The development of accurate and efficient methods of numerical quadrature
NASA Technical Reports Server (NTRS)
Feagin, T.
1973-01-01
Some new methods for performing numerical quadrature of an integrable function over a finite interval are described. Each method provides a sequence of approximations of increasing order to the value of the integral. Each approximation makes use of all previously computed values of the integrand. The points at which new values of the integrand are computed are selected in such a way that the order of the approximation is maximized. The methods are compared with the quadrature methods of Clenshaw and Curtis, Gauss, Patterson, and Romberg using several examples.
An efficient step-size control method in numerical integration for astrodynamical equations
NASA Astrophysics Data System (ADS)
Liu, C. Z.; Cui, D. X.
2002-11-01
Using the curvature of the integral curve, a step-size control method is introduced in this paper. This method will prove to be the efficient scheme in the sense that it saves computation time and improve accuracy of numerical integration.
Efficiency and Accuracy Verification of the Explicit Numerical Manifold Method for Dynamic Problems
NASA Astrophysics Data System (ADS)
Qu, X. L.; Wang, Y.; Fu, G. Y.; Ma, G. W.
2015-05-01
The original numerical manifold method (NMM) employs an implicit time integration scheme to achieve higher computational accuracy, but its efficiency is relatively low, especially when the open-close iterations of contact are involved. To improve its computational efficiency, a modified version of the NMM based on an explicit time integration algorithm is proposed in this study. The lumped mass matrix, internal force and damping vectors are derived for the proposed explicit scheme. A calibration study on P-wave propagation along a rock bar is conducted to investigate the efficiency and accuracy of the developed explicit numerical manifold method (ENMM) for wave propagation problems. Various considerations in the numerical simulations are discussed, and parametric studies are carried out to obtain an insight into the influencing factors on the efficiency and accuracy of wave propagation. To further verify the capability of the proposed ENMM, dynamic stability assessment for a fractured rock slope under seismic effect is analysed. It is shown that, compared to the original NMM, the computational efficiency of the proposed ENMM can be significantly improved.
Efficient numerical method for solving Cauchy problem for the Gamma equation
NASA Astrophysics Data System (ADS)
Koleva, Miglena N.
2011-12-01
In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black-Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ = VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard-Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non-differentiable functions. Results of numerical simulations are given.
AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L2 OPTIMAL MASS TRANSFER PROBLEM*
Haber, Eldad; Rehman, Tauseef; Tannenbaum, Allen
2010-01-01
In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L2 mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61–97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data. PMID:21278828
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
1984-01-01
The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.
Efficient and accurate numerical methods for the Klein-Gordon-Schroedinger equations
Bao, Weizhu . E-mail: bao@math.nus.edu.sg; Yang, Li . E-mail: yangli@nus.edu.sg
2007-08-10
In this paper, we present efficient, unconditionally stable and accurate numerical methods for approximations of the Klein-Gordon-Schroedinger (KGS) equations with/without damping terms. The key features of our methods are based on: (i) the application of a time-splitting spectral discretization for a Schroedinger-type equation in KGS (ii) the utilization of Fourier pseudospectral discretization for spatial derivatives in the Klein-Gordon equation in KGS (iii) the adoption of solving the ordinary differential equations (ODEs) in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying Crank-Nicolson/leap-frog for linear/nonlinear terms for time derivatives. The numerical methods are either explicit or implicit but can be solved explicitly, unconditionally stable, and of spectral accuracy in space and second-order accuracy in time. Moreover, they are time reversible and time transverse invariant when there is no damping terms in KGS, conserve (or keep the same decay rate of) the wave energy as that in KGS without (or with a linear) damping term, keep the same dynamics of the mean value of the meson field, and give exact results for the plane-wave solution. Extensive numerical tests are presented to confirm the above properties of our numerical methods for KGS. Finally, the methods are applied to study solitary-wave collisions in one dimension (1D), as well as dynamics of a 2D problem in KGS.
NASA Astrophysics Data System (ADS)
Zimmermann, Anke; Kuhn, Sandra; Richter, Marten
2016-01-01
Often, the calculation of Coulomb coupling elements for quantum dynamical treatments, e.g., in cluster or correlation expansion schemes, requires the evaluation of a six dimensional spatial integral. Therefore, it represents a significant limiting factor in quantum mechanical calculations. If the size or the complexity of the investigated system increases, many coupling elements need to be determined. The resulting computational constraints require an efficient method for a fast numerical calculation of the Coulomb coupling. We present a computational method to reduce the numerical complexity by decreasing the number of spatial integrals for arbitrary geometries. We use a Green's function formulation of the Coulomb coupling and introduce a generalized scalar potential as solution of a generalized Poisson equation with a generalized charge density as the inhomogeneity. That enables a fast calculation of Coulomb coupling elements and, additionally, a straightforward inclusion of boundary conditions and arbitrarily spatially dependent dielectrics through the Coulomb Green's function. Particularly, if many coupling elements are included, the presented method, which is not restricted to specific symmetries of the model, presents a promising approach for increasing the efficiency of numerical calculations of the Coulomb interaction. To demonstrate the wide range of applications, we calculate internanostructure couplings, such as the Förster coupling, and illustrate the inclusion of symmetry considerations in the method for the Coulomb coupling between bound quantum dot states and unbound continuum states.
Efficient 3D Acoustic Numerical modeling in the Logarithmic-grid using the Expanding Domain Method
NASA Astrophysics Data System (ADS)
Hong, B. R.; Chung, W.; Ko, H.; Bae, H. S.
2015-12-01
In the numerical modeling of seismic wave propagation by the use of a discrete computing domain, dispersion analysis is preceded by the determination of the spatial grid spacings in order to ensure accurate modeling results. Grid spacing is a function of wavelength, and the wavelength depends on the minimum velocity and maximum source frequency. Therefore, as the frequency increases, the number of grids increase and this leads to computational overburden. In order to reduce the computing complexity, coordinate transformation techniques such as Riemannian coordinates and logarithmic grid sets are proposed. Riemannian wave-field extrapolation is a way to reformulate the wave-field by expressing it in Riemannian coordinates. In the logarithmic grid, grid spacing changes logarithmically, so this enables us to reduce the number of grids compared to a conventional grid set. Furthermore, this could completely remove boundary reflections by extending the model dimensions. However, numerical modeling in the logarithmic grid is still inefficient because it is performed for whole model at every individual time step. In this study we applied the expanding domain method to the logarithmic modeling in order to improve computational efficiency. This method, based on amplitude comparison, excludes computations for zero wave-fields by considering a non-zero domain boundary. Numerical examples demonstrated that our new modeling method enhances computational efficiency maintaining accuracy compared with conventional modeling methods. In wider and higher-order dimensions, particularly, the efficiency of our modeling method increased. Our new modeling technique could also be applied to the generation of underwater target echo signals requiring high frequency analysis.
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
1984-01-01
A comparison of the efficiency of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations is presented. The methods examined include two general-purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.
An efficient numerical method for computing dynamics of spin F = 2 Bose-Einstein condensates
Wang Hanquan
2011-07-01
In this paper, we extend the efficient time-splitting Fourier pseudospectral method to solve the generalized Gross-Pitaevskii (GP) equations, which model the dynamics of spin F = 2 Bose-Einstein condensates at extremely low temperature. Using the time-splitting technique, we split the generalized GP equations into one linear part and two nonlinear parts: the linear part is solved with the Fourier pseudospectral method; one of nonlinear parts is solved analytically while the other one is reformulated into a matrix formulation and solved by diagonalization. We show that the method keeps well the conservation laws related to generalized GP equations in 1D and 2D. We also show that the method is of second-order in time and spectrally accurate in space through a one-dimensional numerical test. We apply the method to investigate the dynamics of spin F = 2 Bose-Einstein condensates confined in a uniform/nonuniform magnetic field.
Bao, Weizhu; Chern, I-Liang; Zhang, Yanzhi
2013-11-15
In this paper, we propose efficient numerical methods for computing ground states of spin-1 Bose–Einstein condensates (BECs) with/without the Ioffe–Pritchard magnetic field B(x). When B(x)≠0, a numerical method is introduced to compute the ground states and it is also applied to study properties of ground states. Numerical results suggest that the densities of m{sub F}=±1 components in ground states are identical for any nonzero B(x). In particular, if B(x)≡B≠0 is a constant, the ground states satisfy the single-mode approximation. When B(x)≡0, efficient and simpler numerical methods are presented to solve the ground states of spin-1 BECs based on their ferromagnetic/antiferromagnetic characterizations. Numerical simulations show that our methods are more efficient than those in the literature. In addition, some conjectures are made from our numerical observations.
An Efficient numerical method to calculate the conductivity tensor for disordered topological matter
NASA Astrophysics Data System (ADS)
Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.
2015-03-01
We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.
Devasenapathy, Deepa; Kannan, Kathiravan
2015-01-01
The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN) is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate. PMID:25793221
Estimation of the drift eliminator efficiency using numerical and experimental methods
NASA Astrophysics Data System (ADS)
Stodůlka, Jiří; Vitkovičová, Rut
2016-03-01
The purpose of the drift eliminators is to prevent water from escaping in significant amounts the cooling tower. They are designed to catch the droplets dragged by the tower draft and the efficiency given by the shape of the eliminator is the main evaluation criteria. The ability to eliminate the escaping water droplets is studied using CFD and using the experimental IPI method.
An efficient numerical method for general L(p) regularization in fluorescence molecular tomography.
Baritaux, Jean-Charles; Hassler, Kat; Unser, Michael
2010-04-01
Reconstruction algorithms for fluorescence tomography have to address two crucial issues: 1) the ill-posedness of the reconstruction problem, 2) the large scale of numerical problems arising from imaging of 3-D samples. Our contribution is the design and implementation of a reconstruction algorithm that incorporates general Lp regularization (p ¿ 1). The originality of this work lies in the application of general Lp constraints to fluorescence tomography, combined with an efficient matrix-free strategy that enables the algorithm to deal with large reconstruction problems at reduced memory and computational costs. In the experimental part, we specialize the application of the algorithm to the case of sparsity promoting constraints (L (1)). We validate the adequacy of L (1) regularization for the investigation of phenomena that are well described by a sparse model, using data acquired during phantom experiments. PMID:20236875
An efficient and general numerical method to compute steady uniform vortices
NASA Astrophysics Data System (ADS)
Luzzatto-Fegiz, Paolo; Williamson, Charles H. K.
2011-07-01
Steady uniform vortices are widely used to represent high Reynolds number flows, yet their efficient computation still presents some challenges. Existing Newton iteration methods become inefficient as the vortices develop fine-scale features; in addition, these methods cannot, in general, find solutions with specified Casimir invariants. On the other hand, available relaxation approaches are computationally inexpensive, but can fail to converge to a solution. In this paper, we overcome these limitations by introducing a new discretization, based on an inverse-velocity map, which radically increases the efficiency of Newton iteration methods. In addition, we introduce a procedure to prescribe Casimirs and remove the degeneracies in the steady vorticity equation, thus ensuring convergence for general vortex configurations. We illustrate our methodology by considering several unbounded flows involving one or two vortices. Our method enables the computation, for the first time, of steady vortices that do not exhibit any geometric symmetry. In addition, we discover that, as the limiting vortex state for each flow is approached, each family of solutions traces a clockwise spiral in a bifurcation plot consisting of a velocity-impulse diagram. By the recently introduced "IVI diagram" stability approach [Phys. Rev. Lett. 104 (2010) 044504], each turn of this spiral is associated with a loss of stability for the steady flows. Such spiral structure is suggested to be a universal feature of steady, uniform-vorticity flows.
NASA Technical Reports Server (NTRS)
Maccormack, R. W.
1976-01-01
A fine-mesh method incorporating two new operators, which drastically reduces the computation time, has been developed for solving the time-dependent Navier-Stokes equations at flight Reynolds numbers. The approach time-splits the equations into a hyperbolic part and a parabolic part, solves the hyperbolic part by a new explicit numerical method based on characteristics theory, and solves the parabolic part by a new efficient implicit parabolic method. The method has reduced the computation time by one and two orders of magnitude from that required previously to solve for the interaction of a shock wave with a boundary layer on a flat plate.
Efficient numerical method for computation of thermohydrodynamics of laminar lubricating films
NASA Technical Reports Server (NTRS)
Elrod, Harold G.
1989-01-01
The purpose of this paper is to describe an accurate, yet economical, method for computing temperature effects in laminar lubricating films in two dimensions. The procedure presented here is a sequel to one presented in Leeds in 1986 that was carried out for the one-dimensional case. Because of the marked dependence of lubricant viscosity on temperature, the effect of viscosity variation both across and along a lubricating film can dwarf other deviations from ideal constant-property lubrication. In practice, a thermohydrodynamics program will involve simultaneous solution of the film lubrication problem, together with heat conduction in a solid, complex structure. The extent of computation required makes economy in numerical processing of utmost importance. In pursuit of such economy, we here use techniques similar to those for Gaussian quadrature. We show that, for many purposes, the use of just two properly positioned temperatures (Lobatto points) characterizes well the transverse temperature distribution.
NASA Astrophysics Data System (ADS)
Lai, Wencong; Ogden, Fred L.; Steinke, Robert C.; Talbot, Cary A.
2015-03-01
We have developed a one-dimensional numerical method to simulate infiltration and redistribution in the presence of a shallow dynamic water table. This method builds upon the Green-Ampt infiltration with Redistribution (GAR) model and incorporates features from the Talbot-Ogden (T-O) infiltration and redistribution method in a discretized moisture content domain. The redistribution scheme is more physically meaningful than the capillary weighted redistribution scheme in the T-O method. Groundwater dynamics are considered in this new method instead of hydrostatic groundwater front. It is also computationally more efficient than the T-O method. Motion of water in the vadose zone due to infiltration, redistribution, and interactions with capillary groundwater are described by ordinary differential equations. Numerical solutions to these equations are computationally less expensive than solutions of the highly nonlinear Richards' (1931) partial differential equation. We present results from numerical tests on 11 soil types using multiple rain pulses with different boundary conditions, with and without a shallow water table and compare against the numerical solution of Richards' equation (RE). Results from the new method are in satisfactory agreement with RE solutions in term of ponding time, deponding time, infiltration rate, and cumulative infiltrated depth. The new method, which we call "GARTO" can be used as an alternative to the RE for 1-D coupled surface and groundwater models in general situations with homogeneous soils with dynamic water table. The GARTO method represents a significant advance in simulating groundwater surface water interactions because it very closely matches the RE solution while being computationally efficient, with guaranteed mass conservation, and no stability limitations that can affect RE solvers in the case of a near-surface water table.
NASA Astrophysics Data System (ADS)
Blum, Volker
This talk describes recent advances of a general, efficient, accurate all-electron electronic theory approach based on numeric atom-centered orbitals; emphasis is placed on developments related to materials for energy conversion and their discovery. For total energies and electron band structures, we show that the overall accuracy is on par with the best benchmark quality codes for materials, but scalable to large system sizes (1,000s of atoms) and amenable to both periodic and non-periodic simulations. A recent localized resolution-of-identity approach for the Coulomb operator enables O (N) hybrid functional based descriptions of the electronic structure of non-periodic and periodic systems, shown for supercell sizes up to 1,000 atoms; the same approach yields accurate results for many-body perturbation theory as well. For molecular systems, we also show how many-body perturbation theory for charged and neutral quasiparticle excitation energies can be efficiently yet accurately applied using basis sets of computationally manageable size. Finally, the talk highlights applications to the electronic structure of hybrid organic-inorganic perovskite materials, as well as to graphene-based substrates for possible future transition metal compound based electrocatalyst materials. All methods described here are part of the FHI-aims code. VB gratefully acknowledges contributions by numerous collaborators at Duke University, Fritz Haber Institute Berlin, TU Munich, USTC Hefei, Aalto University, and many others around the globe.
Efficient numerical method for computation of the thermohydrodynamics of laminar lubricating films
NASA Technical Reports Server (NTRS)
Elrod, H. G.
1991-01-01
The purpose of this paper is to describe an accurate, yet economical, method for computing temperature effects in laminar lubricating films in two dimensions. Because of the marked dependence of lubricant viscosity on temperature, the effect of viscosity variation both across and along a lubricating film can dwarf other deviations from ideal constant-property lubrication. In practice, a thermohydrodynamics program will involve simultaneous solution of the film lubrication problem, together with heat conduction in a solid, complex structure. In pursuit of computational economy, techniques similar to those for Gaussian quadrature are used; it is shown that, for many purposes, the use of just two properly positioned temperatures (Lobatto points) characterizes the transverse temperature distribution.
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
NASA Technical Reports Server (NTRS)
Maccormack, R. W.
1976-01-01
A new numerical method used to drastically reduce the computation time required to solve the Navier-Stokes equations at flight Reynolds numbers is described. The new method makes it possible and practical to calculate many important three-dimensional, high Reynolds number flow fields on computers.
NASA Astrophysics Data System (ADS)
Alexandrov, Sergei; Jeng, Yeau-Ren
2013-12-01
Quite a general elastic/plastic material model including evolution equations for internal variables is adopted to predict the distribution of material properties and springback in plane strain bending under tension at large strains. A transformation equation to connect Lagrangian and Eulerian coordinates is used to reduce the original boundary value problem to a system of hyperbolic equations. This system is then solved by the method of characteristics combined with a finite difference scheme. In a particular case of elastic/plastic hardening materials (in this case the only internal variable is the equivalent plastic strain) an analytic solution is available in the literature. Using this solution it is demonstrated that the accuracy of the numerical method is very high.
Numerical methods for molecular dynamics
Skeel, R.D.
1991-01-01
This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.
NASA Astrophysics Data System (ADS)
Seroussi, H. L.; Rignot, E. J.; Morlighem, M.; Larour, E. Y.; Ben Dhia, H.; Aubry, D.
2010-12-01
The recent development of new higher-order, higher-resolution ice sheet models has shown that sophisticated models, such as Full-Stokes, were essential in some parts of the ice sheets, including the grounding line region. These areas are crucial for ice flow projections and can only be rigorously simulated using full 3d models. Higher-order models are well-suited to ice stream dynamics, whereas the shallow-shelf approximation is sufficient for modeling ice shelf flow. Higher-order and full-Stokes model are computationally intensive and prohibitive for large-scale modeling. There is therefore a strong need to combine such different models in order to balance computational cost and physical accuracy for the whole ice sheet. Here we present a new methodology adapted from the Arlequin framework to couple finite element shelfy-stream, higher-order and Full-Stokes models. We achieve this by strongly coupling the different approximations within the same large scale simulation. This technique is applied to the Greenland ice sheet, and compared with single-model approaches. Our new method preserves the conditioning number of the stiffness matrix, and ensures seamless stress regimes across model transition zones, hence improving numerical accuracy compared to existing techniques that use penalties or kinematical constrains. Furthermore, it optimizes the number of degrees of freedom leading to reduced computational cost. This work was performed at the California Institute of Technology's Jet Propulsion Laboratory under a contract with the National Aeronautics and Space Administration's Modeling, Analysis and Prediction (MAP) Program.
Efficient numerical evaluation of Feynman integrals
NASA Astrophysics Data System (ADS)
Li, Zhao; Wang, Jian; Yan, Qi-Shu; Zhao, Xiaoran
2016-03-01
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass. Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)
Numerical methods in structural mechanics
NASA Astrophysics Data System (ADS)
Obraztsov, I. F.
The papers contained in this volume focus on numerical, numerical-analytical, and theoretical methods for dealing with strength, stability, and dynamics problems in the design of the structural elements of flight vehicles. Topics discussed include the solution of homogeneous boundary value problems for systems of ordinary differential equations modified by a difference factorization method, a study of the rupture strength of a welded joint between plates, singular solutions in mixed problems for a wedge and a half-strip, and a thermoelasticity problem for an open-profile cylindrical shell with a localized temperature field.
Numerical methods for turbulent flow
NASA Astrophysics Data System (ADS)
Turner, James C., Jr.
1988-09-01
It has generally become accepted that the Navier-Strokes equations predict the dynamic behavior of turbulent as well as laminar flows of a fluid at a point in space away form a discontinuity such as a shock wave. Turbulence is also closely related to the phenomena of non-uniqueness of solutions of the Navier-Strokes equations. These second order, nonlinear partial differential equations can be solved analytically for only a few simple flows. Turbulent flow fields are much to complex to lend themselves to these few analytical methods. Numerical methods, therefore, offer the only possibility of achieving a solution of turbulent flow equations. In spite of recent advances in computer technology, the direct solution, by discrete methods, of the Navier-Strokes equations for turbulent flow fields is today, and in the foreseeable future, impossible. Thus the only economically feasible way to solve practical turbulent flow problems numerically is to use statistically averaged equations governing mean-flow quantities. The objective is to study some recent developments relating to the use of numerical methods to study turbulent flow.
Numerical methods for multibody systems
NASA Technical Reports Server (NTRS)
Glowinski, Roland; Nasser, Mahmoud G.
1994-01-01
This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.
A numerical method for predicting hypersonic flowfields
NASA Technical Reports Server (NTRS)
Maccormack, Robert W.; Candler, Graham V.
1989-01-01
The flow about a body traveling at hypersonic speed is energetic enough to cause the atmospheric gases to chemically react and reach states in thermal nonequilibrium. The prediction of hypersonic flowfields requires a numerical method capable of solving the conservation equations of fluid flow, the chemical rate equations for specie formation and dissociation, and the transfer of energy relations between translational and vibrational temperature states. Because the number of equations to be solved is large, the numerical method should also be as efficient as possible. The proposed paper presents a fully implicit method that fully couples the solution of the fluid flow equations with the gas physics and chemistry relations. The method flux splits the inviscid flow terms, central differences of the viscous terms, preserves element conservation in the strong chemistry source terms, and solves the resulting block matrix equation by Gauss Seidel line relaxation.
NASA Astrophysics Data System (ADS)
Yu, Jing; Shao, Weijia; Zhou, Yao; Wang, Huijie; Liu, Xiao; Xu, Xiaoliang
2013-11-01
Nano Ag-enhanced energy conversion efficiency (ECE) in one standard commercial pc-Si solar cell utilizing the forward scattering by Ag nanoparticles on surface has been researched experimentally and simulatively in this paper. Directly assembling Ag nanoparticles (with size about 100 nm) on the surface, it is found when the particle surface coverage is 10%, the ECE and the short circuit current density are increased by 2.8% and 1.4%, respectively. Without changing any existing structure of the ready-made solar cell, this facile and efficient method has huger applications than other methods.
Numerical methods used in fusion science numerical modeling
NASA Astrophysics Data System (ADS)
Yagi, M.
2015-04-01
The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.
An efficient numerical technique for calculating thermal spreading resistance
NASA Technical Reports Server (NTRS)
Gale, E. H., Jr.
1977-01-01
An efficient numerical technique for solving the equations resulting from finite difference analyses of fields governed by Poisson's equation is presented. The method is direct (noniterative)and the computer work required varies with the square of the order of the coefficient matrix. The computational work required varies with the cube of this order for standard inversion techniques, e.g., Gaussian elimination, Jordan, Doolittle, etc.
NASA Astrophysics Data System (ADS)
Leal, Allan M. M.; Blunt, Martin J.; LaForce, Tara C.
2013-12-01
We present a robust and efficient method for calculating chemical equilibria of general multiphase systems. The method is based on a stoichiometric approach, which uses Newton's method to solve a system of mass-action equations coupled with a system of equilibrium constraints. A stabilisation procedure is developed to promote convergence of the calculation when a presupposed phase in the chemical system is absent in the equilibrium state. The formulation of the chemical equilibrium problem is developed by presuming no specific details of the involved phases and species. As a consequence, the method is flexible and general enough so that the calculation can be customised with a combination of thermodynamic models that are appropriate for the problem of interest. Finally, we show the use of the method to solve relevant geochemical equilibrium problems for modelling carbon storage in highly saline aquifers.
Time-efficient numerical simulation of diatomic molecular spectra
NASA Astrophysics Data System (ADS)
Beuc, Robert; Movre, Mladen; Horvatić, Berislav
2014-03-01
We present a quantum-mechanical procedure for calculating the photoabsorption spectra of diatomic molecules, entirely based on the Fourier grid Hamiltonian method for obtaining energies and the corresponding wave functions. Discrete and continuous spectrum contributions, which are the result of transitions between bound, free, and quasibound states of diatomic molecules were treated on the same footing. Using the classical Franck-Condon principle and the stationary-phase approximation, we also developed a "semiquantum" simulation method of the spectrum which allows an extremely time-efficient numerical algorithm, reducing the computer time by up to four orders of magnitude. The proposed method was tested on the absorption spectra of potassium molecules.
NASA Astrophysics Data System (ADS)
Gharti, H. N.; Austermann, J.; Komatitsch, D.; Lau, H. C.; Mitrovica, J. X.; Peter, D. B.; Tromp, J.; Xie, Z.; Zampini, S.
2013-12-01
The complete set of governing equations for global dynamic and quasistatic problems --such as post-seismic and post-glacial rebound, tidal loading, and long-period seismology-- involves a coupling between the conservation laws of continuum mechanics and Poisson/Laplace's equation. For dynamic problems, such as seismic wave propagation and the free oscillations of the Earth, it is possible to decouple Poisson's equation using an explicit time marching scheme so that it can be solved independently. For quasistatic problems, such as glacial isostatic adjustment and tidal loading, inertia is neglected, requiring an implicit time marching scheme. In the latter case, Poisson's equation cannot be decoupled. Although an explicit time scheme with an independent Poisson's solver is generally fast, such an approach is limited by conditional stability, such that a very large number of time steps is often necessary. On the other hand, an implicit time scheme coupled with Poisson's equation is generally slow but unconditionally stable. In both cases, the unbounded and large-scale nature of the problem poses numerical challenges, particularly for 3D Earth models. Most of the existing methods use spherical harmonics to solve the unbounded Poisson/Laplace's equation. Such methods are often limited to spherically-symmetric models or have to rely on iterative procedures. In view of these challenges, we develop a parallel software package based on the spectral-element method combined with a mapped infinite-element approach. While the spectral-element method is used within the Earth model, the infinite-element approach is employed in the outer region. In the infinite element approach, a so-called infinite-element layer is used to mimic all of space. The outermost edges of an element in the infinite-element layer are mapped to infinity in order to reproduce the behavior of gravitational potential outside the domain of interest, such that the potential decays to zero at infinity. Gauss
Direct numerical simulations of collision efficiency of cohesive sediments
NASA Astrophysics Data System (ADS)
Zhang, Jin-Feng; Maa, Jerome P.-Y.; Zhang, Qing-He; Shen, Xiao-Teng
2016-09-01
A clear understanding of the collision efficiency of cohesive sediment particles is critical for more accurate simulation of the flocculation processes. It is difficult, if not impossible, to carry out laboratory experiments to determine the collision efficiency for small particles. Direct Numerical Simulation (DNS) is a relatively feasible approach to describe the motion of spherical particles under gravity in calm water, and thus, to study the collision efficiency of these particles. In this study, the Lattice Boltzmann (LB) method is used to calculate the relative trajectories of two approaching particles with different ratios of sizes and densities. Results show that the inter-molecular forces (i.e., van der Waals attractive force, electrostatic repulsive/attractive force, and displacement force), which are usually neglected in previous studies, would affect the trajectories, and thus, lead to an overestimation of the collision efficiency. It is found that to increase the particle size ratio from 0.1 to 0.8 only slightly increases the collision efficiency, since the force caused by fluid-solid interaction between these two particles is reduced. To increase the submerged particle density ratio from 1 to 22, however, would significantly decrease the collision efficiency. Earlier analytical formulations of collision efficiency, which only consider the effects of particle size ratio, have significantly overestimated the collision efficiency (change from 0.01 to 0.6) when the particle size ratio is around 0.5.
Numerical methods for molecular dynamics. Progress report
Skeel, R.D.
1991-12-31
This report summarizes our research progress to date on the use of multigrid methods for three-dimensional elliptic partial differential equations, with particular emphasis on application to the Poisson-Boltzmann equation of molecular biophysics. This research is motivated by the need for fast and accurate numerical solution techniques for three-dimensional problems arising in physics and engineering. In many applications these problems must be solved repeatedly, and the extremely large number of discrete unknowns required to accurately approximate solutions to partial differential equations in three-dimensional regions necessitates the use of efficient solution methods. This situation makes clear the importance of developing methods which are of optimal order (or nearly so), meaning that the number of operations required to solve the discrete problem is on the order of the number of discrete unknowns. Multigrid methods are generally regarded as being in this class of methods, and are in fact provably optimal order for an increasingly large class of problems. The fundamental goal of this research is to develop a fast and accurate numerical technique, based on multi-level principles, for the solutions of the Poisson-Boltzmann equation of molecular biophysics and similar equations occurring in other applications. An outline of the report is as follows. We first present some background material, followed by a survey of the literature on the use of multigrid methods for solving problems similar to the Poisson-Boltzmann equation. A short description of the software we have developed so far is then given, and numerical results are discussed. Finally, our research plans for the coming year are presented.
Numerical methods for problems in computational aeroacoustics
NASA Astrophysics Data System (ADS)
Mead, Jodi Lorraine
1998-12-01
A goal of computational aeroacoustics is the accurate calculation of noise from a jet in the far field. This work concerns the numerical aspects of accurately calculating acoustic waves over large distances and long time. More specifically, the stability, efficiency, accuracy, dispersion and dissipation in spatial discretizations, time stepping schemes, and absorbing boundaries for the direct solution of wave propagation problems are determined. Efficient finite difference methods developed by Tam and Webb, which minimize dispersion and dissipation, are commonly used for the spatial and temporal discretization. Alternatively, high order pseudospectral methods can be made more efficient by using the grid transformation introduced by Kosloff and Tal-Ezer. Work in this dissertation confirms that the grid transformation introduced by Kosloff and Tal-Ezer is not spectrally accurate because, in the limit, the grid transformation forces zero derivatives at the boundaries. If a small number of grid points are used, it is shown that approximations with the Chebyshev pseudospectral method with the Kosloff and Tal-Ezer grid transformation are as accurate as with the Chebyshev pseudospectral method. This result is based on the analysis of the phase and amplitude errors of these methods, and their use for the solution of a benchmark problem in computational aeroacoustics. For the grid transformed Chebyshev method with a small number of grid points it is, however, more appropriate to compare its accuracy with that of high- order finite difference methods. This comparison, for an order of accuracy 10-3 for a benchmark problem in computational aeroacoustics, is performed for the grid transformed Chebyshev method and the fourth order finite difference method of Tam. Solutions with the finite difference method are as accurate. and the finite difference method is more efficient than, the Chebyshev pseudospectral method with the grid transformation. The efficiency of the Chebyshev
Fytas, Nikolaos G; Martín-Mayor, Víctor
2016-06-01
It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used. PMID:27415388
NASA Astrophysics Data System (ADS)
Fytas, Nikolaos G.; Martín-Mayor, Víctor
2016-06-01
It was recently shown [Phys. Rev. Lett. 110, 227201 (2013), 10.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.
Numerical methods for engine-airframe integration
Murthy, S.N.B.; Paynter, G.C.
1986-01-01
Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison of full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment.
A stable and efficient numerical algorithm for unconfined aquifer analysis.
Keating, Elizabeth; Zyvoloski, George
2009-01-01
The nonlinearity of equations governing flow in unconfined aquifers poses challenges for numerical models, particularly in field-scale applications. Existing methods are often unstable, do not converge, or require extremely fine grids and small time steps. Standard modeling procedures such as automated model calibration and Monte Carlo uncertainty analysis typically require thousands of model runs. Stable and efficient model performance is essential to these analyses. We propose a new method that offers improvements in stability and efficiency and is relatively tolerant of coarse grids. It applies a strategy similar to that in the MODFLOW code to the solution of Richard's equation with a grid-dependent pressure/saturation relationship. The method imposes a contrast between horizontal and vertical permeability in gridblocks containing the water table, does not require "dry" cells to convert to inactive cells, and allows recharge to flow through relatively dry cells to the water table. We establish the accuracy of the method by comparison to an analytical solution for radial flow to a well in an unconfined aquifer with delayed yield. Using a suite of test problems, we demonstrate the efficiencies gained in speed and accuracy over two-phase simulations, and improved stability when compared to MODFLOW. The advantages for applications to transient unconfined aquifer analysis are clearly demonstrated by our examples. We also demonstrate applicability to mixed vadose zone/saturated zone applications, including transport, and find that the method shows great promise for these types of problem as well. PMID:19341374
A stable and efficient numerical algorithm for unconfined aquifer analysis
Keating, Elizabeth; Zyvoloski, George
2008-01-01
The non-linearity of equations governing flow in unconfined aquifers poses challenges for numerical models, particularly in field-scale applications. Existing methods are often unstable, do not converge, or require extremely fine grids and small time steps. Standard modeling procedures such as automated model calibration and Monte Carlo uncertainty analysis typically require thousands of forward model runs. Stable and efficient model performance is essential to these analyses. We propose a new method that offers improvements in stability and efficiency, and is relatively tolerant of coarse grids. It applies a strategy similar to that in the MODFLOW code to solution of Richard's Equation with a grid-dependent pressure/saturation relationship. The method imposes a contrast between horizontal and vertical permeability in gridblocks containing the water table. We establish the accuracy of the method by comparison to an analytical solution for radial flow to a well in an unconfined aquifer with delayed yield. Using a suite of test problems, we demonstrate the efficiencies gained in speed and accuracy over two-phase simulations, and improved stability when compared to MODFLOW. The advantages for applications to transient unconfined aquifer analysis are clearly demonstrated by our examples. We also demonstrate applicability to mixed vadose zone/saturated zone applications, including transport, and find that the method shows great promise for these types of problem, as well.
Interleaved numerical renormalization group as an efficient multiband impurity solver
NASA Astrophysics Data System (ADS)
Stadler, K. M.; Mitchell, A. K.; von Delft, J.; Weichselbaum, A.
2016-06-01
Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a "Wilson chain." It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014), 10.1103/PhysRevB.89.121105]. Here we systematically examine the accuracy and efficiency of the "interleaved" NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with "standard" NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are significantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N ) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.
Many-body localization: Entanglement and efficient numerical simulations
NASA Astrophysics Data System (ADS)
Pollmann, Frank
Many-body localization (MBL) occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. To understand this phenomenon, the development of new efficient numerical methods to find highly excited many-body eigenstates is essential. In this talk, we will discuss two complimentary approaches to simulate MBL systems: First, we introduce a variant of the density-matrix renormalization group (DMRG) method that obtains individual highly excited eigenstates of MBL systems to machine precision accuracy at moderate to large disorder. This method explicitly takes advantage of the local spatial structure and the low entanglement which is characteristic for MBL eigenstates. Second, we propose an approach to directly find an approximate compact representation of the diagonalizing unitary by using a variational unitary matrix-product operator.
An Efficient Numerical Approach for Nonlinear Fokker-Planck equations
NASA Astrophysics Data System (ADS)
Otten, Dustin; Vedula, Prakash
2009-03-01
Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.
Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals
NASA Technical Reports Server (NTRS)
Fink, Patrick W.; Wilton, Donald R.; Khayat, Michael A.
2007-01-01
Recently, significant progress has been made in the handling of singular and nearly-singular potential integrals that commonly arise in the Boundary Element Method (BEM). To facilitate object-oriented programming and handling of higher order basis functions, cancellation techniques are favored over techniques involving singularity subtraction. However, gradients of the Newton-type potentials, which produce hypersingular kernels, are also frequently required in BEM formulations. As is the case with the potentials, treatment of the near-hypersingular integrals has proven more challenging than treating the limiting case in which the observation point approaches the surface. Historically, numerical evaluation of these near-hypersingularities has often involved a two-step procedure: a singularity subtraction to reduce the order of the singularity, followed by a boundary contour integral evaluation of the extracted part. Since this evaluation necessarily links basis function, Green s function, and the integration domain (element shape), the approach ill fits object-oriented programming concepts. Thus, there is a need for cancellation-type techniques for efficient numerical evaluation of the gradient of the potential. Progress in the development of efficient cancellation-type procedures for the gradient potentials was recently presented. To the extent possible, a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. However, since the gradient kernel involves singularities of different orders, we also require that the transformation leaves remaining terms that are analytic. The terms "normal" and "tangential" are used herein with reference to the source element. Also, since computational formulations often involve the numerical evaluation of both potentials and their gradients, it is highly desirable that a single integration procedure efficiently handles both.
A numerical method for cardiac mechanoelectric simulations.
Pathmanathan, Pras; Whiteley, Jonathan P
2009-05-01
Much effort has been devoted to developing numerical techniques for solving the equations that describe cardiac electrophysiology, namely the monodomain equations and bidomain equations. Only a limited selection of publications, however, address the development of numerical techniques for mechanoelectric simulations where cardiac electrophysiology is coupled with deformation of cardiac tissue. One problem commonly encountered in mechanoelectric simulations is instability of the coupled numerical scheme. In this study, we develop a stable numerical scheme for mechanoelectric simulations. A number of convergence tests are carried out using this stable technique for simulations where deformations are of the magnitude typically observed in a beating heart. These convergence tests demonstrate that accurate computation of tissue deformation requires a nodal spacing of around 1 mm in the mesh used to calculate tissue deformation. This is a much finer computational grid than has previously been acknowledged, and has implications for the computational efficiency of the resulting numerical scheme. PMID:19263223
Dynamic optimization of bioprocesses: efficient and robust numerical strategies.
Banga, Julio R; Balsa-Canto, Eva; Moles, Carmen G; Alonso, Antonio A
2005-06-29
The dynamic optimization (open loop optimal control) of non-linear bioprocesses is considered in this contribution. These processes can be described by sets of non-linear differential and algebraic equations (DAEs), usually subject to constraints in the state and control variables. A review of the available solution techniques for this class of problems is presented, highlighting the numerical difficulties arising from the non-linear, constrained and often discontinuous nature of these systems. In order to surmount these difficulties, we present several alternative stochastic and hybrid techniques based on the control vector parameterization (CVP) approach. The CVP approach is a direct method which transforms the original problem into a non-linear programming (NLP) problem, which must be solved by a suitable (efficient and robust) solver. In particular, a hybrid technique uses a first global optimization phase followed by a fast second phase based on a local deterministic method, so it can handle the nonconvexity of many of these NLPs. The efficiency and robustness of these techniques is illustrated by solving several challenging case studies regarding the optimal control of fed-batch bioreactors and other bioprocesses. In order to fairly evaluate their advantages, a careful and critical comparison with several other direct approaches is provided. The results indicate that the two-phase hybrid approach presents the best compromise between robustness and efficiency. PMID:15888349
Numerical Methods for Radiation Magnetohydrodynamics in Astrophysics
Klein, R I; Stone, J M
2007-11-20
We describe numerical methods for solving the equations of radiation magnetohydrodynamics (MHD) for astrophysical fluid flow. Such methods are essential for the investigation of the time-dependent and multidimensional dynamics of a variety of astrophysical systems, although our particular interest is motivated by problems in star formation. Over the past few years, the authors have been members of two parallel code development efforts, and this review reflects that organization. In particular, we discuss numerical methods for MHD as implemented in the Athena code, and numerical methods for radiation hydrodynamics as implemented in the Orion code. We discuss the challenges introduced by the use of adaptive mesh refinement in both codes, as well as the most promising directions for future developments.
On Numerical Methods For Hypersonic Turbulent Flows
NASA Astrophysics Data System (ADS)
Yee, H. C.; Sjogreen, B.; Shu, C. W.; Wang, W.; Magin, T.; Hadjadj, A.
2011-05-01
Proper control of numerical dissipation in numerical methods beyond the standard shock-capturing dissipation at discontinuities is an essential element for accurate and stable simulation of hypersonic turbulent flows, including combustion, and thermal and chemical nonequilibrium flows. Unlike rapidly developing shock interaction flows, turbulence computations involve long time integrations. Improper control of numerical dissipation from one time step to another would be compounded over time, resulting in the smearing of turbulent fluctuations to an unrecognizable form. Hypersonic turbulent flows around re- entry space vehicles involve mixed steady strong shocks and turbulence with unsteady shocklets that pose added computational challenges. Stiffness of the source terms and material mixing in combustion pose yet other types of numerical challenges. A low dissipative high order well- balanced scheme, which can preserve certain non-trivial steady solutions of the governing equations exactly, may help minimize some of these difficulties. For stiff reactions it is well known that the wrong propagation speed of discontinuities occurs due to the under-resolved numerical solutions in both space and time. Schemes to improve the wrong propagation speed of discontinuities for systems of stiff reacting flows remain a challenge for algorithm development. Some of the recent algorithm developments for direct numerical simulations (DNS) and large eddy simulations (LES) for the subject physics, including the aforementioned numerical challenges, will be discussed.
New Methods of Energy Efficient Radon Mitigation
Fisk, W.J.; Prill, R.J.; Wooley, J.; Bonnefous, Y.C.; Gadgil, A.J.; Riley, W.J.
1994-05-01
Two new radon mitigation techniques are introduced and their evaluation in a field study complemented by numerical model predictions is described. Based on numerical predictions, installation of a sub gravel membrane at the study site resulted in a factor of two reduction in indoor radon concentrations. Experimental data indicated that installation of 'short-circuit' pipes extending between the subslab gravel and outdoors, caused an additional factor of two decrease in the radon concentration. Consequently, the combination of these two passive radon mitigation features, called the membrane and short-circuit (MASC) technique, was associated with a factor of four reduction in indoor radon concentration. The energy-efficient active radon mitigation method, called efficient active subslab pressurization (EASP), required only 20% of the fan energy of conventional active subslab depressurization and reduced the indoor radon concentration by approximately a factor of 15, including the numerically-predicted impact of the sub-gravel membrane.
Numerical methods for characterization of synchrotron radiation based on the Wigner function method
NASA Astrophysics Data System (ADS)
Tanaka, Takashi
2014-06-01
Numerical characterization of synchrotron radiation based on the Wigner function method is explored in order to accurately evaluate the light source performance. A number of numerical methods to compute the Wigner functions for typical synchrotron radiation sources such as bending magnets, undulators and wigglers, are presented, which significantly improve the computation efficiency and reduce the total computation time. As a practical example of the numerical characterization, optimization of betatron functions to maximize the brilliance of undulator radiation is discussed.
