number regime are difficult to perform and flight testing is expensive. Therefore, numerical methods are often employed for system layout but they require validation against experimental data. Here, we validate the commercial code CFD++ against experimental results for hydrogen combustion in the supersonic combustion facility of the Institute of Aerospace Thermodynamics (ITLR) at the Universität Stuttgart. Fuel is injected through a lobed a strut injector, which provides rapid mixing. Our numerical data shows reasonable agreement with experiments. We further investigate effects of varying equivalence ratios on several important performance parameters.

  15. Direct discontinuous Galerkin method and its variations for second order elliptic equations

    DOE PAGES

    Huang, Hongying; Chen, Zheng; Li, Jin; ...

    2016-08-23

    In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L 2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Mathmore » 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.« less

  16. Direct discontinuous Galerkin method and its variations for second order elliptic equations

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

    Huang, Hongying; Chen, Zheng; Li, Jin

    In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L 2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Mathmore » 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.« less

  17. A level-set method for two-phase flows with moving contact line and insoluble surfactant

    NASA Astrophysics Data System (ADS)

    Xu, Jian-Jun; Ren, Weiqing

    2014-04-01

    A level-set method for two-phase flows with moving contact line and insoluble surfactant is presented. The mathematical model consists of the Navier-Stokes equation for the flow field, a convection-diffusion equation for the surfactant concentration, together with the Navier boundary condition and a condition for the dynamic contact angle derived by Ren et al. (2010) [37]. The numerical method is based on the level-set continuum surface force method for two-phase flows with surfactant developed by Xu et al. (2012) [54] with some cautious treatment for the boundary conditions. The numerical method consists of three components: a flow solver for the velocity field, a solver for the surfactant concentration, and a solver for the level-set function. In the flow solver, the surface force is dealt with using the continuum surface force model. The unbalanced Young stress at the moving contact line is incorporated into the Navier boundary condition. A convergence study of the numerical method and a parametric study are presented. The influence of surfactant on the dynamics of the moving contact line is illustrated using examples. The capability of the level-set method to handle complex geometries is demonstrated by simulating a pendant drop detaching from a wall under gravity.

  18. 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.

  19. Operational modal analysis using SVD of power spectral density transmissibility matrices

    NASA Astrophysics Data System (ADS)

    Araújo, Iván Gómez; Laier, Jose Elias

    2014-05-01

    This paper proposes the singular value decomposition of power spectrum density transmissibility matrices with different references, (PSDTM-SVD), as an identification method of natural frequencies and mode shapes of a dynamic system subjected to excitations under operational conditions. At the system poles, the rows of the proposed transmissibility matrix converge to the same ratio of amplitudes of vibration modes. As a result, the matrices are linearly dependent on the columns, and their singular values converge to zero. Singular values are used to determine the natural frequencies, and the first left singular vectors are used to estimate mode shapes. A numerical example of the finite element model of a beam subjected to colored noise excitation is analyzed to illustrate the accuracy of the proposed method. Results of the PSDTM-SVD method in the numerical example are compared with obtained using frequency domain decomposition (FDD) and power spectrum density transmissibility (PSDT). It is demonstrated that the proposed method does not depend on the excitation characteristics contrary to the FDD method that assumes white noise excitation, and further reduces the risk to identify extra non-physical poles in comparison to the PSDT method. Furthermore, a case study is performed using data from an operational vibration test of a bridge with a simply supported beam system. The real application of a full-sized bridge has shown that the proposed PSDTM-SVD method is able to identify the operational modal parameter. Operational modal parameters identified by the PSDTM-SVD in the real application agree well those identified by the FDD and PSDT methods.

  20. Singularity in structural optimization

    NASA Technical Reports Server (NTRS)

    Patnaik, S. N.; Guptill, J. D.; Berke, L.

    1993-01-01

    The conditions under which global and local singularities may arise in structural optimization are examined. Examples of these singularities are presented, and a framework is given within which the singularities can be recognized. It is shown, in particular, that singularities can be identified through the analysis of stress-displacement relations together with compatibility conditions or the displacement-stress relations derived by the integrated force method of structural analysis. Methods of eliminating the effects of singularities are suggested and illustrated numerically.

  1. Long-time predictions in nonlinear dynamics

    NASA Technical Reports Server (NTRS)

    Szebehely, V.

    1980-01-01

    It is known that nonintegrable dynamical systems do not allow precise predictions concerning their behavior for arbitrary long times. The available series solutions are not uniformly convergent according to Poincare's theorem and numerical integrations lose their meaningfulness after the elapse of arbitrary long times. Two approaches are the use of existing global integrals and statistical methods. This paper presents a generalized method along the first approach. As examples long-time predictions in the classical gravitational satellite and planetary problems are treated.

  2. Calculation of the aerodynamic loading of swept and unswept flexible wings of arbitrary stiffness

    NASA Technical Reports Server (NTRS)

    Diederich, Franklin W

    1950-01-01

    A method is presented for calculating the aerodynamic loading, the divergence speed, and certain stability derivatives of swept and unswept wings and tail surfaces of arbitrary stiffness. Provision is made for using either stiffness curves and root rotation constants or structural influence coefficients in the analysis. Computing forms, tables of numerical constants required in the analysis, and an illustrative example are included to facilitate calculations by means of the method.

  3. System Simulation by Recursive Feedback: Coupling A Set of Stand-Alone Subsystem Simulations

    NASA Technical Reports Server (NTRS)

    Nixon, Douglas D.; Hanson, John M. (Technical Monitor)

    2002-01-01

    Recursive feedback is defined and discussed as a framework for development of specific algorithms and procedures that propagate the time-domain solution for a dynamical system simulation consisting of multiple numerically coupled self-contained stand-alone subsystem simulations. A satellite motion example containing three subsystems (other dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Centralized and distributed versions of coupling structure have been addressed. Numerical results are evaluated by direct comparison with a standard total-system simultaneous-solution approach.

  4. The stability issues in problems of mathematical modeling

    NASA Astrophysics Data System (ADS)

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

    2018-03-01

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

  5. A new operational approach for solving fractional variational problems depending on indefinite integrals

    NASA Astrophysics Data System (ADS)

    Ezz-Eldien, S. S.; Doha, E. H.; Bhrawy, A. H.; El-Kalaawy, A. A.; Machado, J. A. T.

    2018-04-01

    In this paper, we propose a new accurate and robust numerical technique to approximate the solutions of fractional variational problems (FVPs) depending on indefinite integrals with a type of fixed Riemann-Liouville fractional integral. The proposed technique is based on the shifted Chebyshev polynomials as basis functions for the fractional integral operational matrix (FIOM). Together with the Lagrange multiplier method, these problems are then reduced to a system of algebraic equations, which greatly simplifies the solution process. Numerical examples are carried out to confirm the accuracy, efficiency and applicability of the proposed algorithm

  6. Biomimicry in textiles: past, present and potential. An overview

    PubMed Central

    Eadie, Leslie; Ghosh, Tushar K.

    2011-01-01

    The natural world around us provides excellent examples of functional systems built with a handful of materials. Throughout the millennia, nature has evolved to adapt and develop highly sophisticated methods to solve problems. There are numerous examples of functional surfaces, fibrous structures, structural colours, self-healing, thermal insulation, etc., which offer important lessons for the textile products of the future. This paper provides a general overview of the potential of bioinspired textile structures by highlighting a few specific examples of pertinent, inherently sustainable biological systems. Biomimetic research is a rapidly growing field and its true potential in the development of new and sustainable textiles can only be realized through interdisciplinary research rooted in a holistic understanding of nature. PMID:21325320

  7. Biomimicry in textiles: past, present and potential. An overview.

    PubMed

    Eadie, Leslie; Ghosh, Tushar K

    2011-06-06

    The natural world around us provides excellent examples of functional systems built with a handful of materials. Throughout the millennia, nature has evolved to adapt and develop highly sophisticated methods to solve problems. There are numerous examples of functional surfaces, fibrous structures, structural colours, self-healing, thermal insulation, etc., which offer important lessons for the textile products of the future. This paper provides a general overview of the potential of bioinspired textile structures by highlighting a few specific examples of pertinent, inherently sustainable biological systems. Biomimetic research is a rapidly growing field and its true potential in the development of new and sustainable textiles can only be realized through interdisciplinary research rooted in a holistic understanding of nature. © 2011 The Royal Society

  8. Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

    DOE PAGES

    Lu, Zhiming

    2018-01-30

    Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, wemore » derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.« less

  9. An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry

    NASA Astrophysics Data System (ADS)

    Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A.

    2017-07-01

    We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.