A numerical method of detecting singularity
NASA Technical Reports Server (NTRS)
Laporte, M.; Vignes, J.
1978-01-01
A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.
Numerical Processing Efficiency Improved in Experienced Mental Abacus Children
ERIC Educational Resources Information Center
Wang, Yunqi; Geng, Fengji; Hu, Yuzheng; Du, Fenglei; Chen, Feiyan
2013-01-01
Experienced mental abacus (MA) users are able to perform mental arithmetic calculations with unusual speed and accuracy. However, it remains unclear whether their extraordinary gains in mental arithmetic ability are accompanied by an improvement in numerical processing efficiency. To address this question, the present study, using a numerical…
Numerical Algorithms for Precise and Efficient Orbit Propagation and Positioning
NASA Astrophysics Data System (ADS)
Bradley, Ben K.
Motivated by the growing space catalog and the demands for precise orbit determination with shorter latency for science and reconnaissance missions, this research improves the computational performance of orbit propagation through more efficient and precise numerical integration and frame transformation implementations. Propagation of satellite orbits is required for astrodynamics applications including mission design, orbit determination in support of operations and payload data analysis, and conjunction assessment. Each of these applications has somewhat different requirements in terms of accuracy, precision, latency, and computational load. This dissertation develops procedures to achieve various levels of accuracy while minimizing computational cost for diverse orbit determination applications. This is done by addressing two aspects of orbit determination: (1) numerical integration used for orbit propagation and (2) precise frame transformations necessary for force model evaluation and station coordinate rotations. This dissertation describes a recently developed method for numerical integration, dubbed Bandlimited Collocation Implicit Runge-Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. It requires significantly fewer force function evaluations than explicit Runge-Kutta schemes and approaches the efficiency of the 8th-order Gauss-Jackson multistep method. Converting between the Geocentric Celestial Reference System (GCRS) and International Terrestrial Reference System (ITRS) is necessary for many applications in astrodynamics, such as orbit propagation, orbit determination, and analyzing geoscience data from satellite missions. This dissertation provides simplifications to the Celestial Intermediate Origin (CIO) transformation scheme and Earth orientation parameter (EOP) storage for use in positioning and
Numerical Analysis of the Symmetric Methods
NASA Astrophysics Data System (ADS)
Xu, Ji-Hong; Zhang, A.-Li
1995-03-01
Aimed at the initial value problem of the particular second-order ordinary differential equations,y ″=f(x, y), the symmetric methods (Quinlan and Tremaine, 1990) and our methods (Xu and Zhang, 1994) have been compared in detail by integrating the artificial earth satellite orbits in this paper. In the end, we point out clearly that the integral accuracy of numerical integration of the satellite orbits by applying our methods is obviously higher than that by applying the same order formula of the symmetric methods when the integration time-interval is not greater than 12000 periods.
Numerical Methods for Stochastic Partial Differential Equations
Sharp, D.H.; Habib, S.; Mineev, M.B.
1999-07-08
This is the final report of a Laboratory Directed Research and Development (LDRD) project at the Los Alamos National laboratory (LANL). The objectives of this proposal were (1) the development of methods for understanding and control of spacetime discretization errors in nonlinear stochastic partial differential equations, and (2) the development of new and improved practical numerical methods for the solutions of these equations. The authors have succeeded in establishing two methods for error control: the functional Fokker-Planck equation for calculating the time discretization error and the transfer integral method for calculating the spatial discretization error. In addition they have developed a new second-order stochastic algorithm for multiplicative noise applicable to the case of colored noises, and which requires only a single random sequence generation per time step. All of these results have been verified via high-resolution numerical simulations and have been successfully applied to physical test cases. They have also made substantial progress on a longstanding problem in the dynamics of unstable fluid interfaces in porous media. This work has lead to highly accurate quasi-analytic solutions of idealized versions of this problem. These may be of use in benchmarking numerical solutions of the full stochastic PDEs that govern real-world problems.
Numerical methods for supersonic astrophysical jets
NASA Astrophysics Data System (ADS)
Ha, Youngsoo
2003-09-01
The Euler equations of gas dynamics are used for the simulation of general astrophysical fluid flows including high Mach number astrophysical jets with radiative cooling. To accurately compute supersonic jet solutions with sharp resolution of shock waves, three modern numerical methods for gas dynamics were used: (1)a second-order Godunov method in LeVeque's software package CLAWPACK, (2)the Nessyahu-Tadmor-Kurganov (NTK) central hyperbolic scheme, and (3)the WENO-LF (Weighted Essentially Non-Oscillatory Lax-Friedrichs) scheme. Then simulations of supersonic astrophysical jets were compared, first without and then with radiative cooling. CLAWPACK consists of routines for solving time-dependent nonlinear hyperbolic conservation laws based on higher order Godunov methods and approximate Riemann problem solutions; the NTK scheme solves conservation laws using a modified Lax-Friedrichs central difference method without appealing to Riemann problem solutions; and the WENO-LF finite difference scheme is based on the Essentially Non-Oscillatory (ENO) idea by using Lax- Friedrichs flux splitting. The ENO method constructs a solution using the smoothness of the interpolating polynomial on given stencils; on the other hand, the WENO scheme uses a convex combination of the interpolate functions on all candidate stencils. The third-order and fifth-order WENO-LF methods were used to simulate the high Mach number jets. Appropriate numerical methods for incorporating radiative cooling in these numerical methods are also discussed. Interactions of supersonic jets with their environments (jet-“blob” interactions) are shown after modifying the codes to handle high Mach numbers and radiative cooling.
Hyperbolic conservation laws and numerical methods
NASA Technical Reports Server (NTRS)
Leveque, Randall J.
1990-01-01
The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.
A novel gas-droplet numerical method for spray combustion
NASA Technical Reports Server (NTRS)
Chen, C. P.; Shang, H. M.; Jiang, Y.
1991-01-01
This paper presents a non-iterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully-interacting combination of Eulerian fluid and Lagrangian particle calculation. The interaction calculations between the two phases are formulated on a pressure-velocity coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell (PSIC) procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data, as well as efficiency assessments are given for some sprays typical of spray combustion applications.
Simple numerical method for predicting steady compressible flows
NASA Technical Reports Server (NTRS)
Vonlavante, Ernst; Nelson, N. Duane
1986-01-01
A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.
RELAP-7 Numerical Stabilization: Entropy Viscosity Method
R. A. Berry; M. O. Delchini; J. Ragusa
2014-06-01
The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL's modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5's capability and extends the analysis capability for all reactor system simulation scenarios. RELAP-7 utilizes a single phase and a novel seven-equation two-phase flow models as described in the RELAP-7 Theory Manual (INL/EXT-14-31366). The basic equation systems are hyperbolic, which generally require some type of stabilization (or artificial viscosity) to capture nonlinear discontinuities and to suppress advection-caused oscillations. This report documents one of the available options for this stabilization in RELAP-7 -- a new and novel approach known as the entropy viscosity method. Because the code is an ongoing development effort in which the physical sub models, numerics, and coding are evolving, so too must the specific details of the entropy viscosity stabilization method. Here the fundamentals of the method in their current state are presented.
Numerical analysis method for linear induction machines.
NASA Technical Reports Server (NTRS)
Elliott, D. G.
1972-01-01
A numerical analysis method has been developed for linear induction machines such as liquid metal MHD pumps and generators and linear motors. Arbitrary phase currents or voltages can be specified and the moving conductor can have arbitrary velocity and conductivity variations from point to point. The moving conductor is divided into a mesh and coefficients are calculated for the voltage induced at each mesh point by unit current at every other mesh point. Combining the coefficients with the mesh resistances yields a set of simultaneous equations which are solved for the unknown currents.
Numerical methods for finding stationary gravitational solutions
NASA Astrophysics Data System (ADS)
Dias, Óscar J. C.; Santos, Jorge E.; Way, Benson
2016-07-01
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical foundations and give a practical guide for the numerical solution of gravitational boundary value problems. We present these methods by way of example: resolving asymptotically flat black rings, singly spinning lumpy black holes in anti-de Sitter (AdS), and the Gregory–Laflamme zero modes of small rotating black holes in AdS{}5× {S}5. We also include several tools and tricks that have been useful throughout the literature.
MULTIMODECODE: an efficient numerical solver for multifield inflation
NASA Astrophysics Data System (ADS)
Price, Layne C.; Frazer, Jonathan; Xu, Jiajun; Peiris, Hiranya V.; Easther, Richard
2015-03-01
We present MULTIMODECODE, a Fortran 95/2000 package for the numerical exploration of multifield inflation models. This program facilitates efficient Monte Carlo sampling of prior probabilities for inflationary model parameters and initial conditions and is the first publicly available code that can efficiently generate large sample-sets for inflation models with 𝒪 fields. The code numerically solves the equations of motion for the background and first-order perturbations of multi-field inflation models with canonical kinetic terms and arbitrary potentials, providing the adiabatic, isocurvature, and tensor power spectra at the end of inflation. For models with sum-separable potentials MULTIMODECODE also computes the slow-roll prediction via the δ N formalism for easy model exploration and validation. We pay particular attention to the isocurvature perturbations as the system approaches the adiabatic limit, showing how to avoid numerical instabilities that affect some other approaches to this problem. We demonstrate the use of MULTIMODECODE by exploring a few toy models. Finally, we give a concise review of multifield perturbation theory and a user's manual for the program.
Computational methods for aerodynamic design using numerical optimization
NASA Technical Reports Server (NTRS)
Peeters, M. F.
1983-01-01
Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.
Application of numerical methods to elasticity imaging.
Castaneda, Benjamin; Ormachea, Juvenal; Rodríguez, Paul; Parker, Kevin J
2013-03-01
Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity. PMID:24010245
Mathematica with a Numerical Methods Course
NASA Astrophysics Data System (ADS)
Varley, Rodney
2003-04-01
An interdisciplinary "Numerical Methods" course has been shared between physics, mathematics and computer science since 1992 at Hunter C. Recently, the lectures and workshops for this course have become formalized and placed on the internet at http://www.ph.hunter.cuny.edu (follow the links "Course Listings and Websites" >> "PHYS385 (Numerical Methods)". Mathematica notebooks for the lectures are available for automatic download (by "double clicking" the lecture icon) for student use in the classroom or at home. AOL (or Netscape/Explorer) can be used provided Mathematica (or the "free" MathReader) has been made a "helper application". Using Mathematica has the virtue that mathematical equations (no LaTex required) can easily be included with the text and Mathematica's graphing is easy to use. Computational cells can be included within the notebook and students may easily modify the calculation to see the result of "what if..." questions. Homework is sent as Mathematica notebooks to the instructor via the internet and the corrected workshops are returned in the same manner. Most exam questions require computational solutions.
An efficient numerical procedure for thermohydrodynamic analysis of cavitating bearings
NASA Technical Reports Server (NTRS)
Vijayaraghavan, D.
1995-01-01
An efficient and accurate numerical procedure to determine the thermo-hydrodynamic performance of cavitating bearings is described. This procedure is based on the earlier development of Elrod for lubricating films, in which the properties across the film thickness are determined at Lobatto points and their distributions are expressed by collocated polynomials. The cavitated regions and their boundaries are rigorously treated. Thermal boundary conditions at the surfaces, including heat dissipation through the metal to the ambient, are incorporated. Numerical examples are presented comparing the predictions using this procedure with earlier theoretical predictions and experimental data. With a few points across the film thickness and across the journal and the bearing in the radial direction, the temperature profile is very well predicted.
Yao, Yuan; Du, Fenglei; Wang, Chunjie; Liu, Yuqiu; Weng, Jian; Chen, Feiyan
2015-01-01
This study examined whether long-term abacus-based mental calculation (AMC) training improved numerical processing efficiency and at what stage of information processing the effect appeard. Thirty-three children participated in the study and were randomly assigned to two groups at primary school entry, matched for age, gender and IQ. All children went through the same curriculum except that the abacus group received a 2-h/per week AMC training, while the control group did traditional numerical practice for a similar amount of time. After a 2-year training, they were tested with a numerical Stroop task. Electroencephalographic (EEG) and event related potential (ERP) recording techniques were used to monitor the temporal dynamics during the task. Children were required to determine the numerical magnitude (NC) (NC task) or the physical size (PC task) of two numbers presented simultaneously. In the NC task, the AMC group showed faster response times but similar accuracy compared to the control group. In the PC task, the two groups exhibited the same speed and accuracy. The saliency of numerical information relative to physical information was greater in AMC group. With regards to ERP results, the AMC group displayed congruity effects both in the earlier (N1) and later (N2 and LPC (late positive component) time domain, while the control group only displayed congruity effects for LPC. In the left parietal region, LPC amplitudes were larger for the AMC than the control group. Individual differences for LPC amplitudes over left parietal area showed a positive correlation with RTs in the NC task in both congruent and neutral conditions. After controlling for the N2 amplitude, this correlation also became significant in the incongruent condition. Our results suggest that AMC training can strengthen the relationship between symbolic representation and numerical magnitude so that numerical information processing becomes quicker and automatic in AMC children. PMID:26042012
Yao, Yuan; Du, Fenglei; Wang, Chunjie; Liu, Yuqiu; Weng, Jian; Chen, Feiyan
2015-01-01
This study examined whether long-term abacus-based mental calculation (AMC) training improved numerical processing efficiency and at what stage of information processing the effect appeard. Thirty-three children participated in the study and were randomly assigned to two groups at primary school entry, matched for age, gender and IQ. All children went through the same curriculum except that the abacus group received a 2-h/per week AMC training, while the control group did traditional numerical practice for a similar amount of time. After a 2-year training, they were tested with a numerical Stroop task. Electroencephalographic (EEG) and event related potential (ERP) recording techniques were used to monitor the temporal dynamics during the task. Children were required to determine the numerical magnitude (NC) (NC task) or the physical size (PC task) of two numbers presented simultaneously. In the NC task, the AMC group showed faster response times but similar accuracy compared to the control group. In the PC task, the two groups exhibited the same speed and accuracy. The saliency of numerical information relative to physical information was greater in AMC group. With regards to ERP results, the AMC group displayed congruity effects both in the earlier (N1) and later (N2 and LPC (late positive component) time domain, while the control group only displayed congruity effects for LPC. In the left parietal region, LPC amplitudes were larger for the AMC than the control group. Individual differences for LPC amplitudes over left parietal area showed a positive correlation with RTs in the NC task in both congruent and neutral conditions. After controlling for the N2 amplitude, this correlation also became significant in the incongruent condition. Our results suggest that AMC training can strengthen the relationship between symbolic representation and numerical magnitude so that numerical information processing becomes quicker and automatic in AMC children. PMID:26042012
Optimization methods and silicon solar cell numerical models
NASA Technical Reports Server (NTRS)
Girardini, K.; Jacobsen, S. E.
1986-01-01
An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.
A Numerical Method for Solving Elasticity Equations with Interfaces
Li, Zhilin; Wang, Liqun; Wang, Wei
2012-01-01
Solving elasticity equations with interfaces is a challenging problem for most existing methods. Nonetheless, it has wide applications in engineering and science. An accurate and efficient method is desired. In this paper, an efficient non-traditional finite element method with non-body-fitting grids is proposed to solve elasticity equations with interfaces. The main idea is to choose the test function basis to be the standard finite element basis independent of the interface and to choose the solution basis to be piecewise linear satisfying the jump conditions across the interface. The resulting linear system of equations is shown to be positive definite under certain assumptions. Numerical experiments show that this method is second order accurate in the L∞ norm for piecewise smooth solutions. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interface corner. PMID:22707984
Efficient integration method for fictitious domain approaches
NASA Astrophysics Data System (ADS)
Duczek, Sascha; Gabbert, Ulrich
2015-10-01
In the current article, we present an efficient and accurate numerical method for the integration of the system matrices in fictitious domain approaches such as the finite cell method (FCM). In the framework of the FCM, the physical domain is embedded in a geometrically larger domain of simple shape which is discretized using a regular Cartesian grid of cells. Therefore, a spacetree-based adaptive quadrature technique is normally deployed to resolve the geometry of the structure. Depending on the complexity of the structure under investigation this method accounts for most of the computational effort. To reduce the computational costs for computing the system matrices an efficient quadrature scheme based on the divergence theorem (Gauß-Ostrogradsky theorem) is proposed. Using this theorem the dimension of the integral is reduced by one, i.e. instead of solving the integral for the whole domain only its contour needs to be considered. In the current paper, we present the general principles of the integration method and its implementation. The results to several two-dimensional benchmark problems highlight its properties. The efficiency of the proposed method is compared to conventional spacetree-based integration techniques.
Houfek, Karel
2008-09-01
Numerical solution of coupled radial differential equations which are encountered in multichannel scattering problems is presented. Numerical approach is based on the combination of the exterior complex scaling method and the finite-elements method with the discrete variable representation. This method can be used not only to solve multichannel scattering problem but also to find bound states and resonance positions and widths directly by diagonalization of the corresponding complex scaled Hamiltonian. Efficiency and accuracy of this method is demonstrated on an analytically solvable two-channel problem.
Numerical Methods of Computational Electromagnetics for Complex Inhomogeneous Systems
Cai, Wei
2014-05-15
Understanding electromagnetic phenomena is the key in many scientific investigation and engineering designs such as solar cell designs, studying biological ion channels for diseases, and creating clean fusion energies, among other things. The objectives of the project are to develop high order numerical methods to simulate evanescent electromagnetic waves occurring in plasmon solar cells and biological ion-channels, where local field enhancement within random media in the former and long range electrostatic interactions in the latter are of major challenges for accurate and efficient numerical computations. We have accomplished these objectives by developing high order numerical methods for solving Maxwell equations such as high order finite element basis for discontinuous Galerkin methods, well-conditioned Nedelec edge element method, divergence free finite element basis for MHD, and fast integral equation methods for layered media. These methods can be used to model the complex local field enhancement in plasmon solar cells. On the other hand, to treat long range electrostatic interaction in ion channels, we have developed image charge based method for a hybrid model in combining atomistic electrostatics and continuum Poisson-Boltzmann electrostatics. Such a hybrid model will speed up the molecular dynamics simulation of transport in biological ion-channels.
Efficient numerical simulation of heat storage in subsurface georeservoirs
NASA Astrophysics Data System (ADS)
Boockmeyer, A.; Bauer, S.
2015-12-01
The transition of the German energy market towards renewable energy sources, e.g. wind or solar power, requires energy storage technologies to compensate for their fluctuating production. Large amounts of energy could be stored in georeservoirs such as porous formations in the subsurface. One possibility here is to store heat with high temperatures of up to 90°C through borehole heat exchangers (BHEs) since more than 80 % of the total energy consumption in German households are used for heating and hot water supply. Within the ANGUS+ project potential environmental impacts of such heat storages are assessed and quantified. Numerical simulations are performed to predict storage capacities, storage cycle times, and induced effects. For simulation of these highly dynamic storage sites, detailed high-resolution models are required. We set up a model that accounts for all components of the BHE and verified it using experimental data. The model ensures accurate simulation results but also leads to large numerical meshes and thus high simulation times. In this work, we therefore present a numerical model for each type of BHE (single U, double U and coaxial) that reduces the number of elements and the simulation time significantly for use in larger scale simulations. The numerical model includes all BHE components and represents the temporal and spatial temperature distribution with an accuracy of less than 2% deviation from the fully discretized model. By changing the BHE geometry and using equivalent parameters, the simulation time is reduced by a factor of ~10 for single U-tube BHEs, ~20 for double U-tube BHEs and ~150 for coaxial BHEs. Results of a sensitivity study that quantify the effects of different design and storage formation parameters on temperature distribution and storage efficiency for heat storage using multiple BHEs are then shown. It is found that storage efficiency strongly depends on the number of BHEs composing the storage site, their distance and
Optimization methods and silicon solar cell numerical models
NASA Technical Reports Server (NTRS)
Girardini, K.
1986-01-01
The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.
Numerical methods for scattering from electrically large objects
NASA Astrophysics Data System (ADS)
Enguist, Bjorn; Murphy, W. D.; Rokhlin, Vladimir; Vassiliou, Marius S.
1991-05-01
A new and computationally very efficient integral equation numerical method for computing electromagnetic scattering and radar cross section (RCS) was developed. A theory of higher order impedance boundary conditions was derived to handle single and multiple dielectric coatings around conductors. The method was tested in two dimensions using a 14,000-line FORTRAN program and was found to be very promising for electrically large objects. Initial ideas for extensions to three dimensions were explored. Treatments of trailing edge and corner singularities were developed.
The instanton method and its numerical implementation in fluid mechanics
NASA Astrophysics Data System (ADS)
Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias
2015-08-01
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.
The Improvement of Efficiency in the Numerical Computation of Orbit Trajectories
NASA Technical Reports Server (NTRS)
Dyer, J.; Danchick, R.; Pierce, S.; Haney, R.
1972-01-01
An analysis, system design, programming, and evaluation of results are described for numerical computation of orbit trajectories. Evaluation of generalized methods, interaction of different formulations for satellite motion, transformation of equations of motion and integrator loads, and development of efficient integrators are also considered.
NUMERICAL CALCULATION: ASPIRATION EFFICIENCY OF AEROSOLS INTO THIN-WALLED SAMPLING INLETS
Aspiration efficiency of particles from a flowing airstream into a thin-walled sampling inlet is accurately predicted using a numerical model. he model combines the Boundary Integral Equation Method for predicting the velocity field into the inlet with an analytical solution to t...
Dielectric Boundary Forces in Numerical Poisson-Boltzmann Methods: Theory and Numerical Strategies.
Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray
2011-10-01
Continuum modeling of electrostatic interactions based upon the numerical solutions of the Poisson-Boltzmann equation has been widely adopted in biomolecular applications. To extend their applications to molecular dynamics and energy minimization, robust and efficient methodologies to compute solvation forces must be developed. In this study, we have first reviewed the theory for the computation of dielectric boundary forces based on the definition of the Maxwell stress tensor. This is followed by a new formulation of the dielectric boundary force suitable for the finite-difference Poisson-Boltzmann methods. We have validated the new formulation with idealized analytical systems and realistic molecular systems. PMID:22125339
Dielectric boundary force in numerical Poisson-Boltzmann methods: Theory and numerical strategies
NASA Astrophysics Data System (ADS)
Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray
2011-10-01
Continuum modeling of electrostatic interactions based upon the numerical solutions of the Poisson-Boltzmann equation has been widely adopted in biomolecular applications. To extend their applications to molecular dynamics and energy minimization, robust and efficient methodologies to compute solvation forces must be developed. In this study, we have first reviewed the theory for the computation of dielectric boundary force based on the definition of the Maxwell stress tensor. This is followed by a new formulation of the dielectric boundary force suitable for the finite-difference Poisson-Boltzmann methods. We have validated the new formulation with idealized analytical systems and realistic molecular systems.
A numerical efficient way to minimize classical density functional theory
NASA Astrophysics Data System (ADS)
Edelmann, Markus; Roth, Roland
2016-02-01
The minimization of the functional of the grand potential within the framework of classical density functional theory in three spatial dimensions can be numerically very demanding. The Picard iteration, that is often employed, is very simple and robust but can be rather slow. While a number of different algorithms for optimization problems have been suggested, there is still great need for additional strategies. Here, we present an approach based on the limited memory Broyden algorithm that is efficient and relatively simple to implement. We demonstrate the performance of this algorithm with the minimization of an inhomogeneous bulk structure of a fluid with competing interactions. For the problems we studied, we find that the presented algorithm improves performance by roughly a factor of three.
Numerical methods for analyzing electromagnetic scattering
NASA Technical Reports Server (NTRS)
Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.
1985-01-01
Numerical methods to analyze electromagnetic scattering are presented. The dispersions and attenuations of the normal modes in a circular waveguide coated with lossy material were completely analyzed. The radar cross section (RCS) from a circular waveguide coated with lossy material was calculated. The following is observed: (1) the interior irradiation contributes to the RCS much more than does the rim diffraction; (2) at low frequency, the RCS from the circular waveguide terminated by a perfect electric conductor (PEC) can be reduced more than 13 dB down with a coating thickness less than 1% of the radius using the best lossy material available in a 6 radius-long cylinder; (3) at high frequency, a modal separation between the highly attenuated and the lowly attenuated modes is evident if the coating material is too lossy, however, a large RCS reduction can be achieved for a small incident angle with a thin layer of coating. It is found that the waveguide coated with a lossy magnetic material can be used as a substitute for a corrugated waveguide to produce a circularly polarized radiation yield.
An efficient cuckoo search algorithm for numerical function optimization
NASA Astrophysics Data System (ADS)
Ong, Pauline; Zainuddin, Zarita
2013-04-01
Cuckoo search algorithm which reproduces the breeding strategy of the best known brood parasitic bird, the cuckoos has demonstrated its superiority in obtaining the global solution for numerical optimization problems. However, the involvement of fixed step approach in its exploration and exploitation behavior might slow down the search process considerably. In this regards, an improved cuckoo search algorithm with adaptive step size adjustment is introduced and its feasibility on a variety of benchmarks is validated. The obtained results show that the proposed scheme outperforms the standard cuckoo search algorithm in terms of convergence characteristic while preserving the fascinating features of the original method.
NASA Astrophysics Data System (ADS)
Clark, Martyn P.; Kavetski, Dmitri
2010-10-01
A major neglected weakness of many current hydrological models is the numerical method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping schemes in terms of numerical reliability and computational efficiency in the context of conceptual hydrological modeling. Numerical experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the numerical errors of fixed-step explicit schemes commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where numerical errors compensate for model structural errors. Simply running fixed-step explicit schemes with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit schemes with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping schemes investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of numerical errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust numerical implementation.
[Numerical methods for multi-fluid flows]. Final progress report
Pozrikidis, C.
1998-07-21
The central objective of this research has been to develop efficient numerical methods for computing multi-fluid flows with large interfacial deformations, and apply these methods to study the rheology of suspensions of deformable particles with viscous and non-Newtonian interfacial behavior. The mathematical formulation employs boundary-integral, immersed-boundary, and related numerical methods. Particles of interest include liquid drops with constant surface tension and capsules whose interfaces exhibit viscoelastic and incompressible characteristics. In one family of problems, the author has considered the shear-driven and pressure-driven flow of a suspension of two-dimensional liquid drops with ordered and random structure. In a second series of investigations, the author carried out dynamic simulations of two-dimensional, unbounded, doubly-periodic shear flows with random structure. Another family of problems addresses the deformation of three-dimensional capsules whose interfaces exhibit isotropic surface tension, viscous, elastic, or incompressible behavior, in simple shear flow. The numerical results extend previous asymptotic theories for small deformations and illuminate the mechanism of membrane rupture.
NASA Astrophysics Data System (ADS)
Acebrón, Juan A.; Rodríguez-Rozas, Ángel
2013-10-01
An efficient numerical method based on a probabilistic representation for the Vlasov-Poisson system of equations in the Fourier space has been derived. This has been done theoretically for arbitrary dimensional problems, and particularized to unidimensional problems for numerical purposes. Such a representation has been validated theoretically in the linear regime comparing the solution obtained with the classical results of the linear Landau damping. The numerical strategy followed requires generating suitable random trees combined with a Padé approximant for approximating accurately a given divergent series. Such series are obtained by summing the partial contributions to the solution coming from trees with arbitrary number of branches. These contributions, coming in general from multi-dimensional definite integrals, are efficiently computed by a quasi-Monte Carlo method. It is shown how the accuracy of the method can be effectively increased by considering more terms of the series. The new representation was used successfully to develop a Probabilistic Domain Decomposition method suited for massively parallel computers, which improves the scalability found in classical methods. Finally, a few numerical examples based on classical phenomena such as the non-linear Landau damping, and the two streaming instability are given, illustrating the remarkable performance of the algorithm, when compared the results with those obtained using a classical method.
NASA Astrophysics Data System (ADS)
Kornhaas, Michael; Schäfer, Michael; Sternel, Dörte C.
2015-06-01
An integrated hybrid approach for the numerical simulation of aeroacoustics at low Mach numbers is presented. The method is based on a viscous/acoustic splitting. The turbulent incompressible background flow is computed with large eddy simulation, based on the incompressible Navier-Stokes equations, whereas the acoustics are computed from linearized Euler equations with a high-resolution scheme. The focus is on the numerical efficiency of the approach. To accelerate the computations, hierarchical grids and a frozen fluid approach for the acoustics are employed and investigated. For validation and the investigation of the numerical efficiency and accuracy the sound emission of a plate in the turbulent wake of a circular cylinder is employed as a test case.
Numerical methods for the Poisson-Fermi equation in electrolytes
NASA Astrophysics Data System (ADS)
Liu, Jinn-Liang
2013-08-01
The Poisson-Fermi equation proposed by Bazant, Storey, and Kornyshev [Phys. Rev. Lett. 106 (2011) 046102] for ionic liquids is applied to and numerically studied for electrolytes and biological ion channels in three-dimensional space. This is a fourth-order nonlinear PDE that deals with both steric and correlation effects of all ions and solvent molecules involved in a model system. The Fermi distribution follows from classical lattice models of configurational entropy of finite size ions and solvent molecules and hence prevents the long and outstanding problem of unphysical divergence predicted by the Gouy-Chapman model at large potentials due to the Boltzmann distribution of point charges. The equation reduces to Poisson-Boltzmann if the correlation length vanishes. A simplified matched interface and boundary method exhibiting optimal convergence is first developed for this equation by using a gramicidin A channel model that illustrates challenging issues associated with the geometric singularities of molecular surfaces of channel proteins in realistic 3D simulations. Various numerical methods then follow to tackle a range of numerical problems concerning the fourth-order term, nonlinearity, stability, efficiency, and effectiveness. The most significant feature of the Poisson-Fermi equation, namely, its inclusion of steric and correlation effects, is demonstrated by showing good agreement with Monte Carlo simulation data for a charged wall model and an L type calcium channel model.
Advanced numerical methods in mesh generation and mesh adaptation
Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A
2010-01-01
Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge
Efficient Cfd/csd Coupling Methods for Aeroelastic Applications
NASA Astrophysics Data System (ADS)
Chen, Long; Xu, Tianhao; Xie, Jing
2016-06-01
A fast aeroelastic numerical simulation method using CFD/CSD coupling are developed. Generally, aeroelastic numerical simulation costs much time and significant hardware resources with CFD/CSD coupling. In this paper, dynamic grid method, full implicit scheme, parallel technology and improved coupling method are researched for efficiency simulation. An improved Delaunay graph mapping method is proposed for efficient dynamic grid deform. Hybrid grid finite volume method is used to solve unsteady flow fields. The dual time stepping method based on parallel implicit scheme is used in temporal discretization for efficiency simulation. An approximate system of linear equations is solved by the GMRES algorithm with a LU-SGS preconditioner. This method leads to a significant increase in performance over the explicit and LU-SGS implicit methods. A modification of LU-SGS is proposed to improve the parallel performance. Parallel computing overs a very effective way to improve our productivity in doing CFD/CFD coupling analysis. Improved loose coupling method is an efficiency way over the loose coupling method and tight coupling method. 3D wing's aeroelastic phenomenon is simulated by solving Reynolds-averaged Navier-Stokes equations using improved loose coupling method. The flutter boundary is calculated and agrees well with experimental data. The transonic hole is very clear in numerical simulation results.
Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods
NASA Technical Reports Server (NTRS)
Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark
2002-01-01
Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.
Numerical method of characteristics for one-dimensional blood flow
NASA Astrophysics Data System (ADS)
Acosta, Sebastian; Puelz, Charles; Rivière, Béatrice; Penny, Daniel J.; Rusin, Craig G.
2015-08-01
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.
Finite element methods in numerical relativity.
NASA Astrophysics Data System (ADS)
Mann, P. J.
The finite element method is very successful in Newtonian fluid simulations, and can be extended to relativitstic fluid flows. This paper describes the general method, and then outlines some preliminary results for spherically symmetric geometries. The mixed finite element - finite difference scheme is introduced, and used for the description of spherically symmetric collapse. Baker's (Newtonian) shock modelling method and Miller's moving finite element method are also mentioned. Collapse in double-null coordinates requires non-constant time slicing, so the full finite element method in space and time is described.
Numerical matrix method for quantum periodic potentials
NASA Astrophysics Data System (ADS)
Le Vot, Felipe; Meléndez, Juan J.; Yuste, Santos B.
2016-06-01
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the wave functions as finite superpositions of eigenfunctions of the infinite well. A matrix eigenvalue equation then yields the energy levels of the periodic potential within an acceptable accuracy. The methodology has been successfully used to deal with problems based on the well-known Kronig-Penney (KP) model. Besides the original model, these problems are a dimerized KP solid, a KP solid containing a surface, and a KP solid under an external field. A short list of additional problems that can be solved with this procedure is presented.
Method for numerical simulations of metastable states
Heller, U.M.; Seiberg, N.
1983-06-15
We present a numerical simulation of metastable states near a first-order phase transition in the example of a U(1) lattice gauge theory with a generalized action. In order to make measurements in these states possible their decay has to be prevented. We achieve this by using a microcanonical simulation for a finite system. We then obtain the coupling constant (inverse temperature) as a function of the action density. It turns out to be nonmonotonic and hence not uniquely invertible. From it we derive the effective potential for the action density. This effective potential is not always convex, a property that seems to be in contradiction with the standard lore about its convexity. This apparent ''paradox'' is resolved in a discussion about different definitions of the effective potential.
Interpolation Method Needed for Numerical Uncertainty
NASA Technical Reports Server (NTRS)
Groves, Curtis E.; Ilie, Marcel; Schallhorn, Paul A.
2014-01-01
Using Computational Fluid Dynamics (CFD) to predict a flow field is an approximation to the exact problem and uncertainties exist. There is a method to approximate the errors in CFD via Richardson's Extrapolation. This method is based off of progressive grid refinement. To estimate the errors, the analyst must interpolate between at least three grids. This paper describes a study to find an appropriate interpolation scheme that can be used in Richardson's extrapolation or other uncertainty method to approximate errors.
Numerical methods in Markov chain modeling
NASA Technical Reports Server (NTRS)
Philippe, Bernard; Saad, Youcef; Stewart, William J.
1989-01-01
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
Computationally Efficient Numerical Model for the Evolution of Directional Ocean Surface Waves
NASA Astrophysics Data System (ADS)
Malej, M.; Choi, W.; Goullet, A.
2011-12-01
The main focus of this work has been the asymptotic and numerical modeling of weakly nonlinear ocean surface wave fields. In particular, a development of an efficient numerical model for the evolution of nonlinear ocean waves, including extreme waves known as Rogue/Freak waves, is of direct interest. Due to their elusive and destructive nature, the media often portrays Rogue waves as unimaginatively huge and unpredictable monsters of the sea. To address some of these concerns, derivations of reduced phase-resolving numerical models, based on the small wave steepness assumption, are presented and their corresponding numerical simulations via Fourier pseudo-spectral methods are discussed. The simulations are initialized with a well-known JONSWAP wave spectrum and different angular distributions are employed. Both deterministic and Monte-Carlo ensemble average simulations were carried out. Furthermore, this work concerns the development of a new computationally efficient numerical model for the short term prediction of evolving weakly nonlinear ocean surface waves. The derivations are originally based on the work of West et al. (1987) and since the waves in the ocean tend to travel primarily in one direction, the aforementioned new numerical model is derived with an additional assumption of a weak transverse dependence. In turn, comparisons of the ensemble averaged randomly initialized spectra, as well as deterministic surface-to-surface correlations are presented. The new model is shown to behave well in various directional wave fields and can potentially be a candidate for computationally efficient prediction and propagation of extreme ocean surface waves - Rogue/Freak waves.
Validation of a numerical method for unsteady flow calculations
Giles, M.; Haimes, R. . Dept. of Aeronautics and Astronautics)
1993-01-01
This paper describes and validates a numerical method for the calculation of unsteady inviscid and viscous flows. A companion paper compares experimental measurements of unsteady heat transfer on a transonic rotor with the corresponding computational results. The mathematical model is the Reynolds-averaged unsteady Navier-Stokes equations for a compressible ideal gas. Quasi-three-dimensionality is included through the use of a variable streamtube thickness. The numerical algorithm is unusual in two respects: (a) For reasons of efficiency and flexibility, it uses a hybrid Navier-Stokes/Euler method, and (b) to allow for the computation of stator/rotor combinations with arbitrary pitch ratio, a novel space-time coordinate transformation is used. Several test cases are presented to validate the performance of the computer program, UNSFLO. These include: (a) unsteady, inviscid flat plate cascade flows (b) steady and unsteady, viscous flat plate cascade flows, (c) steady turbine heat transfer and loss prediction. In the first two sets of cases comparisons are made with theory, and in the third the comparison is with experimental data.
A numerical method for the study of the circulation of the world ocean
Bryan, K.
1997-08-01
This paper describes a detail computational procedure involving a finite difference numerical schemes to study the circulation models of the world oceans. To obtain an efficient numerical method for low-frequency, large-scale current systems, surfaces gravity-inertial waves are filtered out by the rigid-lid approximation. Special features of the ocean circulation are resolved in the numerical model by allowing for a variable spacing in either the zonal or meridional direction. 20 refs., 5 figs., 1 tab.
A New High-Order Stable Numerical Method for Matrix Inversion
Haghani, F. Khaksar; Soleymani, F.
2014-01-01
A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfth-order convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding Moore-Penrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples. PMID:24688436
Efficient finite element method for grating profile reconstruction
NASA Astrophysics Data System (ADS)
Zhang, Ruming; Sun, Jiguang
2015-12-01
This paper concerns the reconstruction of grating profiles from scattering data. The inverse problem is formulated as an optimization problem with a regularization term. We devise an efficient finite element method (FEM) and employ a quasi-Newton method to solve it. For the direct problems, the FEM stiff and mass matrices are assembled once at the beginning of the numerical procedure. Then only minor changes are made to the mass matrix at each iteration, which significantly saves the computation cost. Numerical examples show that the method is effective and robust.
Efficient procedures for the numerical simulation of mid-size RNA kinetics
2012-01-01
Motivation Methods for simulating the kinetic folding of RNAs by numerically solving the chemical master equation have been developed since the late 90's, notably the programs Kinfold and Treekin with Barriers that are available in the Vienna RNA package. Our goal is to formulate extensions to the algorithms used, starting from the Gillespie algorithm, that will allow numerical simulations of mid-size (~ 60–150 nt) RNA kinetics in some practical cases where numerous distributions of folding times are desired. These extensions can contribute to analyses and predictions of RNA folding in biologically significant problems. Results By describing in a particular way the reduction of numerical simulations of RNA folding kinetics into the Gillespie stochastic simulation algorithm for chemical reactions, it is possible to formulate extensions to the basic algorithm that will exploit memoization and parallelism for efficient computations. These can be used to advance forward from the small examples demonstrated to larger examples of biological interest. Software The implementation that is described and used for the Gillespie algorithm is freely available by contacting the authors, noting that the efficient procedures suggested may also be applicable along with Vienna's Kinfold. PMID:22958879
Modelling asteroid brightness variations. I - Numerical methods
NASA Technical Reports Server (NTRS)
Karttunen, H.
1989-01-01
A method for generating lightcurves of asteroid models is presented. The effects of the shape of the asteroid and the scattering law of a surface element are distinctly separable, being described by chosen functions that can easily be changed. The shape is specified by means of two functions that yield the length of the radius vector and the normal vector of the surface at a given point. The general shape must be convex, but spherical concavities producing macroscopic shadowing can also be modeled.
NASA Technical Reports Server (NTRS)
Maccormack, R. W.
1978-01-01
The calculation of flow fields past aircraft configuration at flight Reynolds numbers is considered. Progress in devising accurate and efficient numerical methods, in understanding and modeling the physics of turbulence, and in developing reliable and powerful computer hardware is discussed. Emphasis is placed on efficient solutions to the Navier-Stokes equations.
Fast Numerical Methods for the Design of Layered Photonic Structures with Rough Interfaces
NASA Technical Reports Server (NTRS)
Komarevskiy, Nikolay; Braginsky, Leonid; Shklover, Valery; Hafner, Christian; Lawson, John
2011-01-01
Modified boundary conditions (MBC) and a multilayer approach (MA) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with arbitrary permittivity tensor. MBC and MA are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.
Two Different Methods for Numerical Solution of the Modified Burgers' Equation
Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi
2014-01-01
A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM. PMID:25162064
A numerical method for power plant simulations
Carcasci, C.; Facchini, B.
1996-03-01
This paper describes a highly flexible computerized method of calculating operating data in a power cycle. The computerized method presented here permits the study of steam, gas and combined plants. Its flexibility is not restricted by any defined cycle scheme. A power plant consists of simple elements (turbine, compressor, combustor chamber, pump, etc.). Each power plant component is represented by its typical equations relating to fundamental mechanical and thermodynamic laws, so a power plant system is represented by algebraic equations, which are the typical equations of components, continuity equations, and data concerning plant conditions. This equation system is not linear, but can be reduced to a linear equation system with variable coefficients. The solution is simultaneous for each component and it is determined by an iterative process. An example of a simple gas turbine cycle demonstrates the applied technique. This paper also presents the user interface based on MS-Windows. The input data, the results, and any characteristic parameters of a complex cycle scheme are also shown.
Numerical methods for analyzing electromagnetic scattering
NASA Technical Reports Server (NTRS)
Lee, S. W.; Lo, Y. T.; Chuang, S. L.; Lee, C. S.
1985-01-01
Attenuation properties of the normal modes in an overmoded waveguide coated with a lossy material were analyzed. It is found that the low-order modes, can be significantly attenuated even with a thin layer of coating if the coating material is not too lossy. A thinner layer of coating is required for large attenuation of the low-order modes if the coating material is magnetic rather than dielectric. The Radar Cross Section (RCS) from an uncoated circular guide terminated by a perfect electric conductor was calculated and compared with available experimental data. It is confirmed that the interior irradiation contributes to the RCS. The equivalent-current method based on the geometrical theory of diffraction (GTD) was chosen for the calculation of the contribution from the rim diffraction. The RCS reduction from a coated circular guide terminated by a PEC are planned schemes for the experiments are included. The waveguide coated with a lossy magnetic material is suggested as a substitute for the corrugated waveguide.
Numerical study of efficiency for a 670 GHz gyrotron
Pu Ruifeng; Nusinovich, Gregory S.; Sinitsyn, Oleksandr V.; Antonsen, Thomas M. Jr.
2011-02-15
In this paper, the results of the efficiency study of a 670 GHz gyrotron operating at TE{sub 31,8}-mode are presented. Calculations are performed by using the self-consistent nonstationary code MAGY. Three cavity configurations were examined. The effects of ohmic losses and electron velocity spread were included in the simulation. The results show that the output efficiency can reach 35% and the velocity spread in the electron beam does not degrade the operation significantly. Furthermore, we verified that the smoothing of the sharp corners for a small tapering angle would reduce mode conversion; the parasitic excitation of neighboring radial modes is less than 1% of the amplitude of the operating mode and the effect on efficiency is small. Lastly, the simulation results show that the after-cavity interaction causes only slight variations in the efficiency.
Numerical study on the influence of boss cap fins on efficiency of controllable-pitch propeller
NASA Astrophysics Data System (ADS)
Xiong, Ying; Wang, Zhanzhi; Qi, Wanjiang
2013-03-01
Numerical simulation is investigated to disclose how propeller boss cap fins (PBCF) operate utilizing Reynolds-averaged Navier-Stokes (RANS) method. In addition, exploration of the influencing mechanism of PBCF on the open water efficiency of one controllable-pitch propeller is analyzed through the open water characteristic curves, blade surface pressure distribution and hub streamline distribution. On this basis, the influence of parameters including airfoil profile, diameter, axial position of installation and circumferential installation angle on the open water efficiency of the controllable-pitch propeller is investigated. Numerical results show: for the controllable-pitch propeller, the thrust generated is at the optimum when the radius of boss cap fins is 1.5 times of propeller hub with an optimal installation position in the axial direction, and its optimal circumferential installation position is the midpoint of the extension line of the front and back ends of two adjacent propeller roots in the front of fin root. Under these optimal parameters, the gain of open water efficiency of the controllable-pitch propeller with different advance velocity coefficients is greater than 0.01, which accounts for approximately an increase of 1%-5% of open water efficiency.
Numerical performance of projection methods in finite element consolidation models
NASA Astrophysics Data System (ADS)
Gambolati, Giuseppe; Pini, Giorgio; Ferronato, Massimiliano
2001-12-01
Projection, or conjugate gradient like, methods are becoming increasingly popular for the efficient solution of large sparse sets of unsymmetric indefinite equations arising from the numerical integration of (initial) boundary value problems. One such problem is soil consolidation coupling a flow and a structural model, typically solved by finite elements (FE) in space and a marching scheme in time (e.g. the Crank-Nicolson scheme). The attraction of a projection method stems from a number of factors, including the ease of implementation, the requirement of limited core memory and the low computational cost if a cheap and effective matrix preconditioner is available. In the present paper, biconjugate gradient stabilized (Bi- CGSTAB) is used to solve FE consolidation equations in 2-D and 3-D settings with variable time integration steps. Three different nodal orderings are selected along with the preconditioner ILUT based on incomplete triangular factorization and variable fill-in. The overall cost of the solver is made up of the preconditioning cost plus the cost to converge which is in turn related to the number of iterations and the elementary operations required by each iteration. The results show that nodal ordering affects the perfor mance of Bi-CGSTAB. For normally conditioned consolidation problems Bi-CGSTAB with the best ILUT preconditioner may converge in a number of iterations up to two order of magnitude smaller than the size of the FE model and proves an accurate, cost-effective and robust alternative to direct methods.
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver. PMID:26034665
Efficient and robust implementation of the TLISMNI method
NASA Astrophysics Data System (ADS)
Aboubakr, Ahmed K.; Shabana, Ahmed A.
2015-09-01
The dynamics of large scale and complex multibody systems (MBS) that include flexible bodies and contact/impact pairs is governed by stiff equations. Because explicit integration methods can be inefficient and often fail in the case of stiff problems, the use of implicit numerical integration methods is recommended in this case. This paper presents a new and efficient implementation of the two-loop implicit sparse matrix numerical integration (TLISMNI) method proposed for the solution of constrained rigid and flexible MBS differential and algebraic equations. The TLISMNI method has desirable features that include avoiding numerical differentiation of the forces, allowing for an efficient sparse matrix implementation, and ensuring that the kinematic constraint equations are satisfied at the position, velocity and acceleration levels. In this method, a sparse Lagrangian augmented form of the equations of motion that ensures that the constraints are satisfied at the acceleration level is used to solve for all the accelerations and Lagrange multipliers. The generalized coordinate partitioning or recursive methods can be used to satisfy the constraint equations at the position and velocity levels. In order to improve the efficiency and robustness of the TLISMNI method, the simple iteration and the Jacobian-Free Newton-Krylov approaches are used in this investigation. The new implementation is tested using several low order formulas that include Hilber-Hughes-Taylor (HHT), L-stable Park, A-stable Trapezoidal, and A-stable BDF methods. The HHT method allows for including numerical damping. Discussion on which method is more appropriate to use for a certain application is provided. The paper also discusses TLISMNI implementation issues including the step size selection, the convergence criteria, the error control, and the effect of the numerical damping. The use of the computer algorithm described in this paper is demonstrated by solving complex rigid and flexible tracked
Numerical Analysis on the Vortex Pattern and Flux Particle Dispersion in KR Method Using MPS Method
NASA Astrophysics Data System (ADS)
Hirata, N.; Xu, Y.; Anzai, K.
2015-06-01
The mechanically-stirring vessel is widely used in many fields, such as chemical reactor, bioreactor, and metallurgy, etc. The type of vortex mode that formed during impeller stirring has great effect on stirring efficiency, chemical reacting rate and air entrapment. Many efforts have been made to numerically simulate the fluid flow in the stirring vessel with classical Eulerian method. However, it is difficult to directly investigate the vortex mode and flux particle dispersion. Therefore, moving particle semi-implicit (MPS) method, which is based on Lagrangian method, is applied to simulate the fluid flow in a KR method in this practice. Top height and bottom heights of vortex surface in a steady state under several rotation speed was taken as key parameters to compare the results of numerical and published results. Flux particle dispersion behaviour under a rotation speed range from 80 to 480 rpm was also compared with the past study. The result shows that the numerical calculation has high consistency with experimental results. It is confirmed that the calculation using MPS method well reflected the vortex mode and flux particle dispersion in a mechanically-stirring vessel.
Numerical Methods for Two-Dimensional Stem Cell Tissue Growth.
Ovadia, Jeremy; Nie, Qing
2014-01-01
Growth of developing and regenerative biological tissues of different cell types is usually driven by stem cells and their local environment. Here, we present a computational framework for continuum tissue growth models consisting of stem cells, cell lineages, and diffusive molecules that regulate proliferation and differentiation through feedback. To deal with the moving boundaries of the models in both open geometries and closed geometries (through polar coordinates) in two dimensions, we transform the dynamic domains and governing equations to fixed domains, followed by solving for the transformation functions to track the interface explicitly. Clustering grid points in local regions for better efficiency and accuracy can be achieved by appropriate choices of the transformation. The equations resulting from the incompressibility of the tissue is approximated by high-order finite difference schemes and is solved using the multigrid algorithms. The numerical tests demonstrate an overall spatiotemporal second-order accuracy of the methods and their capability in capturing large deformations of the tissue boundaries. The methods are applied to two biological systems: stratified epithelia for studying the effects of two different types of stem cell niches and the scaling of a morphogen gradient with the size of the Drosophila imaginal wing disc during growth. Direct simulations of both systems suggest that that the computational framework is robust and accurate, and it can incorporate various biological processes critical to stem cell dynamics and tissue growth. PMID:24415847
A Novel Numerical Method for Fuzzy Boundary Value Problems
NASA Astrophysics Data System (ADS)
Can, E.; Bayrak, M. A.; Hicdurmaz
2016-05-01
In the present paper, a new numerical method is proposed for solving fuzzy differential equations which are utilized for the modeling problems in science and engineering. Fuzzy approach is selected due to its important applications on processing uncertainty or subjective information for mathematical models of physical problems. A second-order fuzzy linear boundary value problem is considered in particular due to its important applications in physics. Moreover, numerical experiments are presented to show the effectiveness of the proposed numerical method on specific physical problems such as heat conduction in an infinite plate and a fin.
Critical study of higher order numerical methods for solving the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1978-01-01
A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.
Application of higher-order numerical methods to the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1978-01-01
A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
Methods for studying close-track efficiency
Mac Mestayer; Konstantin Mikhaylov; Aleksey Stavinskiy; Alexander Vlassov
2004-05-01
Wire chambers used for particle tracking suffer a loss of efficiency when the trajectories of two particles from the same event are very close together in space. We describe two new methods for the study of this close-track efficiency. One is based on the study of a correlation function for particles with different masses as a function of their relative momenta in the laboratory reference system. The other method is based on the analysis of artificial events, constructed by merging raw data from separate events. Both methods and the standard Monte Carlo method were applied to data from the CLAS detector at Jefferson Laboratory. All three methods provide the same result for close-track efficiency with an accuracy sufficient for practical application.
Asymptotic-induced numerical methods for conservation laws
NASA Technical Reports Server (NTRS)
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
An efficient numerical technique for calculating thermal spreading resistance
NASA Technical Reports Server (NTRS)
Gale, E. H., Jr.
1973-01-01
The results of a thermal spreading resistance data generation technique study are reported. The method developed is discussed in detail, illustrative examples given, and the resulting computer program is included.
Photometry of dark atmosphereless planetary bodies: an efficient numerical model
NASA Astrophysics Data System (ADS)
Wilkman, Olli; Muinonen, Karri; Peltoniemi, Jouni
2015-12-01
We present a scattering model for regolith-covered Solar System bodies. It can be used to compute the intensity of light scattered by a surface consisting of packed, mutually shadowing particles. Our intention is to provide a model in which other researchers can apply in studies of Solar System photometry. Our model is a Lommel-Seeliger type model, representing a medium composed of individual scatterers with small single-scattering albedo. This means that it is suitable for dark regolith surfaces such as the Moon and many classes of asteroids. Our model adds an additional term which takes into account the mutual shadowing between the scatterers. The scatterers can have an arbitrary phase function. We use a numerical ray-tracing simulation to compute the shadowing contribution. We present the model in a form which makes implementing it in existing software straightforward and fast. The model in practice is implemented as files containing pre-computed values of the surface reflection coefficient, which can be loaded into a user's program and used to compute the scattering in the desired viewing geometries. As the usage requires only a little simple arithmetic and a table look-up, it is as fast to use as common analytical models.
A critical study of higher-order numerical methods for solving the boundary-layer equations
NASA Technical Reports Server (NTRS)
Wornom, S. F.
1977-01-01
A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
NASA Technical Reports Server (NTRS)
Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.
1992-01-01
The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.
Parallel processing numerical method for confined vortex dynamics and applications
NASA Astrophysics Data System (ADS)
Bistrian, Diana Alina
2013-10-01
This paper explores a combined analytical and numerical technique to investigate the hydrodynamic instability of confined swirling flows, with application to vortex rope dynamics in a Francis turbine diffuser, in condition of sophisticated boundary constraints. We present a new approach based on the method of orthogonal decomposition in the Hilbert space, implemented with a spectral descriptor scheme in discrete space. A parallel implementation of the numerical scheme is conducted reducing the computational time compared to other techniques.
Collocation Method for Numerical Solution of Coupled Nonlinear Schroedinger Equation
Ismail, M. S.
2010-09-30
The coupled nonlinear Schroedinger equation models several interesting physical phenomena presents a model equation for optical fiber with linear birefringence. In this paper we use collocation method to solve this equation, we test this method for stability and accuracy. Numerical tests using single soliton and interaction of three solitons are used to test the resulting scheme.
Investigating Convergence Patterns for Numerical Methods Using Data Analysis
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2013-01-01
The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…
A numerical method for solving singular De`s
Mahaver, W.T.
1996-12-31
A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.
A new numerical method of total solar eclipse photography processing
NASA Astrophysics Data System (ADS)
Druckmüller, M.; Rušin, V.; Minarovjech, M.
2006-10-01
A new numerical method of image processing suitable for visualization of corona images taken during total solar eclipses is presented. This method allows us to study both small- and large-scale coronal structures that remain invisible on original images because of their very high dynamic range of the coronal brightness. The method is based on the use of adaptive filters inspired by human vision and the sensitivity of resulting images is thus very close to that of the human eye during an eclipse. A high precision alignment method for white-light corona images is also discussed. The proposed method highly improves a widely used unsharp masking method employing a radially blurred mask. The results of these numerical image processing techniques are illustrated by a series of images taken during eclipses of the last decade. The method minimizes the risk of processing artifacts.
Numerical analysis of a measured efficiency hysteresis on a bulb turbine model
NASA Astrophysics Data System (ADS)
Houde, S.; Carrier, A.; Buron, J. D.; Deschênes, C.
2014-03-01
Within the framework of the BulbT project, simulations were performed to understand the origin of a measured hysteresis on the efficiency hill chart of a bulb turbine model. This hysteresis is associated with a sharp drop of efficiency located at slightly higher discharge than the best efficiency operating condition. It appears as a variation in the turbine performance whether an operating condition located in the efficiency drop is reached from a lower or a higher discharge. This hysteresis was reproduced numerically using Reynolds Averaged Navier Stokes (RANS) simulations. The paper presents the experimental results, the numerical methodology and a comprehensive analysis of the simulations to shed light on this interesting phenomenon.
Algorithms for the Fractional Calculus: A Selection of Numerical Methods
NASA Technical Reports Server (NTRS)
Diethelm, K.; Ford, N. J.; Freed, A. D.; Luchko, Yu.
2003-01-01
Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes, etc. are formulated in terms of derivatives (and integrals) of fractional (non-integer) order. In this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context. We believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way.
25 Years of Self-organized Criticality: Numerical Detection Methods
NASA Astrophysics Data System (ADS)
McAteer, R. T. James; Aschwanden, Markus J.; Dimitropoulou, Michaila; Georgoulis, Manolis K.; Pruessner, Gunnar; Morales, Laura; Ireland, Jack; Abramenko, Valentyna
2016-01-01
The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.
Comparison of methods for numerical calculation of continuum damping
Bowden, G. W.; Hole, M. J.; Dennis, G. R.; Könies, A.; Gorelenkov, N. N.
2014-05-15
Continuum resonance damping is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this damping, particularly, in the case of the toroidicity-induced shear Alfvén eigenmode. This paper compares results obtained using an analytical perturbative approach with those found using resistive and complex contour numerical approaches. It is found that the perturbative method does not provide accurate agreement with reliable numerical methods for the range of parameters examined. This discrepancy exists even in the limit where damping approaches zero. When the perturbative technique is implemented using a standard finite element method, the damping estimate fails to converge with radial grid resolution. The finite elements used cannot accurately represent the eigenmode in the region of the continuum resonance, regardless of the number of radial grid points used.
NASA Astrophysics Data System (ADS)
Jones, Marvin Quenten, Jr.
The motion and behavior of quantum processes can be described by the Schrodinger equation using the wave function, Psi(x,t). The use of the Schrodinger equation to study quantum phenomena is known as Quantum Mechanics, akin to classical mechanics being the tool to study classical physics. This research focuses on the emphasis of numerical techniques: Finite-Difference, Fast Fourier Transform (spectral method), finite difference schemes such as the Leapfrog method and the Crank-Nicolson scheme and second quantization to solve and analyze the Schrodinger equation for the infinite square well problem, the free particle with periodic boundary conditions, the barrier problem, tight-binding hamiltonians and a potential wall problem. We discuss these techniques and the problems created to test how these different techniques draw both physical and numerical conclusions in a tabular summary. We observed both numerical stability and quantum stability (conservation of energy, probability, momentum, etc.). We found in our results that the Crank-Nicolson scheme is an unconditionally stable scheme and conserves probability (unitary), and momentum, though dissipative with energy. The time-independent problems conserved energy, momentum and were unitary, which is of interest, but we found when time-dependence was introduced, quantum stability (i.e. conservation of mass, momentum, etc.) was not implied by numerical stability. Hence, we observed schemes that were numerically stable, but not quantum stable as well as schemes that were quantum stable, but not numerically stable for all of time, t. We also observed that second quantization removed the issues with stability as the problem was transformed into a discrete problem. Moreover, all quantum information is conserved in second quantization. This method, however, does not work universally for all problems.
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
Extended RKN-type methods for numerical integration of perturbed oscillators
NASA Astrophysics Data System (ADS)
Yang, Hongli; Wu, Xinyuan; You, Xiong; Fang, Yonglei
2009-10-01
In this paper, extended Runge-Kutta-Nyström-type methods for the numerical integration of perturbed oscillators with low frequencies are presented, which inherit the framework of RKN methods and make full use of the special feature of the true flows for both the internal stages and the updates. Following the approach of J. Butcher, E. Hairer and G. Wanner, we develop a new kind of tree set to derive order conditions for the extended Runge-Kutta-Nyström-type methods. The numerical stability and phase properties of the new methods are analyzed. Numerical experiments are accompanied to show the applicability and efficiency of our new methods in comparison with some well-known high quality methods proposed in the scientific literature.
Toward cost-efficient sampling methods
NASA Astrophysics Data System (ADS)
Luo, Peng; Li, Yongli; Wu, Chong; Zhang, Guijie
2015-09-01
The sampling method has been paid much attention in the field of complex network in general and statistical physics in particular. This paper proposes two new sampling methods based on the idea that a small part of vertices with high node degree could possess the most structure information of a complex network. The two proposed sampling methods are efficient in sampling high degree nodes so that they would be useful even if the sampling rate is low, which means cost-efficient. The first new sampling method is developed on the basis of the widely used stratified random sampling (SRS) method and the second one improves the famous snowball sampling (SBS) method. In order to demonstrate the validity and accuracy of two new sampling methods, we compare them with the existing sampling methods in three commonly used simulation networks that are scale-free network, random network, small-world network, and also in two real networks. The experimental results illustrate that the two proposed sampling methods perform much better than the existing sampling methods in terms of achieving the true network structure characteristics reflected by clustering coefficient, Bonacich centrality and average path length, especially when the sampling rate is low.
Efficient stochastic Galerkin methods for random diffusion equations
Xiu Dongbin Shen Jie
2009-02-01
We discuss in this paper efficient solvers for stochastic diffusion equations in random media. We employ generalized polynomial chaos (gPC) expansion to express the solution in a convergent series and obtain a set of deterministic equations for the expansion coefficients by Galerkin projection. Although the resulting system of diffusion equations are coupled, we show that one can construct fast numerical methods to solve them in a decoupled fashion. The methods are based on separation of the diagonal terms and off-diagonal terms in the matrix of the Galerkin system. We examine properties of this matrix and show that the proposed method is unconditionally stable for unsteady problems and convergent for steady problems with a convergent rate independent of discretization parameters. Numerical examples are provided, for both steady and unsteady random diffusions, to support the analysis.
Efficient Methods of Estimating Switchgrass Biomass Supplies
Technology Transfer Automated Retrieval System (TEKTRAN)
Switchgrass (Panicum virgatum L.) is being developed as a biofuel feedstock for the United States. Efficient and accurate methods to estimate switchgrass biomass feedstock supply within a production area will be required by biorefineries. Our main objective was to determine the effectiveness of in...
Efficient Methods to Compute Genomic Predictions
Technology Transfer Automated Retrieval System (TEKTRAN)
Efficient methods for processing genomic data were developed to increase reliability of estimated breeding values and simultaneously estimate thousands of marker effects. Algorithms were derived and computer programs tested on simulated data for 50,000 markers and 2,967 bulls. Accurate estimates of ...
Numerical modeling of magnetic induction tomography using the impedance method.
Ramos, Airton; Wolff, Julia G B
2011-02-01
This article discusses the impedance method in the forward calculation in magnetic induction tomography (MIT). Magnetic field and eddy current distributions were obtained numerically for a sphere in the field of a coil and were compared with an analytical model. Additionally, numerical and experimental results for phase sensitivity in MIT were obtained and compared for a cylindrical object in a planar array of sensors. The results showed that the impedance method provides results that agree very well with reality in the frequency range from 100 kHz to 20 MHz and for low conductivity objects (10 S/m or less). This opens the possibility of using this numerical approach in image reconstruction in MIT. PMID:21229327
NASA Astrophysics Data System (ADS)
Dong, Suchuan
2015-11-01
This talk focuses on simulating the motion of a mixture of N (N>=2) immiscible incompressible fluids with given densities, dynamic viscosities and pairwise surface tensions. We present an N-phase formulation within the phase field framework that is thermodynamically consistent, in the sense that the formulation satisfies the conservations of mass/momentum, the second law of thermodynamics and Galilean invariance. We also present an efficient algorithm for numerically simulating the N-phase system. The algorithm has overcome the issues caused by the variable coefficient matrices associated with the variable mixture density/viscosity and the couplings among the (N-1) phase field variables and the flow variables. We compare simulation results with the Langmuir-de Gennes theory to demonstrate that the presented method produces physically accurate results for multiple fluid phases. Numerical experiments will be presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts to demonstrate the capabilities of the method for studying the interactions among multiple types of fluid interfaces. Support from NSF and ONR is gratefully acknowledged.
Numerical investigation of the thrust efficiency of a laser propelled vehicle
mulroy jr
1990-08-01
The flow situation for a thruster propelled by ablated gas which is energized by a laser pulse is numerically simulated. The flow is axisymmetric and nonsteady, and is assumed to be inviscid due to its high Reynolds number. The high pressure expansion of the laser heated gas generates thrust as it pushes against the vehicle. Gas expansion lateral to the thrust vector causes performance to decrease. The vehicle geometry and the laser pulse characteristics determine the degree to which the flow is one dimensional. As the thruster's parameters are varied, its impulse is calculated and compared to the limiting impulse of a one-dimensional system, and thus the thrust efficiency is computed. Lateral expansion losses computed by simulating the flow of the expanding gas time-accurately on a computer are far less than losses predicted using the method of characteristics, which is the best alternate means of computation. Flows which exhibit a substantial amount of lateral expansion can still yield an expansion efficiency which exceeds 70%. This finding has significant implications on the eventual design of flight hardware. Steger and Warming's flux split numerics for the Euler equations are modified for blast simulations into near vacuum ambient conditions. At the interface between the near vacuum ambient and the wave front, the solution is first order accurate but sufficiently robust to handle pressure ratios exceeding one million and density ratios exceeding 10,000 between the thrust gas and the ambient gas. Elsewhere the solution is second order accurate. The majority of the calculations performed assume an ideal gas equation of state with {gamma} = 1.2. The propellant Lithium Hydride has shown excellent promise in the laboratory, yielding I{sub sp} = 800-1000 sec. Equilibrium and kinetic modeling of LiH is undertaken, with a variable {gamma} of from 1.25 to 1.66 resulting from the kinetic assumptions of ionization equilibrium and frozen chemistry. These additional
COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE
Kritsuk, Alexei G.; Collins, David; Norman, Michael L.; Xu Hao E-mail: dccollins@lanl.gov
2011-08-10
Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the
Advanced numerical methods for three dimensional two-phase flow calculations
Toumi, I.; Caruge, D.
1997-07-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.
Anastassi, Z. A.; Simos, T. E.
2010-09-30
We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.
The TAB method for numerical calculation of spray droplet breakup
NASA Astrophysics Data System (ADS)
Orourke, P. J.; Amsden, A. A.
A short history is given of the major milestones in the development of the stochastic particle method for calculating liquid fuel sprays. The most recent advance has been the discovery of the importance of drop breakup in engine sprays. A new method, called TAB, for calculating drop breakup is presented. Some theoretical properties of the method are derived; its numerical implementation in the computer program KIVA is described; and comparisons are presented between TAB-method calculations and experiments and calculations using another breakup model.
Singularity Preserving Numerical Methods for Boundary Integral Equations
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki (Principal Investigator)
1996-01-01
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
An efficient numerical calculation of gravitational waves from extreme mass ratio inspirals
NASA Astrophysics Data System (ADS)
Fujita, Ryuichi; Hikida, Wataru; Tagoshi, Hideyuki
2009-03-01
Gravitational waves from extreme mass ratio inspirals are one of the important sources of LISA. We should calculate these waves so accurately that we can extract physical information of source by data analysis. Recently, we developed an efficient numerical method to compute gravitational waves from binary systems in which a point particle moves in circular orbits on the equatorial plane of the black hole. In this paper, we apply this method to compute gravitational waves from binary systems in which a point particle moves in general bound geodesic orbits of the black hole. We check the accuracy of our code using spherical symmetry of Schwarzschild black hole such that energy flux radiated by a point particle is independent of the inclination angle from the equatorial plane of black hole. We find that the accuracy of our code may be limited only by truncation of l, k and n -modes, where l is the degree of the spin-weighted spheroidal harmonics, and k and n are harmonics of the polar and radial motion, respectively. Then we evaluate the rate of change of three constants of motion, energy, angular momentum and the Carter constant, due to the emission of gravitational waves from a particle around Kerr black hole. This is the first time to compute the rate of change of the Carter constant using the adiabatic approximation. We also show that we can calculate gravitational waves accurately even in the case of high eccentric orbits. In this work, we truncate l mode up to 20 and estimated that relative accuracy of our numerical results are better than 10-5 even in the high eccentric case, e = 0.9. Our numerical code may be useful to make templates of extreme mass ratio inspirals.
Investigation of highly efficient satellite solution methods
NASA Technical Reports Server (NTRS)
Nacozy, P. E.; Scheifele, G.
1974-01-01
Methods for analyzing the stability of satellites are discussed. The subjects considered are: (1) time elements, (2) stabilization by external energy corrections, and (3) long term global solutions for the synchronous satellite. A set of canonical two-body elements referred to as Delaunay-similar elements is presented. In contrast to the classical Delaunay theory which has time as the independent variable, the D-S theory uses an independent variable which is a generalized true anomaly. The numerical integration of the canonical perturbation equations of these elements is developed.
A numerical method for interface problems in elastodynamics
NASA Technical Reports Server (NTRS)
Mcghee, D. S.
1984-01-01
The numerical implementation of a formulation for a class of interface problems in elastodynamics is discussed. This formulation combines the use of the finite element and boundary integral methods to represent the interior and the exteriro regions, respectively. In particular, the response of a semicylindrical alluvial valley in a homogeneous halfspace to incident antiplane SH waves is considered to determine the accuracy and convergence of the numerical procedure. Numerical results are obtained from several combinations of the incidence angle, frequency of excitation, and relative stiffness between the inclusion and the surrounding halfspace. The results tend to confirm the theoretical estimates that the convergence is of the order H(2) for the piecewise linear elements used. It was also observed that the accuracy descreases as the frequency of excitation increases or as the relative stiffness of the inclusion decreases.
Achieving better cooling of turbine blades using numerical simulation methods
NASA Astrophysics Data System (ADS)
Inozemtsev, A. A.; Tikhonov, A. S.; Sendyurev, C. I.; Samokhvalov, N. Yu.
2013-02-01
A new design of the first-stage nozzle vane for the turbine of a prospective gas-turbine engine is considered. The blade's thermal state is numerically simulated in conjugate statement using the ANSYS CFX 13.0 software package. Critical locations in the blade design are determined from the distribution of heat fluxes, and measures aimed at achieving more efficient cooling are analyzed. Essentially lower (by 50-100°C) maximal temperature of metal has been achieved owing to the results of the performed work.
Path Integrals and Exotic Options:. Methods and Numerical Results
NASA Astrophysics Data System (ADS)
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
An iterative analytic—numerical method for scattering from a target buried beneath a rough surface
NASA Astrophysics Data System (ADS)
Xu, Run-Wen; Guo, Li-Xin; Wang, Rui
2014-11-01
An efficiently iterative analytical—numerical method is proposed for two-dimensional (2D) electromagnetic scattering from a perfectly electric conducting (PEC) target buried under a dielectric rough surface. The basic idea is to employ the Kirchhoff approximation (KA) to accelerate the boundary integral method (BIM). Below the rough surface, an iterative system is designed between the rough surface and the target. The KA is used to simulate the initial field on the rough surface based on the Fresnel theory, while the target is analyzed by the boundary integral method to obtain a precise result. The fields between the rough surface and the target can be linked by the boundary integral equations below the rough surface. The technique presented here is highly efficient in terms of computational memory, time, and versatility. Numerical simulations of two typical models are carried out to validate the method.
Efficient variational Bayesian approximation method based on subspace optimization.
Zheng, Yuling; Fraysse, Aurélia; Rodet, Thomas
2015-02-01
Variational Bayesian approximations have been widely used in fully Bayesian inference for approximating an intractable posterior distribution by a separable one. Nevertheless, the classical variational Bayesian approximation (VBA) method suffers from slow convergence to the approximate solution when tackling large dimensional problems. To address this problem, we propose in this paper a more efficient VBA method. Actually, variational Bayesian issue can be seen as a functional optimization problem. The proposed method is based on the adaptation of subspace optimization methods in Hilbert spaces to the involved function space, in order to solve this optimization problem in an iterative way. The aim is to determine an optimal direction at each iteration in order to get a more efficient method. We highlight the efficiency of our new VBA method and demonstrate its application to image processing by considering an ill-posed linear inverse problem using a total variation prior. Comparisons with state of the art variational Bayesian methods through a numerical example show a notable improvement in computation time. PMID:25532179
Numerical simulation methods for the Rouse model in flow
NASA Astrophysics Data System (ADS)
Howard, Michael P.; Milner, Scott T.
2011-11-01
Simulation of the Rouse model in flow underlies a great variety of numerical investigations of polymer dynamics, in both entangled melts and solutions and in dilute solution. Typically a simple explicit stochastic Euler method is used to evolve the Rouse model. Here we compare this approach to an operator splitting method, which splits the evolution operator into stochastic linear and deterministic nonlinear parts and takes advantage of an analytical solution for the linear Rouse model in terms of the noise history. We show that this splitting method has second-order weak convergence, whereas the Euler method has only first-order weak convergence. Furthermore, the splitting method is unconditionally stable, in contrast to the limited stability range of the Euler method. Similar splitting methods are applicable to a broad class of problems in stochastic dynamics in which noise competes with ordering and flow to determine steady-state order parameter structures.
Numerical study of three-parameter matrix eigenvalue problem by Rayleigh quotient method
NASA Astrophysics Data System (ADS)
Bora, Niranjan; Baruah, Arun Kumar
2016-06-01
In this paper, an attempt is done to find approximate eigenvalues and the corresponding eigenvectors of three-parameter matrix eigenvalue problem by extending Rayleigh Quotient Iteration Method (RQIM), which is generally used to solve generalized eigenvalue problems of the form Ax = λBx. Convergence criteria of RQIM will be derived in terms of matrix 2-norm. We will test the computational efficiency of the Method analytically with the help of numerical examples. All calculations are done in MATLAB software.
Numerical Polynomial Homotopy Continuation Method and String Vacua
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
Homogenized Tomographic Models: a Tool for Efficient Numerical Modeling of Seismic Wave Propagation
NASA Astrophysics Data System (ADS)
Landes, M.; Capdeville, Y.; Shapiro, N.; Guilbert, J.
2013-12-01
Full seismic waveforms are frequently used to characterize details of seismic sources and to discriminate their origin. Prediction of realistic waveforms requires developing algorithms for fast and reliable simulation of seismic wave propagation in 3D models of Earth. Classical 3D seismic tomographic models often use a layered parameterization. However, computing exact wave propagation in layered models may result in mesh complexity and long computing time. These difficulties become crucial when considering regional scales with operational interests. The aim of our study is to develop a parameterization of seismic tomographic models adapted for efficient numerical modeling of the wave propagation within a given frequency range. We use a 'homogenization' approach to construct models smoothed at scale naturally imposed by their propagation characteristics at target frequencies. We start with defining a basis of continuous and smooth functions with a Principal Component Analysis based on the statistic of the homogenized CUB2 tomographic model. Then, we invert surface phase and the group velocities deduced from global tomographic maps with a Monte Carlo method to generate smooth depth profiles with a controlled number of unknowns at all grid points. The set of these profiles form a smooth 3D seismic velocity model designed for numerical wave propagation.
Projected discrete ordinates methods for numerical transport problems
Larsen, E.W.
1985-01-01
A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.
Vectorization on the star computer of several numerical methods for a fluid flow problem
NASA Technical Reports Server (NTRS)
Lambiotte, J. J., Jr.; Howser, L. M.
1974-01-01
A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.
Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly
2016-01-01
This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.
Fast and stable numerical method for neuronal modelling
NASA Astrophysics Data System (ADS)
Hashemi, Soheil; Abdolali, Ali
2016-11-01
Excitable cell modelling is of a prime interest in predicting and targeting neural activity. Two main limits in solving related equations are speed and stability of numerical method. Since there is a tradeoff between accuracy and speed, most previously presented methods for solving partial differential equations (PDE) are focused on one side. More speed means more accurate simulations and therefore better device designing. By considering the variables in finite differenced equation in proper time and calculating the unknowns in the specific sequence, a fast, stable and accurate method is introduced in this paper for solving neural partial differential equations. Propagation of action potential in giant axon is studied by proposed method and traditional methods. Speed, consistency and stability of the methods are compared and discussed. The proposed method is as fast as forward methods and as stable as backward methods. Forward methods are known as fastest methods and backward methods are stable in any circumstances. Complex structures can be simulated by proposed method due to speed and stability of the method.
Automatic numerical integration methods for Feynman integrals through 3-loop
NASA Astrophysics Data System (ADS)
de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.
2015-05-01
We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.
Numerical method for shear bands in ductile metal with inclusions
Plohr, Jee Yeon N; Plohr, Bradley J
2010-01-01
A numerical method for mesoscale simulation of high strain-rate loading of ductile metal containing inclusions is described. Because of small-scale inhomogeneities, such a composite material is prone to localized shear deformation (adiabatic shear bands). The modeling framework is the Generalized Method of Cells of Paley and Aboudi [Mech. Materials, vol. 14, pp. /27-139, 1992], which ensures that the micromechanical response of the material is reflected in the behavior of the composite at the mesoscale. To calculate the effective plastic strain rate when shear bands are present, the analytic and numerical analysis of shear bands by Glimm, Plohr, and Sharp [Mech. Materials, vol. 24, pp. 31-41, 1996] is adapted and extended.
Numerical Method for the Astronomical Almanac and Orbit Calculations
NASA Astrophysics Data System (ADS)
Kim, Kap-Sung
1993-12-01
We have calculated the astronomical almanac 1994 and simulated the trajectory of a satellite orbit considering all perturbative forces with various initial conditions. In this work, Gauss Jackson multistep integration method has been used to calculate our basic equation of motion with high numerical accuracy. It has been found that our results agree well with the Astronomical Almanac Data distributed by JPL of NASA and the orbit simulations have been carried out with fast speed, stability and excellent round-off error accumulation, comparing with other numerical methods. In order to be carried out our works on almanac and orbit calculations easily by anyone who uses a personal computer, we have made a computer program on graphical user interface to provide various menus for detail works selected by a mouse.
Asymptotic and Numerical Methods for Rapidly Rotating Buoyant Flow
NASA Astrophysics Data System (ADS)
Grooms, Ian G.
This thesis documents three investigations carried out in pursuance of a doctoral degree in applied mathematics at the University of Colorado (Boulder). The first investigation concerns the properties of rotating Rayleigh-Benard convection -- thermal convection in a rotating infinite plane layer between two constant-temperature boundaries. It is noted that in certain parameter regimes convective Taylor columns appear which dominate the dynamics, and a semi-analytical model of these is presented. Investigation of the columns and of various other properties of the flow is ongoing. The second investigation concerns the interactions between planetary-scale and mesoscale dynamics in the oceans. Using multiple-scale asymptotics the possible connections between planetary geostrophic and quasigeostrophic dynamics are investigated, and three different systems of coupled equations are derived. Possible use of these equations in conjunction with the method of superparameterization, and extension of the asymptotic methods to the interactions between mesoscale and submesoscale dynamics is ongoing. The third investigation concerns the linear stability properties of semi-implicit methods for the numerical integration of ordinary differential equations, focusing in particular on the linear stability of IMEX (Implicit-Explicit) methods and exponential integrators applied to systems of ordinary differential equations arising in the numerical solution of spatially discretized nonlinear partial differential equations containing both dispersive and dissipative linear terms. While these investigations may seem unrelated at first glance, some reflection shows that they are in fact closely linked. The investigation of rotating convection makes use of single-space, multiple-time-scale asymptotics to deal with dynamics strongly constrained by rotation. Although the context of thermal convection in an infinite layer seems somewhat removed from large-scale ocean dynamics, the asymptotic
NASA Technical Reports Server (NTRS)
Zeng, S.; Wesseling, P.
1993-01-01
The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.
Numerical method for wave forces acting on partially perforated caisson
NASA Astrophysics Data System (ADS)
Jiang, Feng; Tang, Xiao-cheng; Jin, Zhao; Zhang, Li; Chen, Hong-zhou
2015-04-01
The perforated caisson is widely applied to practical engineering because of its great advantages in effectively wave energy consumption and cost reduction. The attentions of many scientists were paid to the fluid-structure interaction between wave and perforated caisson studies, but until now, most concerns have been put on theoretical analysis and experimental model set up. In this paper, interaction between the wave and the partial perforated caisson in a 2D numerical wave flume is investigated by means of the renewed SPH algorithm, and the mathematical equations are in the form of SPH numerical approximation based on Navier-Stokes equations. The validity of the SPH mathematical method is examined and the simulated results are compared with the results of theoretical models, meanwhile the complex hydrodynamic characteristics when the water particles flow in or out of a wave absorbing chamber are analyzed and the wave pressure distribution of the perforated caisson is also addressed here. The relationship between the ratio of total horizontal force acting on caisson under regular waves and its influence factors is examined. The data show that the numerical calculation of the ratio of total horizontal force meets the empirical regression equation very well. The simulations of SPH about the wave nonlinearity and breaking are briefly depicted in the paper, suggesting that the advantages and great potentiality of the SPH method is significant compared with traditional methods.
An alternative numerical method for the stationary pulsar magnetosphere
NASA Astrophysics Data System (ADS)
Takamori, Yohsuke; Okawa, Hirotada; Takamoto, Makoto; Suwa, Yudai
2014-02-01
Stationary pulsar magnetospheres in the force-free system are governed by the pulsar equation. In 1999, Contopoulos, Kazanas, and Fendt (hereafter CKF) numerically solved the pulsar equation and obtained a pulsar magnetosphere model called the CKF solution that has both closed and open magnetic field lines. The CKF solution is a successful solution, but it contains a poloidal current sheet that flows along the last open field line. This current sheet is artificially added to make the current system closed. In this paper, we suggest an alternative method to solve the pulsar equation and construct pulsar magnetosphere models without a current sheet. In our method, the pulsar equation is decomposed into Ampère's law and the force-free condition. We numerically solve these equations simultaneously with a fixed poloidal current. As a result, we obtain a pulsar magnetosphere model without a current sheet, which is similar to the CKF solution near the neutron star and has a jet-like structure at a distance along the pole. In addition, we discuss physical properties of the model and find that the force-free condition breaks down in a vicinity of the light cylinder due to dissipation that is included implicitly in the numerical method.
An efficient method for inverse problems
NASA Technical Reports Server (NTRS)
Daripa, Prabir
1987-01-01
A new inverse method for aerodynamic design of subcritical airfoils is presented. The pressure distribution in this method can be prescribed in a natural way, i.e. as a function of arclength of the as yet unknown body. This inverse problem is shown to be mathematically equivalent to solving a single nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the free stream Mach number M(sub x) and the upstream flow direction theta(sub x). The existence of a solution for any given pressure distribution is discussed. The method is easy to implement and extremely efficient. We present a series of results for which comparisons are made with the known airfoils.
Neonatal thyroid screening: methods-efficiency-failures.
Yordam, N; Ozon, A
2003-12-01
Newborn screening for congenital hypothyroidism (CH) is one of the major achievements of preventive medicine, as the condition occurs frequently (1/4000 newborns) and results in brain damage if not detected and treated in the first few days of life. Measurement of T4 and/or TSH in dried blood spots collected on the second through fifth days of life are the most widely used methods in screening programs for CH currently. Some children with the disease may be missd in any screening program, however, owing to factors related to the disease itself and the methods employed in its detection, as well as factors ascribed to the element of human error, ie screening errors. The methods employed in newborn screening programs for CH, their efficiency in disease detecetion, and biological factors as well as screening errors leading to missed cases are discussed. PMID:16444156
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
NASA Astrophysics Data System (ADS)
Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.
2015-05-01
We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
Lucas, D.S.
2004-10-03
This paper covers the basics of the implementation of the control volume method in the context of the Homogeneous Equilibrium Model (HEM)(T/H) code using the conservation equations of mass, momentum, and energy. This primer uses the advection equation as a template. The discussion will cover the basic equations of the control volume portion of the course in the primer, which includes the advection equation, numerical methods, along with the implementation of the various equations via FORTRAN into computer programs and the final result for a three equation HEM code and its validation.
Integrated numerical methods for hypersonic aircraft cooling systems analysis
NASA Technical Reports Server (NTRS)
Petley, Dennis H.; Jones, Stuart C.; Dziedzic, William M.
1992-01-01
Numerical methods have been developed for the analysis of hypersonic aircraft cooling systems. A general purpose finite difference thermal analysis code is used to determine areas which must be cooled. Complex cooling networks of series and parallel flow can be analyzed using a finite difference computer program. Both internal fluid flow and heat transfer are analyzed, because increased heat flow causes a decrease in the flow of the coolant. The steady state solution is a successive point iterative method. The transient analysis uses implicit forward-backward differencing. Several examples of the use of the program in studies of hypersonic aircraft and rockets are provided.