  10. Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

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

    Lu, Zhiming

    Sensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g. hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, wemore » derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. Finally, the approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.« less

  11. A higher order numerical method for time fractional partial differential equations with nonsmooth data

    NASA Astrophysics Data System (ADS)

    Xing, Yanyuan; Yan, Yubin

    2018-03-01

    Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

  12. A multiresolution method for climate system modeling: application of spherical centroidal Voronoi tessellations

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

    Ringler, Todd; Ju, Lili; Gunzburger, Max

    2008-11-14

    During the next decade and beyond, climate system models will be challenged to resolve scales and processes that are far beyond their current scope. Each climate system component has its prototypical example of an unresolved process that may strongly influence the global climate system, ranging from eddy activity within ocean models, to ice streams within ice sheet models, to surface hydrological processes within land system models, to cloud processes within atmosphere models. These new demands will almost certainly result in the develop of multiresolution schemes that are able, at least regionally, to faithfully simulate these fine-scale processes. Spherical centroidal Voronoimore » tessellations (SCVTs) offer one potential path toward the development of a robust, multiresolution climate system model components. SCVTs allow for the generation of high quality Voronoi diagrams and Delaunay triangulations through the use of an intuitive, user-defined density function. In each of the examples provided, this method results in high-quality meshes where the quality measures are guaranteed to improve as the number of nodes is increased. Real-world examples are developed for the Greenland ice sheet and the North Atlantic ocean. Idealized examples are developed for ocean–ice shelf interaction and for regional atmospheric modeling. In addition to defining, developing, and exhibiting SCVTs, we pair this mesh generation technique with a previously developed finite-volume method. Our numerical example is based on the nonlinear, shallow water equations spanning the entire surface of the sphere. This example is used to elucidate both the potential benefits of this multiresolution method and the challenges ahead.« less

  13. The theoretical study of passive and active optical devices via planewave based transfer (scattering) matrix method and other approaches

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

    Zhuo, Ye

    2011-01-01

    In this thesis, we theoretically study the electromagnetic wave propagation in several passive and active optical components and devices including 2-D photonic crystals, straight and curved waveguides, organic light emitting diodes (OLEDs), and etc. Several optical designs are also presented like organic photovoltaic (OPV) cells and solar concentrators. The first part of the thesis focuses on theoretical investigation. First, the plane-wave-based transfer (scattering) matrix method (TMM) is briefly described with a short review of photonic crystals and other numerical methods to study them (Chapter 1 and 2). Next TMM, the numerical method itself is investigated in details and developed inmore » advance to deal with more complex optical systems. In chapter 3, TMM is extended in curvilinear coordinates to study curved nanoribbon waveguides. The problem of a curved structure is transformed into an equivalent one of a straight structure with spatially dependent tensors of dielectric constant and magnetic permeability. In chapter 4, a new set of localized basis orbitals are introduced to locally represent electromagnetic field in photonic crystals as alternative to planewave basis. The second part of the thesis focuses on the design of optical devices. First, two examples of TMM applications are given. The first example is the design of metal grating structures as replacements of ITO to enhance the optical absorption in OPV cells (chapter 6). The second one is the design of the same structure as above to enhance the light extraction of OLEDs (chapter 7). Next, two design examples by ray tracing method are given, including applying a microlens array to enhance the light extraction of OLEDs (chapter 5) and an all-angle wide-wavelength design of solar concentrator (chapter 8). In summary, this dissertation has extended TMM which makes it capable of treating complex optical systems. Several optical designs by TMM and ray tracing method are also given as a full complement of this work.« less

  14. Some Aspects of Nonlinear Dynamics and CFD

    NASA Technical Reports Server (NTRS)

    Yee, Helen C.; Merriam, Marshal (Technical Monitor)

    1996-01-01

    The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with examples of spurious behavior observed in CFD computations.

  15. Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing

    NASA Technical Reports Server (NTRS)

    Childs, A. G.

    1971-01-01

    A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.

  16. Artificial mismatch hybridization

    DOEpatents

    Guo, Zhen; Smith, Lloyd M.

    1998-01-01

    An improved nucleic acid hybridization process is provided which employs a modified oligonucleotide and improves the ability to discriminate a control nucleic acid target from a variant nucleic acid target containing a sequence variation. The modified probe contains at least one artificial mismatch relative to the control nucleic acid target in addition to any mismatch(es) arising from the sequence variation. The invention has direct and advantageous application to numerous existing hybridization methods, including, applications that employ, for example, the Polymerase Chain Reaction, allele-specific nucleic acid sequencing methods, and diagnostic hybridization methods.

  17. An evaluation of dynamic mutuality measurements and methods in cyclic time series

    NASA Astrophysics Data System (ADS)

    Xia, Xiaohua; Huang, Guitian; Duan, Na

    2010-12-01

    Several measurements and techniques have been developed to detect dynamic mutuality and synchronicity of time series in econometrics. This study aims to compare the performances of five methods, i.e., linear regression, dynamic correlation, Markov switching models, concordance index and recurrence quantification analysis, through numerical simulations. We evaluate the abilities of these methods to capture structure changing and cyclicity in time series and the findings of this paper would offer guidance to both academic and empirical researchers. Illustration examples are also provided to demonstrate the subtle differences of these techniques.

  18. Sparse Covariance Matrix Estimation With Eigenvalue Constraints

    PubMed Central

    LIU, Han; WANG, Lie; ZHAO, Tuo

    2014-01-01

    We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholding and projection algorithm based on the alternating direction method of multipliers. Empirically, we conduct thorough numerical experiments on simulated datasets as well as real data examples to illustrate the usefulness of our method. Supplementary materials for the article are available online. PMID:25620866

  19. Boundary element modelling of dynamic behavior of piecewise homogeneous anisotropic elastic solids

    NASA Astrophysics Data System (ADS)

    Igumnov, L. A.; Markov, I. P.; Litvinchuk, S. Yu

    2018-04-01

    A traditional direct boundary integral equations method is applied to solve three-dimensional dynamic problems of piecewise homogeneous linear elastic solids. The materials of homogeneous parts are considered to be generally anisotropic. The technique used to solve the boundary integral equations is based on the boundary element method applied together with the Radau IIA convolution quadrature method. A numerical example of suddenly loaded 3D prismatic rod consisting of two subdomains with different anisotropic elastic properties is presented to verify the accuracy of the proposed formulation.

  20. Iterative algorithms for computing the feedback Nash equilibrium point for positive systems

    NASA Astrophysics Data System (ADS)

    Ivanov, I.; Imsland, Lars; Bogdanova, B.

    2017-03-01

    The paper studies N-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilising solution of a set of generalised algebraic Riccati equations. The latter is related to the Nash equilibrium point of the considered game model. Moreover, we derive the sufficient conditions for convergence of the proposed methods. Finally, we discuss two numerical examples so as to illustrate the performance of both of the algorithms.

  1. Particle-based and meshless methods with Aboria

    NASA Astrophysics Data System (ADS)

    Robinson, Martin; Bruna, Maria

    Aboria is a powerful and flexible C++ library for the implementation of particle-based numerical methods. The particles in such methods can represent actual particles (e.g. Molecular Dynamics) or abstract particles used to discretise a continuous function over a domain (e.g. Radial Basis Functions). Aboria provides a particle container, compatible with the Standard Template Library, spatial search data structures, and a Domain Specific Language to specify non-linear operators on the particle set. This paper gives an overview of Aboria's design, an example of use, and a performance benchmark.

  2. Harmony Search Method: Theory and Applications

    PubMed Central

    Gao, X. Z.; Govindasamy, V.; Xu, H.; Wang, X.; Zenger, K.

    2015-01-01

    The Harmony Search (HS) method is an emerging metaheuristic optimization algorithm, which has been employed to cope with numerous challenging tasks during the past decade. In this paper, the essential theory and applications of the HS algorithm are first described and reviewed. Several typical variants of the original HS are next briefly explained. As an example of case study, a modified HS method inspired by the idea of Pareto-dominance-based ranking is also presented. It is further applied to handle a practical wind generator optimal design problem. PMID:25945083

  3. Symmetry- and essentially-bound-preserving flux-corrected remapping of momentum in staggered ALE hydrodynamics

    NASA Astrophysics Data System (ADS)

    Velechovský, J.; Kuchařík, M.; Liska, R.; Shashkov, M.; Váchal, P.

    2013-12-01

    We present a new flux-corrected approach for remapping of velocity in the framework of staggered arbitrary Lagrangian-Eulerian methods. The main focus of the paper is the definition and preservation of coordinate invariant local bounds for velocity vector and development of momentum remapping method such that the radial symmetry of the radially symmetric flows is preserved when remapping from one equiangular polar mesh to another. The properties of this new method are demonstrated on a set of selected numerical cyclic remapping tests and a full hydrodynamic example.

  4. Fuzzy Hungarian Method for Solving Intuitionistic Fuzzy Travelling Salesman Problem

    NASA Astrophysics Data System (ADS)

    Prabakaran, K.; Ganesan, K.

    2018-04-01

    The travelling salesman problem is to identify the shortest route that the salesman journey all the places and return the starting place with minimum cost. We develop a fuzzy version of Hungarian algorithm for the solution of intuitionistic fuzzy travelling salesman problem using triangular intuitionistic fuzzy numbers without changing them to classical travelling salesman problem. The purposed method is easy to empathize and to implement for finding solution of intuitionistic travelling salesman problem happening in real life situations. To illustrate the proposed method numerical example are provided.

  5. Unconditionally stable WLP-FDTD method for the modeling of electromagnetic wave propagation in gyrotropic materials.

    PubMed

    Li, Zheng-Wei; Xi, Xiao-Li; Zhang, Jin-Sheng; Liu, Jiang-fan

    2015-12-14

    The unconditional stable finite-difference time-domain (FDTD) method based on field expansion with weighted Laguerre polynomials (WLPs) is applied to model electromagnetic wave propagation in gyrotropic materials. The conventional Yee cell is modified to have the tightly coupled current density components located at the same spatial position. The perfectly matched layer (PML) is formulated in a stretched-coordinate (SC) system with the complex-frequency-shifted (CFS) factor to achieve good absorption performance. Numerical examples are shown to validate the accuracy and efficiency of the proposed method.