NASA Astrophysics Data System (ADS)
Min, Xiaoyi
This thesis first presents the study of the interaction of electromagnetic waves with three-dimensional heterogeneous, dielectric, magnetic, and lossy bodies by surface integral equation modeling. Based on the equivalence principle, a set of coupled surface integral equations is formulated and then solved numerically by the method of moments. Triangular elements are used to model the interfaces of the heterogeneous body, and vector basis functions are defined to expand the unknown current in the formulation. The validity of this formulation is verified by applying it to concentric spheres for which an exact solution exists. The potential applications of this formulation to a partially coated sphere and a homogeneous human body are discussed. Next, this thesis also introduces an efficient new set of integral equations for treating the scattering problem of a perfectly conducting body coated with a thin magnetically lossy layer. These electric field integral equations and magnetic field integral equations are numerically solved by the method of moments (MoM). To validate the derived integral equations, an alternative method to solve the scattering problem of an infinite circular cylinder coated with a thin magnetic lossy layer has also been developed, based on the eigenmode expansion. Results for the radar cross section and current densities via the MoM and the eigenmode expansion method are compared. The agreement is excellent. The finite difference time domain method is subsequently implemented to solve a metallic object coated with a magnetic thin layer and numerical results are compared with that by the MoM. Finally, this thesis presents an application of the finite-difference time-domain approach to the problem of electromagnetic receiving and scattering by a cavity -backed antenna situated on an infinite conducting plane. This application involves modifications of Yee's model, which applies the difference approximations of field derivatives to differential
NASA Astrophysics Data System (ADS)
Čársky, Petr
2010-09-01
The UGU term was used as a model of the UGT term, and its evaluation by numerical quadrature was examined systematically with a training set of eight molecules. Minimum numbers of points have been determined for radial Gauss-Legendre and angular Lebedev quadratures that preserve the accuracy needed for practical applications. These quadratures are recommended for efficient calculation of electron scattering by polyatomic molecules.
Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems
Hykes, J. M.; Ferrer, R. M.
2013-07-01
The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is {sup 98}Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)
Numerical integration of population models satisfying conservation laws: NSFD methods.
Mickens, Ronald E
2007-10-01
Population models arising in ecology, epidemiology and mathematical biology may involve a conservation law, i.e. the total population is constant. In addition to these cases, other situations may occur for which the total population, asymptotically in time, approach a constant value. Since it is rarely the situation that the equations of motion can be analytically solved to obtain exact solutions, it follows that numerical techniques are needed to provide solutions. However, numerical procedures are only valid if they can reproduce fundamental properties of the differential equations modeling the phenomena of interest. We show that for population models, involving a dynamical conservation law the use of nonstandard finite difference (NSFD) methods allows the construction of discretization schemes such that they are dynamically consistent (DC) with the original differential equations. The paper will briefly discuss the NSFD methodology, the concept of DC, and illustrate their application to specific problems for population models. PMID:22876826
Time-dependent corona models - A numerical method
NASA Astrophysics Data System (ADS)
Korevaar, P.; van Leer, B.
1988-07-01
A time-dependent numerical method for calculating gas flows is described. The method is implicit and especially suitable for finding stationary flow solutions. Although the method is general in its application to ideal compressible fluids, this paper applies it to a stellar atmosphere, heated to coronal temperatures by dissipation of mechanical energy. The integration scheme is based on conservative upwind spatial differencing. The upwind switching is provided by Van Leer's method of differentiable flux-splitting. It is shown that the code can handle large differences in density: up to 14 orders of magnitude. Special attention is paid to the boundary conditions, which are made completely transparent to disturbances. Besides some test-results, converged solutions for various values of the initial mechanical flux are presented which are in good agreement with previous time-independent calculations.
Ryabinkin, Ilya G; Nagesh, Jayashree; Izmaylov, Artur F
2015-11-01
We have developed a numerical differentiation scheme that eliminates evaluation of overlap determinants in calculating the time-derivative nonadiabatic couplings (TDNACs). Evaluation of these determinants was the bottleneck in previous implementations of mixed quantum-classical methods using numerical differentiation of electronic wave functions in the Slater determinant representation. The central idea of our approach is, first, to reduce the analytic time derivatives of Slater determinants to time derivatives of molecular orbitals and then to apply a finite-difference formula. Benchmark calculations prove the efficiency of the proposed scheme showing impressive several-order-of-magnitude speedups of the TDNAC calculation step for midsize molecules. PMID:26538034
NASA Astrophysics Data System (ADS)
Lathuilière, Cyril; Baraille, Rémy; Le Boyer, Arnaud
2015-04-01
The French navy hydrographic service uses a modified version of the Hybrid coordinate ocean model (HYCOM) for operational oceanographic applications. In the framework of the COMODO project, a series of test cases has been carried out to measure the numerical efficiency of the model. It addresses a wide panel of oceanic processes (baroclinic eddy, baroclinic jet, coastal upwelling, internal tides) and is useful to examine most of numerical schemes (advection schemes, time stepping, pressure gradient, …). The objectives of this study are first to assess the numerical performance of the present model to guide the modelers to make the suitable choices, and second to examine how the performances may be improved in the next years. We examine the sensitivity of the main choices for Hycom (2th or 4th order advection schemes, and viscosity values) in baroclinic eddy and baroclinic jet test cases. Both test cases are run using increasing resolution. The highest resolution provides a reference for studying the coarser resolutions. In the baroclinic vortex test case, the second order vector form scheme is well performing whereas the 4th order scheme appears to be more accurate in the baroclinic jet test case. This is probably due to the lack of fine scale energy in the baroclinic vortex test case allowing simulations with very tiny dissipation rates. We focus then on the sensitivity of the performance to vertical coordinate choices. The ability of Hycom to switch between isopycnal coordinate and quasi geopotential coordinate provides useful insights for example on the sensitivity of numerical diapycnal mixing to remapping scheme. This is particularly visible on the internal tide test case. The type of vertical coordinate is also important for potential vorticity structures. The shape of the baroclinic vortex is found to be different in geopotential and isopycnal coordinates. At coarse resolution, the potential vorticity structures seem to be better resolved in isopycnal
Novel Parallel Numerical Methods for Radiation& Neutron Transport
Brown, P N
2001-03-06
In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both.
NASA Astrophysics Data System (ADS)
Tang, Xiaojun
2016-04-01
The main purpose of this work is to provide multiple-interval integral Gegenbauer pseudospectral methods for solving optimal control problems. The latest developed single-interval integral Gauss/(flipped Radau) pseudospectral methods can be viewed as special cases of the proposed methods. We present an exact and efficient approach to compute the mesh pseudospectral integration matrices for the Gegenbauer-Gauss and flipped Gegenbauer-Gauss-Radau points. Numerical results on benchmark optimal control problems confirm the ability of the proposed methods to obtain highly accurate solutions.
High-performance Integrated numerical methods for Two-phase Flow in Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
Chueh, Chih-Che; Djilali, Ned; Bangerth, Wolfgang
2010-11-01
Modelling of two-phase flow in heterogeneous porous media has been playing a decisive role in a variety of areas. However, how to efficiently and accurately solve the governing equation in the flow in porous media remains a challenge. In order to ensure the accurate representative flow field and simultaneously increase the computational efficiency, we incorporate a number of state-of-the-art techniques into a numerical framework on which more complicated models in the field of multi-phase flow in porous media will be based. Such a numerical framework consists of a h-adaptive refinement method, an entropy-based artificial diffusive term, a new adaptive operator splitting method and efficient preconditioners. In particular, it is emphasized that we propose a new efficient adaptive operator splitting to avoid solving a time-consuming pressure-velocity part every saturation time step and, most importantly, we also provide a theoretically numerical analysis as well as proof. A few benchmarks will be demonstrated in the presentation.
Numerical analysis on the cutting and finishing efficiency of MRAFF process
NASA Astrophysics Data System (ADS)
Lih, F. L.
2016-03-01
The aim of the present research is to conduct a numerical study of the characteristic of a two-phase magnetorheological fluid with different operation conditions by the finite volume method called SIMPLE with an add-on MHD code.
A numerical method to study the dynamics of capillary fluid systems
NASA Astrophysics Data System (ADS)
Herrada, M. A.; Montanero, J. M.
2016-02-01
We propose a numerical approach to study both the nonlinear dynamics and linear stability of capillary fluid systems. In the nonlinear analysis, the time-dependent fluid region is mapped onto a fixed numerical domain through a coordinate transformation. The hydrodynamic equations are spatially discretized with the Chebyshev spectral collocation technique, while an implicit time advancement is performed using second-order backward finite differences. The resulting algebraic equations are solved with the iterative Newton-Raphson technique. The most novel aspect of the method is the fact that the elements of the Jacobian of the discretized system of equations are symbolic functions calculated before running the simulation. These functions are evaluated numerically in the Newton-Raphson iterations to find the solution at each time step, which reduces considerably the computing time. Besides, this numerical procedure can be easily adapted to solve the eigenvalue problem which determines the linear global modes of the capillary system. Therefore, both the nonlinear dynamics and the linear stability analysis can be conducted with essentially the same algorithm. We validate this numerical approach by studying the dynamics of a liquid bridge close to its minimum volume stability limit. The results are virtually the same as those obtained with other methods. The proposed approach proves to be much more computationally efficient than those other methods. Finally, we show the versatility of the method by calculating the linear global modes of a gravitational jet.
Flexible, reconfigurable, power efficient transmitter and method
NASA Technical Reports Server (NTRS)
Bishop, James W. (Inventor); Zaki, Nazrul H. Mohd (Inventor); Newman, David Childress (Inventor); Bundick, Steven N. (Inventor)
2011-01-01
A flexible, reconfigurable, power efficient transmitter device and method is provided. In one embodiment, the method includes receiving outbound data and determining a mode of operation. When operating in a first mode the method may include modulation mapping the outbound data according a modulation scheme to provide first modulation mapped digital data, converting the first modulation mapped digital data to an analog signal that comprises an intermediate frequency (IF) analog signal, upconverting the IF analog signal to produce a first modulated radio frequency (RF) signal based on a local oscillator signal, amplifying the first RF modulated signal to produce a first RF output signal, and outputting the first RF output signal via an isolator. In a second mode of operation method may include modulation mapping the outbound data according a modulation scheme to provide second modulation mapped digital data, converting the second modulation mapped digital data to a first digital baseband signal, conditioning the first digital baseband signal to provide a first analog baseband signal, modulating one or more carriers with the first analog baseband signal to produce a second modulated RF signal based on a local oscillator signal, amplifying the second RF modulated signal to produce a second RF output signal, and outputting the second RF output signal via the isolator. The digital baseband signal may comprise an in-phase (I) digital baseband signal and a quadrature (Q) baseband signal.
Comparison of four stable numerical methods for Abel's integral equation
NASA Technical Reports Server (NTRS)
Murio, Diego A.; Mejia, Carlos E.
1991-01-01
The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.
Numerical Analysis of a Finite Element/Volume Penalty Method
NASA Astrophysics Data System (ADS)
Maury, Bertrand
The penalty method makes it possible to incorporate a large class of constraints in general purpose Finite Element solvers like freeFEM++. We present here some contributions to the numerical analysis of this method. We propose an abstract framework for this approach, together with some general error estimates based on the discretization parameter ɛ and the space discretization parameter h. As this work is motivated by the possibility to handle constraints like rigid motion for fluid-particle flows, we shall pay a special attention to a model problem of this kind, where the constraint is prescribed over a subdomain. We show how the abstract estimate can be applied to this situation, in the case where a non-body-fitted mesh is used. In addition, we describe how this method provides an approximation of the Lagrange multiplier associated to the constraint.
Numerical methods for high-dimensional probability density function equations
NASA Astrophysics Data System (ADS)
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016-01-01
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Improved numerical method for subchannel cross-flow calculations
Kaya, S.; Anghaie, S.
1986-01-01
COBRA-OSU is a fast running computer code for coupled kinetic and thermal-hydraulic analysis of nuclear reactor core subchannels, currently under development at Oregon State University. This code is a modified version of COBRA-IV with two major improved features. First, COBRA-OSU uses the Gaussian elimination method instead of Gauss-Seidel iteration for subchannel cross-flow calculation. Second, COBRA-OSU has an additional model for regionwise point reactor kinetics which includes all major feedback reactivity effects on calculation of the axial power profile during the course of a transient. This paper summarizes the improved numerical features of the COBRA-OSU code.
On a New Numerical Method for Solving General Variational Inequalities
NASA Astrophysics Data System (ADS)
Bnouhachem, Abdellah; Noor, Muhammad Aslam; Khalfaoui, Mohamed; Sheng, Zhaohan
In this paper, we suggest and analyze a new extragradient method for solving the general variational inequalities involving two operators. We also prove the global convergence of the proposed modified method under certain mild conditions. We used a self-adaptive technique to adjust parameter ρ at each iteration. It is proved theoretically that the lower-bound of the progress obtained by the proposed method is greater than that by the extragradient method. An example is given to illustrate the efficiency and its comparison with the extragradient method. Since the general variational inequalities include the classical variational inequalities and complementarity problems as special cases, our results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as an improvement and refinement of the previously known results in this field.
Willis, Catherine; Rubin, Jacob
1987-01-01
In this paper we consider examples of chemistry-affected transport processes in porous media. A moving boundary problem which arises during transport with precipitation-dissolution reactions is solved by three different numerical methods. Two of these methods (one explicit and one implicit) are based on an integral formulation of mass balance and lead to an approximation of a weak solution. These methods are compared to a front-tracking scheme. Although the two approaches are conceptually different, the numerical solutions showed good agreement. As the ratio of dispersion to convection decreases, the methods based on the integral formulation become computationally more efficient. Specific reactions were modeled to examine the dependence of the system on the physical and chemical parameters.
An Efficient Coupled Dipole Method: TCDM
NASA Astrophysics Data System (ADS)
Kim, Hye-Young
2015-03-01
An overview of a memory-efficient and cost-effective method, called Trace-Coupled Dipole Method (TCDM), which can accurately predict the van der Waals (VDW) forces between dielectric materials will be presented. CDM is an intrinsically atomistic method which includes all the many-body interaction terms self-consistently. TCDM, an alternative way to execute CDM, is to obtain VDW interaction energy by calculating the trace of a 3NX3N matrix, rather than its eigenvalues. It will be demonstrated that the power series expansion in TCDM is equivalent to that of the perturbation theory. The advantage of adopting TCDM over the conventional perturbation theory or CDM will also be discussed. The use of TCDM will make it practical for any interested future users to calculate the accurate VDW interaction in large systems like those found in computer simulation studies without serious increase in computational burden. This research is supported by the Louisiana Board of Regents-RCS Grant (LEQSF(2012-15)-RD-A-19).
An Efficient Method for Computing All Reducts
NASA Astrophysics Data System (ADS)
Bao, Yongguang; Du, Xiaoyong; Deng, Mingrong; Ishii, Naohiro
In the process of data mining of decision table using Rough Sets methodology, the main computational effort is associated with the determination of the reducts. Computing all reducts is a combinatorial NP-hard computational problem. Therefore the only way to achieve its faster execution is by providing an algorithm, with a better constant factor, which may solve this problem in reasonable time for real-life data sets. The purpose of this presentation is to propose two new efficient algorithms to compute reducts in information systems. The proposed algorithms are based on the proposition of reduct and the relation between the reduct and discernibility matrix. Experiments have been conducted on some real world domains in execution time. The results show it improves the execution time when compared with the other methods. In real application, we can combine the two proposed algorithms.
NASA Astrophysics Data System (ADS)
Ding, Ye; Zhu, Limin; Zhang, Xiaojian; Ding, Han
2012-09-01
As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.
Efficient sensitivity analysis method for chaotic dynamical systems
NASA Astrophysics Data System (ADS)
Liao, Haitao
2016-05-01
The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results in an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.
Numerical methods for the simulation of a coalescence-driven droplet size distribution
NASA Astrophysics Data System (ADS)
Bordás, Róbert; John, Volker; Schmeyer, Ellen; Thévenin, Dominique
2013-06-01
The droplet size distribution in a turbulent flow field is considered and modeled by means of a population balance system. This paper studies different numerical methods for the 4D population balance equation and their impact on an output of interest, the time-space-averaged droplet size distribution at the outlet, which is known from experiments. These methods include different interpolations of the experimental data at the inlet, various discretizations in time and space, and different schemes for computing the coalescence integrals. It will be shown that noticeable changes in the output of interest might occur. In addition, the computational efficiency of the studied methods is discussed.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
D. S. Lucas
2004-10-01
A graduate level course for Thermal Hydraulics (T/H) was taught through Idaho State University in the spring of 2004. A numerical approach was taken for the content of this course since the students were employed at the Idaho National Laboratory and had been users of T/H codes. The majority of the students had expressed an interest in learning about the Courant Limit, mass error, semi-implicit and implicit numerical integration schemes in the context of a computer code. Since no introductory text was found the author developed notes taught from his own research and courses taught for Westinghouse on the subject. The course started with a primer on control volume methods and the construction of a Homogeneous Equilibrium Model (HEM) (T/H) code. The primer was valuable for giving the students the basics behind such codes and their evolution to more complex codes for Thermal Hydraulics and Computational Fluid Dynamics (CFD). The course covered additional material including the Finite Element Method and non-equilibrium (T/H). The control volume primer and the construction of a three-equation (mass, momentum and energy) HEM code are the subject of this paper . The Fortran version of the code covered in this paper is elementary compared to its descendants. The steam tables used are less accurate than the available commercial version written in C Coupled to a Graphical User Interface (GUI). The Fortran version and input files can be downloaded at www.microfusionlab.com.
NASA Astrophysics Data System (ADS)
Muthuvalu, Mohana Sundaram; Aruchunan, Elayaraja; Akhir, Mohd Kamalrulzaman Md; Sulaiman, Jumat; Karim, Samsul Ariffin Abdul
2014-10-01
In this paper, application of the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is extended by solving second order composite closed Newton-Cotes quadrature (2-CCNC) system. The performance of HSSOR method in solving 2-CCNC system is comparatively studied by their application on linear Fredholm integral equations of the second kind. The derivation and implementation of the method are discussed. In addition, numerical results by solving two test problems are included and compared with the standard Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) methods. Numerical results demonstrate that HSSOR method is an efficient method among the tested methods.
Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
NASA Astrophysics Data System (ADS)
Wu, Lei; White, Craig; Scanlon, Thomas J.; Reese, Jason M.; Zhang, Yonghao
2013-10-01
The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method [36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard-Jones, and rigid attracting potentials. The accuracy of the fast spectral method is checked by comparing our numerical solutions of the space-homogeneous Boltzmann equation with the exact Bobylev-Krook-Wu solutions for a gas of Maxwell molecules. It is found that the accuracy is improved by replacing the trapezoidal rule with Gauss-Legendre quadrature in the calculation of the kernel mode, and the conservation of momentum and energy are ensured by the Lagrangian multiplier method without loss of spectral accuracy. The relax-to-equilibrium processes of different collision kernels with the same value of shear viscosity are then compared; the numerical results indicate that different forms of the collision kernels can be used as long as the shear viscosity (not only the value, but also its temperature dependence) is recovered. An iteration scheme is employed to obtain stationary solutions of the space-inhomogeneous Boltzmann equation, where the numerical errors decay exponentially. Four classical benchmarking problems are investigated: the normal shock wave, and the planar Fourier/Couette/force-driven Poiseuille flows. For normal shock waves, our numerical results are compared with a finite difference solution of the Boltzmann equation for hard sphere molecules, experimental data, and molecular dynamics simulation of argon using the realistic Lennard-Jones potential. For planar Fourier/Couette/force-driven Poiseuille flows, our results are compared with the direct simulation Monte Carlo method. Excellent agreements are observed in all test cases
Numerical modeling of spray combustion with an advanced VOF method
NASA Technical Reports Server (NTRS)
Chen, Yen-Sen; Shang, Huan-Min; Shih, Ming-Hsin; Liaw, Paul
1995-01-01
This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.
An Efficient Numerical Solution To The Stochastic Coagulation Equation Based On Set of Moments
NASA Astrophysics Data System (ADS)
Rodin, A. V.
Stochastic coagulation equation (SCE) describes numerous processes of geophysi- cal and astrophysical interest, e.g. clouds and aerosol media. Although substantial progress is achieved in understanding microphysics of particular systems governed by the SCE, their interactive simulation in large-scale fluid dynamics models is hard to implement due to high computational cost demanded by calculation of the evolv- ing size distribution of interacting particles. On the other hand, in many cases SCE results in unimodal distributions of simple form, which macroscopic properties are determined by only few lower moments. Seeking for computationally efficient nu- merical scheme for ab initio simulation of the stochastic coagulation in large-scale models, a purely spectral conservative solution to the SCE based on a limited set of lower moments has been developed and tested against conventional gridpoint scheme. The method is based on offline averaging of a multidimensional quadratic function generated by the SCE over subset of test distributions constrained by moment rela- tionships. Effects of advection and sedimentation, as well as implications for the case of superlinear kernels leading to runaway coagulation, are discussed.
Asymmetric MRI magnet design using a hybrid numerical method.
Zhao, H; Crozier, S; Doddrell, D M
1999-12-01
This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. PMID:10579958
An unconditionally stable method for numerically solving solar sail spacecraft equations of motion
NASA Astrophysics Data System (ADS)
Karwas, Alex
Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach
NASA Astrophysics Data System (ADS)
Mehrling, T. J.; Robson, R. E.; Erbe, J.-H.; Osterhoff, J.
2016-09-01
This paper introduces a semi-analytic numerical approach (SANA) for the rapid computation of the transverse emittance of beams with finite energy spread in plasma wakefield accelerators in the blowout regime. The SANA method is used to model the beam emittance evolution when injected into and extracted from realistic plasma profiles. Results are compared to particle-in-cell simulations, establishing the accuracy and efficiency of the procedure. In addition, it is demonstrated that the tapering of vacuum-to-plasma and plasma-to-vacuum transitions is a viable method for the mitigation of emittance growth of beams during their injection and extraction from and into plasma cells.
A method for improving time-stepping numerics
NASA Astrophysics Data System (ADS)
Williams, P. D.
2012-04-01
In contemporary numerical simulations of the atmosphere, evidence suggests that time-stepping errors may be a significant component of total model error, on both weather and climate time-scales. This presentation will review the available evidence, and will then suggest a simple but effective method for substantially improving the time-stepping numerics at no extra computational expense. The most common time-stepping method is the leapfrog scheme combined with the Robert-Asselin (RA) filter. This method is used in the following atmospheric models (and many more): ECHAM, MAECHAM, MM5, CAM, MESO-NH, HIRLAM, KMCM, LIMA, SPEEDY, IGCM, PUMA, COSMO, FSU-GSM, FSU-NRSM, NCEP-GFS, NCEP-RSM, NSEAM, NOGAPS, RAMS, and CCSR/NIES-AGCM. Although the RA filter controls the time-splitting instability in these models, it also introduces non-physical damping and reduces the accuracy. This presentation proposes a simple modification to the RA filter. The modification has become known as the RAW filter (Williams 2011). When used in conjunction with the leapfrog scheme, the RAW filter eliminates the non-physical damping and increases the amplitude accuracy by two orders, yielding third-order accuracy. (The phase accuracy remains second-order.) The RAW filter can easily be incorporated into existing models, typically via the insertion of just a single line of code. Better simulations are obtained at no extra computational expense. Results will be shown from recent implementations of the RAW filter in various atmospheric models, including SPEEDY and COSMO. For example, in SPEEDY, the skill of weather forecasts is found to be significantly improved. In particular, in tropical surface pressure predictions, five-day forecasts made using the RAW filter have approximately the same skill as four-day forecasts made using the RA filter (Amezcua, Kalnay & Williams 2011). These improvements are encouraging for the use of the RAW filter in other models.
Unsaturated Shear Strength and Numerical Analysis Methods for Unsaturated Soils
NASA Astrophysics Data System (ADS)
Kim, D.; Kim, G.; Kim, D.; Baek, H.; Kang, S.
2011-12-01
The angles of shearing resistance(φb) and internal friction(φ') appear to be identical in low suction range, but the angle of shearing resistance shows non-linearity as suction increases. In most numerical analysis however, a fixed value for the angle of shearing resistance is applied even in low suction range for practical reasons, often leading to a false conclusion. In this study, a numerical analysis has been undertaken employing the estimated shear strength curve of unsaturated soils from the residual water content of SWCC proposed by Vanapalli et al.(1996). The result was also compared with that from a fixed value of φb. It is suggested that, in case it is difficult to measure the unsaturated shear strength curve through the triaxial soil tests, the estimated shear strength curve using the residual water content can be a useful alternative. This result was applied for analyzing the slope stablity of unsaturated soils. The effects of a continuous rainfall on slope stability were analyzed using a commercial program "SLOPE/W", with the coupled infiltration analysis program "SEEP/W" from the GEO-SLOPE International Ltd. The results show that, prior to the infiltration by the intensive rainfall, the safety factors using the estimated shear strength curve were substantially higher than that from the fixed value of φb at all time points. After the intensive infiltration, both methods showed a similar behavior.
A Hybrid Numerical Analysis Method for Structural Health Monitoring
NASA Technical Reports Server (NTRS)
Forth, Scott C.; Staroselsky, Alexander
2001-01-01
A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.
Space-time adaptive numerical methods for geophysical applications.
Castro, C E; Käser, M; Toro, E F
2009-11-28
In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space-time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost. PMID:19840984
Development of numerical methods to problems of micromechanics
NASA Astrophysics Data System (ADS)
Garcia-Martinez, Jose Ramon
In this dissertation we utilize the finite element method to investigate three micromechanical problems. In Chapter 2, we study the compliance contribution tensor H of multiple branched cracks. The cracks grow from a deltoid pore at their center into a triple crack. For plain strain conditions, two-dimensional models of the branched crack are modeled and solved in ABAQUS. The displacement field over the surface of the branched crack and the deltoid is curve fitted to carry out the integral surface of the compliance contribution tensor H. The predicted values are in good agreement with analytical solution. In Chapter 3 a three-dimensional finite element program using an unaligned mesh with an eight-node isoparametric element is developed to study the compliance contribution tensor H of cavities with superellipsoid shapes. A mesh clustering algorithm to increase the number of elements inside and near the superellipsoid surface to obtain a mesh independent solution is used. The numerical results are compared with the analytical solution of a sphere; the error of the numerical approximation varied from 8 to 11%. It is found that the number of elements inside the superellipsoid are insufficient. An algorithm to mesh independently the volumes inside and outside the cube is proposed to increase the accuracy in the calculation of H. As n1 and n2 increase, the numerical solutions show that, H1111 → 0 and H2211 → 0. Although, for these concave shapes no analytical solution exists a bound of 0 for the terms H 1111 and H2211 is suggested. Finally, in Chapter 4 a numerical verification of the cross-property connection between the effective fluid permeability and the effective electrical conductivity is study. A molecular dynamics algorithm is used to generate a set of different microstructural patterns. The volumetric average over a cubic volume is used to obtain the effective electrical conductivity and the effective fluid permeability. The tortuosity of the porous phase
Simultaneous source-mask optimization: a numerical combining method
NASA Astrophysics Data System (ADS)
Mülders, Thomas; Domnenko, Vitaliy; Küchler, Bernd; Klimpel, Thomas; Stock, Hans-Jürgen; Poonawala, Amyn A.; Taravade, Kunal N.; Stanton, William A.
2010-09-01
A new method for simultaneous Source-Mask Optimization (SMO) is presented. In order to produce optimum imaging fidelity with respect to exposure lattitude, depth of focus (DoF) and mask error enhancement factor (MEEF) the presented method aims to leverage both, the available degrees of freedom of a pixelated source and those available for the mask layout. The approach described in this paper is designed as to work with dissected mask polygons. The dissection of the mask patterns is to be performed in advance (before SMO) with the Synopsys Proteus OPC engine, providing the available degrees of freedom for mask pattern optimization. This is similar to mask optimization done for optical proximity correction (OPC). Additionally, however, the illumination source will be simultaneously optimized. The SMO approach borrows many of the performance enhancement methods of OPC software for mask correction, but is especially designed as to simultaneously optimize a pixelated source shape as nowadays available in production environments. Designed as a numerical optimization approach the method is able to assess in acceptable times several hundreds of thousands source-mask combinations for small, critical layout snippets. This allows a global optimization scheme to be applied to the SMO problem which is expected to better explore the optimization space and thus to yield an improved solution quality compared to local optimizations methods. The method is applied to an example system for investigating the impact of source constraints on the SMO results. Also, it is investigated how well possibly conflicting goals of low MEEF and large DoF can be balanced.
NASA Astrophysics Data System (ADS)
Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.
2010-10-01
Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.
NASA Astrophysics Data System (ADS)
Burago, N. G.; Nikitin, I. S.; Yakushev, V. L.
2016-06-01
Techniques that improve the accuracy of numerical solutions and reduce their computational costs are discussed as applied to continuum mechanics problems with complex time-varying geometry. The approach combines shock-capturing computations with the following methods: (1) overlapping meshes for specifying complex geometry; (2) elastic arbitrarily moving adaptive meshes for minimizing the approximation errors near shock waves, boundary layers, contact discontinuities, and moving boundaries; (3) matrix-free implementation of efficient iterative and explicit-implicit finite element schemes; (4) balancing viscosity (version of the stabilized Petrov-Galerkin method); (5) exponential adjustment of physical viscosity coefficients; and (6) stepwise correction of solutions for providing their monotonicity and conservativeness.
A method for data handling numerical results in parallel OpenFOAM simulations
NASA Astrophysics Data System (ADS)
Anton, Alin; Muntean, Sebastian
2015-12-01
Parallel computational fluid dynamics simulations produce vast amount of numerical result data. This paper introduces a method for reducing the size of the data by replaying the interprocessor traffic. The results are recovered only in certain regions of interest configured by the user. A known test case is used for several mesh partitioning scenarios using the OpenFOAM toolkit®[1]. The space savings obtained with classic algorithms remain constant for more than 60 Gb of floating point data. Our method is most efficient on large simulation meshes and is much better suited for compressing large scale simulation results than the regular algorithms.
NASA Technical Reports Server (NTRS)
Golik, W. L.
1996-01-01
A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with finite differences, and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and efficiency. Different smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.
A method for data handling numerical results in parallel OpenFOAM simulations
Anton, Alin; Muntean, Sebastian
2015-12-31
Parallel computational fluid dynamics simulations produce vast amount of numerical result data. This paper introduces a method for reducing the size of the data by replaying the interprocessor traffic. The results are recovered only in certain regions of interest configured by the user. A known test case is used for several mesh partitioning scenarios using the OpenFOAM toolkit{sup ®}[1]. The space savings obtained with classic algorithms remain constant for more than 60 Gb of floating point data. Our method is most efficient on large simulation meshes and is much better suited for compressing large scale simulation results than the regular algorithms.
Introduction to finite-difference methods for numerical fluid dynamics
Scannapieco, E.; Harlow, F.H.
1995-09-01
This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.
Advanced numerical methods and software approaches for semiconductor device simulation
CAREY,GRAHAM F.; PARDHANANI,A.L.; BOVA,STEVEN W.
2000-03-23
In this article the authors concisely present several modern strategies that are applicable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of upwind and artificial dissipation schemes, generalization of the traditional Scharfetter-Gummel approach, Petrov-Galerkin and streamline-upwind Petrov Galerkin (SUPG), entropy variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. They have included numerical examples from the recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and they emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, they briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.
a Numerical Method for Stability Analysis of Pinned Flexible Mechanisms
NASA Astrophysics Data System (ADS)
Beale, D. G.; Lee, S. W.
1996-05-01
A technique is presented to investigate the stability of mechanisms with pin-jointed flexible members. The method relies on a special floating frame from which elastic link co-ordinates are defined. Energies are easily developed for use in a Lagrange equation formulation, leading to a set of non-linear and mixed ordinary differential-algebraic equations of motion with constraints. Stability and bifurcation analysis is handled using a numerical procedure (generalized co-ordinate partitioning) that avoids the tedious and difficult task of analytically reducing the system of equations to a number equalling the system degrees of freedom. The proposed method was then applied to (1) a slider-crank mechanism with a flexible connecting rod and crank of constant rotational speed, and (2) a four-bar linkage with a flexible coupler with a constant speed crank. In both cases, a single pinned-pinned beam bending mode is employed to develop resonance curves and stability boundaries in the crank length-crank speed parameter plane. Flip and fold bifurcations are common occurrences in both mechanisms. The accuracy of the proposed method was also verified by comparison with previous experimental results [1].
Numerical Simulations of Granular Dynamics: Method and Tests
NASA Astrophysics Data System (ADS)
Richardson, Derek C.; Walsh, K. J.; Murdoch, N.; Michel, P.; Schwartz, S. R.
2010-10-01
We present a new particle-based numerical method for the simulation of granular dynamics, with application to motions of particles (regolith) on small solar system bodies and planetary surfaces [1]. The method employs the parallel N-body tree code pkdgrav [2] to search for collisions and compute particle trajectories. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. Several tests of the method are presented, including a model granular "atmosphere” that achieves correct energy equipartition, and a series of tumbler simulations that compare favorably with actual laboratory experiments [3]. DCR and SRS acknowledge NASA Grant No. NNX08AM39G and NSF Grant No. AST0524875; KJW, the Poincaré Fellowship at OCA; NM, Thales Alenia Space and The Open University; and PM and NM, the French Programme National de Planétologie. References: [1] Richardson et al. (2010), Icarus, submitted; [2] Cf. Richardson et al. (2009), P&SS 57, 183 and references therein; [3] Brucks et al. (2007), PRE 75, 032301-1-032301-4.
Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation
Carey, Graham F.; Pardhanani, A. L.; Bova, S. W.
2000-01-01
In this article we concisely present several modern strategies that are applicable to driftdominated carrier transport in higher-order deterministic models such as the driftdiffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of “upwind” and artificial dissipation schemes, generalization of the traditional Scharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind Petrov Galerkin (SUPG), “entropy” variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of themore » methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.« less
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.
Numerical Comparison of Periodic MoM (Method of Moments) and BMIA (Banded Matrix Iteration Method)
NASA Technical Reports Server (NTRS)
Kim, Y.; Rodriguez, E.; Michel, T.
1995-01-01
The most popular numerical technique in rough surface scattering is the Method of Moments (MoM). Since the scattering patch size is finite, the edge current must be suppressed to obtain accurate scattering cross sections. Two standard ways to minimize the edge current are periodic boundary conditions and incident wave tapering. We compare the accuracy & computational requirements of these methods.
A new numerical method for calculating extrema of received power for polarimetric SAR
Zhang, Y.; Zhang, Jiahua; Lu, Zhiming; Gong, W.
2009-01-01
A numerical method called cross-step iteration is proposed to calculate the maximal/minimal received power for polarized imagery based on a target's Kennaugh matrix. This method is much more efficient than the systematic method, which searches for the extrema of received power by varying the polarization ellipse angles of receiving and transmitting polarizations. It is also more advantageous than the Schuler method, which has been adopted by the PolSARPro package, because the cross-step iteration method requires less computation time and can derive both the maximal and minimal received powers, whereas the Schuler method is designed to work out only the maximal received power. The analytical model of received-power optimization indicates that the first eigenvalue of the Kennaugh matrix is the supremum of the maximal received power. The difference between these two parameters reflects the depolarization effect of the target's backscattering, which might be useful for target discrimination. ?? 2009 IEEE.
Borazjani, Iman; Westerdale, John; McMahon, Eileen M.; Rajaraman, Prathish K.; Heys, Jeffrey J.
2013-01-01
The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation. The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics. Improved understanding of LV hemodynamics is expected to provide important clinical diagnostic and prognostic information. We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV), due to its potential for broad and practical utility. Future research directions to advance patient-specific LV simulations include development of methods capable of resolving heart valves, higher temporal resolution, automated generation of three-dimensional (3D) geometry, and incorporating actual flow measurements into the numerical solution of the 3D cardiovascular fluid dynamics. PMID:23690874
Methods for increased computational efficiency of multibody simulations
NASA Astrophysics Data System (ADS)
Epple, Alexander
This thesis is concerned with the efficient numerical simulation of finite element based flexible multibody systems. Scaling operations are systematically applied to the governing index-3 differential algebraic equations in order to solve the problem of ill conditioning for small time step sizes. The importance of augmented Lagrangian terms is demonstrated. The use of fast sparse solvers is justified for the solution of the linearized equations of motion resulting in significant savings of computational costs. Three time stepping schemes for the integration of the governing equations of flexible multibody systems are discussed in detail. These schemes are the two-stage Radau IIA scheme, the energy decaying scheme, and the generalized-a method. Their formulations are adapted to the specific structure of the governing equations of flexible multibody systems. The efficiency of the time integration schemes is comprehensively evaluated on a series of test problems. Formulations for structural and constraint elements are reviewed and the problem of interpolation of finite rotations in geometrically exact structural elements is revisited. This results in the development of a new improved interpolation algorithm, which preserves the objectivity of the strain field and guarantees stable simulations in the presence of arbitrarily large rotations. Finally, strategies for the spatial discretization of beams in the presence of steep variations in cross-sectional properties are developed. These strategies reduce the number of degrees of freedom needed to accurately analyze beams with discontinuous properties, resulting in improved computational efficiency.
Numerical Methods for Forward and Inverse Problems in Discontinuous Media
Chartier, Timothy P.
2011-03-08
The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.
Numerical methods for determining interstitial oxygen in silicon
Stevenson, J.O.; Medernach, J.W.
1995-01-01
The interstitial oxygen (O{sub i}) concentration in Czochralski silicon and the subsequent SiO{sub x} precipitation are important parameters for integrated circuit fabrication. Uncontrolled SiO{sub x} precipitation during processing can create detrimental mechanical and electrical effects that contribute to poor performance. An inability to consistently and accurately measure the initial O{sub i} concentration in heavily doped silicon has led to contradictory results regarding the effects of dopant type and concentration on SiO{sub x} precipitation. The authors have developed a software package for reliably determining and comparing O{sub i} in heavily doped silicon. The SiFTIR{copyright} code implements three independent oxygen analysis methods in a single integrated package. Routine oxygen measurements are desirable over a wide range of silicon resistivities, but there has been confusion concerning which of the three numerical methods is most suitable for the low resistivity portion of the continuum. A major strength of the software is an ability to rapidly produce results for all three methods using only a single Fourier Transform Infrared Spectroscopy (FTIR) spectrum as input. This ability to perform three analyses on a single data set allows a detailed comparison of the three methods across the entire range of resistivities in question. Integrated circuit manufacturers could use the enabling technology provided by SiFTIR{copyright} to monitor O{sub i} content. Early detection of O{sub i} using this diagnostic could be beneficial in controlling SiO{sub x} precipitation during integrated circuit processing.
An efficient method for solving the steady Euler equations
NASA Technical Reports Server (NTRS)
Liou, M.-S.
1986-01-01
An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.
Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics
NASA Astrophysics Data System (ADS)
Rangan, Aaditya V.; Cai, David; Tao, Louis
2007-02-01
Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of
NASA Astrophysics Data System (ADS)
Katsaounis, T. D.
2005-02-01
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
A numerically efficient damping model for acoustic resonances in microfluidic cavities
NASA Astrophysics Data System (ADS)
Hahn, P.; Dual, J.
2015-06-01
Bulk acoustic wave devices are typically operated in a resonant state to achieve enhanced acoustic amplitudes and high acoustofluidic forces for the manipulation of microparticles. Among other loss mechanisms related to the structural parts of acoustofluidic devices, damping in the fluidic cavity is a crucial factor that limits the attainable acoustic amplitudes. In the analytical part of this study, we quantify all relevant loss mechanisms related to the fluid inside acoustofluidic micro-devices. Subsequently, a numerical analysis of the time-harmonic visco-acoustic and thermo-visco-acoustic equations is carried out to verify the analytical results for 2D and 3D examples. The damping results are fitted into the framework of classical linear acoustics to set up a numerically efficient device model. For this purpose, all damping effects are combined into an acoustofluidic loss factor. Since some components of the acoustofluidic loss factor depend on the acoustic mode shape in the fluid cavity, we propose a two-step simulation procedure. In the first step, the loss factors are deduced from the simulated mode shape. Subsequently, a second simulation is invoked, taking all losses into account. Owing to its computational efficiency, the presented numerical device model is of great relevance for the simulation of acoustofluidic particle manipulation by means of acoustic radiation forces or acoustic streaming. For the first time, accurate 3D simulations of realistic micro-devices for the quantitative prediction of pressure amplitudes and the related acoustofluidic forces become feasible.
A numerically efficient damping model for acoustic resonances in microfluidic cavities
Hahn, P. Dual, J.
2015-06-15
Bulk acoustic wave devices are typically operated in a resonant state to achieve enhanced acoustic amplitudes and high acoustofluidic forces for the manipulation of microparticles. Among other loss mechanisms related to the structural parts of acoustofluidic devices, damping in the fluidic cavity is a crucial factor that limits the attainable acoustic amplitudes. In the analytical part of this study, we quantify all relevant loss mechanisms related to the fluid inside acoustofluidic micro-devices. Subsequently, a numerical analysis of the time-harmonic visco-acoustic and thermo-visco-acoustic equations is carried out to verify the analytical results for 2D and 3D examples. The damping results are fitted into the framework of classical linear acoustics to set up a numerically efficient device model. For this purpose, all damping effects are combined into an acoustofluidic loss factor. Since some components of the acoustofluidic loss factor depend on the acoustic mode shape in the fluid cavity, we propose a two-step simulation procedure. In the first step, the loss factors are deduced from the simulated mode shape. Subsequently, a second simulation is invoked, taking all losses into account. Owing to its computational efficiency, the presented numerical device model is of great relevance for the simulation of acoustofluidic particle manipulation by means of acoustic radiation forces or acoustic streaming. For the first time, accurate 3D simulations of realistic micro-devices for the quantitative prediction of pressure amplitudes and the related acoustofluidic forces become feasible.
AN ACCURATE AND EFFICIENT ALGORITHM FOR NUMERICAL SIMULATION OF CONDUCTION-TYPE PROBLEMS. (R824801)
A modification of the finite analytic numerical method for conduction-type (diffusion) problems is presented. The finite analytic discretization scheme is derived by means of the Fourier series expansion for the most general case of nonuniform grid and variabl...