  6. On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach

    NASA Astrophysics Data System (ADS)

    Gerstmayr, Johannes; Irschik, Hans

    2008-12-01

    In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.

  7. Numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains.

    PubMed

    Li, Hongwei; Guo, Yue

    2017-12-01

    The numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains is considered by applying the artificial boundary method in this paper. In order to design the local absorbing boundary conditions for the coupled nonlinear Schrödinger equations, we generalize the unified approach previously proposed [J. Zhang et al., Phys. Rev. E 78, 026709 (2008)PLEEE81539-375510.1103/PhysRevE.78.026709]. Based on the methodology underlying the unified approach, the original problem is split into two parts, linear and nonlinear terms, and we then achieve a one-way operator to approximate the linear term to make the wave out-going, and finally we combine the one-way operator with the nonlinear term to derive the local absorbing boundary conditions. Then we reduce the original problem into an initial boundary value problem on the bounded domain, which can be solved by the finite difference method. The stability of the reduced problem is also analyzed by introducing some auxiliary variables. Ample numerical examples are presented to verify the accuracy and effectiveness of our proposed method.

  8. Streaming potential modeling in fractured rock: Insights into the identification of hydraulically active fractures

    NASA Astrophysics Data System (ADS)

    Roubinet, D.; Linde, N.; Jougnot, D.; Irving, J.

    2016-05-01

    Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools for modeling streaming potentials in fractured media prevents quantitative interpretation and limits our understanding of how the SP method can be used in this regard. To address this issue, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid flow and associated self-potential problems in fractured rock. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interactions. This implies that fractures associated with strong SP amplitudes are likely to be hydraulically conductive, attracting fluid flow from the surrounding matrix.

  9. Real-time 3-D space numerical shake prediction for earthquake early warning

    NASA Astrophysics Data System (ADS)

    Wang, Tianyun; Jin, Xing; Huang, Yandan; Wei, Yongxiang

    2017-12-01

    In earthquake early warning systems, real-time shake prediction through wave propagation simulation is a promising approach. Compared with traditional methods, it does not suffer from the inaccurate estimation of source parameters. For computation efficiency, wave direction is assumed to propagate on the 2-D surface of the earth in these methods. In fact, since the seismic wave propagates in the 3-D sphere of the earth, the 2-D space modeling of wave direction results in inaccurate wave estimation. In this paper, we propose a 3-D space numerical shake prediction method, which simulates the wave propagation in 3-D space using radiative transfer theory, and incorporate data assimilation technique to estimate the distribution of wave energy. 2011 Tohoku earthquake is studied as an example to show the validity of the proposed model. 2-D space model and 3-D space model are compared in this article, and the prediction results show that numerical shake prediction based on 3-D space model can estimate the real-time ground motion precisely, and overprediction is alleviated when using 3-D space model.

  10. Implicit level set algorithms for modelling hydraulic fracture propagation.

    PubMed

    Peirce, A

    2016-10-13

    Hydraulic fractures are tensile cracks that propagate in pre-stressed solid media due to the injection of a viscous fluid. Developing numerical schemes to model the propagation of these fractures is particularly challenging due to the degenerate, hypersingular nature of the coupled integro-partial differential equations. These equations typically involve a singular free boundary whose velocity can only be determined by evaluating a distinguished limit. This review paper describes a class of numerical schemes that have been developed to use the multiscale asymptotic behaviour typically encountered near the fracture boundary as multiple physical processes compete to determine the evolution of the fracture. The fundamental concepts of locating the free boundary using the tip asymptotics and imposing the tip asymptotic behaviour in a weak form are illustrated in two quite different formulations of the governing equations. These formulations are the displacement discontinuity boundary integral method and the extended finite-element method. Practical issues are also discussed, including new models for proppant transport able to capture 'tip screen-out'; efficient numerical schemes to solve the coupled nonlinear equations; and fast methods to solve resulting linear systems. Numerical examples are provided to illustrate the performance of the numerical schemes. We conclude the paper with open questions for further research. This article is part of the themed issue 'Energy and the subsurface'. © 2016 The Author(s).

  11. Implicit level set algorithms for modelling hydraulic fracture propagation

    PubMed Central

    2016-01-01

    Hydraulic fractures are tensile cracks that propagate in pre-stressed solid media due to the injection of a viscous fluid. Developing numerical schemes to model the propagation of these fractures is particularly challenging due to the degenerate, hypersingular nature of the coupled integro-partial differential equations. These equations typically involve a singular free boundary whose velocity can only be determined by evaluating a distinguished limit. This review paper describes a class of numerical schemes that have been developed to use the multiscale asymptotic behaviour typically encountered near the fracture boundary as multiple physical processes compete to determine the evolution of the fracture. The fundamental concepts of locating the free boundary using the tip asymptotics and imposing the tip asymptotic behaviour in a weak form are illustrated in two quite different formulations of the governing equations. These formulations are the displacement discontinuity boundary integral method and the extended finite-element method. Practical issues are also discussed, including new models for proppant transport able to capture ‘tip screen-out’; efficient numerical schemes to solve the coupled nonlinear equations; and fast methods to solve resulting linear systems. Numerical examples are provided to illustrate the performance of the numerical schemes. We conclude the paper with open questions for further research.  This article is part of the themed issue ‘Energy and the subsurface’. PMID:27597787

  12. Applications of a Sequence of Points in Teaching Linear Algebra, Numerical Methods and Discrete Mathematics

    ERIC Educational Resources Information Center

    Shi, Yixun

    2009-01-01

    Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, "Using a sequence of number pairs as an example in teaching mathematics". Math. Comput. Educ., 39 (2005), pp. 198-205; Y. Shi, "Case study projects for college mathematics courses based on a particular…

  13. Model-Based Heterogeneous Data Fusion for Reliable Force Estimation in Dynamic Structures under Uncertainties

    PubMed Central

    Khodabandeloo, Babak; Melvin, Dyan; Jo, Hongki

    2017-01-01

    Direct measurements of external forces acting on a structure are infeasible in many cases. The Augmented Kalman Filter (AKF) has several attractive features that can be utilized to solve the inverse problem of identifying applied forces, as it requires the dynamic model and the measured responses of structure at only a few locations. But, the AKF intrinsically suffers from numerical instabilities when accelerations, which are the most common response measurements in structural dynamics, are the only measured responses. Although displacement measurements can be used to overcome the instability issue, the absolute displacement measurements are challenging and expensive for full-scale dynamic structures. In this paper, a reliable model-based data fusion approach to reconstruct dynamic forces applied to structures using heterogeneous structural measurements (i.e., strains and accelerations) in combination with AKF is investigated. The way of incorporating multi-sensor measurements in the AKF is formulated. Then the formulation is implemented and validated through numerical examples considering possible uncertainties in numerical modeling and sensor measurement. A planar truss example was chosen to clearly explain the formulation, while the method and formulation are applicable to other structures as well. PMID:29149088

  14. Multi-objective and Perishable Fuzzy Inventory Models Having Weibull Life-time With Time Dependent Demand, Demand Dependent Production and Time Varying Holding Cost: A Possibility/Necessity Approach

    NASA Astrophysics Data System (ADS)

    Pathak, Savita; Mondal, Seema Sarkar

    2010-10-01

    A multi-objective inventory model of deteriorating item has been developed with Weibull rate of decay, time dependent demand, demand dependent production, time varying holding cost allowing shortages in fuzzy environments for non- integrated and integrated businesses. Here objective is to maximize the profit from different deteriorating items with space constraint. The impreciseness of inventory parameters and goals for non-integrated business has been expressed by linear membership functions. The compromised solutions are obtained by different fuzzy optimization methods. To incorporate the relative importance of the objectives, the different cardinal weights crisp/fuzzy have been assigned. The models are illustrated with numerical examples and results of models with crisp/fuzzy weights are compared. The result for the model assuming them to be integrated business is obtained by using Generalized Reduced Gradient Method (GRG). The fuzzy integrated model with imprecise inventory cost is formulated to optimize the possibility necessity measure of fuzzy goal of the objective function by using credibility measure of fuzzy event by taking fuzzy expectation. The results of crisp/fuzzy integrated model are illustrated with numerical examples and results are compared.

  15. A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale

    DOE PAGES

    Cheung, James; Frischknecht, Amalie L.; Perego, Mauro; ...

    2017-07-20

    Here, we develop and demonstrate a new, hybrid simulation approach for charged fluids, which combines the accuracy of the nonlocal, classical density functional theory (cDFT) with the efficiency of the Poisson–Nernst–Planck (PNP) equations. The approach is motivated by the fact that the more accurate description of the physics in the cDFT model is required only near the charged surfaces, while away from these regions the PNP equations provide an acceptable representation of the ionic system. We formulate the hybrid approach in two stages. The first stage defines a coupled hybrid model in which the PNP and cDFT equations act independentlymore » on two overlapping domains, subject to suitable interface coupling conditions. At the second stage we apply the principles of the alternating Schwarz method to the hybrid model by using the interface conditions to define the appropriate boundary conditions and volume constraints exchanged between the PNP and the cDFT subdomains. Numerical examples with two representative examples of ionic systems demonstrate the numerical properties of the method and its potential to reduce the computational cost of a full cDFT calculation, while retaining the accuracy of the latter near the charged surfaces.« less

  16. A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale

    NASA Astrophysics Data System (ADS)

    Cheung, James; Frischknecht, Amalie L.; Perego, Mauro; Bochev, Pavel

    2017-11-01

    We develop and demonstrate a new, hybrid simulation approach for charged fluids, which combines the accuracy of the nonlocal, classical density functional theory (cDFT) with the efficiency of the Poisson-Nernst-Planck (PNP) equations. The approach is motivated by the fact that the more accurate description of the physics in the cDFT model is required only near the charged surfaces, while away from these regions the PNP equations provide an acceptable representation of the ionic system. We formulate the hybrid approach in two stages. The first stage defines a coupled hybrid model in which the PNP and cDFT equations act independently on two overlapping domains, subject to suitable interface coupling conditions. At the second stage we apply the principles of the alternating Schwarz method to the hybrid model by using the interface conditions to define the appropriate boundary conditions and volume constraints exchanged between the PNP and the cDFT subdomains. Numerical examples with two representative examples of ionic systems demonstrate the numerical properties of the method and its potential to reduce the computational cost of a full cDFT calculation, while retaining the accuracy of the latter near the charged surfaces.

  17. The concept of culture: a core issue in health disparities.

    PubMed

    Page, J Bryan

    2005-06-01

    Contemporary discourse contains numerous examples of use of the concept of culture by social and behavioral scientists. Simple reification, where the speaker makes culture into a thing capable of action exemplifies one usage in public discourse. Some quantitative social scientists attempt to characterize people's cultural identities by means of a single categorical variable, which often "lumps" people into categories such as "Hispanic" or "Black" that in fact have numerous culturally bounded subcategories. Approaches that emphasize cultural process are preferable to those who attempt to categorize; more complex measures of acculturation help investigators to make convincing analyses of circumstances in which health disparities occur. Examples in which investigators make appropriate use of cultural characterizations demonstrate their utility in investigating health disparities in Haitian American women, injecting and noninjecting drug users, Hispanic youth, and adult Hispanics at risk of HIV infection. Focus on culture in the study of health disparities can identify entanglements between structural factors such as poverty and lack of education and cultural factors such as beliefs about health. Qualitative methods coupled with quantitative methods have great potential to improve investigators' grasp of cultural nuance while capturing the distribution of qualitatively derived behaviors.

  18. A hybrid, coupled approach for modeling charged fluids from the nano to the mesoscale

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

    Cheung, James; Frischknecht, Amalie L.; Perego, Mauro

    Here, we develop and demonstrate a new, hybrid simulation approach for charged fluids, which combines the accuracy of the nonlocal, classical density functional theory (cDFT) with the efficiency of the Poisson–Nernst–Planck (PNP) equations. The approach is motivated by the fact that the more accurate description of the physics in the cDFT model is required only near the charged surfaces, while away from these regions the PNP equations provide an acceptable representation of the ionic system. We formulate the hybrid approach in two stages. The first stage defines a coupled hybrid model in which the PNP and cDFT equations act independentlymore » on two overlapping domains, subject to suitable interface coupling conditions. At the second stage we apply the principles of the alternating Schwarz method to the hybrid model by using the interface conditions to define the appropriate boundary conditions and volume constraints exchanged between the PNP and the cDFT subdomains. Numerical examples with two representative examples of ionic systems demonstrate the numerical properties of the method and its potential to reduce the computational cost of a full cDFT calculation, while retaining the accuracy of the latter near the charged surfaces.« less

  19. One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control

    NASA Technical Reports Server (NTRS)

    Taasan, Shlomo

    1991-01-01

    The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

  20. Numerical Polynomial Homotopy Continuation Method and String Vacua

    DOE PAGES

    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

  1. Considerations for the application of finite element beam modeling to vibration analysis of flight vehicle structures. Ph.D. Thesis - Case Western Reserve Univ.

    NASA Technical Reports Server (NTRS)

    Kvaternik, R. G.

    1976-01-01

    The manner of representing a flight vehicle structure as an assembly of beam, spring, and rigid-body components for vibration analysis is described. The development is couched in terms of a substructures methodology which is based on the finite-element stiffness method. The particular manner of employing beam, spring, and rigid-body components to model such items as wing structures, external stores, pylons supporting engines or external stores, and sprung masses associated with launch vehicle fuel slosh is described by means of several simple qualitative examples. A detailed numerical example consisting of a tilt-rotor VTOL aircraft is included to provide a unified illustration of the procedure for representing a structure as an equivalent system of beams, springs, and rigid bodies, the manner of forming the substructure mass and stiffness matrices, and the mechanics of writing the equations of constraint which enforce deflection compatibility at the junctions of the substructures. Since many structures, or selected components of structures, can be represented in this manner for vibration analysis, the modeling concepts described and their application in the numerical example shown should prove generally useful to the dynamicist.

  2. A Review of Computational Methods in Materials Science: Examples from Shock-Wave and Polymer Physics

    PubMed Central

    Steinhauser, Martin O.; Hiermaier, Stefan

    2009-01-01

    This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment. PMID:20054467

  3. Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

    NASA Astrophysics Data System (ADS)

    Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

    2017-10-01

    This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

  4. On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

    NASA Technical Reports Server (NTRS)

    Gunzburger, M. D.; Nicolaides, R. A.

    1986-01-01

    Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

  5. System Simulation by Recursive Feedback: Coupling a Set of Stand-Alone Subsystem Simulations

    NASA Technical Reports Server (NTRS)

    Nixon, D. D.

    2001-01-01

    Conventional construction of digital dynamic system simulations often involves collecting differential equations that model each subsystem, arran g them to a standard form, and obtaining their numerical gin solution as a single coupled, total-system simultaneous set. Simulation by numerical coupling of independent stand-alone subsimulations is a fundamentally different approach that is attractive because, among other things, the architecture naturally facilitates high fidelity, broad scope, and discipline independence. Recursive feedback is defined and discussed as a candidate approach to multidiscipline dynamic system simulation by numerical coupling of self-contained, single-discipline subsystem simulations. A satellite motion example containing three subsystems (orbit dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Distributed and centralized implementations of coupling have been considered. Numerical results are evaluated by direct comparison with a standard total-system, simultaneous-solution approach.

  6. A gradient enhanced plasticity-damage microplane model for concrete

    NASA Astrophysics Data System (ADS)

    Zreid, Imadeddin; Kaliske, Michael

    2018-03-01

    Computational modeling of concrete poses two main types of challenges. The first is the mathematical description of local response for such a heterogeneous material under all stress states, and the second is the stability and efficiency of the numerical implementation in finite element codes. The paper at hand presents a comprehensive approach addressing both issues. Adopting the microplane theory, a combined plasticity-damage model is formulated and regularized by an implicit gradient enhancement. The plasticity part introduces a new microplane smooth 3-surface cap yield function, which provides a stable numerical solution within an implicit finite element algorithm. The damage part utilizes a split, which can describe the transition of loading between tension and compression. Regularization of the model by the implicit gradient approach eliminates the mesh sensitivity and numerical instabilities. Identification methods for model parameters are proposed and several numerical examples of plain and reinforced concrete are carried out for illustration.

  7. Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

    NASA Technical Reports Server (NTRS)

    Dlugach, Janna M.; Mishchenko, Michael I.

    2017-01-01

    In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

  8. Computation of subsonic flow around airfoil systems with multiple separation

    NASA Technical Reports Server (NTRS)

    Jacob, K.

    1982-01-01

    A numerical method for computing the subsonic flow around multi-element airfoil systems was developed, allowing for flow separation at one or more elements. Besides multiple rear separation also sort bubbles on the upper surface and cove bubbles can approximately be taken into account. Also, compressibility effects for pure subsonic flow are approximately accounted for. After presentation the method is applied to several examples and improved in some details. Finally, the present limitations and desirable extensions are discussed.

  9. NECAP 4.1: NASA's energy-cost analysis program user's manual

    NASA Technical Reports Server (NTRS)

    Jensen, R. N.; Henninger, R. H.; Miner, D. L.

    1983-01-01

    The Enery Cost Analysis Program (NECAP) is a powerful computerized method to determine and to minimize building energy consumption. The program calculates hourly heat gain or losses taking into account the building thermal resistance and mass, using hourly weather and a "response factor' method. Internal temperatures are allowed to vary in accordance with thermostat settings and equipment capacity. A simplified input procedure and numerous other technical improvements are presented. This Users Manual describes the program and provides examples.

  10. An efficient solution procedure for the thermoelastic analysis of truss space structures

    NASA Technical Reports Server (NTRS)

    Givoli, D.; Rand, O.

    1992-01-01

    A solution procedure is proposed for the thermal and thermoelastic analysis of truss space structures in periodic motion. In this method, the spatial domain is first descretized using a consistent finite element formulation. Then the resulting semi-discrete equations in time are solved analytically by using Fourier decomposition. Geometrical symmetry is taken advantage of completely. An algorithm is presented for the calculation of heat flux distribution. The method is demonstrated via a numerical example of a cylindrically shaped space structure.