Hybrid Numerical Methods for Multiscale Simulations of Subsurface Biogeochemical Processes
Scheibe, Timothy D.; Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.; Redden, George D.; Meakin, Paul
2007-08-01
Many subsurface flow and transport problems of importance today involve coupled non-linear flow, transport, and reaction in media exhibiting complex heterogeneity. In particular, problems involving biological mediation of reactions fall into this class of problems. Recent experimental research has revealed important details about the physical, chemical, and biological mechanisms involved in these processes at a variety of scales ranging from molecular to laboratory scales. However, it has not been practical or possible to translate detailed knowledge at small scales into reliable predictions of field-scale phenomena important for environmental management applications. A large assortment of numerical simulation tools have been developed, each with its own characteristic scale including molecular (e.g., molecular dynamics), microbial (e.g., cellular automata or particle individual-based models), pore (e.g., lattice-Boltzmann, pore network models, and discrete particle methods such as smoothed particle hydrodynamics) and continuum scales (e.g., traditional partial differential equations solved by finite difference or finite element methods). While many problems can be effectively addressed by one of these models at a single scale, some problems may require explicit integration of models across multiple scales. We are developing a hybrid multi-scale subsurface reactive transport modeling framework that integrates models with diverse representations of physics, chemistry and biology at different scales (sub-pore, pore and continuum). The modeling framework is being designed to take advantage of advanced computational technologies including parallel code components using the Common Component Architecture, parallel solvers, gridding, data and workflow management, and visualization. This paper describes the specific methods/codes being used at each scale, techniques used to directly and adaptively couple across model scales, and preliminary results of application to a
Numerical Weather Predictions Evaluation Using Spatial Verification Methods
NASA Astrophysics Data System (ADS)
Tegoulias, I.; Pytharoulis, I.; Kotsopoulos, S.; Kartsios, S.; Bampzelis, D.; Karacostas, T.
2014-12-01
During the last years high-resolution numerical weather prediction simulations have been used to examine meteorological events with increased convective activity. Traditional verification methods do not provide the desired level of information to evaluate those high-resolution simulations. To assess those limitations new spatial verification methods have been proposed. In the present study an attempt is made to estimate the ability of the WRF model (WRF -ARW ver3.5.1) to reproduce selected days with high convective activity during the year 2010 using those feature-based verification methods. Three model domains, covering Europe, the Mediterranean Sea and northern Africa (d01), the wider area of Greece (d02) and central Greece - Thessaly region (d03) are used at horizontal grid-spacings of 15km, 5km and 1km respectively. By alternating microphysics (Ferrier, WSM6, Goddard), boundary layer (YSU, MYJ) and cumulus convection (Kain--Fritsch, BMJ) schemes, a set of twelve model setups is obtained. The results of those simulations are evaluated against data obtained using a C-Band (5cm) radar located at the centre of the innermost domain. Spatial characteristics are well captured but with a variable time lag between simulation results and radar data. Acknowledgements: This research is cofinanced by the European Union (European Regional Development Fund) and Greek national funds, through the action "COOPERATION 2011: Partnerships of Production and Research Institutions in Focused Research and Technology Sectors" (contract number 11SYN_8_1088 - DAPHNE) in the framework of the operational programme "Competitiveness and Entrepreneurship" and Regions in Transition (OPC II, NSRF 2007--2013).
Transforming Mean and Osculating Elements Using Numerical Methods
NASA Technical Reports Server (NTRS)
Ely, Todd A.
2010-01-01
Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order
Transforming Mean and Osculating Elements Using Numerical Methods
NASA Astrophysics Data System (ADS)
Ely, Todd A.
2015-03-01
Mean element propagation of perturbed two body orbits has as its mathematical basis the averaging theory of nonlinear dynamical systems. Mean elements define an orbit's long-term evolution characteristics consisting of both secular and long-period effects. Using averaging theory, a near-identity transformation can be found that transforms between the mean elements and their osculating counterparts that augment the mean elements with short period effects. The ability to perform the conversion is necessary so that orbit design conducted in either mean elements or osculating can be effectively converted between each element type. In the present work, the near-identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the mean or osculating elements to first-order.
Trigonometrically fitted two step hybrid method for the numerical integration of second order IVPs
NASA Astrophysics Data System (ADS)
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2016-06-01
In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct trigonometrically fitted two step hybrid methods. We apply the new methods on the numerical integration of several test problems.
A Numerical Method for Determining Diffusivity from Annealing Experiments
NASA Astrophysics Data System (ADS)
Harris-Kuhlman, K. R.; Kulcinski, G. L.
1998-12-01
Terrestrial analogs of lunar ilmenite (FeTiO3) have been implanted with solar-wind energy 4He at 4 keV and 3He at 3 keV using Plasma Source Ion Implantation (PSII). Isochronal annealing of the samples revealed thermally induced 4He evolution similar to the helium release of the Apollo 11 regoliths reported by Pepin, et. al., [1970]. These annealing experiments are analyzed with a three dimensional numerical method based on Fick's law for diffusion. An iterative method is used to calculate the diffusivity. The code uses an assumed diffusivity to calculate the amount of gas released during a temperature step. The initial depth profile of the implanted species is generated using the TRIM electronic stopping code [Ziegler, 1996]. The calculated value is compared to the measured value and a linear regression is used to calculate a new diffusivity until there is convergence within a specified tolerance level. The diffusivity as a function of temperature is then fitted to an Arrhenius equation. Analysis of results for 4 keV 4He on ilmenite shows two distinct regions of Arrehnius behavior with activation energies of 0.5 +/- 0.1 eV at emperatures below 800 deg C and 1.5 +/- 0.2 eV at temperatures from 800 deg C to 1100 deg C. Pepin, R. O., L. E. Nyquist, D. Phinney, and D. C. Black (1970) "Rare Gases in Apollo 11 Lunar Material," Proceedings of the Apollo 11 Lunar Science Conference, 2, pp. 1435-1454. Ziegler, J. P. (1996) SRIM Instruction Manual: The Stopping and Range of Ions in Matter, (Yorktown, New York: IBM - Research); based on Ziegler, J. P., J. P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids, (New York: Pergamon Press, 1985).
On the efficient and reliable numerical solution of rate-and-state friction problems
NASA Astrophysics Data System (ADS)
Pipping, Elias; Kornhuber, Ralf; Rosenau, Matthias; Oncken, Onno
2016-03-01
We present a mathematically consistent numerical algorithm for the simulation of earthquake rupture with rate-and-state friction. Its main features are adaptive time stepping, a novel algebraic solution algorithm involving nonlinear multigrid and a fixed point iteration for the rate-and-state decoupling. The algorithm is applied to a laboratory scale subduction zone which allows us to compare our simulations with experimental results. Using physical parameters from the experiment, we find a good fit of recurrence time of slip events as well as their rupture width and peak slip. Computations in 3-D confirm efficiency and robustness of our algorithm.
Numerical discussion of a new method for amplitude estimation in noise-corrupted waveform signal
NASA Astrophysics Data System (ADS)
Le Gland, F.
A seemingly promising algorithm, whose purpose is to estimate the constant amplitude of a waveform signal, corrupted by both additive noise and phase-noise is presented. Principally comparisons with other algorithms, based on numerical simulations, are reported. It should be emphasized that this method (which appears to belong to the general class of maximum likelihood estimators) is highly efficient, even when the phase-noise is large. It is also more expensive, in terms of computational time, while there seems to be reasonable hope for an improvement in this direction.
Asuero, A G; Navas, M J; Jiminez-Trillo, J L
1986-02-01
The spectrophotometric methods applicable to the numerical evaluation of acidity constants of monobasic acids are briefly reviewed. The equations are presented in a form suitable for easy calculation with a programmable pocket calculator. The aim of this paper is to cover a gap in the education analytical literature. PMID:18964064
Active Problem Solving and Applied Research Methods in a Graduate Course on Numerical Methods
ERIC Educational Resources Information Center
Maase, Eric L.; High, Karen A.
2008-01-01
"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…
NASA Astrophysics Data System (ADS)
Arbabi, Amir; Horie, Yu; Ball, Alexander J.; Bagheri, Mahmood; Faraon, Andrei
2015-05-01
Flat optical devices thinner than a wavelength promise to replace conventional free-space components for wavefront and polarization control. Transmissive flat lenses are particularly interesting for applications in imaging and on-chip optoelectronic integration. Several designs based on plasmonic metasurfaces, high-contrast transmitarrays and gratings have been recently implemented but have not provided a performance comparable to conventional curved lenses. Here we report polarization-insensitive, micron-thick, high-contrast transmitarray micro-lenses with focal spots as small as 0.57 λ. The measured focusing efficiency is up to 82%. A rigorous method for ultrathin lens design, and the trade-off between high efficiency and small spot size (or large numerical aperture) are discussed. The micro-lenses, composed of silicon nano-posts on glass, are fabricated in one lithographic step that could be performed with high-throughput photo or nanoimprint lithography, thus enabling widespread adoption.
Arbabi, Amir; Horie, Yu; Ball, Alexander J; Bagheri, Mahmood; Faraon, Andrei
2015-01-01
Flat optical devices thinner than a wavelength promise to replace conventional free-space components for wavefront and polarization control. Transmissive flat lenses are particularly interesting for applications in imaging and on-chip optoelectronic integration. Several designs based on plasmonic metasurfaces, high-contrast transmitarrays and gratings have been recently implemented but have not provided a performance comparable to conventional curved lenses. Here we report polarization-insensitive, micron-thick, high-contrast transmitarray micro-lenses with focal spots as small as 0.57 λ. The measured focusing efficiency is up to 82%. A rigorous method for ultrathin lens design, and the trade-off between high efficiency and small spot size (or large numerical aperture) are discussed. The micro-lenses, composed of silicon nano-posts on glass, are fabricated in one lithographic step that could be performed with high-throughput photo or nanoimprint lithography, thus enabling widespread adoption. PMID:25947118
Conway, A; Wang, T; Deo, N; Cheung, C; Nikolic, R
2008-06-24
This work reports numerical simulations of a novel three-dimensionally integrated, {sup 10}boron ({sup 10}B) and silicon p+, intrinsic, n+ (PIN) diode micropillar array for thermal neutron detection. The inter-digitated device structure has a high probability of interaction between the Si PIN pillars and the charged particles (alpha and {sup 7}Li) created from the neutron - {sup 10}B reaction. In this work, the effect of both the 3-D geometry (including pillar diameter, separation and height) and energy loss mechanisms are investigated via simulations to predict the neutron detection efficiency and gamma discrimination of this structure. The simulation results are demonstrated to compare well with the measurement results. This indicates that upon scaling the pillar height, a high efficiency thermal neutron detector is possible.
NASA Astrophysics Data System (ADS)
Kramer, Alex; Thumm, Uwe
2016-05-01
We discuss a class of window-transform-based ``virtual detector'' methods for computing momentum-resolved dissociation and ionization spectra by numerically analyzing the motion of nuclear or electronic quantum-mechanical wavepackets at the periphery of their numerical grids. While prior applications of such surface-flux methods considered semi-classical limits to derive ionization and dissociation spectra, we systematically include quantum-mechanical corrections and extensions to higher dimensions, discussing numerical convergence properties and the computational efficiency of our method in comparison with alternative schemes for obtaining momentum distributions. Using the example of atomic ionization by co- and counter-rotating circularly polarized laser pulses, we scrutinize the efficiency of common finite-difference schemes for solving the time-dependent Schrödinger equation in virtual detection and standard Fourier-transformation methods for extracting momentum spectra. Supported by the DoE, NSF, and Alexander von Humboldt foundation.
NASA Astrophysics Data System (ADS)
Lazarus, A.; Miller, J. T.; Reis, P. M.
2013-08-01
We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by parameterizing the position of the centerline and making use of quaternions to represent the orientation of the material frame. The equilibrium equations and the stability of their solutions are derived from the mechanical energy which takes into account the contributions due to internal moments (bending and twist), external forces and torques. Our use of quaternions allows for the equilibrium equations to be written in a quadratic form and solved efficiently with an asymptotic numerical continuation method. This finite element perturbation method gives interactive access to semi-analytical equilibrium branches, in contrast with the individual solution points obtained from classical minimization or predictor-corrector techniques. By way of example, we apply our numerics to address the specific problem of a naturally curved and heavy rod under extreme twisting and perform a detailed comparison against our own precision model experiments of this system. Excellent quantitative agreement is found between experiments and simulations for the underlying 3D buckling instabilities and the characterization of the resulting complex configurations. We believe that our framework is a powerful alternative to other methods for the computation of nonlinear equilibrium 3D shapes of rods in practical scenarios.
Power Measurement Methods for Energy Efficient Applications
Calandrini, Guilherme; Gardel, Alfredo; Bravo, Ignacio; Revenga, Pedro; Lázaro, José L.; Toledo-Moreo, F. Javier
2013-01-01
Energy consumption constraints on computing systems are more important than ever. Maintenance costs for high performance systems are limiting the applicability of processing devices with large dissipation power. New solutions are needed to increase both the computation capability and the power efficiency. Moreover, energy efficient applications should balance performance vs. consumption. Therefore power data of components are important. This work presents the most remarkable alternatives to measure the power consumption of different types of computing systems, describing the advantages and limitations of available power measurement systems. Finally, a methodology is proposed to select the right power consumption measurement system taking into account precision of the measure, scalability and controllability of the acquisition system. PMID:23778191
NUMERICAL METHODS FOR THE SIMULATION OF HIGH INTENSITY HADRON SYNCHROTRONS.
LUCCIO, A.; D'IMPERIO, N.; MALITSKY, N.
2005-09-12
Numerical algorithms for PIC simulation of beam dynamics in a high intensity synchrotron on a parallel computer are presented. We introduce numerical solvers of the Laplace-Poisson equation in the presence of walls, and algorithms to compute tunes and twiss functions in the presence of space charge forces. The working code for the simulation here presented is SIMBAD, that can be run as stand alone or as part of the UAL (Unified Accelerator Libraries) package.
An efficient method for solving the steady Euler equations
NASA Technical Reports Server (NTRS)
Liou, M. S.
1986-01-01
An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.
Energy efficiency assessment methods and tools evaluation
McMordie, K.L.; Richman, E.E.; Keller, J.M.; Dixon, D.R.
1994-08-01
Many different methods of assessing the energy savings potential at federal installations, and identifying attractive projects for capital investment have been used by the different federal agencies. These methods range from high-level estimating tools to detailed design tools, both manual and software assisted. These methods have different purposes and provide results that are used for different parts of the project identification, and implementation process. Seven different assessment methods are evaluated in this study. These methods were selected by the program managers at the DoD Energy Policy Office, and DOE Federal Energy Management Program (FEMP). Each of the methods was applied to similar buildings at Bolling Air Force Base (AFB), unless it was inappropriate or the method was designed to make an installation-wide analysis, rather than focusing on particular buildings. Staff at Bolling AFB controlled the collection of data.
Cilfone, Nicholas A.; Kirschner, Denise E.; Linderman, Jennifer J.
2015-01-01
Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level. PMID:26366228
NASA Technical Reports Server (NTRS)
Wright, William B.
1988-01-01
Transient, numerical simulations of the deicing of composite aircraft components by electrothermal heating have been performed in a 2-D rectangular geometry. Seven numerical schemes and four solution methods were used to find the most efficient numerical procedure for this problem. The phase change in the ice was simulated using the Enthalpy method along with the Method for Assumed States. Numerical solutions illustrating deicer performance for various conditions are presented. Comparisons are made with previous numerical models and with experimental data. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.
Efficient positional misalignment correction method for Fourier ptychographic microscopy
Sun, Jiasong; Chen, Qian; Zhang, Yuzhen; Zuo, Chao
2016-01-01
Fourier ptychographic microscopy (FPM) is a newly developed super-resolution technique, which employs angularly varying illuminations and a phase retrieval algorithm to surpass the diffraction limit of a low numerical aperture (NA) objective lens. In current FPM imaging platforms, accurate knowledge of LED matrix’s position is critical to achieve good recovery quality. Furthermore, considering such a wide field-of-view (FOV) in FPM, different regions in the FOV have different sensitivity of LED positional misalignment. In this work, we introduce an iterative method to correct position errors based on the simulated annealing (SA) algorithm. To improve the efficiency of this correcting process, large number of iterations for several images with low illumination NAs are firstly implemented to estimate the initial values of the global positional misalignment model through non-linear regression. Simulation and experimental results are presented to evaluate the performance of the proposed method and it is demonstrated that this method can both improve the quality of the recovered object image and relax the LED elements’ position accuracy requirement while aligning the FPM imaging platforms. PMID:27446659
Numerical Research of Steam and Gas Plant Efficiency of Triple Cycle for Extreme North Regions
NASA Astrophysics Data System (ADS)
Galashov, Nikolay; Tsibulskii, Svjatoslav; Matveev, Aleksandr; Masjuk, Vladimir
2016-02-01
The present work shows that temperature decrease of heat rejection in a cycle is necessary for energy efficiency of steam turbine plants. Minimum temperature of heat rejection at steam turbine plant work on water steam is 15°C. Steam turbine plant of triple cycle where lower cycle of steam turbine plant is organic Rankine cycle on low-boiling substance with heat rejection in air condenser, which safely allows rejecting heat at condensation temperatures below 0°C, has been offered. Mathematical model of steam and gas plant of triple cycle, which allows conducting complex researches with change of working body appearance and parameters defining thermodynamic efficiency of cycles, has been developed. On the basis of the model a program of parameters and index cycles design of steam and gas plants has been developed in a package of electron tables Excel. Numerical studies of models showed that energy efficiency of steam turbine plants of triple cycle strongly depend on low-boiling substance type in a lower cycle. Energy efficiency of steam and gas plants net 60% higher can be received for steam and gas plants on the basis of gas turbine plant NK-36ST on pentane and its condensation temperature below 0°C. It was stated that energy efficiency of steam and gas plants net linearly depends on condensation temperature of low-boiling substance type and temperature of gases leaving reco very boiler. Energy efficiency increases by 1% at 10% decrease of condensation temperature of pentane, and it increases by 0.88% at 15°C temperature decrease of gases leaving recovery boiler.
Hydraulic design, numerical simulation and BVF diagnosis of high efficiency centrifugal pump
NASA Astrophysics Data System (ADS)
Zhang, Y. X.; Chen, L.; Zhou, X.; Jiangand, C. W.; Su, M.
2012-11-01
Under the Two-dimensional Flow Theory and the Velocity Coefficient Theory, a centrifugal-pump impeller has been designed, based on the parameters of IS150-125-250 centrifugal pump. And self-compiled programs have been used to complete the hydraulic design of the whole flow passage of centrifugal pump. The space bending and twisting characteristics of the design blade are more obvious. Then, numerical simulation is applied to the inner flow field of the two pumps using RANS (Reynolds Averaged N-S) Equation with a standard k-ε two-equation turbulence model. The compare of the numerical simulation data of two centrifugal pumps, getting from 13 working points including design condition, shows that, the design pump has higher head and efficiency in the range of lower flow rate. Based on the numerical results of the inner flow of the design pump and model pump, the boundary vorticity flux (BVF) diagnostics has been used to analyze the BVF distribution of suction surface and pressure surface of two pumps. The result shows that, the BVF distribution of the design pump is more uniform and smooth, with smaller peak value.
A Fast Numerical Method for a Nonlinear Black-Scholes Equation
NASA Astrophysics Data System (ADS)
Koleva, Miglena N.; Vulkov, Lubin G.
2009-11-01
In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed.
SAMSAN- MODERN NUMERICAL METHODS FOR CLASSICAL SAMPLED SYSTEM ANALYSIS
NASA Technical Reports Server (NTRS)
Frisch, H. P.
1994-01-01
SAMSAN was developed to aid the control system analyst by providing a self consistent set of computer algorithms that support large order control system design and evaluation studies, with an emphasis placed on sampled system analysis. Control system analysts have access to a vast array of published algorithms to solve an equally large spectrum of controls related computational problems. The analyst usually spends considerable time and effort bringing these published algorithms to an integrated operational status and often finds them less general than desired. SAMSAN reduces the burden on the analyst by providing a set of algorithms that have been well tested and documented, and that can be readily integrated for solving control system problems. Algorithm selection for SAMSAN has been biased toward numerical accuracy for large order systems with computational speed and portability being considered important but not paramount. In addition to containing relevant subroutines from EISPAK for eigen-analysis and from LINPAK for the solution of linear systems and related problems, SAMSAN contains the following not so generally available capabilities: 1) Reduction of a real non-symmetric matrix to block diagonal form via a real similarity transformation matrix which is well conditioned with respect to inversion, 2) Solution of the generalized eigenvalue problem with balancing and grading, 3) Computation of all zeros of the determinant of a matrix of polynomials, 4) Matrix exponentiation and the evaluation of integrals involving the matrix exponential, with option to first block diagonalize, 5) Root locus and frequency response for single variable transfer functions in the S, Z, and W domains, 6) Several methods of computing zeros for linear systems, and 7) The ability to generate documentation "on demand". All matrix operations in the SAMSAN algorithms assume non-symmetric matrices with real double precision elements. There is no fixed size limit on any matrix in any
Considerations of Methods of Improving Helicopter Efficiency
NASA Technical Reports Server (NTRS)
Dingeldein, Richard C.
1961-01-01
Recent NASA helicopter research indicates that significant improvements in hovering efficiency, up to 7 percent, are available from the use of a special airfoil section formed by combining an NACA 632A015 thickness distribution with an NACA 230 mean line. This airfoil should be considered for flying-crane-type helicopters. Application of standard leading-edge roughness causes a large drop in efficiency; however, the cambered rotor is shown to retain its superiority over a rotor having a symmetrical airfoil when both rotors have leading-edge roughness. A simple analysis of available rotor static-thrust data indicates a greatly reduced effect of compressibility effects on the rotor profile-drag power than predicted from calculations. Preliminary results of an experimental study of helicopter parasite drag indicate the practicability of achieving an equivalent flat-plate parasite-drag area of less than 4 square feet for a rotor-head-pylon-fuselage configuration (landing gear retracted) in the 2,000-pound minimum-flying-weight class. The large drag penalty of a conventional skid-type landing (3.6 square feet) can be reduced by two-thirds by careful design. Clean, fair, and smooth fuselages that tend to have narrow, deep cross sections are shown to have advantages from the standpoint of drag and download. A ferry range of the order of 1,500 miles is indicated to be practicable for the small helicopter considered.
Numerical analysis of polarization gratings using the finite-difference time-domain method
Oh, Chulwoo; Escuti, Michael J.
2007-10-15
We report the first full numerical analysis of polarization gratings (PGs), and study their most general properties and limits by using the finite-difference time-domain (FDTD) method. In this way, we avoid limiting assumptions on material properties or grating dimensions (e.g., no paraxial approximations) and provide a more complete understanding of PG diffraction behavior. We identify the fundamental delineation between diffraction regimes (thin versus thick) for anisotropic gratings and determine the conditions for {approx_equal}100% diffraction efficiency in the framework of the coupled-wave {rho} and Q parameters. Diffraction characteristics including the efficiency, spectral response, and polarization sensitivity are investigated for the two primary types of PGs with linear and circular birefringence. The angular response and finite-grating behavior (i.e., pixelation) are also examined. Comparisons with previous analytic approximations, where applicable, show good agreement.
Wu, Yu-Shu; Forsyth, Peter A.
2006-04-13
Numerical issues with modeling transport of chemicals or solute in realistic large-scale subsurface systems have been a serious concern, even with the continual progress made in both simulation algorithms and computer hardware in the past few decades. The problem remains and becomes even more difficult when dealing with chemical transport in a multiphase flow system using coarse, multidimensional regular or irregular grids, because of the known effects of numerical dispersion associated with moving plume fronts. We have investigated several total-variation-diminishing (TVD) or flux-limiter schemes by implementing and testing them in the T2R3D code, one of the TOUGH2 family of codes. The objectives of this paper are (1) to investigate the possibility of applying these TVD schemes, using multi-dimensional irregular unstructured grids, and (2) to help select more accurate spatial averaging methods for simulating chemical transport given a numerical grid or spatial discretization. We present an application example to show that such TVD schemes are able to effectively reduce numerical dispersion.
Liu, Haofei; Sun, Wei
2016-01-01
In this study, we evaluated computational efficiency of finite element (FE) simulations when a numerical approximation method was used to obtain the tangent moduli. A fiber-reinforced hyperelastic material model for nearly incompressible soft tissues was implemented for 3D solid elements using both the approximation method and the closed-form analytical method, and validated by comparing the components of the tangent modulus tensor (also referred to as the material Jacobian) between the two methods. The computational efficiency of the approximation method was evaluated with different perturbation parameters and approximation schemes, and quantified by the number of iteration steps and CPU time required to complete these simulations. From the simulation results, it can be seen that the overall accuracy of the approximation method is improved by adopting the central difference approximation scheme compared to the forward Euler approximation scheme. For small-scale simulations with about 10,000 DOFs, the approximation schemes could reduce the CPU time substantially compared to the closed-form solution, due to the fact that fewer calculation steps are needed at each integration point. However, for a large-scale simulation with about 300,000 DOFs, the advantages of the approximation schemes diminish because the factorization of the stiffness matrix will dominate the solution time. Overall, as it is material model independent, the approximation method simplifies the FE implementation of a complex constitutive model with comparable accuracy and computational efficiency to the closed-form solution, which makes it attractive in FE simulations with complex material models. PMID:26692168
Efficient pseudospectral methods for density functional calculations
Murphy, R. B.; Cao, Y.; Beachy, M. D.; Ringnalda, M. N.; Friesner, R. A.
2000-06-15
Novel improvements of the pseudospectral method for assembling the Coulomb operator are discussed. These improvements consist of a fast atom centered multipole method and a variation of the Head-Gordan J-engine analytic integral evaluation. The details of the methodology are discussed and performance evaluations presented for larger molecules within the context of DFT energy and gradient calculations. (c) 2000 American Institute of Physics.
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.
2010-01-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward-difference-formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications. PMID:20577570
NASA Astrophysics Data System (ADS)
Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.
2010-07-01
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.
Stress analysis and damage evaluation of flawed composite laminates by hybrid-numerical methods
NASA Technical Reports Server (NTRS)
Yang, Yii-Ching
1992-01-01
Structural components in flight vehicles is often inherited flaws, such as microcracks, voids, holes, and delamination. These defects will degrade structures the same as that due to damages in service, such as impact, corrosion, and erosion. It is very important to know how a structural component can be useful and survive after these flaws and damages. To understand the behavior and limitation of these structural components researchers usually do experimental tests or theoretical analyses on structures with simulated flaws. However, neither approach has been completely successful. As Durelli states that 'Seldom does one method give a complete solution, with the most efficiency'. Examples of this principle is seen in photomechanics which additional strain-gage testing can only average stresses at locations of high concentration. On the other hand, theoretical analyses including numerical analyses are implemented with simplified assumptions which may not reflect actual boundary conditions. Hybrid-Numerical methods which combine photomechanics and numerical analysis have been used to correct this inefficiency since 1950's. But its application is limited until 1970's when modern computer codes became available. In recent years, researchers have enhanced the data obtained from photoelasticity, laser speckle, holography and moire' interferometry for input of finite element analysis on metals. Nevertheless, there is only few of literature being done on composite laminates. Therefore, this research is dedicated to this highly anisotropic material.
Taylor, G.; Dong, C.; Sun, S.
2010-03-18
A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods, i.e. mixed finite element (MFE) and the finite volume methods. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocities field for both the fractures and matrix which are crucial to the convection part of the transport equation. The finite volume method and the standard MFE method are used to approximate the convection and dispersion terms respectively. The model is used to investigate the interaction of adsorption with transport and to extract information on effective adsorption distribution coefficients. Numerical examples in different fractured media illustrate the robustness and efficiency of the proposed numerical model.
On Efficient Multigrid Methods for Materials Processing Flows with Small Particles
NASA Technical Reports Server (NTRS)
Thomas, James (Technical Monitor); Diskin, Boris; Harik, VasylMichael
2004-01-01
Multiscale modeling of materials requires simulations of multiple levels of structural hierarchy. The computational efficiency of numerical methods becomes a critical factor for simulating large physical systems with highly desperate length scales. Multigrid methods are known for their superior efficiency in representing/resolving different levels of physical details. The efficiency is achieved by employing interactively different discretizations on different scales (grids). To assist optimization of manufacturing conditions for materials processing with numerous particles (e.g., dispersion of particles, controlling flow viscosity and clusters), a new multigrid algorithm has been developed for a case of multiscale modeling of flows with small particles that have various length scales. The optimal efficiency of the algorithm is crucial for accurate predictions of the effect of processing conditions (e.g., pressure and velocity gradients) on the local flow fields that control the formation of various microstructures or clusters.
Bahşı, Ayşe Kurt; Yalçınbaş, Salih
2016-01-01
In this study, the Fibonacci collocation method based on the Fibonacci polynomials are presented to solve for the fractional diffusion equations with variable coefficients. The fractional derivatives are described in the Caputo sense. This method is derived by expanding the approximate solution with Fibonacci polynomials. Using this method of the fractional derivative this equation can be reduced to a set of linear algebraic equations. Also, an error estimation algorithm which is based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation algorithm. If the exact solution of the problem is not known, the absolute error function of the problems can be approximately computed by using the Fibonacci polynomial solution. By using this error estimation function, we can find improved solutions which are more efficient than direct numerical solutions. Numerical examples, figures, tables are comparisons have been presented to show efficiency and usable of proposed method. PMID:27610294
IMPROVED NUMERICAL METHODS FOR MODELING RIVER-AQUIFER INTERACTION.
Tidwell, Vincent C.; Sue Tillery; Phillip King
2008-09-01
A new option for Local Time-Stepping (LTS) was developed to use in conjunction with the multiple-refined-area grid capability of the U.S. Geological Survey's (USGS) groundwater modeling program, MODFLOW-LGR (MF-LGR). The LTS option allows each local, refined-area grid to simulate multiple stress periods within each stress period of a coarser, regional grid. This option is an alternative to the current method of MF-LGR whereby the refined grids are required to have the same stress period and time-step structure as the coarse grid. The MF-LGR method for simulating multiple-refined grids essentially defines each grid as a complete model, then for each coarse grid time-step, iteratively runs each model until the head and flux changes at the interfacing boundaries of the models are less than some specified tolerances. Use of the LTS option is illustrated in two hypothetical test cases consisting of a dual well pumping system and a hydraulically connected stream-aquifer system, and one field application. Each of the hypothetical test cases was simulated with multiple scenarios including an LTS scenario, which combined a monthly stress period for a coarse grid model with a daily stress period for a refined grid model. The other scenarios simulated various combinations of grid spacing and temporal refinement using standard MODFLOW model constructs. The field application simulated an irrigated corridor along the Lower Rio Grande River in New Mexico, with refinement of a small agricultural area in the irrigated corridor.The results from the LTS scenarios for the hypothetical test cases closely replicated the results from the true scenarios in the refined areas of interest. The head errors of the LTS scenarios were much smaller than from the other scenarios in relation to the true solution, and the run times for the LTS models were three to six times faster than the true models for the dual well and stream-aquifer test cases, respectively. The results of the field application
Efficiency improvement in a vibration power generator for a linear MR damper: numerical study
NASA Astrophysics Data System (ADS)
Sapiński, Bogdan; Krupa, Stanisław
2013-04-01
This paper summarizes a numerical analysis of the electromagnetic field, voltage and circuit properties and the cogging force in a vibration power generator comprising permanent magnets and a coil with a foil winding. The device converts the energy harvested from vibrations into electrical energy which is next used to vary the damping characteristics of a linear MR damper attached to the generator. The objective of the study is to propose a sufficiently efficient generator whose finally developed (target) version could be integrated with a small-scale MR damper to build a single device. Two design options for the device are numerically studied, the previously engineered generator 1 and the newly devised generator 2. Generator 1 incorporates two magnet systems having four magnets each and a single-section coil, while generator 2 comprises three magnet systems with four magnets each and a two-section coil. Calculations were performed to determine the electromagnetic field, voltage and current properties and the cogging force in the generators. The electromagnetic field parameters include the distribution of the magnetic field, the electrical potential field and the current density in the open turn and closed turn of the generators’ coils. The voltage and current properties include electromotive force (emf) in the generators and the voltage, current, instantaneous power and energy of the magnetic field in the MR damper control coil which is represented by resistance parameter R and inductance parameter L. The cogging force expresses the magnetic interactions between the permanent magnet systems and ferromagnetic structural components of the generators. The occurrence of this force is very unfavourable and attempts should be made to reduce it through control of the parameters of the magnetic circuit components. On one hand, comparison of the numerical results for the electromagnetic field parameters and voltage and current properties revealed that for the
New efficient optimizing techniques for Kalman filters and numerical weather prediction models
NASA Astrophysics Data System (ADS)
Famelis, Ioannis; Galanis, George; Liakatas, Aristotelis
2016-06-01
The need for accurate local environmental predictions and simulations beyond the classical meteorological forecasts are increasing the last years due to the great number of applications that are directly or not affected: renewable energy resource assessment, natural hazards early warning systems, global warming and questions on the climate change can be listed among them. Within this framework the utilization of numerical weather and wave prediction systems in conjunction with advanced statistical techniques that support the elimination of the model bias and the reduction of the error variability may successfully address the above issues. In the present work, new optimization methods are studied and tested in selected areas of Greece where the use of renewable energy sources is of critical. The added value of the proposed work is due to the solid mathematical background adopted making use of Information Geometry and Statistical techniques, new versions of Kalman filters and state of the art numerical analysis tools.
Efficient solution on solving 3D Maxwell equations using stable semi-implicit splitting method
NASA Astrophysics Data System (ADS)
Cen, Wei; Gu, Ning
2016-05-01
In this paper, we propose an efficient solution on solving 3-dimensional (3D) time-domain Maxwell equations using the semi-implicit Crank-Nicholson (CN) method for time domain discretization with advantage of unconditional time stability. By applying the idea of fractional steps method (FSM) to the CN scheme, the proposed method provides a much simpler and efficient implementation than a direct implementation of the CN scheme. Compared with the alternating-direction implicit (ADI) method and explicit finite-difference time-domain approach (FDTD), it significantly saves the computational resource like memory and CPU time while remains similar numerical accuracy.
NASA Technical Reports Server (NTRS)
Thompson, J. F.; Mcwhorter, J. C.; Siddiqi, S. A.; Shanks, S. P.
1973-01-01
Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.
Some variance reduction methods for numerical stochastic homogenization.
Blanc, X; Le Bris, C; Legoll, F
2016-04-28
We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here. PMID:27002065
An Improved Numerical Integration Method for Springback Predictions
NASA Astrophysics Data System (ADS)
Ibrahim, R.; Smith, L. M.; Golovashchenko, Sergey F.
2011-08-01
In this investigation, the focus is on the springback of steel sheets in V-die air bending. A full replication to a numerical integration algorithm presented rigorously in [1] to predict the springback in air bending was performed and confirmed successfully. Algorithm alteration and extensions were proposed here. The altered approach used in solving the moment equation numerically resulted in springback values much closer to the trend presented by the experimental data, Although investigation here extended to use a more realistic work-hardening model, the differences in the springback values obtained by both hardening models were almost negligible. The algorithm was extended to be applied on thin sheets down to 0.8 mm. Results show that this extension is possible as verified by FEA and other published experiments on TRIP steel sheets.
Efficient discretization in finite difference method
NASA Astrophysics Data System (ADS)
Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris
2015-04-01
Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.
On numerical methods in non-Newtonian flows
NASA Astrophysics Data System (ADS)
Fileas, G.
1982-12-01
The constitutive equations for non-Newtonian flows are presented and the various flow models derived from continuum mechanics and molecular theories are considered and evaluated. Detailed account is given of numerical simulation employing differential and integral models of different kinds of non-Newtonian flows using finite difference and finite element techniques. Procedures for computer set ups are described and references are given for finite difference, finite element and molecular theory based programs for several kinds of flow. Achievements and unreached goals in the field of numerical simulation of non-Newtonian flows are discussed and the lack of numerical work in the fields of suspension flows and heat transfer is pointed out. Finally, FFOCUS is presented as a newly built computer program which can simulate freezing flows of Newtonian fluids through various geometries and is aimed to be further developed to handle non-Newtonian freezing flows and certain types of suspension phenomena involved in corium flow after a hypothetical core melt down accident in a pressurized water reactor.
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Kumar, Jai
2014-11-01
In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
Method of increasing the efficiency of a liquid hydrocarbon fuel
Sakata, H.
1986-02-11
This patent describes a method of increasing the efficiency of a liquid hydrocarbon fuel. The method consists of the steps of repeatedly and alternately subjecting the fuel to a magnetic field and to radioactive rays.
Numerical simulation of diffusion MRI signals using an adaptive time-stepping method.
Li, Jing-Rebecca; Calhoun, Donna; Poupon, Cyril; Le Bihan, Denis
2014-01-20
The effect on the MRI signal of water diffusion in biological tissues in the presence of applied magnetic field gradient pulses can be modelled by a multiple compartment Bloch-Torrey partial differential equation. We present a method for the numerical solution of this equation by coupling a standard Cartesian spatial discretization with an adaptive time discretization. The time discretization is done using the explicit Runge-Kutta-Chebyshev method, which is more efficient than the forward Euler time discretization for diffusive-type problems. We use this approach to simulate the diffusion MRI signal from the extra-cylindrical compartment in a tissue model of the brain gray matter consisting of cylindrical and spherical cells and illustrate the effect of cell membrane permeability. PMID:24351275
Numerical simulation of diffusion MRI signals using an adaptive time-stepping method
NASA Astrophysics Data System (ADS)
Li, Jing-Rebecca; Calhoun, Donna; Poupon, Cyril; Le Bihan, Denis
2014-01-01
The effect on the MRI signal of water diffusion in biological tissues in the presence of applied magnetic field gradient pulses can be modelled by a multiple compartment Bloch-Torrey partial differential equation. We present a method for the numerical solution of this equation by coupling a standard Cartesian spatial discretization with an adaptive time discretization. The time discretization is done using the explicit Runge-Kutta-Chebyshev method, which is more efficient than the forward Euler time discretization for diffusive-type problems. We use this approach to simulate the diffusion MRI signal from the extra-cylindrical compartment in a tissue model of the brain gray matter consisting of cylindrical and spherical cells and illustrate the effect of cell membrane permeability.
Sun, Jiasong; Chen, Qian; Zhang, Yuzhen; Zuo, Chao
2016-03-15
In this Letter, an accurate and highly efficient numerical phase aberration compensation method is proposed for digital holographic microscopy. Considering that most parts of the phase aberration resides in the low spatial frequency domain, a Fourier-domain mask is introduced to extract the aberrated frequency components, while rejecting components that are unrelated to the phase aberration estimation. Principal component analysis (PCA) is then performed only on the reduced-sized spectrum, and the aberration terms can be extracted from the first principal component obtained. Finally, by oversampling the reduced-sized aberration terms, the precise phase aberration map is obtained and thus can be compensated by multiplying with its conjugation. Because the phase aberration is estimated from the limited but more relevant raw data, the compensation precision is improved and meanwhile the computation time can be significantly reduced. Experimental results demonstrate that our proposed technique could achieve both high compensating accuracy and robustness compared with other developed compensation methods. PMID:26977692
NASA Astrophysics Data System (ADS)
Li, Xinxiu
2012-10-01
Physical processes with memory and hereditary properties can be best described by fractional differential equations due to the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional differential equations using cubic B-spline wavelet. Analytical expressions of fractional derivatives in Caputo sense for cubic B-spline functions are presented. The main characteristic of the approach is that it converts such problems into a system of algebraic equations which is suitable for computer programming. It not only simplifies the problem but also speeds up the computation. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation.
Kelkar, K.M. )
1990-01-01
Heat exchange that occurs between materials with largely differing thermal conductivities is commonly encountered in engineering practice.Conventional iterative solution methods perform poorly for the numerical solution for such problems. Results for computations for test problems indicate that the proposed solution procedure enables efficient solution of heat transfer problems with large conductivity differences for which the conventional line-by-line method proves ineffective.
Botello-Smith, Wesley M.; Luo, Ray
2016-01-01
Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966
Botello-Smith, Wesley M; Luo, Ray
2015-10-26
Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membranes into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multigrid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966
Numerical Study of Boundary Layer Interaction with Shocks: Method Improvement and Test Computation
NASA Technical Reports Server (NTRS)
Adams, N. A.
1995-01-01
The objective is the development of a high-order and high-resolution method for the direct numerical simulation of shock turbulent-boundary-layer interaction. Details concerning the spatial discretization of the convective terms can be found in Adams and Shariff (1995). The computer code based on this method as introduced in Adams (1994) was formulated in Cartesian coordinates and thus has been limited to simple rectangular domains. For more general two-dimensional geometries, as a compression corner, an extension to generalized coordinates is necessary. To keep the requirements or limitations for grid generation low, the extended formulation should allow for non-orthogonal grids. Still, for simplicity and cost efficiency, periodicity can be assumed in one cross-flow direction. For easy vectorization, the compact-ENO coupling algorithm as used in Adams (1994) treated whole planes normal to the derivative direction with the ENO scheme whenever at least one point of this plane satisfied the detection criterion. This is apparently too restrictive for more general geometries and more complex shock patterns. Here we introduce a localized compact-ENO coupling algorithm, which is efficient as long as the overall number of grid points treated by the ENO scheme is small compared to the total number of grid points. Validation and test computations with the final code are performed to assess the efficiency and suitability of the computer code for the problems of interest. We define a set of parameters where a direct numerical simulation of a turbulent boundary layer along a compression corner with reasonably fine resolution is affordable.
Efficient implementation of minimal polynomial and reduced rank extrapolation methods
NASA Technical Reports Server (NTRS)
Sidi, Avram
1990-01-01
The minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are two effective techniques that have been used in accelerating the convergence of vector sequences, such as those that are obtained from iterative solution of linear and nonlinear systems of equation. Their definitions involve some linear least squares problems, and this causes difficulties in their numerical implementation. Timewise efficient and numerically stable implementations for MPE and RRE are developed. A computer program written in FORTRAN 77 is also appended and applied to some model problems.
The Cauchy-Lagrangian method for numerical analysis of Euler flow
NASA Astrophysics Data System (ADS)
Podvigina, O.; Zheligovsky, V.; Frisch, U.
2016-02-01
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle, only limited spatial smoothness of the initial data. Efficient generation of high-order time-Taylor coefficients is made possible by a recurrence relation that follows from the Cauchy invariants formulation of the Euler equation (Zheligovsky and Frisch, 2014 [44]). Truncated time-Taylor series of very high order allow the use of time steps vastly exceeding the Courant-Friedrichs-Lewy limit, without compromising the accuracy of the solution. Tests performed on the two-dimensional Euler equation indicate that the Cauchy-Lagrangian method is more - and occasionally much more - efficient and less prone to instability than Eulerian Runge-Kutta methods, and less prone to rapid growth of rounding errors than the high-order Eulerian time-Taylor algorithm. We also develop tools of analysis adapted to the Cauchy-Lagrangian method, such as the monitoring of the radius of convergence of the time-Taylor series. Certain other fluid equations can be handled similarly.