  11. Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem.

    PubMed

    Altürk, Ahmet

    2016-01-01

    Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.

  12. On Solutions for the Transient Response of Beams

    NASA Technical Reports Server (NTRS)

    Leonard, Robert W.

    1959-01-01

    Williams type modal solutions of the elementary and Timoshenko beam equations are presented for the response of several uniform beams to a general applied load. Example computations are shown for a free-free beam subject to various concentrated loads at its center. Discussion includes factors influencing the convergence of modal solutions and factors to be considered in a choice of beam theory. Results obtained by two numerical procedures, the traveling-wave method and Houbolt's method, are also presented and discussed.

  13. Transfer matrix method for four-flux radiative transfer.

    PubMed

    Slovick, Brian; Flom, Zachary; Zipp, Lucas; Krishnamurthy, Srini

    2017-07-20

    We develop a transfer matrix method for four-flux radiative transfer, which is ideally suited for studying transport through multiple scattering layers. The model predicts the specular and diffuse reflection and transmission of multilayer composite films, including interface reflections, for diffuse or collimated incidence. For spherical particles in the diffusion approximation, we derive closed-form expressions for the matrix coefficients and show remarkable agreement with numerical Monte Carlo simulations for a range of absorption values and film thicknesses, and for an example multilayer slab.

  14. Arbitrary-level hanging nodes for adaptive hphp-FEM approximations in 3D

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

    Pavel Kus; Pavel Solin; David Andrs

    2014-11-01

    In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hphp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.

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

    Kalugin, A. V., E-mail: Kalugin-AV@nrcki.ru; Tebin, V. V.

    The specific features of calculation of the effective multiplication factor using the Monte Carlo method for weakly coupled and non-asymptotic multiplying systems are discussed. Particular examples are considered and practical recommendations on detection and Monte Carlo calculation of systems typical in numerical substantiation of nuclear safety for VVER fuel management problems are given. In particular, the problems of the choice of parameters for the batch mode and the method for normalization of the neutron batch, as well as finding and interpretation of the eigenvalue spectrum for the integral fission matrix, are discussed.

  16. Two dimensional fully nonlinear numerical wave tank based on the BEM

    NASA Astrophysics Data System (ADS)

    Sun, Zhe; Pang, Yongjie; Li, Hongwei

    2012-12-01

    The development of a two dimensional numerical wave tank (NWT) with a rocker or piston type wavemaker based on the high order boundary element method (BEM) and mixed Eulerian-Lagrangian (MEL) is examined. The cauchy principle value (CPV) integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the corner problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.

  17. Numerical model of the polymer electro-optic waveguide

    NASA Astrophysics Data System (ADS)

    Fan, Guofang; Li, Yuan; Han, Bing; Wang, Qi; Liu, Xinhou; Zhen, Zhen

    2012-09-01

    A numerical design model is presented for the polymer waveguide in an electro-optic modulator. The effective index method is used to analyze the height of the core waveguide and rib waveguide, an improved Marcatili method is presented to design the rib waveguide width in order to keep the strong single mode operation and have a good match with the standard fiber. Also, the thickness of the upper cladding layer is discussed through calculating the effective index of the multilayer planar waveguide structure has been obtained by setting the optical loss due to the metallic absorption to an acceptable value (<0.1 dB/cm). As a consequence, we take the EO polymer waveguide structure of UV15:CLD/APC:UFC170 as an example, an optimized design is reported.

  18. Numerical method of applying shadow theory to all regions of multilayered dielectric gratings in conical mounting.

    PubMed

    Wakabayashi, Hideaki; Asai, Masamitsu; Matsumoto, Keiji; Yamakita, Jiro

    2016-11-01

    Nakayama's shadow theory first discussed the diffraction by a perfectly conducting grating in a planar mounting. In the theory, a new formulation by use of a scattering factor was proposed. This paper focuses on the middle regions of a multilayered dielectric grating placed in conical mounting. Applying the shadow theory to the matrix eigenvalues method, we compose new transformation and improved propagation matrices of the shadow theory for conical mounting. Using these matrices and scattering factors, being the basic quantity of diffraction amplitudes, we formulate a new description of three-dimensional scattering fields which is available even for cases where the eigenvalues are degenerate in any region. Some numerical examples are given for cases where the eigenvalues are degenerate in the middle regions.

  19. Numerical treatment of a geometrically nonlinear planar Cosserat shell model

    NASA Astrophysics Data System (ADS)

    Sander, Oliver; Neff, Patrizio; Bîrsan, Mircea

    2016-05-01

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

  20. Penalty methods for the numerical solution of American multi-asset option problems

    NASA Astrophysics Data System (ADS)

    Nielsen, Bjørn Fredrik; Skavhaug, Ola; Tveito, Aslak

    2008-12-01

    We derive and analyze a penalty method for solving American multi-asset option problems. A small, non-linear penalty term is added to the Black-Scholes equation. This approach gives a fixed solution domain, removing the free and moving boundary imposed by the early exercise feature of the contract. Explicit, implicit and semi-implicit finite difference schemes are derived, and in the case of independent assets, we prove that the approximate option prices satisfy some basic properties of the American option problem. Several numerical experiments are carried out in order to investigate the performance of the schemes. We give examples indicating that our results are sharp. Finally, the experiments indicate that in the case of correlated underlying assets, the same properties are valid as in the independent case.

  1. Potential flow about arbitrary biplane wing sections

    NASA Technical Reports Server (NTRS)

    Garrick, I E

    1937-01-01

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

  2. Microhartree precision in density functional theory calculations

    NASA Astrophysics Data System (ADS)

    Gulans, Andris; Kozhevnikov, Anton; Draxl, Claudia

    2018-04-01

    To address ultimate precision in density functional theory calculations we employ the full-potential linearized augmented plane-wave + local-orbital (LAPW + lo) method and justify its usage as a benchmark method. LAPW + lo and two completely unrelated numerical approaches, the multiresolution analysis (MRA) and the linear combination of atomic orbitals, yield total energies of atoms with mean deviations of 0.9 and 0.2 μ Ha , respectively. Spectacular agreement with the MRA is reached also for total and atomization energies of the G2-1 set consisting of 55 molecules. With the example of α iron we demonstrate the capability of LAPW + lo to reach μ Ha /atom precision also for periodic systems, which allows also for the distinction between the numerical precision and the accuracy of a given functional.

  3. Advantages of multigrid methods for certifying the accuracy of PDE modeling

    NASA Technical Reports Server (NTRS)

    Forester, C. K.

    1981-01-01

    Numerical techniques for assessing and certifying the accuracy of the modeling of partial differential equations (PDE) to the user's specifications are analyzed. Examples of the certification process with conventional techniques are summarized for the three dimensional steady state full potential and the two dimensional steady Navier-Stokes equations using fixed grid methods (FG). The advantages of the Full Approximation Storage (FAS) scheme of the multigrid technique of A. Brandt compared with the conventional certification process of modeling PDE are illustrated in one dimension with the transformed potential equation. Inferences are drawn for how MG will improve the certification process of the numerical modeling of two and three dimensional PDE systems. Elements of the error assessment process that are common to FG and MG are analyzed.

  4. High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bran R. (Technical Monitor)

    2002-01-01

    We present high-order semi-discrete central-upwind numerical schemes for approximating solutions of multi-dimensional Hamilton-Jacobi (HJ) equations. This scheme is based on the use of fifth-order central interpolants like those developed in [1], in fluxes presented in [3]. These interpolants use the weighted essentially nonoscillatory (WENO) approach to avoid spurious oscillations near singularities, and become "central-upwind" in the semi-discrete limit. This scheme provides numerical approximations whose error is as much as an order of magnitude smaller than those in previous WENO-based fifth-order methods [2, 1]. Thee results are discussed via examples in one, two and three dimensions. We also pregnant explicit N-dimensional formulas for the fluxes, discuss their monotonicity and tl!e connection between this method and that in [2].

  5. Solutions of interval type-2 fuzzy polynomials using a new ranking method

    NASA Astrophysics Data System (ADS)

    Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

    2015-10-01

    A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

  6. On importance assessment of aging multi-state system

    NASA Astrophysics Data System (ADS)

    Frenkel, Ilia; Khvatskin, Lev; Lisnianski, Anatoly

    2017-01-01

    Modern high-tech equipment requires precise temperature control and effective cooling below the ambient temperature. Greater cooling efficiencies will allow equipment to be operated for longer periods without overheating, providing a greater return on investment and increased in availability of the equipment. This paper presents application of the Lz-transform method to importance assessment of aging multi-state water-cooling system used in one of Israeli hospitals. The water cooling system consists of 3 principal sub-systems: chillers, heat exchanger and pumps. The performance of the system and the sub-systems is measured by their produced cooling capacity. Heat exchanger is an aging component. Straightforward Markov method applied to solve this problem will require building of a system model with numerous numbers of states and solving a corresponding system of multiple differential equations. Lz-transform method, which is used for calculation of the system elements importance, drastically simplified the solution. Numerical example is presented to illustrate the described approach.

  7. A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

    NASA Astrophysics Data System (ADS)

    Huang, Weizhang; Kamenski, Lennard; Lang, Jens

    2010-03-01

    A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauß-Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.

  8. Some problems in applications of the linear variational method

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

  9. A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

    NASA Astrophysics Data System (ADS)

    Peng, Heng; Liu, Yinghua; Chen, Haofeng

    2018-05-01

    In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.

  10. Method for Identification of Results of Dynamic Overloads in Assessment of Safety Use of the Mine Auxiliary Transportation System

    NASA Astrophysics Data System (ADS)

    Tokarczyk, Jarosław

    2016-12-01

    Method for identification the effects of dynamic overload affecting the people, which may occur in the emergency state of suspended monorail is presented in the paper. The braking curve using MBS (Multi-Body System) simulation was determined. For this purpose a computational model (MBS) of suspended monorail was developed and two different variants of numerical calculations were carried out. An algorithm of conducting numerical simulations to assess the effects of dynamic overload acting on the suspended monorails' users is also posted in the paper. An example of computational model FEM (Finite Element Method) composed of technical mean and the anthropometrical model ATB (Articulated Total Body) is shown. The simulation results are presented: graph of HIC (Head Injury Criterion) parameter and successive phases of dislocation of ATB model. Generator of computational models for safety criterion, which enables preparation of input data and remote starting the simulation, is proposed.

  11. Acoustic coupled fluid-structure interactions using a unified fast multipole boundary element method.

    PubMed

    Wilkes, Daniel R; Duncan, Alec J

    2015-04-01

    This paper presents a numerical model for the acoustic coupled fluid-structure interaction (FSI) of a submerged finite elastic body using the fast multipole boundary element method (FMBEM). The Helmholtz and elastodynamic boundary integral equations (BIEs) are, respectively, employed to model the exterior fluid and interior solid domains, and the pressure and displacement unknowns are coupled between conforming meshes at the shared boundary interface to achieve the acoustic FSI. The low frequency FMBEM is applied to both BIEs to reduce the algorithmic complexity of the iterative solution from O(N(2)) to O(N(1.5)) operations per matrix-vector product for N boundary unknowns. Numerical examples are presented to demonstrate the algorithmic and memory complexity of the method, which are shown to be in good agreement with the theoretical estimates, while the solution accuracy is comparable to that achieved by a conventional finite element-boundary element FSI model.

  12. The spectral cell method in nonlinear earthquake modeling

    NASA Astrophysics Data System (ADS)

    Giraldo, Daniel; Restrepo, Doriam

    2017-12-01

    This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

  13. Immunomagnetic separation for MEMS-based biosensor of waterborne pathogens detection

    NASA Astrophysics Data System (ADS)

    Guo, Jianjiang; Zhang, Rongbiao

    2017-07-01

    Rapid isolation and detection of special pathogens present in environmental drinking water is critical for water quality monitoring. Numerical analysis and experimental investigations on immunomagnetic capture and isolation of waterborne pathogens with magnetic nanoparticles (MNPs) in microfluidic channel are performed. A finite-element COMSOL-based model is established to demonstrate the novel method of on-chip capturing pathogens using MNPs together with periodic pulse magnetic field. Simulation results determine the optimum magnetic pole current and switching frequency for magnetic separation. With the magnetic isolation experiment platform built up, as a pathogen example of Escherichia coli O157:H7, the performance of the method is experimentally verified. Both numerical and experimental results are found to agree reasonably well. Results of these investigations show that the capture efficiency of the immunomagnetic separation method is more than 92%, which could be encouraging for the design and optimization of MEMS-based biosensor of waterborne pathogen detection.

  14. Noniterative Multireference Coupled Cluster Methods on Heterogeneous CPU-GPU Systems

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

    Bhaskaran-Nair, Kiran; Ma, Wenjing; Krishnamoorthy, Sriram

    2013-04-09

    A novel parallel algorithm for non-iterative multireference coupled cluster (MRCC) theories, which merges recently introduced reference-level parallelism (RLP) [K. Bhaskaran-Nair, J.Brabec, E. Aprà, H.J.J. van Dam, J. Pittner, K. Kowalski, J. Chem. Phys. 137, 094112 (2012)] with the possibility of accelerating numerical calculations using graphics processing unit (GPU) is presented. We discuss the performance of this algorithm on the example of the MRCCSD(T) method (iterative singles and doubles and perturbative triples), where the corrections due to triples are added to the diagonal elements of the MRCCSD (iterative singles and doubles) effective Hamiltonian matrix. The performance of the combined RLP/GPU algorithmmore » is illustrated on the example of the Brillouin-Wigner (BW) and Mukherjee (Mk) state-specific MRCCSD(T) formulations.« less

  15. A Fast MHD Code for Gravitationally Stratified Media using Graphical Processing Units: SMAUG

    NASA Astrophysics Data System (ADS)

    Griffiths, M. K.; Fedun, V.; Erdélyi, R.

    2015-03-01

    Parallelization techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPUs), possessing hundreds of processor cores. The opportunity has been recognized by the computational sciences and engineering communities, who have recently harnessed successfully the numerical performance of GPUs. For example, parallel magnetohydrodynamic (MHD) algorithms are important for numerical modelling of highly inhomogeneous solar, astrophysical and geophysical plasmas. Here, we describe the implementation of SMAUG, the Sheffield Magnetohydrodynamics Algorithm Using GPUs. SMAUG is a 1-3D MHD code capable of modelling magnetized and gravitationally stratified plasma. The objective of this paper is to present the numerical methods and techniques used for porting the code to this novel and highly parallel compute architecture. The methods employed are justified by the performance benchmarks and validation results demonstrating that the code successfully simulates the physics for a range of test scenarios including a full 3D realistic model of wave propagation in the solar atmosphere.

  16. Numerical algorithms for computations of feedback laws arising in control of flexible systems

    NASA Technical Reports Server (NTRS)

    Lasiecka, Irena

    1989-01-01

    Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

  17. Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver

    NASA Technical Reports Server (NTRS)

    Kim, S.-W.

    1991-01-01

    A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.

  18. Numerical Solution of Systems of Loaded Ordinary Differential Equations with Multipoint Conditions

    NASA Astrophysics Data System (ADS)

    Assanova, A. T.; Imanchiyev, A. E.; Kadirbayeva, Zh. M.

    2018-04-01

    A system of loaded ordinary differential equations with multipoint conditions is considered. The problem under study is reduced to an equivalent boundary value problem for a system of ordinary differential equations with parameters. A system of linear algebraic equations for the parameters is constructed using the matrices of the loaded terms and the multipoint condition. The conditions for the unique solvability and well-posedness of the original problem are established in terms of the matrix made up of the coefficients of the system of linear algebraic equations. The coefficients and the righthand side of the constructed system are determined by solving Cauchy problems for linear ordinary differential equations. The solutions of the system are found in terms of the values of the desired function at the initial points of subintervals. The parametrization method is numerically implemented using the fourth-order accurate Runge-Kutta method as applied to the Cauchy problems for ordinary differential equations. The performance of the constructed numerical algorithms is illustrated by examples.

  19. BOOK REVIEW: Numerical Recipes in C++: The Art of Scientific Computing (2nd edn)1 Numerical Recipes Example Book (C++) (2nd edn)2 Numerical Recipes Multi-Language Code CD ROM with LINUX or UNIX Single-Screen License Revised Version3Numerical Recipes in C++: The Art of Scientific Computing (2nd edn) Numerical Recipes Example Book (C++) (2nd edn) Numerical Recipes Multi-Language Code CD ROM with LINUX or UNIX Single-Screen License Revised Version

    NASA Astrophysics Data System (ADS)

    Press, William H.; Teukolsky, Saul A.; Vettering, William T.; Flannery, Brian P.

    2003-05-01

    The two Numerical Recipes books are marvellous. The principal book, The Art of Scientific Computing, contains program listings for almost every conceivable requirement, and it also contains a well written discussion of the algorithms and the numerical methods involved. The Example Book provides a complete driving program, with helpful notes, for nearly all the routines in the principal book. The first edition of Numerical Recipes: The Art of Scientific Computing was published in 1986 in two versions, one with programs in Fortran, the other with programs in Pascal. There were subsequent versions with programs in BASIC and in C. The second, enlarged edition was published in 1992, again in two versions, one with programs in Fortran (NR(F)), the other with programs in C (NR(C)). In 1996 the authors produced Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing as a supplement, called Volume 2, with the original (Fortran) version referred to as Volume 1. Numerical Recipes in C++ (NR(C++)) is another version of the 1992 edition. The numerical recipes are also available on a CD ROM: if you want to use any of the recipes, I would strongly advise you to buy the CD ROM. The CD ROM contains the programs in all the languages. When the first edition was published I bought it, and have also bought copies of the other editions as they have appeared. Anyone involved in scientific computing ought to have a copy of at least one version of Numerical Recipes, and there also ought to be copies in every library. If you already have NR(F), should you buy the NR(C++) and, if not, which version should you buy? In the preface to Volume 2 of NR(F), the authors say 'C and C++ programmers have not been far from our minds as we have written this volume, and we think that you will find that time spent in absorbing its principal lessons will be amply repaid in the future as C and C++ eventually develop standard parallel extensions'. In the preface and introduction to NR(C++), the authors point out some of the problems in the use of C++ in scientific computing. I have not found any mention of parallel computing in NR(C++). Fortran has quite a lot going for it. As someone who has used it in most of its versions from Fortran II, I have seen it develop and leave behind other languages promoted by various enthusiasts: who now uses Algol or Pascal? I think it unlikely that C++ will disappear: it was devised as a systems language, and can also be used for other purposes such as scientific computing. It is possible that Fortran will disappear, but Fortran has the strengths that it can develop, that there are extensive Fortran subroutine libraries, and that it has been developed for parallel computing. To argue with programmers as to which is the best language to use is sterile. If you wish to use C++, then buy NR(C++), but you should also look at volume 2 of NR(F). If you are a Fortran programmer, then make sure you have NR(F), volumes 1 and 2. But whichever language you use, make sure you have one version or the other, and the CD ROM. The Example Book provides listings of complete programs to run nearly all the routines in NR, frequently based on cases where an anlytical solution is available. It is helpful when developing a new program incorporating an unfamiliar routine to see that routine actually working, and this is what the programs in the Example Book achieve. I started teaching computational physics before Numerical Recipes was published. If I were starting again, I would make heavy use of both The Art of Scientific Computing and of the Example Book. Every computational physics teaching laboratory should have both volumes: the programs in the Example Book are included on the CD ROM, but the extra commentary in the book itself is of considerable value. P Borcherds