Numerical simulation of fluid-structure interaction with the volume penalization method
NASA Astrophysics Data System (ADS)
Engels, Thomas; Kolomenskiy, Dmitry; Schneider, Kai; Sesterhenn, Jörn
2015-01-01
We present a novel scheme for the numerical simulation of fluid-structure interaction problems. It extends the volume penalization method, a member of the family of immersed boundary methods, to take into account flexible obstacles. We show how the introduction of a smoothing layer, physically interpreted as surface roughness, allows for arbitrary motion of the deformable obstacle. The approach is carefully validated and good agreement with various results in the literature is found. A simple one-dimensional solid model is derived, capable of modeling arbitrarily large deformations and imposed motion at the leading edge, as it is required for the simulation of simplified models for insect flight. The model error is shown to be small, while the one-dimensional character of the model features a reasonably easy implementation. The coupled fluid-solid interaction solver is shown not to introduce artificial energy in the numerical coupling, and validated using a widely used benchmark. We conclude with the application of our method to models for insect flight and study the propulsive efficiency of one and two wing sections.
Application of Numerical Integration and Data Fusion in Unit Vector Method
NASA Astrophysics Data System (ADS)
Zhang, J.
2012-01-01
The Unit Vector Method (UVM) is a series of orbit determination methods which are designed by Purple Mountain Observatory (PMO) and have been applied extensively. It gets the conditional equations for different kinds of data by projecting the basic equation to different unit vectors, and it suits for weighted process for different kinds of data. The high-precision data can play a major role in orbit determination, and accuracy of orbit determination is improved obviously. The improved UVM (PUVM2) promoted the UVM from initial orbit determination to orbit improvement, and unified the initial orbit determination and orbit improvement dynamically. The precision and efficiency are improved further. In this thesis, further research work has been done based on the UVM: Firstly, for the improvement of methods and techniques for observation, the types and decision of the observational data are improved substantially, it is also asked to improve the decision of orbit determination. The analytical perturbation can not meet the requirement. So, the numerical integration for calculating the perturbation has been introduced into the UVM. The accuracy of dynamical model suits for the accuracy of the real data, and the condition equations of UVM are modified accordingly. The accuracy of orbit determination is improved further. Secondly, data fusion method has been introduced into the UVM. The convergence mechanism and the defect of weighted strategy have been made clear in original UVM. The problem has been solved in this method, the calculation of approximate state transition matrix is simplified and the weighted strategy has been improved for the data with different dimension and different precision. Results of orbit determination of simulation and real data show that the work of this thesis is effective: (1) After the numerical integration has been introduced into the UVM, the accuracy of orbit determination is improved obviously, and it suits for the high-accuracy data of
NASA Astrophysics Data System (ADS)
Shukla, H. S.; Tamsir, Mohammad; Srivastava, Vineet K.; Rashidi, Mohammad Mehdi
2016-04-01
In this paper, we propose a modified cubic B-spline differential quadrature method (MCB-DQM) to solve three-dimensional (3D) coupled viscous Burger equation with appropriate initial and boundary conditions. In this method, modified cubic B-spline is treated as a basis function in the differential quadrature method (DQM) to compute the weighting coefficients. In this way, the Burger equation is reduced into a system of ordinary differential equations. An optimal strong stability-preserving Runge-Kutta (SSP-RK) method is employed to solve the resulting system of ordinary differential equations. In order to illustrate the accuracy and efficiency of the proposed method, a numerical problem is considered. From the numerical experiment, it is found that the computed result is in good agreement with the exact solution. Stability analysis of the method is also carried out using the matrix stability analysis method and found to be unconditionally stable.
Magnetohydrodynamic (MHD) modelling of solar active phenomena via numerical methods
NASA Technical Reports Server (NTRS)
Wu, S. T.
1988-01-01
Numerical ideal MHD models for the study of solar active phenomena are summarized. Particular attention is given to the following physical phenomena: (1) local heating of a coronal loop in an isothermal and stratified atmosphere, and (2) the coronal dynamic responses due to magnetic field movement. The results suggest that local heating of a magnetic loop will lead to the enhancement of the density of the neighboring loops through MHD wave compression. It is noted that field lines can be pinched off and may form a self-contained magnetized plasma blob that may move outward into interplanetary space.
Numerical methods for a general class of porous medium equations
Rose, M. E.
1980-03-01
The partial differential equation par. deltau/par. deltat + par. delta(f(u))/par. deltax = par. delta(g(u)par. deltau/par. deltax)/par. deltax, where g(u) is a non-negative diffusion coefficient that may vanish for one or more values of u, was used to model fluid flow through a porous medium. Error estimates for a numerical procedure to approximate the solution are derived. A revised version of this report will appear in Computers and Mathematics with Applications.
Efficient hybrid-symbolic methods for quantum mechanical calculations
NASA Astrophysics Data System (ADS)
Scott, T. C.; Zhang, Wenxing
2015-06-01
We present hybrid symbolic-numerical tools to generate optimized numerical code for rapid prototyping and fast numerical computation starting from a computer algebra system (CAS) and tailored to any given quantum mechanical problem. Although a major focus concerns the quantum chemistry methods of H. Nakatsuji which has yielded successful and very accurate eigensolutions for small atoms and molecules, the tools are general and may be applied to any basis set calculation with a variational principle applied to its linear and non-linear parameters.
Projection methods for the numerical solution of Markov chain models
NASA Technical Reports Server (NTRS)
Saad, Youcef
1989-01-01
Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.
An efficient method for computation of the manipulator inertia matrix
NASA Technical Reports Server (NTRS)
Fijany, Amir; Bejczy, Antal K.
1989-01-01
An efficient method of computation of the manipulator inertia matrix is presented. Using spatial notations, the method leads to the definition of the composite rigid-body spatial inertia, which is a spatial representation of the notion of augmented body. The previously proposed methods, the physical interpretations leading to their derivation, and their redundancies are analyzed. The proposed method achieves a greater efficiency by eliminating the redundancy in the intrinsic equations as well as by a better choice of coordinate frame for their projection. In this case, removing the redundancy leads to greater efficiency of the computation in both serial and parallel senses.
Numerical conformal mapping methods for exterior and doubly connected regions
DeLillo, T.K.; Pfaltzgraff, J.A.
1996-12-31
Methods are presented and analyzed for approximating the conformal map from the exterior of the disk to the exterior a smooth, simple closed curve and from an annulus to a bounded, doubly connected region with smooth boundaries. The methods are Newton-like methods for computing the boundary correspondences and conformal moduli similar to Fornberg`s method for the interior of the disk. We show that the linear systems are discretizations of the identity plus a compact operator and, hence, that the conjugate gradient method converges superlinearly.
Method for numerical simulation of two-term exponentially correlated colored noise
Yilmaz, B.; Ayik, S.; Abe, Y.; Gokalp, A.; Yilmaz, O.
2006-04-15
A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications.
WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method
NASA Astrophysics Data System (ADS)
Crevoisier, David; Voltz, Marc
2013-04-01
To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute
Efficient modelling of gravity effects due to topographic masses using the Gauss-FFT method
NASA Astrophysics Data System (ADS)
Wu, Leyuan
2016-04-01
We present efficient Fourier-domain algorithms for modelling gravity effects due to topographic masses. The well-known Parker's formula originally based on the standard fast Fourier transform (FFT) algorithm is modified by applying the Gauss-FFT method instead. Numerical precision of the forward and inverse Fourier transforms embedded in Parker's formula and its extended forms are significantly improved by the Gauss-FFT method. The topographic model is composed of two major aspects, the geometry and the density. Versatile geometric representations, including the mass line model, the mass prism model, the polyhedron model and smoother topographic models interpolated from discrete data sets using high-order splines or pre-defined by analytical functions, in combination with density distributions that vary both laterally and vertically in rather arbitrary ways following exponential or general polynomial functions, now can be treated in a consistent framework by applying the Gauss-FFT method. The method presented has been numerically checked by space-domain analytical and hybrid analytical/numerical solutions already established in the literature. Synthetic and real model tests show that both the Gauss-FFT method and the standard FFT method run much faster than space-domain solutions, with the Gauss-FFT method being superior in numerical accuracy. When truncation errors are negligible, the Gauss-FFT method can provide forward results almost identical to space-domain analytical or semi-numerical solutions in much less time.
Zeng, Y; Albertus, P; Klein, R; Chaturvedi, N; Kojic, A; Bazant, MZ; Christensen, J
2013-06-07
Mathematical models of batteries which make use of the intercalation of a species into a solid phase need to solve the corresponding mass transfer problem. Because solving this equation can significantly add to the computational cost of a model, various methods have been devised to reduce the computational time. In this paper we focus on a comparison of the formulation, accuracy, and order of the accuracy for two numerical methods of solving the spherical diffusion problem with a constant or non-constant diffusion coefficient: the finite volume method and the control volume method. Both methods provide perfect mass conservation and second order accuracy in mesh spacing, but the control volume method provides the surface concentration directly, has a higher accuracy for a given numbers of mesh points and can also be easily extended to variable mesh spacing. Variable mesh spacing can significantly reduce the number of points that are required to achieve a given degree of accuracy in the surface concentration (which is typically coupled to the other battery equations) by locating more points where the concentration gradients are highest. (C) 2013 The Electrochemical Society. All rights reserved.
An efficient method to evaluate energy variances for extrapolation methods
NASA Astrophysics Data System (ADS)
Puddu, G.
2012-08-01
The energy variance extrapolation method consists of relating the approximate energies in many-body calculations to the corresponding energy variances and inferring eigenvalues by extrapolating to zero variance. The method needs a fast evaluation of the energy variances. For many-body methods that expand the nuclear wavefunctions in terms of deformed Slater determinants, the best available method for the evaluation of energy variances scales with the sixth power of the number of single-particle states. We propose a new method which depends on the number of single-particle orbits and the number of particles rather than the number of single-particle states. We discuss as an example the case of 4He using the chiral N3LO interaction in a basis consisting up to 184 single-particle states.
Pusa, M.; Leppaenen, J.
2012-07-01
The Chebyshev Rational Approximation Method (CRAM) has been recently introduced by the authors for solving the burnup equations with excellent results. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices and it can be characterized as the best rational approximation on the negative real axis. The coefficients of the rational approximation are fixed and have been reported for various approximation orders. In addition to these coefficients, implementing the method only requires a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM approximation. The introduced direct method is based on sparse Gaussian elimination where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of the proposed Gaussian elimination method is discussed based on considering the numerical properties of burnup matrices. Suitable algorithms are presented for computing the symbolic factorization and numerical elimination in order to facilitate the implementation of CRAM and its adoption into routine use. The accuracy and efficiency of the described technique are demonstrated by computing the CRAM approximations for a large test case with over 1600 nuclides. (authors)
Numerical method to digital photoelasticity using plane polariscope.
Júnior, P A A Magalhães; Vieira, F G; Magalhães, C A; Ribeiro, J S; Rios, I G
2016-06-13
This research aims to find a new way to get the intensity equations for the phase-shifting model in digital photoelasticity. The procedure is based on the rotation of the analyzer itself. From the intensity equations, the isoclinic and isochromatic equations parameters are deduced by applying a new numerical technique. This approach can be done to calculate how many images allow the resolution of the polariscope. Each image indicates the stress forces in the object. In this study the plane polariscope was used. The amount of images will determinate the number of errors and uncertainties of the study, due to the observation that the veracity of the equations increases considerably with a large amout of images. Several analyses are performed with different amounts of photographic images. The results showed the possibility to measure stress forces with high precision using plane polariscopes. PMID:27410283
Analysis of free turbulent shear flows by numerical methods
NASA Technical Reports Server (NTRS)
Korst, H. H.; Chow, W. L.; Hurt, R. F.; White, R. A.; Addy, A. L.
1973-01-01
Studies are described in which the effort was essentially directed to classes of problems where the phenomenologically interpreted effective transport coefficients could be absorbed by, and subsequently extracted from (by comparison with experimental data), appropriate coordinate transformations. The transformed system of differential equations could then be solved without further specifications or assumptions by numerical integration procedures. An attempt was made to delineate different regimes for which specific eddy viscosity models could be formulated. In particular, this would account for the carryover of turbulence from attached boundary layers, the transitory adjustment, and the asymptotic behavior of initially disturbed mixing regions. Such models were subsequently used in seeking solutions for the prescribed two-dimensional test cases, yielding a better insight into overall aspects of the exchange mechanisms.
MODELING COLLISIONAL CASCADES IN DEBRIS DISKS: THE NUMERICAL METHOD
Gaspar, Andras; Psaltis, Dimitrios; Oezel, Feryal; Rieke, George H.; Cooney, Alan E-mail: dpsaltis@as.arizona.edu E-mail: grieke@as.arizona.edu
2012-04-10
We develop a new numerical algorithm to model collisional cascades in debris disks. Because of the large dynamical range in particle masses, we solve the integro-differential equations describing erosive and catastrophic collisions in a particle-in-a-box approach, while treating the orbital dynamics of the particles in an approximate fashion. We employ a new scheme for describing erosive (cratering) collisions that yields a continuous set of outcomes as a function of colliding masses. We demonstrate the stability and convergence characteristics of our algorithm and compare it with other treatments. We show that incorporating the effects of erosive collisions results in a decay of the particle distribution that is significantly faster than with purely catastrophic collisions.
Vernekar, R; Krüger, T
2015-09-01
We investigate the effect of particle volume fraction on the efficiency of deterministic lateral displacement (DLD) devices. DLD is a popular passive sorting technique for microfluidic applications. Yet, it has been designed for treating dilute suspensions, and its efficiency for denser samples is not well known. We perform 3D simulations based on the immersed-boundary, lattice-Boltzmann and finite-element methods to model the flow of red blood cells (RBCs) in different DLD devices. We quantify the DLD efficiency in terms of appropriate "failure" probabilities and RBC counts in designated device outlets. Our main result is that the displacement mode breaks down upon an increase of RBC volume fraction, while the zigzag mode remains relatively robust. This suggests that the separation of larger particles (such as white blood cells) from a dense RBC background is simpler than separating smaller particles (such as platelets) from the same background. The observed breakdown stems from non-deterministic particle collisions interfering with the designed deterministic nature of DLD devices. Therefore, we postulate that dense suspension effects generally hamper efficient particle separation in devices based on deterministic principles. PMID:26143149
NASA Astrophysics Data System (ADS)
Imada, Masatoshi; Kashima, Tsuyoshi
2000-09-01
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after a numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from the optimized linear combination of retained states in the truncated Hilbert space with a numerically chosen basis. This algorithm does not suffer from the negative sign problem and can be applied to any type of Hamiltonian in any dimension. The efficiency is tested in examples of the Hubbard model where the basis of Slater determinants is numerically optimized. We show results on fast convergence and accuracy achieved with a small number of retained states.
NASA Astrophysics Data System (ADS)
Nagel, T.; Böttcher, N.; Görke, U. J.; Kolditz, O.
2014-12-01
The design process of geotechnical installations includes the application of numerical simulation tools for safety assessment, dimensioning and long term effectiveness estimations. Underground salt caverns can be used for the storage of natural gas, hydrogen, oil, waste or compressed air. For their design one has to take into account fluctuating internal pressures due to different levels of filling, the stresses imposed by the surrounding rock mass, irregular geometries and possibly heterogeneous material properties [3] in order to estimate long term cavern convergence as well as locally critical wall stresses. Constitutive models applied to rock salt are usually viscoplastic in nature and most often based on a Burgers-type rheological model extended by non-linear viscosity functions and/or plastic friction elements. Besides plastic dilatation, healing and damage are sometimes accounted for as well [2]. The scales of the geotechnical system to be simulated and the laboratory tests from which material parameters are determined are vastly different. The most common material testing modalities to determine material parameters in geoengineering are the uniaxial and the triaxial compression tests. Some constitutive formulations in widespread use are formulated based on equivalent rather than tensorial quantities valid under these specific test conditions and are subsequently applied to heterogeneous underground systems and complex 3D load cases. We show here that this procedure is inappropriate and can lead to erroneous results. We further propose alternative formulations of the constitutive models in question that restore their validity under arbitrary loading conditions. For an efficient numerical simulation, the discussed constitutive models are integrated locally with a Newton-Raphson algorithm that directly provides the algorithmically consistent tangent matrix for the global Newton iteration of the displacement based finite element formulation. Finally, the finite
Numerical simulations of immiscible displacement in the cavities via lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Liang, Hong; Chai, Zhenhua; Shi, Baochang; Guo, Zhaoli; Li, Qiuxiang
2015-12-01
In this paper, the immiscible displacements in the different cavities are studied by the pseudo-potential lattice Boltzmann (LB) model. We first validate the model with a two-dimensional (2D) layered flow, and find that the numerical results agree well with the corresponding analytical solutions. Then, we perform some numerical simulations to study the immiscible displacements in the cavities, and focus on the effects of the surface wettability, capillary number and density ratio on the displacement efficiency. The numerical results show that the displacement efficiency increases with the increase of the capillary number at first and then presents a decrease with the capillary number when it is large enough. The increase of the contact angle θ1 or decrease of the density ratio increases the displacement efficiency but decreases the critical capillary number. Finally, it is also found that both the size and geometry of cavity have a significant influence on the displacement efficiency.
Exploring the Use of Discontinuous Galerkin Methods for Numerical Relativity
NASA Astrophysics Data System (ADS)
Hebert, Francois; Kidder, Lawrence; Teukolsky, Saul; SXS Collaboration
2015-04-01
The limited accuracy of relativistic hydrodynamic simulations constrains our insight into several important research problems, including among others our ability to generate accurate template waveforms for black hole-neutron star mergers, or our understanding of supernova explosion mechanisms. In many codes the algorithms used to evolve the matter, based on the finite volume method, struggle to reach the desired accuracy. We aim to show improved accuracy by using a discontinuous Galerkin method. This method's attractiveness comes from its combination of spectral convergence properties for smooth solutions and robust stability properties for shocks. We present the status of our work implementing a testbed GR-hydro code using discontinuous Galerkin.
A numerical method for eigenvalue problems in modeling liquid crystals
Baglama, J.; Farrell, P.A.; Reichel, L.; Ruttan, A.; Calvetti, D.
1996-12-31
Equilibrium configurations of liquid crystals in finite containments are minimizers of the thermodynamic free energy of the system. It is important to be able to track the equilibrium configurations as the temperature of the liquid crystals decreases. The path of the minimal energy configuration at bifurcation points can be computed from the null space of a large sparse symmetric matrix. We describe a new variant of the implicitly restarted Lanczos method that is well suited for the computation of extreme eigenvalues of a large sparse symmetric matrix, and we use this method to determine the desired null space. Our implicitly restarted Lanczos method determines adoptively a polynomial filter by using Leja shifts, and does not require factorization of the matrix. The storage requirement of the method is small, and this makes it attractive to use for the present application.
Numerical Stability and Convergence of Approximate Methods for Conservation Laws
NASA Astrophysics Data System (ADS)
Galkin, V. A.
We present the new approach to background of approximate methods convergence based on functional solutions theory for conservation laws. The applications to physical kinetics, gas and fluid dynamics are considered.
Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case
Fernández-Nieto, Enrique D.
2014-05-01
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.
Efficiency assessment of vertical barriers on the basis of flow and transport numerical modeling
NASA Astrophysics Data System (ADS)
Koda, Eugeniusz; Kołanka, Tomasz; Osiński, Piotr
2012-10-01
The construction of cut-off walls is a common solution applied in such disciplines as land reclamation and landfill containment. Most commonly the construction of vertical barriers is based on cut-off wall mono or diphase technology with the use of bentonite-cement mixture as a filling material. The content of the paper is focused on groundwater flow and transport numerical modeling conducted on landfill areas where vertical bentonite barriers were constructed. The modeling process was conducted with the use of FEMWATER software which employs analysis based on finite element method. There are two examples of the software application presented in the paper which concern such case studies, i.e., reclamation of Radiowo and Łubna landfill sites. These examples are provided to prove that the appropriate investigation of ground conditions as well as definition of initial and boundary conditions and correct selection of material parameters to be fed into the software, are crucial for the overall modeling process. Moreover, the comparison of results obtained from the numerical modeling and the groundwater monitoring on site is presented for one of the case studies.
Tempest - Efficient Computation of Atmospheric Flows Using High-Order Local Discretization Methods
NASA Astrophysics Data System (ADS)
Ullrich, P. A.; Guerra, J. E.
2014-12-01
The Tempest Framework composes several compact numerical methods to easily facilitate intercomparison of atmospheric flow calculations on the sphere and in rectangular domains. This framework includes the implementations of Spectral Elements, Discontinuous Galerkin, Flux Reconstruction, and Hybrid Finite Element methods with the goal of achieving optimal accuracy in the solution of atmospheric problems. Several advantages of this approach are discussed such as: improved pressure gradient calculation, numerical stability by vertical/horizontal splitting, arbitrary order of accuracy, etc. The local numerical discretization allows for high performance parallel computation and efficient inclusion of parameterizations. These techniques are used in conjunction with a non-conformal, locally refined, cubed-sphere grid for global simulations and standard Cartesian grids for simulations at the mesoscale. A complete implementation of the methods described is demonstrated in a non-hydrostatic setting.
Numerical Study of Usage Efficiency of Multistage Filters on Mineral Leaching Process
NASA Astrophysics Data System (ADS)
Inkarbekov, Medet; Kuljabekov, Alibek; Alibayeva, Karlygash; Kaltayev, Aidarkhan
2013-11-01
The numerical study of the usage efficiency of the multistage filters setting technology is carried out on the basis of mathematical simulation. And its application on in-situ mineral leaching process is considered. So long as mineral bearing sandstone in deposit mostly is separated by interbedded layers of sands and clays, it's expedient to use multistage filters setting technology at the mineral extraction. A comparison of the extraction degree at single and multistage filters is implemented. The results of calculations show that the distribution of flow (inflow) on well height is not uniform. In the calculations the well accepted as high-permeability channel, depending on the construction of the filter. Obtained results for a multistage filters setting qualitatively conform to the experimental findings. Wellbore is considered as a surface with a constant reduced pressure in the bottomhole formation zone. But such assumption does not show a qualitative picture of the fluid flow in the bottomhole zone [Brovin K.G., Grabovnikov V.A., 1997]. To construct an accurate mathematical model it's necessary to use Navier-Stokes equation for the interior of a vertical wellbore, and the filtration law for modeling the filtration in the reservoir. Strictly speaking, it would have had to sew two laws on the contact surface of a rock and filter. Such review requires enormous computing, as far as computational grid must be sufficiently thick to cover the interior of the wellbore.
Validation of a Numerical Method for Determining Liner Impedance
NASA Technical Reports Server (NTRS)
Watson, Willie R.; Jones, Michael G.; Tanner, Sharon E.; Parrott, Tony L.
1996-01-01
This paper reports the initial results of a test series to evaluate a method for determining the normal incidence impedance of a locally reacting acoustically absorbing liner, located on the lower wall of a duct in a grazing incidence, multi-modal, non-progressive acoustic wave environment without flow. This initial evaluation is accomplished by testing the methods' ability to converge to the known normal incidence impedance of a solid steel plate, and to the normal incidence impedance of an absorbing test specimen whose impedance was measured in a conventional normal incidence tube. The method is shown to converge to the normal incident impedance values and thus to be an adequate tool for determining the impedance of specimens in a grazing incidence, multi-modal, nonprogressive acoustic wave environment for a broad range of source frequencies.
Structure of the Gabor matrix and efficient numerical algorithms for discrete Gabor expansions
NASA Astrophysics Data System (ADS)
Qiu, Sigang; Feichtinger, Hans G.
1994-09-01
The standard way to obtain suitable coefficients for the (non-orthogonal) Gabor expansion of a general signal for a given Gabor atom g and a pair of lattice constants in the (discrete) time/frequency plane, requires to compute the dual Gabor window function g- first. In this paper, we present an explicit description of the sparsity, the block and banded structure of the Gabor frame matrix G. On this basis efficient algorithms are developed for computing g- by solving the linear equation g- * G equals g with the conjugate- gradients method. Using the dual Gabor wavelet, a fast Gabor reconstruction algorithm with very low computational complexity is proposed.
Improved numerical methods for turbulent viscous recirculating flows
NASA Technical Reports Server (NTRS)
Turan, A.; Vandoormaal, J. P.
1988-01-01
The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.
NASA Astrophysics Data System (ADS)
Mendoza-Suárez, A.; Pérez-Aguilar, H.
2016-09-01
We present several numerical integral methods for the study of a photonic crystal waveguide, formed by two parallel conducting plates and an array of circular inclusions involving a conducting material and a metamaterial. Band structures and reflectance were calculated, for infinite and finite photonic crystal waveguides, respectively. The numerical results obtained show that the numerical methods applied provide good accuracy and efficiency. An interesting detail that resulted from this study was the appearance of a propagating mode in a band gap due to defects in the middle of the photonic crystal waveguide. This is equivalent to dope a semiconductor to introduce allowed energy states within a band gap. Our main interest in this work is to model photonic crystal waveguides that involve left-handed materials (LHMs). For the specific LHM considered, a surface plasmon mode on the vacuum-LHM interface was found.
Numerical solution of 2D-vector tomography problem using the method of approximate inverse
NASA Astrophysics Data System (ADS)
Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna
2016-08-01
We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.
Cox, T.J.; Runkel, R.L.
2008-01-01
Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.
A finite volume method for numerical grid generation
NASA Astrophysics Data System (ADS)
Beale, S. B.
1999-07-01
A novel method to generate body-fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables , and is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re-zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid-correction procedure. The scalar variables are re-mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet-Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local-boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point-by-point and whole-field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright
Evaluating numerical ODE/DAE methods, algorithms and software
NASA Astrophysics Data System (ADS)
Soderlind, Gustaf; Wang, Lina
2006-01-01
Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one method is better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris paribus conditions. Moreover, testing is an empirical science and as such requires a formal test protocol; without it conclusions are questionable, invalid or even false.We argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. The goals are computational stability, reproducibility, and improved software quality. We also focus on different error criteria and norms, and discuss modifications to DASPK and RADAU5. Finally, some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems.
NASA Astrophysics Data System (ADS)
Fox, R. O.; Laurent, F.; Massot, M.
2008-03-01
The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v,u;x,t) of droplet volume and velocity. Eulerian multi-fluid models have already been rigorously derived from this equation in Laurent et al. [F. Laurent, M. Massot, P. Villedieu, Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays, J. Comput. Phys. 194 (2004) 505-543]. The first key feature of the paper is the application of direct quadrature method of moments (DQMOM) introduced by Marchisio and Fox [D.L. Marchisio, R.O. Fox, Solution of population balance equations using the direct quadrature method of moments, J. Aerosol Sci. 36 (2005) 43-73] to the Williams spray equation. Both the multi-fluid method and DQMOM yield systems of Eulerian conservation equations with complicated interaction terms representing coalescence. In order to focus on the difficulties associated with treating size-dependent coalescence and to avoid numerical uncertainty issues associated with two-way coupling, only one-way coupling between the droplets and a given gas velocity field is considered. In order to validate and compare these approaches, the chosen configuration is a self-similar 2D axisymmetrical decelerating nozzle with sprays having various size distributions, ranging from smooth ones up to Dirac delta functions. The second key feature of the paper is a thorough comparison of the two approaches for various test-cases to a reference solution obtained through a classical stochastic Lagrangian solver. Both Eulerian models prove to describe adequately spray coalescence and yield a very interesting alternative to the Lagrangian solver. The third key point of the study is a detailed description of the limitations associated with each method, thus giving criteria for
A survey of numerical methods for shock physics applications
Hertel, E.S. Jr.
1997-10-01
Hydrocodes or more accurately, shock physics analysis packages, have been widely used in the US Department of Energy (DOE) laboratories and elsewhere around the world for over 30 years. Initial applications included weapons effects studies where the pressure levels were high enough to disregard the material strength, hence the term hydrocode. Over the last 30 years, Sandia has worked extensively to develop and apply advanced hydrocodes to armor/anti-armor interactions, warhead design, high explosive initiation, and nuclear weapon safety issues. The needs of the DOE have changed over the last 30 years, especially over the last decade. A much stronger emphasis is currently placed on the details of material deformation and high explosive initiation phenomena. The hydrocodes of 30 years ago have now evolved into sophisticated analysis tools that can replace testing in some situations and complement it in all situations. A brief history of the development of hydrocodes in the US will be given. The author also discusses and compares the four principal methods in use today for the solution of the conservation equations of mass, momentum, and energy for shock physics applications. The techniques discussed are the Eulerian methods currently employed by the Sandia multi-dimensional shock physics analysis package known as CTH; the element based Lagrangian method currently used by codes like DYNA; the element free Lagrangian method (also known as smooth particle hydrodynamics) used by codes like the Los Alamos code SPHINX; and the Arbitrary Lagrangian Eulerian methods used by codes like the Lawrence Livermore code CALE or the Sandia code ALEGRA.
Applications of numerical methods to simulate the movement of contaminants in groundwater.
Sun, N Z
1989-01-01
This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327
Numerical design method for thermally loaded plate-cylinder intersections
Baldur, R.; Laberge, C.A.; Lapointe, D. )
1988-11-01
This paper is an extension of work on stresses in corner radii described by the authors previously. Whereas the original study concerned itself with pressure effects only and the second reference gave the initial version of the work dealing with the thermal effects, this report gives more recent results concerning specifically thermal loads. As before, the results are limited to inside corner radii between cylinders and flat heat closures. Similarly, the analysis is based on a systematic series of finite element calculations with the significant parameters covering the field of useful design boundaries. The results are condensed into a rapid method for the determination of peak stresses needed for performing fatigue analysis in pressure vessels subjected to a significant, variable thermal load. The paper takes into account the influence of the film coefficient, temporal temperature variations, and material properties. A set of coefficients provides a convenient method of stress evaluation suitable for design purposes.
Numerical optimization methods for critical currents in superconductors
NASA Astrophysics Data System (ADS)
Kimmel, Gregory; Sadovskyy, Ivan; Koshelev, Alex; Glatz, Andreas
In this work, I present optimization methods for maximizing the critical current in high-temperature superconductors for energy applications. The critical current in the presence of an external magnetic field is mostly defined by the pinning landscape (pinscape) within the superconductor, which prevents magnetic vortices from moving and, therefore, increases its critical current. Our approach is to generate different pinscapes and obtain the resulting critical current by large-scale time-dependent Ginzburg-Landau equations. Pinning centers could be any combination of defects, including spherical and columnar defects. The parameters controlling the pinscape are adaptively adjusted in order to find the optimal parameter set, which maximizes the critical current. Here, we compare different optimization methods and discuss their performance. Work was supported by the Scientific Discovery through Advanced Computing (SciDAC) program funded by U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences.
NASA Astrophysics Data System (ADS)
Ge, Liang; Sotiropoulos, Fotis
2007-08-01
A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow
Extremal polynomials and methods of optimization of numerical algorithms
Lebedev, V I
2004-10-31
Chebyshev-Markov-Bernstein-Szegoe polynomials C{sub n}(x) extremal on [-1,1] with weight functions w(x)=(1+x){sup {alpha}}(1- x){sup {beta}}/{radical}(S{sub l}(x)) where {alpha},{beta}=0,1/2 and S{sub l}(x)={pi}{sub k=1}{sup m}(1-c{sub k}T{sub l{sub k}}(x))>0 are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight p(x)=w{sup 2}(x)(1-x{sup 2}){sup -1/2}. The parameters of optimal Chebyshev iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko-Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshev filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.
Extremal polynomials and methods of optimization of numerical algorithms
NASA Astrophysics Data System (ADS)
Lebedev, V. I.
2004-10-01
Chebyshëv-Markov-Bernstein-Szegö polynomials C_n(x) extremal on \\lbrack -1,1 \\rbrack with weight functions w(x)=(1+x)^\\alpha(1- x)^\\beta/\\sqrt{S_l(x)} where \\alpha,\\beta=0,\\frac12 and S_l(x)=\\prod_{k=1}^m(1-c_kT_{l_k}(x))>0 are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight p(x)=w^2(x)(1-x^2)^{-1/2}. The parameters of optimal Chebyshëv iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko-Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshëv filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.
B-spline methods and zonal grids for numerical simulations of turbulent flows
NASA Astrophysics Data System (ADS)
Kravchenko, Arthur Grigorievich
1998-12-01
A novel numerical technique is developed for simulations of complex turbulent flows on zonal embedded grids. This technique is based on the Galerkin method with basis functions constructed using B-splines. The technique permits fine meshes to be embedded in physically significant flow regions without placing a large number of grid points in the rest of the computational domain. The numerical technique has been tested successfully in simulations of a fully developed turbulent channel flow. Large eddy simulations of turbulent channel flow at Reynolds numbers up to Rec = 110,000 (based on centerline velocity and channel half-width) show good agreement with the existing experimental data. These tests indicate that the method provides an efficient information transfer between zones without accumulation of errors in the regions of sudden grid changes. The numerical solutions on multi-zone grids are of the same accuracy as those on a single-zone grid but require less computer resources. The performance of the numerical method in a generalized coordinate system is assessed in simulations of laminar flows over a circular cylinder at low Reynolds numbers and three-dimensional simulations at ReD = 300 (based on free-stream velocity and cylinder diameter). The drag coefficients, the size of the recirculation region, and the vortex shedding frequency all agree well with the experimental data and previous simulations of these flows. Large eddy simulations of a flow over a circular cylinder at a sub-critical Reynolds number, ReD = 3900, are performed and compared with previous upwind-biased and central finite-difference computations. In the very near-wake, all three simulations are in agreement with each other and agree fairly well with the PIV experimental data of Lourenco & Shih (1993). Farther downstream, the results of the B- spline computations are in better agreement with the hot- wire experiment of Ong & Wallace (1996) than those obtained in finite-difference simulations
Numerical simulation of fluid-structure interactions with stabilized finite element method
NASA Astrophysics Data System (ADS)
Sváček, Petr
2016-03-01
This paper is interested to the interactions of the incompressible flow with a flexibly supported airfoil. The bending and the torsion modes are considered. The problem is mathematically described. The numerical method is based on the finite element method. A combination of the streamline-upwind/Petrov-Galerkin and pressure stabilizing/Petrov-Galerkin method is used for the stabilization of the finite element method. The numerical results for a three-dimensional problem of flow over an airfoil are shown.
An efficient ensemble of radial basis functions method based on quadratic programming
NASA Astrophysics Data System (ADS)
Shi, Renhe; Liu, Li; Long, Teng; Liu, Jian
2016-07-01
Radial basis function (RBF) surrogate models have been widely applied in engineering design optimization problems to approximate computationally expensive simulations. Ensemble of radial basis functions (ERBF) using the weighted sum of stand-alone RBFs improves the approximation performance. To achieve a good trade-off between the accuracy and efficiency of the modelling process, this article presents a novel efficient ERBF method to determine the weights through solving a quadratic programming subproblem, denoted ERBF-QP. Several numerical benchmark functions are utilized to test the performance of the proposed ERBF-QP method. The results show that ERBF-QP can significantly improve the modelling efficiency compared with several existing ERBF methods. Moreover, ERBF-QP also provides satisfactory performance in terms of approximation accuracy. Finally, the ERBF-QP method is applied to a satellite multidisciplinary design optimization problem to illustrate its practicality and effectiveness for real-world engineering applications.
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)
2002-01-01
Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.
NASA Technical Reports Server (NTRS)
Fridlind, Ann; Seifert, Axel; Ackerman, Andrew; Jensen, Eric
2004-01-01
Numerical models that resolve cloud particles into discrete mass size distributions on an Eulerian grid provide a uniquely powerful means of studying the closely coupled interaction of aerosols, cloud microphysics, and transport that determine cloud properties and evolution. However, such models require many experimentally derived paramaterizations in order to properly represent the complex interactions of droplets within turbulent flow. Many of these parameterizations remain poorly quantified, and the numerical methods of solving the equations for temporal evolution of the mass size distribution can also vary considerably in terms of efficiency and accuracy. In this work, we compare results from two size-resolved microphysics models that employ various widely-used parameterizations and numerical solution methods for several aspects of stochastic collection.
A new numerical method for wave propagation through assemblies of cylinders and spheres
NASA Astrophysics Data System (ADS)
Yano, Takeru; Prosperetti, Andrea
2002-05-01
PHYSALIS is a new method for the numerical solution of a variety of problems (potential theory, Navier-Stokes equations, and others) involving cylindrical or spherical internal boundaries [A. Prosperetti and H. N. Oguz, J. Comput. Phys. 167, 196-216 (2001)]. At the heart of the method is the use of an exact analytical solution to transfer the boundary conditions from the surface of the inclusions to the neighboring grid nodes. This step avoids the difficulty deriving from the complex geometrical relationship between the internal boundaries and the underlying regular grid, with the added benefit that fast solvers can be used. In this work the method is adapted to two-dimensional acoustic scattering by cylinders as governed by the Helmholtz equation. As in prior applications, the method reveals itself highly efficient and of a relatively simple implementation. These features are illustrated on several problems. In particular, it is shown that the computational time grows much less than linearly with the number of cylinders, which permits the simulation of complex multiple scattering problems without large computational resources. [Work supported by The Japan Ministry of Education, Culture, Sports, Science and Technology, and by ONR.
Design of braided composite tubes by numerical analysis method
Hamada, Hiroyuki; Fujita, Akihiro; Maekawa, Zenichiro; Nakai, Asami; Yokoyama, Atsushi
1995-11-01
Conventional composite laminates have very poor strength through thickness and as a result are limited in their application for structural parts with complex shape. In this paper, the design for braided composite tube was proposed. The concept of analysis model which involved from micro model to macro model was presented. This method was applied to predict bending rigidity and initial fracture stress under bending load of the braided tube. The proposed analytical procedure can be included as a unit in CAE system for braided composites.
[General calculation method of diffraction efficiency of concave blazed gratings].
Li, Ting; Huang, Yuan-Shen; Xu, Bang-Lian; Li, Bai-Cheng; Zhang, Da-Wei; Tao, Chun-Xian; Ling, Jin-Zhong; Zhuang, Song-Lin
2013-07-01
In order to make diffraction energy of concave gratings more concentrated in the desired order, the present paper puts forward that the concave blazed grating with variable groove angles could be fabricated on the concave substrates by mechanical ruling method, and the theoretical method of simultaneously calculating the diffraction efficiency in the main section and non-main section is deduced by using Fresnel-Kirchhoff's diffraction formula, which makes up the shortage of the diffraction efficiency calculated only in the main section. Finally, the diffraction efficiency curves varied with wavelength is simulated by Matlab software, and the variation laws of the diffraction efficiency are compared for different production methods and application parameters, which provides a valuable reference for the design and production of the concave gratings. PMID:24059218
An Efficient Inverse Aerodynamic Design Method For Subsonic Flows
NASA Technical Reports Server (NTRS)
Milholen, William E., II
2000-01-01
Computational Fluid Dynamics based design methods are maturing to the point that they are beginning to be used in the aircraft design process. Many design methods however have demonstrated deficiencies in the leading edge region of airfoil sections. The objective of the present research is to develop an efficient inverse design method which is valid in the leading edge region. The new design method is a streamline curvature method, and a new technique is presented for modeling the variation of the streamline curvature normal to the surface. The new design method allows the surface coordinates to move normal to the surface, and has been incorporated into the Constrained Direct Iterative Surface Curvature (CDISC) design method. The accuracy and efficiency of the design method is demonstrated using both two-dimensional and three-dimensional design cases.
A fast method of numerical quadrature for p-version finite element matrices
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1993-01-01
A new technique of numerical quadrature especially suited for p-version finite element matrices is presented. This new technique separates the integrand into two parts, and numerically operates on each part separately. The objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function. The efficiency of the new technique is compared with Gaussian quadrature and found to take a small fraction of the computational effort.
A complete method for efficient fuzzy modal analysis
NASA Astrophysics Data System (ADS)
Massa, F.; Ruffin, K.; Tison, T.; Lallemand, B.
2008-01-01
The objective of this paper is to determine both the fuzzy eigenvalues and eigenvectors of a finite element model defined with fuzzy parameters. The proposed method introduces the concepts of mode shape pairing and the functional dependence of eigensolutions with respect to design parameters. High-order approximations are then introduced to limit the computational cost associated with variability management. Numerical test cases are used to highlight the abilities of this method to predict behaviour modifications due to variations in the physical parameters.
NASA Astrophysics Data System (ADS)
Hagan, Jonathan; Priede, Jānis
2013-12-01
We analyze weakly nonlinear stability of a flow of viscous conducting liquid driven by pressure gradient in the channel between two parallel walls subject to a transverse magnetic field. Using a non-standard numerical approach, we compute the linear growth rate correction and the first Landau coefficient, which in a sufficiently strong magnetic field vary with the Hartmann number as μ 1˜ (0.814-i19.8)× 10^{-3}textit {Ha} and μ 2˜ (2.73-i1.50)× 10^{-5}textit {Ha}^{-4}. These coefficients describe a subcritical transverse velocity perturbation with the equilibrium amplitude |A|2=Re [μ 1]/Re [μ 2](textit {Re}c-textit {Re})˜ 29.8textit {Ha}5(textit {Re}c-textit {Re}), which exists at Reynolds numbers below the linear stability threshold textit {Re}c˜ 4.83× 104textit {Ha}. We find that the flow remains subcritically unstable regardless of the magnetic field strength. Our method for computing Landau coefficients differs from the standard one by the application of the solvability condition to the discretized rather than continuous problem. This allows us to bypass both the solution of the adjoint problem and the subsequent evaluation of the integrals defining the inner products, which results in a significant simplification of the method.