  20. Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

    NASA Technical Reports Server (NTRS)

    Orr, Jeb S.; Powers, Joseph F.; Yang, Hong Q

    2015-01-01

    A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments is based upon a novel approach that relies on the global momentum conservation of the closed fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. A numerical example illustrates the method's application to prediction of bulk fluid behavior during a spacecraft ullage settling maneuver.

  1. Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

    NASA Technical Reports Server (NTRS)

    Orr, Jeb S.; Powers, Joseph F.; Yang, Hong Q.

    2015-01-01

    A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments relies upon the global momentum conservation of the fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. Numerical examples illustrate the method's application to predicting bulk fluid motion including lateral propellant slosh in low-g conditions.

  2. Analysis and algorithms for a regularized Cauchy problem arising from a non-linear elliptic PDE for seismic velocity estimation

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

    Cameron, M.K.; Fomel, S.B.; Sethian, J.A.

    2009-01-01

    In the present work we derive and study a nonlinear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax-Friedrichs method. The key features of this scheme is the Lax-Friedrichs averaging and the wide stencil in space. The second approachmore » is a spectral Chebyshev method with truncated series. We show that our schemes work because of (1) the special input corresponding to a positive finite seismic velocity, (2) special initial conditions corresponding to the image rays, (3) the fact that our finite-difference scheme contains small error terms which damp the high harmonics; truncation of the Chebyshev series, and (4) the need to compute the solution only for a short interval of time. We test our numerical scheme on a collection of analytic examples and demonstrate a dramatic improvement in accuracy in the estimation of the sound speed inside the Earth in comparison with the conventional Dix inversion. Our test on the Marmousi example confirms the effectiveness of the proposed approach.« less

  3. GO2OGS 1.0: a versatile workflow to integrate complex geological information with fault data into numerical simulation models

    NASA Astrophysics Data System (ADS)

    Fischer, T.; Naumov, D.; Sattler, S.; Kolditz, O.; Walther, M.

    2015-11-01

    We offer a versatile workflow to convert geological models built with the ParadigmTM GOCAD© (Geological Object Computer Aided Design) software into the open-source VTU (Visualization Toolkit unstructured grid) format for usage in numerical simulation models. Tackling relevant scientific questions or engineering tasks often involves multidisciplinary approaches. Conversion workflows are needed as a way of communication between the diverse tools of the various disciplines. Our approach offers an open-source, platform-independent, robust, and comprehensible method that is potentially useful for a multitude of environmental studies. With two application examples in the Thuringian Syncline, we show how a heterogeneous geological GOCAD model including multiple layers and faults can be used for numerical groundwater flow modeling, in our case employing the OpenGeoSys open-source numerical toolbox for groundwater flow simulations. The presented workflow offers the chance to incorporate increasingly detailed data, utilizing the growing availability of computational power to simulate numerical models.

  4. Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

    NASA Astrophysics Data System (ADS)

    Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah

    2018-04-01

    This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual artifact banding phenomenon unlike the proposed method and USRM. In all, the proposed permeability and porosity fields generation coupled with the numerical simulator developed will aid in developing efficient mobility control schemes to improve on poor volumetric sweep efficiency in porous media.

  5. Electromagnetic Inverse Methods and Applications for Inhomogeneous Media Probing and Synthesis.

    NASA Astrophysics Data System (ADS)

    Xia, Jake Jiqing

    The electromagnetic inverse scattering problems concerned in this thesis are to find unknown inhomogeneous permittivity and conductivity profiles in a medium from the scattering data. Both analytical and numerical methods are studied in the thesis. The inverse methods can be applied to geophysical medium probing, non-destructive testing, medical imaging, optical waveguide synthesis and material characterization. An introduction is given in Chapter 1. The first part of the thesis presents inhomogeneous media probing. The Riccati equation approach is discussed in Chapter 2 for a one-dimensional planar profile inversion problem. Two types of the Riccati equations are derived and distinguished. New renormalized formulae based inverting one specific type of the Riccati equation are derived. Relations between the inverse methods of Green's function, the Riccati equation and the Gel'fand-Levitan-Marchenko (GLM) theory are studied. In Chapter 3, the renormalized source-type integral equation (STIE) approach is formulated for inversion of cylindrically inhomogeneous permittivity and conductivity profiles. The advantages of the renormalized STIE approach are demonstrated in numerical examples. The cylindrical profile inversion problem has an application for borehole inversion. In Chapter 4 the renormalized STIE approach is extended to a planar case where the two background media are different. Numerical results have shown fast convergence. This formulation is applied to inversion of the underground soil moisture profiles in remote sensing. The second part of the thesis presents the synthesis problem of inhomogeneous dielectric waveguides using the electromagnetic inverse methods. As a particular example, the rational function representation of reflection coefficients in the GLM theory is used. The GLM method is reviewed in Chapter 5. Relations between modal structures and transverse reflection coefficients of an inhomogeneous medium are established in Chapter 6. A stratified medium model is used to derive the guidance condition and the reflection coefficient. Results obtained in Chapter 6 provide the physical foundation for applying the inverse methods for the waveguide design problem. In Chapter 7, a global guidance condition for continuously varying medium is derived using the Riccati equation. It is further shown that the discrete modes in an inhomogeneous medium have the same wave vectors as the poles of the transverse reflection coefficient. An example of synthesizing an inhomogeneous dielectric waveguide using a rational reflection coefficient is presented. A summary of the thesis is given in Chapter 8. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

  6. Thermal engineering research. [Runge-Kutta investigation of gas flow inside multilayer insulation system for rocket booster fuel tanks

    NASA Technical Reports Server (NTRS)

    Shih, C. C.

    1973-01-01

    A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given, and comparisons with experimental data were made.

  7. Numerical simulation of groundwater flow in strongly anisotropic aquifers using multiple-point flux approximation method

    NASA Astrophysics Data System (ADS)

    Lin, S. T.; Liou, T. S.

    2017-12-01

    Numerical simulation of groundwater flow in anisotropic aquifers usually suffers from the lack of accuracy of calculating groundwater flux across grid blocks. Conventional two-point flux approximation (TPFA) can only obtain the flux normal to the grid interface but completely neglects the one parallel to it. Furthermore, the hydraulic gradient in a grid block estimated from TPFA can only poorly represent the hydraulic condition near the intersection of grid blocks. These disadvantages are further exacerbated when the principal axes of hydraulic conductivity, global coordinate system, and grid boundary are not parallel to one another. In order to refine the estimation the in-grid hydraulic gradient, several multiple-point flux approximation (MPFA) methods have been developed for two-dimensional groundwater flow simulations. For example, the MPFA-O method uses the hydraulic head at the junction node as an auxiliary variable which is then eliminated using the head and flux continuity conditions. In this study, a three-dimensional MPFA method will be developed for numerical simulation of groundwater flow in three-dimensional and strongly anisotropic aquifers. This new MPFA method first discretizes the simulation domain into hexahedrons. Each hexahedron is further decomposed into a certain number of tetrahedrons. The 2D MPFA-O method is then extended to these tetrahedrons, using the unknown head at the intersection of hexahedrons as an auxiliary variable along with the head and flux continuity conditions to solve for the head at the center of each hexahedron. Numerical simulations using this new MPFA method have been successfully compared with those obtained from a modified version of TOUGH2.

  8. A Sequential Optimization Sampling Method for Metamodels with Radial Basis Functions

    PubMed Central

    Pan, Guang; Ye, Pengcheng; Yang, Zhidong

    2014-01-01

    Metamodels have been widely used in engineering design to facilitate analysis and optimization of complex systems that involve computationally expensive simulation programs. The accuracy of metamodels is strongly affected by the sampling methods. In this paper, a new sequential optimization sampling method is proposed. Based on the new sampling method, metamodels can be constructed repeatedly through the addition of sampling points, namely, extrema points of metamodels and minimum points of density function. Afterwards, the more accurate metamodels would be constructed by the procedure above. The validity and effectiveness of proposed sampling method are examined by studying typical numerical examples. PMID:25133206

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

    NASA Astrophysics Data System (ADS)

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

    2001-02-01

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

  10. Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems

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

    Wolf, Elizabeth Skubak, E-mail: ewolf@saintmarys.edu; Anderson, David F., E-mail: anderson@math.wisc.edu

    2015-01-21

    Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations of model output quantities with respect to model parameters, are useful in this setting for a variety of applications. In this paper, we introduce a class of hybrid pathwise differentiation methods for the numerical estimation of parametric sensitivities. The new hybrid methods combine elements from the three main classes of procedures for sensitivity estimation and have a number of desirable qualities. First, the new methods are unbiased formore » a broad class of problems. Second, the methods are applicable to nearly any physically relevant biochemical CTMC model. Third, and as we demonstrate on several numerical examples, the new methods are quite efficient, particularly if one wishes to estimate the full gradient of parametric sensitivities. The methods are rather intuitive and utilize the multilevel Monte Carlo philosophy of splitting an expectation into separate parts and handling each in an efficient manner.« less

  11. An extended GS method for dense linear systems

    NASA Astrophysics Data System (ADS)

    Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

    2009-09-01

    Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

  12. Numerical methods for coupled fracture problems

    NASA Astrophysics Data System (ADS)

    Viesca, Robert C.; Garagash, Dmitry I.

    2018-04-01

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

  13. Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

    NASA Astrophysics Data System (ADS)

    Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

    2015-11-01

    We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

  14. Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation.

    PubMed

    Bergeron, Dominic; Tremblay, A-M S

    2016-08-01

    Analytic continuation of numerical data obtained in imaginary time or frequency has become an essential part of many branches of quantum computational physics. It is, however, an ill-conditioned procedure and thus a hard numerical problem. The maximum-entropy approach, based on Bayesian inference, is the most widely used method to tackle that problem. Although the approach is well established and among the most reliable and efficient ones, useful developments of the method and of its implementation are still possible. In addition, while a few free software implementations are available, a well-documented, optimized, general purpose, and user-friendly software dedicated to that specific task is still lacking. Here we analyze all aspects of the implementation that are critical for accuracy and speed and present a highly optimized approach to maximum entropy. Original algorithmic and conceptual contributions include (1) numerical approximations that yield a computational complexity that is almost independent of temperature and spectrum shape (including sharp Drude peaks in broad background, for example) while ensuring quantitative accuracy of the result whenever precision of the data is sufficient, (2) a robust method of choosing the entropy weight α that follows from a simple consistency condition of the approach and the observation that information- and noise-fitting regimes can be identified clearly from the behavior of χ^{2} with respect to α, and (3) several diagnostics to assess the reliability of the result. Benchmarks with test spectral functions of different complexity and an example with an actual physical simulation are presented. Our implementation, which covers most typical cases for fermions, bosons, and response functions, is available as an open source, user-friendly software.

  15. Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation

    NASA Astrophysics Data System (ADS)

    Bergeron, Dominic; Tremblay, A.-M. S.

    2016-08-01

    Analytic continuation of numerical data obtained in imaginary time or frequency has become an essential part of many branches of quantum computational physics. It is, however, an ill-conditioned procedure and thus a hard numerical problem. The maximum-entropy approach, based on Bayesian inference, is the most widely used method to tackle that problem. Although the approach is well established and among the most reliable and efficient ones, useful developments of the method and of its implementation are still possible. In addition, while a few free software implementations are available, a well-documented, optimized, general purpose, and user-friendly software dedicated to that specific task is still lacking. Here we analyze all aspects of the implementation that are critical for accuracy and speed and present a highly optimized approach to maximum entropy. Original algorithmic and conceptual contributions include (1) numerical approximations that yield a computational complexity that is almost independent of temperature and spectrum shape (including sharp Drude peaks in broad background, for example) while ensuring quantitative accuracy of the result whenever precision of the data is sufficient, (2) a robust method of choosing the entropy weight α that follows from a simple consistency condition of the approach and the observation that information- and noise-fitting regimes can be identified clearly from the behavior of χ2 with respect to α , and (3) several diagnostics to assess the reliability of the result. Benchmarks with test spectral functions of different complexity and an example with an actual physical simulation are presented. Our implementation, which covers most typical cases for fermions, bosons, and response functions, is available as an open source, user-friendly software.

  16. Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

    NASA Astrophysics Data System (ADS)

    Faghih Shojaei, Mostafa; Yavari, Arash

    2018-05-01

    We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.

  17. Sensitivity of control-augmented structure obtained by a system decomposition method

    NASA Technical Reports Server (NTRS)

    Sobieszczanskisobieski, Jaroslaw; Bloebaum, Christina L.; Hajela, Prabhat

    1988-01-01

    The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam's dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The method's principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

  18. Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems

    NASA Astrophysics Data System (ADS)

    Bäcker, A.

    Summary: We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two-dimensional area-preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area-preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illustrate the eigenvalue distribution for two types of perturbed cat maps, one leading to COE and the other to CUE statistics. For the eigenfunctions of quantum maps we study the distribution of the eigenvectors and compare them with the corresponding random matrix distributions. The Husimi representation allows for a direct comparison of the localization of the eigenstates in phase space with the corresponding classical structures. Examples for a perturbed cat map and the standard map with different parameters are shown. Billiard systems and the corresponding quantum billiards are another important class of systems (which are also relevant to applications, for example in mesoscopic physics). We provide a detailed exposition of the boundary integral method, which is one important method to determine the eigenvalues and eigenfunctions of the Helmholtz equation. We discuss several methods to determine the eigenvalues from the Fredholm equation and illustrate them for the stadium billiard. The occurrence of spurious solutions is discussed in detail and illustrated for the circular billiard, the stadium billiard, and the annular sector billiard. We emphasize the role of the normal derivative function to compute the normalization of eigenfunctions, momentum representations or autocorrelation functions in a very efficient and direct way. Some examples for these quantities are given and discussed.

  19. Analysis of periodically excited non-linear systems by a parametric continuation technique

    NASA Astrophysics Data System (ADS)

    Padmanabhan, C.; Singh, R.

    1995-07-01

    The dynamic behavior and frequency response of harmonically excited piecewise linear and/or non-linear systems has been the subject of several recent investigations. Most of the prior studies employed harmonic balance or Galerkin schemes, piecewise linear techniques, analog simulation and/or direct numerical integration (digital simulation). Such techniques are somewhat limited in their ability to predict all of the dynamic characteristics, including bifurcations leading to the occurrence of unstable, subharmonic, quasi-periodic and/or chaotic solutions. To overcome this problem, a parametric continuation scheme, based on the shooting method, is applied specifically to a periodically excited piecewise linear/non-linear system, in order to improve understanding as well as to obtain the complete dynamic response. Parameter regions exhibiting bifurcations to harmonic, subharmonic or quasi-periodic solutions are obtained quite efficiently and systematically. Unlike other techniques, the proposed scheme can follow period-doubling bifurcations, and with some modifications obtain stable quasi-periodic solutions and their bifurcations. This knowledge is essential in establishing conditions for the occurrence of chaotic oscillations in any non-linear system. The method is first validated through the Duffing oscillator example, the solutions to which are also obtained by conventional one-term harmonic balance and perturbation methods. The second example deals with a clearance non-linearity problem for both harmonic and periodic excitations. Predictions from the proposed scheme match well with available analog simulation data as well as with multi-term harmonic balance results. Potential savings in computational time over direct numerical integration is demonstrated for some of the example cases. Also, this work has filled in some of the solution regimes for an impact pair, which were missed previously in the literature. Finally, one main limitation associated with the proposed procedure is discussed.

  20. On Calculation Methods and Results for Straight Cylindrical Roller Bearing Deflection, Stiffness, and Stress

    NASA Technical Reports Server (NTRS)

    Krantz, Timothy L.

    2011-01-01

    The purpose of this study was to assess some calculation methods for quantifying the relationships of bearing geometry, material properties, load, deflection, stiffness, and stress. The scope of the work was limited to two-dimensional modeling of straight cylindrical roller bearings. Preparations for studies of dynamic response of bearings with damaged surfaces motivated this work. Studies were selected to exercise and build confidence in the numerical tools. Three calculation methods were used in this work. Two of the methods were numerical solutions of the Hertz contact approach. The third method used was a combined finite element surface integral method. Example calculations were done for a single roller loaded between an inner and outer raceway for code verification. Next, a bearing with 13 rollers and all-steel construction was used as an example to do additional code verification, including an assessment of the leading order of accuracy of the finite element and surface integral method. Results from that study show that the method is at least first-order accurate. Those results also show that the contact grid refinement has a more significant influence on precision as compared to the finite element grid refinement. To explore the influence of material properties, the 13-roller bearing was modeled as made from Nitinol 60, a material with very different properties from steel and showing some potential for bearing applications. The codes were exercised to compare contact areas and stress levels for steel and Nitinol 60 bearings operating at equivalent power density. As a step toward modeling the dynamic response of bearings having surface damage, static analyses were completed to simulate a bearing with a spall or similar damage.

Top