NASA Technical Reports Server (NTRS)
Wie, Yong-Sun
1990-01-01
A procedure for calculating 3-D, compressible laminar boundary layer flow on general fuselage shapes is described. The boundary layer solutions can be obtained in either nonorthogonal 'body oriented' coordinates or orthogonal streamline coordinates. The numerical procedure is 'second order' accurate, efficient and independent of the cross flow velocity direction. Numerical results are presented for several test cases, including a sharp cone, an ellipsoid of revolution, and a general aircraft fuselage at angle of attack. Comparisons are made between numerical results obtained using nonorthogonal curvilinear 'body oriented' coordinates and streamline coordinates.
On the numerical dispersion and the spectral fidelity of the Particle-In-Cell method
NASA Astrophysics Data System (ADS)
Huang, Chengkun; Meyers, M. D.; Zeng, Y.; Yi, S.; Albright, B. J.
2015-11-01
The Particle-In-Cell (PIC) method is widely used in plasma modeling. However, the PIC method exhibits grid type numerical instabilities, including the finite grid instability and the numerical Cherenkov instability that can render unphysical simulation results or disrupt the simulation. A faithful numerical dispersion of the electromagnetic PIC algorithm is obtained and analyzed to obtain the insight about the numerical instabilities inherent in such a computation model. Using this dispersion, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. Compared with the gridless model, we show that the lack of spectral fidelity relative to the real system due to the aliasing effect is a major cause of the numerical instabilities in the PIC model. Work supported by the U.S. Department of Energy through the LDRD program at Los Alamos National Laboratory.
Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em
2014-08-01
The Karhunen–Lòeve (KL) decomposition provides a low-dimensional representation for random fields as it is optimal in the mean square sense. Although for many stochastic systems of practical interest, described by stochastic partial differential equations (SPDEs), solutions possess this low-dimensional character, they also have a strongly time-dependent form and to this end a fixed-in-time basis may not describe the solution in an efficient way. Motivated by this limitation of standard KL expansion, Sapsis and Lermusiaux (2009) [26] developed the dynamically orthogonal (DO) field equations which allow for the simultaneous evolution of both the spatial basis where uncertainty ‘lives’ but also the stochastic characteristics of uncertainty. Recently, Cheng et al. (2013) [28] introduced an alternative approach, the bi-orthogonal (BO) method, which performs the exact same tasks, i.e. it evolves the spatial basis and the stochastic characteristics of uncertainty. In the current work we examine the relation of the two approaches and we prove theoretically and illustrate numerically their equivalence, in the sense that one method is an exact reformulation of the other. We show this by deriving a linear and invertible transformation matrix described by a matrix differential equation that connects the BO and the DO solutions. We also examine a pathology of the BO equations that occurs when two eigenvalues of the solution cross, resulting in an instantaneous, infinite-speed, internal rotation of the computed spatial basis. We demonstrate that despite the instantaneous duration of the singularity this has important implications on the numerical performance of the BO approach. On the other hand, it is observed that the BO is more stable in nonlinear problems involving a relatively large number of modes. Several examples, linear and nonlinear, are presented to illustrate the DO and BO methods as well as their equivalence.
NASA Technical Reports Server (NTRS)
Lacasse, James M.
1995-01-01
A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations. Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies. The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from the CFD discretized flow equations, recast in adjoint form, and solved using direct matrix inversion techniques. This investigation is performed to demonstrate an aerodynamic shape optimization technique on a multiblock domain and its applicability to complex geometries. The objectives are accomplished by shape optimizing two aerodynamic configurations. First, the shape optimization of a transonic airfoil is performed to investigate the behavior of the method in highly nonlinear flows and the effect of different grid blocking strategies on the procedure. Secondly, shape optimization of a two-element configuration in subsonic flow is completed. Cases are presented for this configuration to demonstrate the effect of simultaneously reshaping interfering elements. The aerodynamic shape optimization is shown to produce supercritical type airfoils in the transonic flow from an initially symmetric airfoil. Multiblocking effects the path of optimization while providing similar results at the conclusion. Simultaneous reshaping of elements is shown to be more effective than individual element reshaping due to the inclusion of mutual interference effects.
An efficient method for flanking sequence isolation in barley
Technology Transfer Automated Retrieval System (TEKTRAN)
An adapter ligation method was developed to determine native barley (Hordeum vulgare) sequences flanking Ds insertions and barley ESTs. This method is simple and efficient, with the majority of queries returning valid sequence information. This report describes the protocol in detail, quantifies its...
Effective vs. Efficient: Teaching Methods of Solving Linear Equations
ERIC Educational Resources Information Center
Ivey, Kathy M. C.
2003-01-01
The choice of teaching an effective method--one that most students can master--or an efficient method--one that takes the fewest steps--occurs daily in Algebra I classrooms. This decision may not be made in the abstract, however, but rather in a ready-to-hand mode. This study examines how teachers solve linear equations when the purpose is…
Numerical Quadrature and Operator Splitting in Finite Element Methods for Cardiac Electrophysiology
Krishnamoorthi, Shankarjee; Sarkar, Mainak; Klug, William S.
2015-01-01
SUMMARY We examine carefully the numerical accuracy and computational efficiency of alternative formulations of the finite-element solution procedure for the mono-domain equations of cardiac electrophysiology (EP), focusing on the interaction of spatial quadrature implementations with operator splitting, examining both nodal and Gauss quadrature methods, and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of “lumped” approximations of consistent capacitance and mass matrices. Most generally we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state-variable ODEs. We identify two lumped approximation schemes that exhibit superior accuracy, rivaling that of the most expensive variationally consistent implementations. Finally we illustrate some of the physiological consequences of discretization error in EP simulation relevant to cardiac arrhythmia and fibrillation. These results suggest caution with the use of semi-automated free-form tetrahedral and hexahedral meshing algorithms available in most commercially available meshing software, which produce non-uniform meshes having a large distribution of element sizes. PMID:23873868
NASA Astrophysics Data System (ADS)
Lai, Yongzeng; Zeng, Yan; Xi, Xiaojing
2011-11-01
In this paper, we discuss control variate methods for Asian option pricing under exponential jump diffusion model for the underlying asset prices. Numerical results show that the new control variate XNCV is much more efficient than the classical control variate XCCV when used in pricing Asian options. For example, the variance reduction ratios by XCCV are no more than 120 whereas those by XNCV vary from 15797 to 49171 on average over sample sizes 1024, 2048, 4096, 8192, 16384 and 32768.
NASA Astrophysics Data System (ADS)
Zhi, Jie; Zhao, Libin; Zhang, Jianyu; Liu, Zhanli
2016-06-01
In this paper, a new numerical method that combines a surface-based cohesive model and extended finite element method (XFEM) without predefining the crack paths is presented to simulate the microscopic damage evolution in composites under uniaxial transverse tension. The proposed method is verified to accurately capture the crack kinking into the matrix after fiber/matrix debonding. A statistical representative volume element (SRVE) under periodic boundary conditions is used to approximate the microstructure of the composites. The interface parameters of the cohesive models are investigated, in which the initial interface stiffness has a great effect on the predictions of the fiber/matrix debonding. The detailed debonding states of SRVE with strong and weak interfaces are compared based on the surface-based and element-based cohesive models. The mechanism of damage in composites under transverse tension is described as the appearance of the interface cracks and their induced matrix micro-cracking, both of which coalesce into transversal macro-cracks. Good agreement is found between the predictions of the model and the in situ experimental observations, demonstrating the efficiency of the presented model for simulating the microscopic damage evolution in composites.
Mazzurana, M; Sandrini, L; Vaccari, A; Malacarne, C; Cristoforetti, L; Pontalti, R
2003-10-01
Complex permittivity values have a dominant role in the overall consideration of interaction between radiofrequency electromagnetic fields and living matter, and in related applications such as electromagnetic dosimetry. There are still some concerns about the accuracy of published data and about their variability due to the heterogeneous nature of biological tissues. The aim of this study is to provide an alternative semi-automatic method by which numerical dielectric human models for dosimetric studies can be obtained. Magnetic resonance imaging (MRI) tomography was used to acquire images. A new technique was employed to correct nonuniformities in the images and frequency-dependent transfer functions to correlate image intensity with complex permittivity were used. The proposed method provides frequency-dependent models in which permittivity and conductivity vary with continuity--even in the same tissue--reflecting the intrinsic realistic spatial dispersion of such parameters. The human model is tested with an FDTD (finite difference time domain) algorithm at different frequencies; the results of layer-averaged and whole-body-averaged SAR (specific absorption rate) are compared with published work, and reasonable agreement has been found. Due to the short time needed to obtain a whole body model, this semi-automatic method may be suitable for efficient study of various conditions that can determine large differences in the SAR distribution, such as body shape, posture, fat-to-muscle ratio, height and weight. PMID:14579858
Cruel, Magali; Bensidhoum, Morad; Nouguier-Lehon, Cécile; Dessombz, Olivier; Becquart, Pierre; Petite, Hervé; Hoc, Thierry
2015-09-01
Controlling the mechanical environment in bioreactors represents a key element in the reactors' optimization. Positive effects of fluid flow in three-dimensional bioreactors have been observed, but local stresses at cell scale remain unknown. These effects led to the development of numerical tools to assess the micromechanical environment of cells in bioreactors. Recently, new possible scaffold geometry has emerged: granular packings. In the present study, the primary goal was to compare the efficiency of such a scaffold to the other ones from literature in terms of wall shear stress levels and distributions. To that aim, three different types of granular packings were generated through discrete element method, and computational fluid dynamics was used to simulate the flow within these packings. Shear stress levels and distributions were determined. A linear relationship between shear stress and inlet velocity was observed, and its slope was similar to published data. The distributions of normalized stress were independent of the inlet velocity and were highly comparable to those of widely used porous scaffolds. Granular packings present similar features to more classical porous scaffolds and have the advantage of being easy to manipulate and seed. The methods of this work are generalizable to the study of other granular packing configurations. PMID:25634115
Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels.
Liu, Jinn-Liang; Eisenberg, Bob
2015-07-01
Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent Ca(2+) may cause more unstable discrete Ca(2+) fluxes than that of monovalent Na(+). Two different methods-called the SMIB and multiscale methods-are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are
Numerical methods for the design and analysis of wings at supersonic speeds
NASA Technical Reports Server (NTRS)
Carlson, H. W.; Miller, D. S.
1974-01-01
Numerical methods for the design and analysis of arbitrary-planform wings at supersonic speeds are reviewed. Certain deficiencies are revealed, particularly in application to wings with slightly subsonic leading edges. Recently devised numerical techniques which overcome the major part of these deficiencies are presented. The original development as well as the more recent revisions are subjected to a thorough review.
A study of numerical methods for hyperbolic conservation laws with stiff source terms
NASA Technical Reports Server (NTRS)
Leveque, R. J.; Yee, H. C.
1988-01-01
The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.
A Method for Determining Optimal Residential Energy Efficiency Packages
Polly, B.; Gestwick, M.; Bianchi, M.; Anderson, R.; Horowitz, S.; Christensen, C.; Judkoff, R.
2011-04-01
This report describes an analysis method for determining optimal residential energy efficiency retrofit packages and, as an illustrative example, applies the analysis method to a 1960s-era home in eight U.S. cities covering a range of International Energy Conservation Code (IECC) climate regions. The method uses an optimization scheme that considers average energy use (determined from building energy simulations) and equivalent annual cost to recommend optimal retrofit packages specific to the building, occupants, and location.
An efficient multilevel optimization method for engineering design
NASA Technical Reports Server (NTRS)
Vanderplaats, G. N.; Yang, Y. J.; Kim, D. S.
1988-01-01
An efficient multilevel deisgn optimization technique is presented. The proposed method is based on the concept of providing linearized information between the system level and subsystem level optimization tasks. The advantages of the method are that it does not require optimum sensitivities, nonlinear equality constraints are not needed, and the method is relatively easy to use. The disadvantage is that the coupling between subsystems is not dealt with in a precise mathematical manner.
Some numerical methods for integrating systems of first-order ordinary differential equations
NASA Technical Reports Server (NTRS)
Clark, N. W.
1969-01-01
Report on numerical methods of integration includes the extrapolation methods of Bulirsch-Stoer and Neville. A comparison is made nith the Runge-Kutta and Adams-Moulton methods, and circumstances are discussed under which the extrapolation method may be preferred.
NASA Astrophysics Data System (ADS)
Totaro, N.; Guyader, J. L.
2012-06-01
Given the need to decrease energy consumption in the automobile industry, vehicle weight has become an important issue. Regarding acoustic comfort, the weight of noise reduction devices must be minimized inside vehicle compartments. Consequently, these devices, for example those using poro-elastic materials, must be designed carefully to maximize their influence on noise reduction. The present paper describes a method developed to obtain an efficient positioning of a given surface (or mass) of absorbing material characterized by its surface impedance. This technique is based on the Patch Transfer Function method used to couple complex vibro-acoustic sub-domains and which has been successfully applied in the European ViSPeR and Silence projects. First, a numerical analysis of the possibilities of this method is performed on a non-rectangular cavity with rigid walls after which an experimental validation of this numerical analysis is performed to evaluate the accuracy of the method under real conditions.
NASA Technical Reports Server (NTRS)
Rosenbaum, J. S.
1976-01-01
If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.
Assessing methods to measure motor efficiency in situ
Douglass, J.; Wohlgemuth, C.; Wainwright, G.
1997-07-01
Managing electric motor systems is one of the most important aspects of improving reliability and increasing energy efficiency in the industrial environment. Unfortunately, unknown performance data for existing motors often frustrates good motor systems management intentions. Determining motor efficiency is not easy. Nonetheless, several existing methods and dedicated instruments estimated in-situ efficiency well enough to support economic decisions. The off-voltage conditions did not subvert results as much as the authors have expected. However, performance of the different methods varied by the motor under test, revealing that developers need to tune their designs for better accuracy with older, rewound, and/or damaged motors. For most methods, the best correlation with lab-determined efficiency was for the new energy efficient 300 HP motor. With the diverse veteran motors the methods diverged more, not only from lab efficiency, but also from each other. The most accurate methods were more invasive, requiring shutdown and uncoupling. However, with a structured motor systems management program, these procedures could be accomplished conveniently at different times with the results combined later to compute efficiency. For example, winding resistance could be measured and recorded at the receiving inspection of new and repaired motors. No-load power consumption could be accomplished either at the repair shop or during initial or post-repair installation. Performance under load could be recorded any time the motor is installed and operating at normal load. The authors believe that all methods can benefit from more validation studies with a diversity of typical veteran motors (i.e. other than new, efficient, and healthy motors). Where divergence occurs, case studies should pursue the causes of divergence. Several methods perform well enough that their adoption should be encouraged. However, the need to keep the techniques simple and user friendly for use in the
NASA Astrophysics Data System (ADS)
Zhao, Xuzhe
High efficiency hydrogen storage method is significant in development of fuel cell vehicle. Seeking for a high energy density material as the fuel becomes the key of wide spreading fuel cell vehicle. LiBH4 + MgH 2 system is a strong candidate due to their high hydrogen storage density and the reaction between them is reversible. However, LiBH4 + MgH 2 system usually requires the high temperature and hydrogen pressure for hydrogen release and uptake reaction. In order to reduce the requirements of this system, nanoengineering is the simple and efficient method to improve the thermodynamic properties and reduce kinetic barrier of reaction between LiBH4 and MgH2. Based on ab initio density functional theory (DFT) calculations, the previous study has indicated that the reaction between LiBH4 and MgH2 can take place at temperature near 200°C or below. However, the predictions have been shown to be inconsistent with many experiments. Therefore, it is the first time that our experiment using ball milling with aerosol spraying (BMAS) to prove the reaction between LiBH4 and MgH2 can happen during high energy ball milling at room temperature. Through this BMAS process we have found undoubtedly the formation of MgB 2 and LiH during ball milling of MgH2 while aerosol spraying of the LiBH4/THF solution. Aerosol nanoparticles from LiBH 4/THF solution leads to form Li2B12H12 during BMAS process. The Li2B12H12 formed then reacts with MgH2 in situ during ball milling to form MgB 2 and LiH. Discrete element modeling (DEM) is a useful tool to describe operation of various ball milling processes. EDEM is software based on DEM to predict power consumption, liner and media wear and mill output. In order to further improve the milling efficiency of BMAS process, EDEM is conducted to make analysis for complicated ball milling process. Milling speed and ball's filling ratio inside the canister as the variables are considered to determine the milling efficiency. The average and maximum
Assessment of an efficient numerical solution of the 1D Richards' equation on bare soil
NASA Astrophysics Data System (ADS)
Varado, N.; Braud, I.; Ross, P. J.; Haverkamp, R.
2006-05-01
A new numerical scheme has been proposed by Ross [Ross, P.J., 2003. Modeling soil water and solute transport—fast, simplified numerical solutions. Agronomy Journal 95, 1352-1361] to solve the 1D Richards' equation [Richards, L.A., 1931. Capillary conduction of liquids through porous medium. Physics 1, 318-333]. This non-iterative solution uses the description of soil properties proposed by Brooks and Corey [Brooks, R.H., Corey, A.T., 1964. Hydraulic properties of porous media. Colorado State University, Fort Collins]. It allows the derivation of an analytical expression for the Kirchhoff potential used in the calculation of water fluxes. The degree of saturation is used as the dependent variable when the soil is unsaturated and the Kirchhoff potential is used in case of saturation. A space and time discretisation scheme leads to a tridiagonal set of linear equations that is solved non-iteratively. We propose in this paper an extensive test of this numerical method, evaluated only on a single case by Ross. The tests are conducted in two steps. First, the solution is assessed against two analytical solutions. The first one [Basha, H.A., 1999. Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface. Water Resources Research 35(1), 75-93] provides the water content profile when simplified soil characteristics such as the exponential law of Gardner [Gardner, W.R., 1958. Some steady-state solutions of the unsaturated moisture flow equations with application to evaporation from a water table. Soil Science 85, 228-232] are used. The Ross solution is compared to this solution on eight different soils that were fitted to this law. Analytical solution with the Brooks and Corey models is not available at the moment for the moisture profile but some exist for cumulative infiltration. Therefore, the second analytical solution, used in this study, is the one developed by Parlange et al. [Parlange, J.-Y., Haverkamp, R., Touma, J
An Efficient Simulation Budget Allocation Method Incorporating Regression for Partitioned Domains*
Brantley, Mark W.; Lee, Loo Hay; Chen, Chun-Hung; Xu, Jie
2014-01-01
Simulation can be a very powerful tool to help decision making in many applications but exploring multiple courses of actions can be time consuming. Numerous ranking & selection (R&S) procedures have been developed to enhance the simulation efficiency of finding the best design. To further improve efficiency, one approach is to incorporate information from across the domain into a regression equation. However, the use of a regression metamodel also inherits some typical assumptions from most regression approaches, such as the assumption of an underlying quadratic function and the simulation noise is homogeneous across the domain of interest. To extend the limitation while retaining the efficiency benefit, we propose to partition the domain of interest such that in each partition the mean of the underlying function is approximately quadratic. Our new method provides approximately optimal rules for between and within partitions that determine the number of samples allocated to each design location. The goal is to maximize the probability of correctly selecting the best design. Numerical experiments demonstrate that our new approach can dramatically enhance efficiency over existing efficient R&S methods. PMID:24936099
An efficient method for evaluating RRAM crossbar array performance
NASA Astrophysics Data System (ADS)
Song, Lin; Zhang, Jinyu; Chen, An; Wu, Huaqiang; Qian, He; Yu, Zhiping
2016-06-01
An efficient method is proposed in this paper to mitigate computational burden in resistive random access memory (RRAM) array simulation. In the worst case scenario, a 4 Mb RRAM array with line resistance is greatly reduced using this method. For 1S1R-RRAM array structures, static and statistical parameters in both reading and writing processes are simulated. Error analysis is performed to prove the reliability of the algorithm when line resistance is extremely small compared with the junction resistance. Results show that high precision is maintained even if the size of RRAM array is reduced by one thousand times, which indicates significant improvements in both computational efficiency and memory requirements.
NASA Technical Reports Server (NTRS)
Gottlieb, D.; Turkel, E.
1980-01-01
New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.
A numerical method for approximating antenna surfaces defined by discrete surface points
NASA Technical Reports Server (NTRS)
Lee, R. Q.; Acosta, R.
1985-01-01
A simple numerical method for the quadratic approximation of a discretely defined reflector surface is described. The numerical method was applied to interpolate the surface normal of a parabolic reflector surface from a grid of nine closest surface points to the point of incidence. After computing the surface normals, the geometrical optics and the aperture integration method using the discrete Fast Fourier Transform (FFT) were applied to compute the radiaton patterns for a symmetric and an offset antenna configurations. The computed patterns are compared to that of the analytic case and to the patterns generated from another numerical technique using the spline function approximation. In the paper, examples of computations are given. The accuracy of the numerical method is discussed.
Analysis of coupling efficiency on hemispherical fiber lens by method of lines.
Lambak, Zainuddin; Abdul Rahman, Faidz; Mokhtar, Mohd Ridzuan; Tengku, Imran A
2009-02-16
The method of lines (MoL) has been developed to study coupling efficiency on hemispherical lens. In this paper, the physical shape of the lens is approximated by cascading a number of straight waveguide segments. The perfectly matched layer (PML) is applied as an absorber for the MoL to reduce numerical reflection in the simulation region. Analysis is done by calculating coupling efficiency at the plane of integration where the coupling efficiency is an overlap integral between laser diode field and fiber field. The result of coupling efficiency in this analysis is compared to the experiment and ABCD matrix. It is found that MoL gives good result accuracy. PMID:19219196
Numerical methods for simulating blood flow at macro, micro, and multi scales.
Imai, Yohsuke; Omori, Toshihiro; Shimogonya, Yuji; Yamaguchi, Takami; Ishikawa, Takuji
2016-07-26
In the past decade, numerical methods for the computational biomechanics of blood flow have progressed to overcome difficulties in diverse applications from cellular to organ scales. Such numerical methods may be classified by the type of computational mesh used for the fluid domain, into fixed mesh methods, moving mesh (boundary-fitted mesh) methods, and mesh-free methods. The type of computational mesh used is closely related to the characteristics of each method. We herein provide an overview of numerical methods recently used to simulate blood flow at macro and micro scales, with a focus on computational meshes. We also discuss recent progress in the multi-scale modeling of blood flow. PMID:26705108
Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels
NASA Astrophysics Data System (ADS)
Liu, Jinn-Liang; Eisenberg, Bob
2015-07-01
Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent Ca2 + may cause more unstable discrete Ca2 + fluxes than that of monovalent Na+. Two different methods—called the SMIB and multiscale methods—are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are
Efficient forced vibration reanalysis method for rotating electric machines
NASA Astrophysics Data System (ADS)
Saito, Akira; Suzuki, Hiromitsu; Kuroishi, Masakatsu; Nakai, Hideo
2015-01-01
Rotating electric machines are subject to forced vibration by magnetic force excitation with wide-band frequency spectrum that are dependent on the operating conditions. Therefore, when designing the electric machines, it is inevitable to compute the vibration response of the machines at various operating conditions efficiently and accurately. This paper presents an efficient frequency-domain vibration analysis method for the electric machines. The method enables the efficient re-analysis of the vibration response of electric machines at various operating conditions without the necessity to re-compute the harmonic response by finite element analyses. Theoretical background of the proposed method is provided, which is based on the modal reduction of the magnetic force excitation by a set of amplitude-modulated standing-waves. The method is applied to the forced response vibration of the interior permanent magnet motor at a fixed operating condition. The results computed by the proposed method agree very well with those computed by the conventional harmonic response analysis by the FEA. The proposed method is then applied to the spin-up test condition to demonstrate its applicability to various operating conditions. It is observed that the proposed method can successfully be applied to the spin-up test conditions, and the measured dominant frequency peaks in the frequency response can be well captured by the proposed approach.
Implicit methods for efficient musculoskeletal simulation and optimal control
van den Bogert, Antonie J.; Blana, Dimitra; Heinrich, Dieter
2011-01-01
The ordinary differential equations for musculoskeletal dynamics are often numerically stiff and highly nonlinear. Consequently, simulations require small time steps, and optimal control problems are slow to solve and have poor convergence. In this paper, we present an implicit formulation of musculoskeletal dynamics, which leads to new numerical methods for simulation and optimal control, with the expectation that we can mitigate some of these problems. A first order Rosenbrock method was developed for solving forward dynamic problems using the implicit formulation. It was used to perform real-time dynamic simulation of a complex shoulder arm system with extreme dynamic stiffness. Simulations had an RMS error of only 0.11 degrees in joint angles when running at real-time speed. For optimal control of musculoskeletal systems, a direct collocation method was developed for implicitly formulated models. The method was applied to predict gait with a prosthetic foot and ankle. Solutions were obtained in well under one hour of computation time and demonstrated how patients may adapt their gait to compensate for limitations of a specific prosthetic limb design. The optimal control method was also applied to a state estimation problem in sports biomechanics, where forces during skiing were estimated from noisy and incomplete kinematic data. Using a full musculoskeletal dynamics model for state estimation had the additional advantage that forward dynamic simulations, could be done with the same implicitly formulated model to simulate injuries and perturbation responses. While these methods are powerful and allow solution of previously intractable problems, there are still considerable numerical challenges, especially related to the convergence of gradient-based solvers. PMID:22102983
NASA Astrophysics Data System (ADS)
Zhang, Qian-Jiang; Dai, Shi-Kun; Chen, Long-Wei; Qiang, Jian-Ke; Li, Kun; Zhao, Dong-Dong
2016-06-01
To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.
Efficient harvesting methods for early-stage snake and turtle embryos.
Matsubara, Yoshiyuki; Kuroiwa, Atsushi; Suzuki, Takayuki
2016-04-01
Reptile development is an intriguing research target for understating the unique morphogenesis of reptiles as well as the evolution of vertebrates. However, there are numerous difficulties associated with studying development in reptiles. The number of available reptile eggs is usually quite limited. In addition, the reptile embryo is tightly adhered to the eggshell, making it a challenge to isolate reptile embryos intact. Furthermore, there have been few reports describing efficient procedures for isolating intact embryos especially prior to pharyngula stage. Thus, the aim of this review is to present efficient procedures for obtaining early-stage reptilian embryos intact. We first describe the method for isolating early-stage embryos of the Japanese striped snake. This is the first detailed method for obtaining embryos prior to oviposition in oviparous snake species. Second, we describe an efficient strategy for isolating early-stage embryos of the soft-shelled turtle. PMID:27059539
Efficient Approach To Discover Novel Agrochemical Candidates: Intermediate Derivatization Method.
Liu, Changling; Guan, Aiying; Yang, Jindong; Chai, Baoshan; Li, Miao; Li, Huichao; Yang, Jichun; Xie, Yong
2016-01-13
Intensive competition of intellectual property, easy development of agrochemical resistance, and stricter regulations of environmental concerns make the successful rate for agrochemical discovery extremely lower using traditional agrochemical discovery methods. Therefore, there is an urgent need to find a novel approach to guide agrochemical discovery with high efficiency to quickly keep pace with the changing market. On the basis of these situations, here we summarize the intermediate derivatization method (IDM) between conventional methods in agrochemicals and novel ones in pharmaceuticals. This method is relatively efficient with short time in discovery phase, reduced cost, especially good innovated structure, and better performance. In this paper, we summarize and illustrate "what is the IDM" and "why to use" and "how to use" it to accelerate the discovery of new biologically active molecules, focusing on agrochemicals. Furthermore, we display several research projects in our novel agrochemical discovery programs with improved success rate under guidance of this strategy in recent years. PMID:25517210
Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory
NASA Astrophysics Data System (ADS)
Lin, Lin; Shao, Sihong; E, Weinan
2013-07-01
We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt2, Au2, TlF, and Bi2Se3 indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.
An efficient surrogate-based method for computing rare failure probability
NASA Astrophysics Data System (ADS)
Li, Jing; Li, Jinglai; Xiu, Dongbin
2011-10-01
In this paper, we present an efficient numerical method for evaluating rare failure probability. The method is based on a recently developed surrogate-based method from Li and Xiu [J. Li, D. Xiu, Evaluation of failure probability via surrogate models, J. Comput. Phys. 229 (2010) 8966-8980] for failure probability computation. The method by Li and Xiu is of hybrid nature, in the sense that samples of both the surrogate model and the true physical model are used, and its efficiency gain relies on using only very few samples of the true model. Here we extend the capability of the method to rare probability computation by using the idea of importance sampling (IS). In particular, we employ cross-entropy (CE) method, which is an effective method to determine the biasing distribution in IS. We demonstrate that, by combining with the CE method, a surrogate-based IS algorithm can be constructed and is highly efficient for rare failure probability computation—it incurs much reduced simulation efforts compared to the traditional CE-IS method. In many cases, the new method is capable of capturing failure probability as small as 10 -12 ˜ 10 -6 with only several hundreds samples.
Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory
Lin, Lin; Shao, Sihong; E, Weinan
2012-11-06
We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt$_{2}$, Au$_{2}$, TlF, and Bi$_{2}$Se$_{3}$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.
Numerical method for estimating the size of chaotic regions of phase space
Henyey, F.S.; Pomphrey, N.
1987-10-01
A numerical method for estimating irregular volumes of phase space is derived. The estimate weights the irregular area on a surface of section with the average return time to the section. We illustrate the method by application to the stadium and oval billiard systems and also apply the method to the continuous Henon-Heiles system. 15 refs., 10 figs. (LSP)
Efficiency of shock wave attenuation in ducts by various methods
NASA Astrophysics Data System (ADS)
Frolov, S. M.
1993-02-01
Different methods of shock wave attenuation in ducts are compared in terms of efficiency. The methods investigated include expansion of the duct cross section, the use of perforated side walls, and the use of porous screens and screen cascades. The attentuation of air shock waves is estimated by using a unified approach which provides satisfactory agreement with experimental data. Based on the results of the study, a nomogram is plotted which can be used for practical calculations.
Estimating School Efficiency: A Comparison of Methods Using Simulated Data.
ERIC Educational Resources Information Center
Bifulco, Robert; Bretschneider, Stuart
2001-01-01
Uses simulated data to assess the adequacy of two econometric and linear-programming techniques (data-envelopment analysis and corrected ordinary least squares) for measuring performance-based school reform. In complex data sets (simulated to contain measurement error and endogeneity), these methods are inadequate efficiency measures. (Contains 40…
NASA Astrophysics Data System (ADS)
Grenga, Temistocle
The aim of this research is to further develop a dynamically adaptive algorithm based on wavelets that is able to solve efficiently multi-dimensional compressible reactive flow problems. This work demonstrates the great potential for the method to perform direct numerical simulation (DNS) of combustion with detailed chemistry and multi-component diffusion. In particular, it addresses the performance obtained using a massive parallel implementation and demonstrates important savings in memory storage and computational time over conventional methods. In addition, fully-resolved simulations of challenging three dimensional problems involving mixing and combustion processes are performed. These problems are particularly challenging due to their strong multiscale characteristics. For these solutions, it is necessary to combine the advanced numerical techniques applied to modern computational resources.
76 FR 21673 - Alternative Efficiency Determination Methods and Alternate Rating Methods
Federal Register 2010, 2011, 2012, 2013, 2014
2011-04-18
...-substantiation of an AEDM or ARM as a result of a change in standard or test procedure. 76 FR 12492 (March 7...; ] DEPARTMENT OF ENERGY 10 CFR Part 431 RIN 1904-AC46 Alternative Efficiency Determination Methods and Alternate Rating Methods AGENCY: Office of Energy Efficiency and Renewable Energy, Department of Energy....
An efficient method of noroviruses recovery from oysters and clams
NASA Astrophysics Data System (ADS)
Zhou, Deqing; Ma, Liping; Zhao, Feng; Yao, Lin; Su, Laijin; Li, Xinguang
2013-03-01
Noroviruses (NoVs) are widespread causes of nonbacterial gastroenteritis. Outbreaks of NoVs caused diseases are commonly ascribed to the consumption of contaminated shellfish. The concentration and RNA extraction of NoVs are crucial steps of detecting NoVs in shellfish. This study aimed to select a simple, rapid and highly efficient recovery method of NoVs detection with real-time RT-PCR. Four methods of recovering GI.3 and GII.4 NoVs from spiked digestive tissues of oysters and clams, respectively, were compared, of them, the method involving proteinase K and PEG 8000 was found the most efficient. With this method, 9.3% and 13.1% of GI.3 and GII.4 NoVs were recovered from oysters and 9.6% and 12.3% of GI.3 and GII.4 NoVs were recovered from clams, respectively. This method was further used to detect NoVs in 84 oysters ( Crassostrea gigas) and 86 clams ( Ruditapes philippinarum) collected from 10 coastal cities in China from Jan. 2011 to Feb. 2012. The NoVs isolation rates were 10.47% of clams (9/86) and 7.14% of oysters (6/84). All the detected NoVs belonged to genotype GII. The NoVs recovery method selected is efficient for NoVs detection in oysters and clams.
Geometry optimization of bimetallic clusters using an efficient heuristic method
NASA Astrophysics Data System (ADS)
Lai, Xiangjing; Xu, Ruchu; Huang, Wenqi
2011-10-01
In this paper, an efficient heuristic algorithm for geometry optimization of bimetallic clusters is proposed. The algorithm is mainly composed of three ingredients: the monotonic basin-hopping method with guided perturbation (MBH-GP), surface optimization method, and iterated local search (ILS) method, where MBH-GP and surface optimization method are used to optimize the geometric structure of a cluster, and the ILS method is used to search the optimal homotop for a fixed geometric structure. The proposed method is applied to Cu38-nAun (0 ≤ n ≤ 38), Ag55-nAun (0 ≤ n ≤ 55), and Cu55-nAun (0 ≤ n ≤ 55) clusters modeled by the many-body Gupta potential. Comparison with the results reported in the literature indicates that the present method is highly efficient and a number of new putative global minima missed in the previous papers are found. The present method should be a promising tool for the theoretical determination of ground-state structure of bimetallic clusters. Additionally, some key elements and properties of the present method are also analyzed.
A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems
Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing
2012-01-01
An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849
The alias method: A fast, efficient Monte Carlo sampling technique
Rathkopf, J.A.; Edwards, A.L. ); Smidt, R.K. )
1990-11-16
The alias method is a Monte Carlo sampling technique that offers significant advantages over more traditional methods. It equals the accuracy of table lookup and the speed of equal probable bins. The original formulation of this method sampled from discrete distributions and was easily extended to histogram distributions. We have extended the method further to applications more germane to Monte Carlo particle transport codes: continuous distributions. This paper presents the alias method as originally derived and our extensions to simple continuous distributions represented by piecewise linear functions. We also present a method to interpolate accurately between distributions tabulated at points other than the point of interest. We present timing studies that demonstrate the method's increased efficiency over table lookup and show further speedup achieved through vectorization. 6 refs., 2 figs., 1 tab.
Methods of Efficient Study Habits and Physics Learning
NASA Astrophysics Data System (ADS)
Zettili, Nouredine
2010-02-01
We want to discuss the methods of efficient study habits and how they can be used by students to help them improve learning physics. In particular, we deal with the most efficient techniques needed to help students improve their study skills. We focus on topics such as the skills of how to develop long term memory, how to improve concentration power, how to take class notes, how to prepare for and take exams, how to study scientific subjects such as physics. We argue that the students who conscientiously use the methods of efficient study habits achieve higher results than those students who do not; moreover, a student equipped with the proper study skills will spend much less time to learn a subject than a student who has no good study habits. The underlying issue here is not the quantity of time allocated to the study efforts by the students, but the efficiency and quality of actions so that the student can function at peak efficiency. These ideas were developed as part of Project IMPACTSEED (IMproving Physics And Chemistry Teaching in SEcondary Education), an outreach grant funded by the Alabama Commission on Higher Education. This project is motivated by a major pressing local need: A large number of high school physics teachers teach out of field. )
NASA Astrophysics Data System (ADS)
Schuster, Jonathan; Bellotti, Enrico
2013-06-01
We have investigated the quantum effiency in HgCdTe photovoltaic pixel arrays employing a photon-trapping structure realized with a periodic array of pillars intended to provide broadband operation. We have found that the quantum efficiency depends heavily on the passivation of the pillar surface. Pillars passivated with anodicoxide have a large fixed positive charge on the pillar surface. We use our three-dimensional numerical simulation model to study the effect of surface charge and surface recombination velocity on the exterior of the pillars. We then evaluate the quantum efficiency of this structure subject to different surface conditions. We have found that by themselves, the surface charge and surface recombination are detrimental to the quantum efficiency but the quantum efficiency is recovered when both phenomena are present. We will discuss the effects of these phenomena and the trade offs that exist between the two.
Application of numerical methods for diffusion-based modeling of skin permeation.
Frasch, H Frederick; Barbero, Ana M
2013-02-01
The application of numerical methods for mechanistic, diffusion-based modeling of skin permeation is reviewed. Methods considered here are finite difference, method of lines, finite element, finite volume, random walk, cellular automata, and smoothed particle hydrodynamics. First the methods are briefly explained with rudimentary mathematical underpinnings. Current state of the art numerical models are described, and then a chronological overview of published models is provided. Key findings and insights of reviewed models are highlighted. Model results support a primarily transcellular pathway with anisotropic lipid transport. Future endeavors would benefit from a fundamental analysis of drug/vehicle/skin interactions. PMID:22261307
Numerical Solution of Problems in Calculus of Variations by Homotopy Perturbation Method
Jafari, M. A.; Aminataei, A.
2008-09-01
In this work we use Homotopy Perturbation Method (HPM) to solve differential equations that arise in variational problems. To illustrate the method some examples are provided. The results show the efficiency and accuracy of the HPM. HPM can be considered an alternative method to Adomian decomposition method. Both of these methods can obtain analytic form of the solution in some cases.
NASA Astrophysics Data System (ADS)
Li, Jianbo; Liu, Jun; Lin, Gao
2013-12-01
Consideration of structure-foundation-soil dynamic interaction is a basic requirement in the evaluation of the seismic safety of nuclear power facilities. An efficient and accurate dynamic interaction numerical model in the time domain has become an important topic of current research. In this study, the scaled boundary finite element method (SBFEM) is improved for use as an effective numerical approach with good application prospects. This method has several advantages, including dimensionality reduction, accuracy of the radial analytical solution, and unlike other boundary element methods, it does not require a fundamental solution. This study focuses on establishing a high performance scaled boundary finite element interaction analysis model in the time domain based on the acceleration unit-impulse response matrix, in which several new solution techniques, such as a dimensionless method to solve the interaction force, are applied to improve the numerical stability of the actual soil parameters and reduce the amount of calculation. Finally, the feasibility of the time domain methods are illustrated by the response of the nuclear power structure and the accuracy of the algorithms are dynamically verified by comparison with the refinement of a large-scale viscoelastic soil model.
Lim, Hooi Been; Baumann, Dirk; Li, Er-Ping
2011-03-01
Wireless body area network (WBAN) is a new enabling system with promising applications in areas such as remote health monitoring and interpersonal communication. Reliable and optimum design of a WBAN system relies on a good understanding and in-depth studies of the wave propagation around a human body. However, the human body is a very complex structure and is computationally demanding to model. This paper aims to investigate the effects of the numerical model's structure complexity and feature details on the simulation results. Depending on the application, a simplified numerical model that meets desired simulation accuracy can be employed for efficient simulations. Measurements of ultra wideband (UWB) signal propagation along a human arm are performed and compared to the simulation results obtained with numerical arm models of different complexity levels. The influence of the arm shape and size, as well as tissue composition and complexity is investigated. PMID:21062677
A Computationally Efficient Method for Polyphonic Pitch Estimation
NASA Astrophysics Data System (ADS)
Zhou, Ruohua; Reiss, Joshua D.; Mattavelli, Marco; Zoia, Giorgio
2009-12-01
This paper presents a computationally efficient method for polyphonic pitch estimation. The method employs the Fast Resonator Time-Frequency Image (RTFI) as the basic time-frequency analysis tool. The approach is composed of two main stages. First, a preliminary pitch estimation is obtained by means of a simple peak-picking procedure in the pitch energy spectrum. Such spectrum is calculated from the original RTFI energy spectrum according to harmonic grouping principles. Then the incorrect estimations are removed according to spectral irregularity and knowledge of the harmonic structures of the music notes played on commonly used music instruments. The new approach is compared with a variety of other frame-based polyphonic pitch estimation methods, and results demonstrate the high performance and computational efficiency of the approach.
Method for Determining Optimal Residential Energy Efficiency Retrofit Packages
Polly, B.; Gestwick, M.; Bianchi, M.; Anderson, R.; Horowitz, S.; Christensen, C.; Judkoff, R.
2011-04-01
Businesses, government agencies, consumers, policy makers, and utilities currently have limited access to occupant-, building-, and location-specific recommendations for optimal energy retrofit packages, as defined by estimated costs and energy savings. This report describes an analysis method for determining optimal residential energy efficiency retrofit packages and, as an illustrative example, applies the analysis method to a 1960s-era home in eight U.S. cities covering a range of International Energy Conservation Code (IECC) climate regions. The method uses an optimization scheme that considers average energy use (determined from building energy simulations) and equivalent annual cost to recommend optimal retrofit packages specific to the building, occupants, and location. Energy savings and incremental costs are calculated relative to a minimum upgrade reference scenario, which accounts for efficiency upgrades that would occur in the absence of a retrofit because of equipment wear-out and replacement with current minimum standards.
Efficient algorithm of the transcorrelated method for periodic systems
NASA Astrophysics Data System (ADS)
Ochi, Masayuki; Sodeyama, Keitaro; Sakuma, Rei; Tsuneyuki, Shinji
2012-03-01
The transcorrelated (TC) method is one of the promising wave-function-based approaches for the first-principles electronic structure calculations. In this method, the many-body wave function is approximated as the Jastrow-Slater type and one-electron orbitals in the Slater determinant are optimized with a one-body self-consistent-field equation such as that in the Hartree-Fock (HF) method. Although the TC method has yielded good results for both molecules and solids, its computational cost in solid-state calculations, being of order O(N_k^3N_b^3) with Nk and Nb the respective numbers of k-points and bands, has for some years hindered its wide application in condensed matter physics. Although an efficient algorithm was proposed for a Gaussian basis set, that algorithm is not applicable to a plane-wave basis that is suited to and widely used in solid-state calculations. In this paper, we present a new efficient algorithm of the TC method for the plane-wave basis or an arbitrary basis function set expanded in terms of plane waves, with which the computational cost of the TC method scales as O(N_k^2N_b^2). This is the same as that of the HF method. We applied the TC method with the new algorithm to obtain converged band structure and cell parameters of some semiconductors.
Efficient algorithm of the transcorrelated method for periodic systems.
Ochi, Masayuki; Sodeyama, Keitaro; Sakuma, Rei; Tsuneyuki, Shinji
2012-03-01
The transcorrelated (TC) method is one of the promising wave-function-based approaches for the first-principles electronic structure calculations. In this method, the many-body wave function is approximated as the Jastrow-Slater type and one-electron orbitals in the Slater determinant are optimized with a one-body self-consistent-field equation such as that in the Hartree-Fock (HF) method. Although the TC method has yielded good results for both molecules and solids, its computational cost in solid-state calculations, being of order O(N(k)(3)N(b)(3)) with N(k) and N(b) the respective numbers of k-points and bands, has for some years hindered its wide application in condensed matter physics. Although an efficient algorithm was proposed for a Gaussian basis set, that algorithm is not applicable to a plane-wave basis that is suited to and widely used in solid-state calculations. In this paper, we present a new efficient algorithm of the TC method for the plane-wave basis or an arbitrary basis function set expanded in terms of plane waves, with which the computational cost of the TC method scales as O(N(k)(2)N(b) (2)). This is the same as that of the HF method. We applied the TC method with the new algorithm to obtain converged band structure and cell parameters of some semiconductors. PMID:22401430
NASA Astrophysics Data System (ADS)
Basore, P. A.
1987-07-01
This is the final report summarizing concentrator solar cell research activity at Iowa State University under contract to Sandia National Laboratories from March 1985 to September 1986. A new one-dimensional semiconductor device analysis program for personal computers, PC-1D, is presented with emphasis on its application to modeling solar cells. Two applications of this program are described: (1) the validation of a new fast-transient technique for determining the relative importance of recombination in the emitter and base regions of planar silicon solar cells; and (2) the estimation of practical efficiency goals for production solar cells both for concentrators and one-sun applications. A laboratory investigation into etching v-shaped grooves in (100)-oriented silicon is also described.
Numerical Methods for a Kohn-Sham Density Functional Model Based on Optimal Transport.
Chen, Huajie; Friesecke, Gero; Mendl, Christian B
2014-10-14
In this paper, we study numerical discretizations to solve density functional models in the "strictly correlated electrons" (SCE) framework. Unlike previous studies, our work is not restricted to radially symmetric densities. In the SCE framework, the exchange-correlation functional encodes the effects of the strong correlation regime by minimizing the pairwise Coulomb repulsion, resulting in an optimal transport problem. We give a mathematical derivation of the self-consistent Kohn-Sham-SCE equations, construct an efficient numerical discretization for this type of problem for N = 2 electrons, and apply it to the H2 molecule in its dissociating limit. PMID:26588133
NASA Astrophysics Data System (ADS)
Shukla, K.; Wang, Y.; Jaiswal, P.
2014-12-01
In a porous medium the seismic energy not only propagates through matrix but also through pore-fluids. The differential movement between sediment grains of the matrix and interstitial fluid generates a diffusive wave which is commonly referred to as the slow P-wave. A combined system of equation which includes both elastic and diffusive phases is known as the poroelasticity. Analyzing seismic data through poroelastic modeling results in accurate interpretation of amplitude and separation of wave modes, leading to more accurate estimation of geomehanical properties of rocks. Despite its obvious multi-scale application, from sedimentary reservoir characterization to deep-earth fractured crust, poroelasticity remains under-developed primarily due to the complex nature of its constituent equations. We present a detail formulation of poroleastic wave equations for isotropic media by combining the Biot's and Newtonian mechanics. System of poroelastic wave equation constitutes for eight time dependent hyperbolic PDEs in 2D whereas in case of 3D number goes up to thirteen. Eigen decomposition of Jacobian of these systems confirms the presence of an additional slow-P wave phase with velocity lower than shear wave, posing stability issues on numerical scheme. To circumvent the issue, we derived a numerical scheme using nodal discontinuous Galerkin approach by adopting the triangular meshes in 2D which is extended to tetrahedral for 3D problems. In our nodal DG approach the basis function over a triangular element is interpolated using Legendre-Gauss-Lobatto (LGL) function leading to a more accurate local solutions than in the case of simple DG. We have tested the numerical scheme for poroelastic media in 1D and 2D case, and solution obtained for the systems offers high accuracy in results over other methods such as finite difference , finite volume and pseudo-spectral. The nodal nature of our approach makes it easy to convert the application into a multi-threaded algorithm
Godunov-type numerical methods for a model of granular flow
NASA Astrophysics Data System (ADS)
Adimurthi, A.; Aggarwal, Aekta; Veerappa Gowda, G. D.
2016-01-01
We propose and analyze finite volume Godunov type methods based on discontinuous flux for a 2 × 2 system of non-linear partial differential equations proposed by Hadeler and Kuttler to model the dynamics of growing sandpiles generated by a vertical source on a flat bounded rectangular table. The scheme is made well-balanced by modifying the flux function locally by including source term as a part of the convection term. Its extension to multi-dimensions is not straightforward for which an approach has been introduced here based on Transport Rays. This approach is compared with another approach for inclusion of source term which uses the idea of inverting the divergence operator relying on the Curl-free component of the Helmholtz decomposition of the source term. Numerical experiments are presented to illustrate the efficiency of the proposed scheme for both unsteady and steady state calculations and to make comparisons with the previously studied finite difference and semi-Lagrangian approaches by Falcone and Finzi Vita.
Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
NASA Astrophysics Data System (ADS)
Deuretzbacher, F.; Becker, D.; Santos, L.
2016-08-01
One-dimensional spinor gases with strong δ interaction fermionize and form a spin chain. The spatial degrees of freedom of this atom chain can be described by a mapping to spinless noninteracting fermions and the spin degrees of freedom are described by a spin-chain model with nearest-neighbor interactions. Here, we compute momentum and occupation-number distributions of up to 16 strongly interacting spinor fermions and bosons as a function of their spin imbalance, the strength of an externally applied magnetic field gradient, the length of their spin, and for different excited states of the multiplet. We show that the ground-state momentum distributions resemble those of the corresponding noninteracting systems, apart from flat background distributions, which extend to high momenta. Moreover, we show that the spin order of the spin chain—in particular antiferromagnetic spin order—may be deduced from the momentum and occupation-number distributions of the system. Finally, we present efficient numerical methods for the calculation of the single-particle densities and one-body density matrix elements and of the local exchange coefficients of the spin chain for large systems containing more than 20 strongly interacting particles in arbitrary confining potentials.
Method for assessing in-service motor efficiency and in-service motor/load efficiency
Kueck, John D.; Otaduy, Pedro J.
1997-01-01
A method and apparatus for assessing the efficiency of an in-service motor. The operating characteristics of the in-service motor are remotely measured. The operating characteristics are then applied to an equivalent circuit for electrical motors. Finally the equivalent circuit is evaluated to determine the performance characteristics of said in-service motor. Based upon the evaluation an individual is able to determine the rotor speed, power output, efficiency, and toque of the in-service motor. Additionally, an individual is able to confirm the calculations by comparing measured values with values obtained as a result of the motor equivalent circuit evaluation.
NASA Astrophysics Data System (ADS)
Bao, WeiZhu; Cai, YongYong; Jia, XiaoWei; Yin, Jia
2016-08-01
We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation in the nonrelativistic limit regime, involving a small dimensionless parameter $0<\\varepsilon\\ll 1$ which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e. there are propagating waves with wavelength $O(\\varepsilon^2)$ and $O(1)$ in time and space, respectively. We begin with the conservative Crank-Nicolson finite difference (CNFD) method and establish rigorously its error estimate which depends explicitly on the mesh size $h$ and time step $\\tau$ as well as the small parameter $0<\\varepsilon\\le 1$. Based on the error bound, in order to obtain `correct' numerical solutions in the nonrelativistic limit regime, i.e. $0<\\varepsilon\\ll 1$, the CNFD method requests the $\\varepsilon$-scalability: $\\tau=O(\\varepsilon^3)$ and $h=O(\\sqrt{\\varepsilon})$. Then we propose and analyze two numerical methods for the discretization of the nonlinear Dirac equation by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and time-splitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their $\\varepsilon$-scalability is improved to $\\tau=O(\\varepsilon^2)$ and $h=O(1)$ when $0<\\varepsilon\\ll 1$ compared with the CNFD method. Extensive numerical results are reported to confirm our error estimates.
Efficient method for assessing channel instability near bridges
Robinson, Bret A.; Thompson, R.E., Jr.
1993-01-01
Efficient methods for data collection and processing are required to complete channel-instability assessments at 5,600 bridge sites in Indiana at an affordable cost and within a reasonable time frame while maintaining the quality of the assessments. To provide this needed efficiency and quality control, a data-collection form was developed that specifies the data to be collected and the order of data collection. This form represents a modification of previous forms that grouped variables according to type rather than by order of collection. Assessments completed during two field seasons showed that greater efficiency was achieved by using a fill-in-the-blank form that organizes the data to be recorded in a specified order: in the vehicle, from the roadway, in the upstream channel, under the bridge, and in the downstream channel.
An efficient method for simulation of noisy coupled multi-dimensional oscillators
NASA Astrophysics Data System (ADS)
Stinchcombe, Adam R.; Forger, Daniel B.
2016-09-01
We present an efficient computational method for the study of populations of noisy coupled oscillators. By taking a population density approach in which the probability density of observing an oscillator at a point of state space is the primary variable instead of the states of all of the oscillators, we are able to seamlessly account for intrinsic noise within the oscillators and global coupling within the population. The population is assumed to consist of a large number of oscillators so that the noise process is well sampled over the population. Our numerical method is able to solve the governing equation even in the challenging case of limit cycle oscillators with a large number of state variables. Instead of simulating a prohibitive number of oscillators, our particle method simulates relatively few particles allowing for the efficient solution of the governing equation.
NASA Technical Reports Server (NTRS)
Thomas, P. D.
1980-01-01
A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.
NASA Astrophysics Data System (ADS)
Hermand, Jean-Pierre; Berrada, Mohamed; Meyer, Matthias; Asch, Mark
2005-09-01
Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK '94 experimental conditions.
3D-radiative transfer in terrestrial atmosphere: An efficient parallel numerical procedure
NASA Astrophysics Data System (ADS)
Bass, L. P.; Germogenova, T. A.; Nikolaeva, O. V.; Kokhanovsky, A. A.; Kuznetsov, V. S.
2003-04-01
Light propagation and scattering in terrestrial atmosphere is usually studied in the framework of the 1D radiative transfer theory [1]. However, in reality particles (e.g., ice crystals, solid and liquid aerosols, cloud droplets) are randomly distributed in 3D space. In particular, their concentrations vary both in vertical and horizontal directions. Therefore, 3D effects influence modern cloud and aerosol retrieval procedures, which are currently based on the 1D radiative transfer theory. It should be pointed out that the standard radiative transfer equation allows to study these more complex situations as well [2]. In recent year the parallel version of the 2D and 3D RADUGA code has been developed. This version is successfully used in gammas and neutrons transport problems [3]. Applications of this code to radiative transfer in atmosphere problems are contained in [4]. Possibilities of code RADUGA are presented in [5]. The RADUGA code system is an universal solver of radiative transfer problems for complicated models, including 2D and 3D aerosol and cloud fields with arbitrary scattering anisotropy, light absorption, inhomogeneous underlying surface and topography. Both delta type and distributed light sources can be accounted for in the framework of the algorithm developed. The accurate numerical procedure is based on the new discrete ordinate SWDD scheme [6]. The algorithm is specifically designed for parallel supercomputers. The version RADUGA 5.1(P) can run on MBC1000M [7] (768 processors with 10 Gb of hard disc memory for each processor). The peak productivity is equal 1 Tfl. Corresponding scalar version RADUGA 5.1 is working on PC. As a first example of application of the algorithm developed, we have studied the shadowing effects of clouds on neighboring cloudless atmosphere, depending on the cloud optical thickness, surface albedo, and illumination conditions. This is of importance for modern satellite aerosol retrieval algorithms development. [1] Sobolev
NASA Technical Reports Server (NTRS)
English, Robert E; Cavicchi, Richard H
1951-01-01
Empirical methods of Ainley and Kochendorfer and Nettles were used to predict performances of nine turbine designs. Measured and predicted performances were compared. Appropriate values of blade-loss parameter were determined for the method of Kochendorfer and Nettles. The measured design-point efficiencies were lower than predicted by as much as 0.09 (Ainley and 0.07 (Kochendorfer and Nettles). For the method of Kochendorfer and Nettles, appropriate values of blade-loss parameter ranged from 0.63 to 0.87 and the off-design performance was accurately predicted.
Models and numerical methods for the simulation of loss-of-coolant accidents in nuclear reactors
NASA Astrophysics Data System (ADS)
Seguin, Nicolas
2014-05-01
model, this numerical scheme is also efficient in terms of CPU time. Eventually, simpler models can locally replace the more complex model in order to simplify the overall computation, using some appropriate local error indicators developed in [5], without reducing the accuracy. References 1. Ishii, M., Hibiki, T., Thermo-fluid dynamics of two-phase flow, Springer, New-York, 2006. 2. Gallouët, T. and Hérard, J.-M., Seguin, N., Numerical modeling of two-phase flows using the two-fluid two-pressure approach, Math. Models Methods Appl. Sci., Vol. 14, 2004. 3. Seguin, N., Étude d'équations aux dérivées partielles hyperboliques en mécanique des fluides, Habilitation à diriger des recherches, UPMC-Paris 6, 2011. 4. Coquel, F., Hérard, J-M., Saleh, K., Seguin, N., A Robust Entropy-Satisfying Finite Volume Scheme for the Isentropic Baer-Nunziato Model, ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 48, 2013. 5. Mathis, H., Cancès, C., Godlewski, E., Seguin, N., Dynamic model adaptation for multiscale simulation of hyperbolic systems with relaxation, preprint, 2013.
A numerical method for the time coarsening of transport processes at the atomistic scale
NASA Astrophysics Data System (ADS)
Gonzalez-Ferreiro, B.; Romero, I.; Ortiz, M.
2016-05-01
We propose a novel numerical scheme for the simulation of slow transport processes at the atomistic scale. The scheme is based on a model for non-equilibrium statistical thermodynamics recently proposed by the authors, and extends it by formulating a variational integrator, i.e. a discrete functional whose optimality conditions provide all the governing equations of the problem. The method is employed to study surface segregation of AuAg alloys and its convergence is confirmed numerically.
NASA Astrophysics Data System (ADS)
Maksimov, F. A.; Churakov, D. A.; Shevelev, Yu. D.
2011-02-01
Complex-geometry design and grid generation are addressed. The gasdynamic equations are solved, and the numerical results are compared with experimental data. For aerodynamic problems, a suite of mathematical and information technology tools is proposed for the support and management of geometric models of actual objects. Based on the mathematical modeling methods developed, numerical experiments can be performed for a wide class of geometric forms and the aerodynamic properties of aircraft can be predicted with allowance for the viscosity effects.
Efficient solution of parabolic equations by Krylov approximation methods
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Y.
1990-01-01
Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.
An optimized efficient dual junction InGaN/CIGS solar cell: A numerical simulation
NASA Astrophysics Data System (ADS)
Farhadi, Bita; Naseri, Mosayeb
2016-08-01
The photovoltaic performance of an efficient double junction InGaN/CIGS solar cell including a CdS antireflector top cover layer is studied using Silvaco ATLAS software. In this study, to gain a desired structure, the different design parameters, including the CIGS various band gaps, the doping concentration and the thickness of CdS layer are optimized. The simulation indicates that under current matching condition, an optimum efficiency of 40.42% is achieved.
Steady and Unsteady Numerical Solution of Generalized Newtonian Fluids Flow by Runge-Kutta method
NASA Astrophysics Data System (ADS)
Keslerová, R.; Kozel, K.; Prokop, V.
2010-09-01
In this paper the laminar viscous incompressible flow for generalized Newtonian (Newtonian and non-Newtonian) fluids is considered. The governing system of equations is the system of Navier-Stokes equations and the continuity equation. The steady and unsteady numerical solution for this system is computed by finite volume method combined with an artificial compressibility method. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. The dual time-stepping method is considered for unsteady computation. The high artificial compressibility coefficient is used in the artificial compressibility method applied in the dual time τ. The steady and unsteady numerical results of Newtonian and non-Newtonian (shear thickening and shear thinning) fluids flow in the branching channel are presented.
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Iwashige, Kengo; Ikeda, Takashi
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
A general spectral method for the numerical simulation of one-dimensional interacting fermions
NASA Astrophysics Data System (ADS)
Clason, Christian; von Winckel, Gregory
2012-08-01
This software implements a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. The approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An efficient Matlab program for the assembly of the stiffness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. This program allows the accurate discretization of systems with multiple fermions subject to arbitrary potentials, e.g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the time-dependent Schrödinger equation. The new version includes a Python implementation of the presented approach. New version program summaryProgram title: assembleFermiMatrix Catalogue identifier: AEKO_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKO_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 332 No. of bytes in distributed program, including test data, etc.: 5418 Distribution format: tar.gz Programming language: MATLAB/GNU Octave, Python Computer: Any architecture supported by MATLAB, GNU Octave or Python Operating system: Any supported by MATLAB, GNU Octave or Python RAM: Depends on the data Classification: 4.3, 2.2. External routines: Python 2.7+, NumPy 1.3+, SciPy 0.10+ Catalogue identifier of previous version: AEKO_v1_0 Journal reference of previous version: Comput. Phys. Commun. 183 (2012) 405 Does the new version supersede the previous version?: Yes Nature of problem: The direct numerical
A study of numerical methods for hyperbolic conservation laws with stiff source terms
NASA Technical Reports Server (NTRS)
Leveque, R. J.; Yee, H. C.
1990-01-01
In the present study of the behavior of typical numerical methods in the case of a model advection equation having a parameter-dependent source term, two approaches to the incorporation of the source terms are used: MacCormack-type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. The latter are found to perform slightly better. The model scalar equation is used to show that the incorrectness of the propagation speeds of discontinuities observed in the stiff case is due to the introduction of nonequilibrium values through numerical dissipation in the advection step.
Numerical implementation of the method of fictitious domains for elliptic equations
NASA Astrophysics Data System (ADS)
Temirbekov, Almas N.
2016-08-01
In the paper, we study the elliptical type equation with strongly changing coefficients. We are interested in studying such equation because the given type equations are yielded when we use the fictitious domain method. In this paper we suggest a special method for numerical solution of the elliptic equation with strongly changing coefficients. We have proved the theorem for the assessment of developed iteration process convergence rate. We have developed computational algorithm and numerical calculations have been done to illustrate the effectiveness of the suggested method.
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.
NASA Astrophysics Data System (ADS)
Plakhov, Iu. V.; Mytsenko, A. V.; Shel'Pov, V. A.
A numerical integration method is developed that is more accurate than Everhart's (1974) implicit single-sequence approach for integrating orbits. This method can be used to solve problems of space geodesy based on the use of highly precise laser observations.
ERIC Educational Resources Information Center
Jarvelin, Kalervo
1986-01-01
Describes a method for advance estimation of user charges for queries in relational data model-based numeric databases when charges are based on data retrieved. Use of this approach is demonstrated by sample queries to an imaginary marketing database. The principles and methods of this approach and its relevance are discussed. (MBR)
Energy conserving numerical methods for the computation of complex vortical flows
NASA Astrophysics Data System (ADS)
Allaneau, Yves
One of the original goals of this thesis was to develop numerical tools to help with the design of micro air vehicles. Micro Air Vehicles (MAVs) are small flying devices of only a few inches in wing span. Some people consider that as their size becomes smaller and smaller, it would be increasingly more difficult to keep all the classical control surfaces such as the rudders, the ailerons and the usual propellers. Over the years, scientists took inspiration from nature. Birds, by flapping and deforming their wings, are capable of accurate attitude control and are able to generate propulsion. However, the biomimicry design has its own limitations and it is difficult to place a hummingbird in a wind tunnel to study precisely the motion of its wings. Our approach was to use numerical methods to tackle this challenging problem. In order to precisely evaluate the lift and drag generated by the wings, one needs to be able to capture with high fidelity the extremely complex vortical flow produced in the wake. This requires a numerical method that is stable yet not too dissipative, so that the vortices do not get diffused in an unphysical way. We solved this problem by developing a new Discontinuous Galerkin scheme that, in addition to conserving mass, momentum and total energy locally, also preserves kinetic energy globally. This property greatly improves the stability of the simulations, especially in the special case p=0 when the approximation polynomials are taken to be piecewise constant (we recover a finite volume scheme). In addition to needing an adequate numerical scheme, a high fidelity solution requires many degrees of freedom in the computations to represent the flow field. The size of the smallest eddies in the flow is given by the Kolmogoroff scale. Capturing these eddies requires a mesh counting in the order of Re³ cells, where Re is the Reynolds number of the flow. We show that under-resolving the system, to a certain extent, is acceptable. However our
An Efficient Method to Study Nondiffusive Motion of Brownian Particles
NASA Astrophysics Data System (ADS)
Lisý, Vladimír; Tóthová, Jana
2016-02-01
The experimental access to short timescales has pointed to the inadequacy of the standard Langevin theory of the Brownian motion (BM) in fluids. The hydrodynamic theory of the BM describes well the observed motion of the particles; however, the published approach should be improved in several points. In particular, it leads to incorrect correlation properties of the thermal noise driving the particles. In our contribution we present an efficient method, which is applicable to linear generalized Langevin equations describing the BM of particles with any kind of memory and apply it to interpret the experiments where nondiffusive BM of particles was observed. It is shown that the applicability of the method is much broader, allowing, among all, to obtain efficient solutions of various problems of anomalous BM.
Computational methods for efficient structural reliability and reliability sensitivity analysis
NASA Technical Reports Server (NTRS)
Wu, Y.-T.
1993-01-01
This paper presents recent developments in efficient structural reliability analysis methods. The paper proposes an efficient, adaptive importance sampling (AIS) method that can be used to compute reliability and reliability sensitivities. The AIS approach uses a sampling density that is proportional to the joint PDF of the random variables. Starting from an initial approximate failure domain, sampling proceeds adaptively and incrementally with the goal of reaching a sampling domain that is slightly greater than the failure domain to minimize over-sampling in the safe region. Several reliability sensitivity coefficients are proposed that can be computed directly and easily from the above AIS-based failure points. These probability sensitivities can be used for identifying key random variables and for adjusting design to achieve reliability-based objectives. The proposed AIS methodology is demonstrated using a turbine blade reliability analysis problem.
Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2
NASA Technical Reports Server (NTRS)
Karki, K. C.; Patankar, S. V.; Runchal, A. K.; Mongia, H. C.
1988-01-01
The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.
Estimation of coupling efficiency of optical fiber by far-field method
NASA Astrophysics Data System (ADS)
Kataoka, Keiji
2010-09-01
Coupling efficiency to a single-mode optical fiber can be estimated with the field amplitudes at far-field of an incident beam and optical fiber mode. We call it the calculation by far-field method (FFM) in this paper. The coupling efficiency by FFM is formulated including effects of optical aberrations, vignetting of the incident beam, and misalignments of the optical fiber such as defocus, lateral displacements, and angle deviation in arrangement of the fiber. As the results, it is shown the coupling efficiency is proportional to the central intensity of the focused spot, i.e., Strehl intensity of a virtual beam determined by the incident beam and mode of the optical fiber. Using the FFM, a typical optics in which a laser beam is coupled to an optical fiber with a lens of finite numerical aperture (NA) is analyzed for several cases of amplitude distributions of the incident light.
A Diffusion Approximation and Numerical Methods for Adaptive Neuron Models with Stochastic Inputs
Rosenbaum, Robert
2016-01-01
Characterizing the spiking statistics of neurons receiving noisy synaptic input is a central problem in computational neuroscience. Monte Carlo approaches to this problem are computationally expensive and often fail to provide mechanistic insight. Thus, the field has seen the development of mathematical and numerical approaches, often relying on a Fokker-Planck formalism. These approaches force a compromise between biological realism, accuracy and computational efficiency. In this article we develop an extension of existing diffusion approximations to more accurately approximate the response of neurons with adaptation currents and noisy synaptic currents. The implementation refines existing numerical schemes for solving the associated Fokker-Planck equations to improve computationally efficiency and accuracy. Computer code implementing the developed algorithms is made available to the public. PMID:27148036
A Diffusion Approximation and Numerical Methods for Adaptive Neuron Models with Stochastic Inputs.
Rosenbaum, Robert
2016-01-01
Characterizing the spiking statistics of neurons receiving noisy synaptic input is a central problem in computational neuroscience. Monte Carlo approaches to this problem are computationally expensive and often fail to provide mechanistic insight. Thus, the field has seen the development of mathematical and numerical approaches, often relying on a Fokker-Planck formalism. These approaches force a compromise between biological realism, accuracy and computational efficiency. In this article we develop an extension of existing diffusion approximations to more accurately approximate the response of neurons with adaptation currents and noisy synaptic currents. The implementation refines existing numerical schemes for solving the associated Fokker-Planck equations to improve computationally efficiency and accuracy. Computer code implementing the developed algorithms is made available to the public. PMID:27148036
Tian, Fang-Bao; Luo, Haoxiang; Zhu, Luoding; Liao, James C.; Lu, Xi-Yun
2012-01-01
We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish. PMID:23564971
NASA Astrophysics Data System (ADS)
Tian, Shuling; Wu, Yizhao; Xia, Jian
A parallel Navier-Stokes solver based on dynamic overset unstructured grids method is presented to simulate the unsteady turbulent flow field around helicopter in forward flight. The grid method has the advantages of unstructured grid and Chimera grid and is suitable to deal with multiple bodies in relatively moving. Unsteady Navier-Stokes equations are solved on overset unstructured grids by an explicit dual time-stepping, finite volume method. Preconditioning method applied to inner iteration of the dual-time stepping is used to speed up the convergence of numerical simulation. The Spalart-Allmaras one-equation turbulence model is used to evaluate the turbulent viscosity. Parallel computation is based on the dynamic domain decomposition method in overset unstructured grids system at each physical time step. A generic helicopter Robin with a four-blade rotor in forward flight is considered to validate the method presented in this paper. Numerical simulation results show that the parallel dynamic overset unstructured grids method is very efficient for the simulation of helicopter flow field and the results are reliable.
Efficient extraction method to collect sugar from sweet sorghum
2013-01-01
Background Sweet sorghum is a domesticated grass containing a sugar-rich juice that can be readily utilized for ethanol production. Most of the sugar is stored inside the cells of the stalk tissue and can be difficult to release, a necessary step before conventional fermentation. While this crop holds much promise as an arid land sugar source for biofuel production, a number of challenges must be overcome. One lies in the inherent labile nature of the sugars in the stalks leading to a short usable storage time. Also, collection of sugars from the sweet sorghum stalks is usually accomplished by mechanical squeezing, but generally does not collect all of the available sugars. Results In this paper, we present two methods that address these challenges for utilization of sweet sorghum for biofuel production. The first method demonstrates a means to store sweet sorghum stalks in the field under semi-arid conditions. The second provides an efficient water extraction method that can collect as much of the available sugar as feasible. Operating parameters investigated include temperature, stalk size, and solid–liquid ratio that impact both the rate of sugar release and the maximal amount recovered with a goal of low water use. The most desirable conditions include 30°C, 0.6 ratio of solid to liquid (w/w), which collects 90 % of the available sugar. Variations in extraction methods did not alter the efficiency of the eventual ethanol fermentation. Conclusions The water extraction method has the potential to be used for sugar extraction from both fresh sweet sorghum stalks and dried ones. When combined with current sugar extraction methods, the overall ethanol production efficiency would increase compared to current field practices. PMID:23305036
Tudela, Ignacio; Sáez, Verónica; Esclapez, María Deseada; Díez-García, María Isabel; Bonete, Pedro; González-García, José
2014-05-01
Numerical methods for the calculation of the acoustic field inside sonoreactors have rapidly emerged in the last 15 years. This paper summarizes some of the most important works on this topic presented in the past, along with the diverse numerical works that have been published since then, reviewing the state of the art from a qualitative point of view. In this sense, we illustrate and discuss some of the models recently developed by the scientific community to deal with some of the complex events that take place in a sonochemical reactor such as the vibration of the reactor walls and the nonlinear phenomena inherent to the presence of ultrasonic cavitation. In addition, we point out some of the upcoming challenges that must be addressed in order to develop a reliable tool for the proper designing of efficient sonoreactors and the scale-up of sonochemical processes. PMID:24355287
A convenient and efficient purification method for chemically labeled oligonucleotides.
Hwang, Jihee; Kang, Junhee; Kim, Seong Keun; Kim, Younggyu
2013-05-01
We developed an efficient, cost-effective, and rapid purification method for chemically-labeled oligonucleotides that requires less time than conventional procedures such as ethanol precipitation or size-exclusion chromatography. Based on the hydrophilic and hydrophobic properties of DNA and amine-reactive fluorophores, we show that n-butanol saturated with distilled water may be used to remove unreacted fluorophores by sequestering them in the organic phase, while labeled DNA remains in the aqueous phase. This phase extraction method is simple, fast, and allows for processing multiple samples simultaneously, a necessity for high-throughput labeling strategies. PMID:23662899
Methods and compositions for efficient nucleic acid sequencing
Drmanac, Radoje
2002-01-01
Disclosed are novel methods and compositions for rapid and highly efficient nucleic acid sequencing based upon hybridization with two sets of small oligonucleotide probes of known sequences. Extremely large nucleic acid molecules, including chromosomes and non-amplified RNA, may be sequenced without prior cloning or subcloning steps. The methods of the invention also solve various current problems associated with sequencing technology such as, for example, high noise to signal ratios and difficult discrimination, attaching many nucleic acid fragments to a surface, preparing many, longer or more complex probes and labelling more species.
Methods and compositions for efficient nucleic acid sequencing
Drmanac, Radoje
2006-07-04
Disclosed are novel methods and compositions for rapid and highly efficient nucleic acid sequencing based upon hybridization with two sets of small oligonucleotide probes of known sequences. Extremely large nucleic acid molecules, including chromosomes and non-amplified RNA, may be sequenced without prior cloning or subcloning steps. The methods of the invention also solve various current problems associated with sequencing technology such as, for example, high noise to signal ratios and difficult discrimination, attaching many nucleic acid fragments to a surface, preparing many, longer or more complex probes and labelling more species.
An analytical method to predict efficiency of aircraft gearboxes
NASA Technical Reports Server (NTRS)
Anderson, N. E.; Loewenthal, S. H.; Black, J. D.
1984-01-01
A spur gear efficiency prediction method previously developed by the authors was extended to include power loss of planetary gearsets. A friction coefficient model was developed for MIL-L-7808 oil based on disc machine data. This combined with the recent capability of predicting losses in spur gears of nonstandard proportions allows the calculation of power loss for complete aircraft gearboxes that utilize spur gears. The method was applied to the T56/501 turboprop gearbox and compared with measured test data. Bearing losses were calculated with large scale computer programs. Breakdowns of the gearbox losses point out areas for possible improvement.
Method for the determination of photomultiplier collection efficiency, F.
Wright, A G
2010-04-10
Photomultiplier collection efficiency, F, is a fundamental, but difficult, parameter to measure with certainty. A method for its determination, based on the gain of the first dynode, has been devised and applied to two different types of photomultiplier. The measurements are substantially free from the sources of error, which have compromised previously reported results by other authors. F may be determined by the proposed method with an accuracy of better than +/-3% for any photomultiplier tube with sufficient gain to uncover its single electron response. PMID:20390005
NASA Astrophysics Data System (ADS)
Kumar, Nitin; Singh, Udaybir; Kumar, Anil; Bhattacharya, Ranajoy; Singh, T. P.; Sinha, A. K.
2013-02-01
The design of 120 GHz, 1 MW gyrotron for plasma fusion application is presented in this paper. The mode selection is carried out considering the aim of minimum mode competition, minimum cavity wall heating, etc. On the basis of the selected operating mode, the interaction cavity design and beam-wave interaction computation are carried out by using the PIC code. The design of triode type Magnetron Injection Gun (MIG) is also presented. Trajectory code EGUN, synthesis code MIGSYN and data analysis code MIGANS are used in the MIG designing. Further, the design of MIG is also validated by using the another trajectory code TRAK. The design results of beam dumping system (collector) and RF window are also presented. Depressed collector is designed to enhance the overall tube efficiency. The design study confirms >1 MW output power with tube efficiency around 50% (with collector efficiency).
An efficient empirical Bayes method for genomewide association studies.
Wang, Q; Wei, J; Pan, Y; Xu, S
2016-08-01
Linear mixed model (LMM) is one of the most popular methods for genomewide association studies (GWAS). Numerous forms of LMM have been developed; however, there are two major issues in GWAS that have not been fully addressed before. The two issues are (i) the genomic background noise and (ii) low statistical power after Bonferroni correction. We proposed an empirical Bayes (EB) method by assigning each marker effect a normal prior distribution, resulting in shrinkage estimates of marker effects. We found that such a shrinkage approach can selectively shrink marker effects and reduce the noise level to zero for majority of non-associated markers. In the meantime, the EB method allows us to use an 'effective number of tests' to perform Bonferroni correction for multiple tests. Simulation studies for both human and pig data showed that EB method can significantly increase statistical power compared with the widely used exact GWAS methods, such as GEMMA and FaST-LMM-Select. Real data analyses in human breast cancer identified improved detection signals for markers previously known to be associated with breast cancer. We therefore believe that EB method is a valuable tool for identifying the genetic basis of complex traits. PMID:26582716
Development of a numerical method for the prediction of turbulent flows in dump diffusers
NASA Astrophysics Data System (ADS)
Ando, Yasunori; Kawai, Masafumi; Sato, Yukinori; Toh, Hidemi
1987-01-01
In order to obtain an effective tool to design dump diffusers for gas turbine combustors, a finite-volume numerical calculation method has been developed for the solution of two-dimensional/axisymmetric incompressible steady Navier-Stokes equation in general curvilinear coordinate system. This method was applied to the calculations of turbulent flows in a two-dimensional dump diffuser with uniform and distorted inlet velocity profiles as well as an annular dump diffuser with uniform inlet velocity profile, and the calculated results were compared with experimental data. The numerical results showed a good agreement with experimental data in case of both inlet velocity profiles; eventually, the numerical method was confirmed to be an effective tool for the development of dump diffusers which can predict the flow pattern, velocity distribution and the pressure loss.
A method for generating numerical pilot opinion ratings using the optimal pilot model
NASA Technical Reports Server (NTRS)
Hess, R. A.
1976-01-01
A method for generating numerical pilot opinion ratings using the optimal pilot model is introduced. The method is contained in a rating hypothesis which states that the numerical rating which a human pilot assigns to a specific vehicle and task can be directly related to the numerical value of the index of performance resulting from the optimal pilot modeling procedure as applied to that vehicle and task. The hypothesis is tested using the data from four piloted simulations. The results indicate that the hypothesis is reasonable, but that the predictive capability of the method is a strong function of the accuracy of the pilot model itself. This accuracy is, in turn, dependent upon the parameters which define the optimal modeling problem. A procedure for specifying the parameters for the optimal pilot model in the absence of experimental data is suggested.
A numerical study of the European option by the MLPG method with moving kriging interpolation.
Phaochoo, P; Luadsong, A; Aschariyaphotha, N
2016-01-01
In this paper, the meshless local Petrov-Galerkin (MLPG) method is applied for solving a generalized Black-Scholes equation in financial problems. This equation is a PDE governing the price evolution of a European call or a European put under the Black-Scholes model. The θ-weighted method and MLPG are used for discretizing the governing equation in time variable and option pricing, respectively. We show that the spectral radius of amplification matrix with the discrete operator is less than 1. This ensures that this numerical scheme is stable. Numerical experiments are performed with time varying volatility and the results are compared with the analytical and the numerical results of other methods. PMID:27064892
Bang, Jin-Young; Chung, Chin-Wook
2010-12-15
Electron energy distribution functions (EEDFs) were determined from probe characteristics using a numerical ac superimposed method with a distortion correction of high derivative terms by varying amplitude of a sinusoidal perturbation voltage superimposed onto the dc sweep voltage, depending on the related electron energy. Low amplitude perturbation applied around the plasma potential represented the low energy peak of the EEDF exactly, and high amplitude perturbation applied around the floating potential was effective to suppress noise or distortion of the probe characteristic, which is fatal to the tail electron distribution. When a small random noise was imposed over the stabilized prove characteristic, the numerical differentiation method was not suitable to determine the EEDF, while the numerical ac superimposed method was able to obtain a highly precise EEDF.
Efficient two-component relativistic method for large systems
Nakai, Hiromi
2015-12-31
This paper reviews a series of theoretical studies to develop efficient two-component (2c) relativistic method for large systems by the author’s group. The basic theory is the infinite-order Douglas-Kroll-Hess (IODKH) method for many-electron Dirac-Coulomb Hamiltonian. The local unitary transformation (LUT) scheme can effectively produce the 2c relativistic Hamiltonian, and the divide-and-conquer (DC) method can achieve linear-scaling of Hartree-Fock and electron correlation methods. The frozen core potential (FCP) theoretically connects model potential calculations with the all-electron ones. The accompanying coordinate expansion with a transfer recurrence relation (ACE-TRR) scheme accelerates the computations of electron repulsion integrals with high angular momenta and long contractions.
A numerical simulation method and analysis of a complete thermoacoustic-Stirling engine.
Ling, Hong; Luo, Ercang; Dai, Wei
2006-12-22
Thermoacoustic prime movers can generate pressure oscillation without any moving parts on self-excited thermoacoustic effect. The details of the numerical simulation methodology for thermoacoustic engines are presented in the paper. First, a four-port network method is used to build the transcendental equation of complex frequency as a criterion to judge if temperature distribution of the whole thermoacoustic system is correct for the case with given heating power. Then, the numerical simulation of a thermoacoustic-Stirling heat engine is carried out. It is proved that the numerical simulation code can run robustly and output what one is interested in. Finally, the calculated results are compared with the experiments of the thermoacoustic-Stirling heat engine (TASHE). It shows that the numerical simulation can agrees with the experimental results with acceptable accuracy. PMID:16996099
DG method for the numerical solution of the state problem in shape optimization
NASA Astrophysics Data System (ADS)
Hozman, J.; ŠimÅ¯nková, M.
2015-11-01
In this article we are concerned with the discontinuous Galerkin (DG) method in connection with the numerical solution of the state problem in the field of shape optimization techniques. The presented state problem is described by the stationary energy equation of the system of the mould, glass piece, plunger and plunger cavity arising from the forming process in the glass industry. The attention is paid to the development of the numerical scheme based on the piecewise polynomial, generally discontinuous approximation, which enables to better resolve various phenomena typical for such a heterogeneous medium problem, compared with standard common numerical techniques. The studied problem is supplemented with the preliminary numerical results demonstrating the potency of the proposed scheme.
Numerical wave tank based on a conserved wave-absorbing method
NASA Astrophysics Data System (ADS)
Hu, Zhe; Tang, Wen-yong; Xue, Hong-xiang; Zhang, Xiao-ying
2016-03-01
Recently the numerical wave tank has become a widely-used tool to study waves as well as wave-structure interactions, and the wave-absorbing method is very important as its effect on the quality of waves generated. The relaxation method and the derived momentum source method are often utilized, however, the damping weight is constant during calculation and repeated trials are required to obtain an acceptable wave-absorbing effect. To address the abovementioned issues, a conserved wave-absorbing method is developed. The damping weight is determined by solving the mass conservation equation of the absorbing region at every time step. Based on this method, a two-dimensional numerical wave tank is established by using the VB language to simulate various waves by which the validation of this method is evaluated.
NASA Astrophysics Data System (ADS)
Kindrachuk, Vitaliy M.; Galanov, Boris A.
2014-02-01
A computationally efficient solution scheme is presented for the mechanical problems whose formulations include the Kuhn-Tucker or Signorini-Fichera conditions. It is proposed to reformulate these problems replacing inequalities in these conditions by equations with respect to new unknowns. The solutions of the modified problems have simple physical meanings and determine uniquely the unknowns of the original problems. The approach avoids application of multi-valued operators (inclusions or inequalities) in formulation of the problems. Hence, the modified formulations are suitable for numerical analysis using established powerful mathematical methods and corresponding solvers developed for solving systems of non-linear equations.
A numerically efficient finite element hydroelastic analysis. Volume 1: Theory and results
NASA Technical Reports Server (NTRS)
Coppolino, R. N.
1976-01-01
Symmetric finite element matrix formulations for compressible and incompressible hydroelasticity are developed on the basis of Toupin's complementary formulation of classical mechanics. Results of implementation of the new technique in the NASTRAN structural analysis program are presented which demonstrate accuracy and efficiency.
High-efficiency solar cell and method for fabrication
Hou, H.Q.; Reinhardt, K.C.
1999-08-31
A high-efficiency 3- or 4-junction solar cell is disclosed with a theoretical AM0 energy conversion efficiency of about 40%. The solar cell includes p-n junctions formed from indium gallium arsenide nitride (InGaAsN), gallium arsenide (GaAs) and indium gallium aluminum phosphide (InGaAlP) separated by n-p tunnel junctions. An optional germanium (Ge) p-n junction can be formed in the substrate upon which the other p-n junctions are grown. The bandgap energies for each p-n junction are tailored to provide substantially equal short-circuit currents for each p-n junction, thereby eliminating current bottlenecks and improving the overall energy conversion efficiency of the solar cell. Additionally, the use of an InGaAsN p-n junction overcomes super-bandgap energy losses that are present in conventional multi-junction solar cells. A method is also disclosed for fabricating the high-efficiency 3- or 4-junction solar cell by metal-organic chemical vapor deposition (MOCVD). 4 figs.
High-efficiency solar cell and method for fabrication
Hou, Hong Q.; Reinhardt, Kitt C.
1999-01-01
A high-efficiency 3- or 4-junction solar cell is disclosed with a theoretical AM0 energy conversion efficiency of about 40%. The solar cell includes p-n junctions formed from indium gallium arsenide nitride (InGaAsN), gallium arsenide (GaAs) and indium gallium aluminum phosphide (InGaAlP) separated by n-p tunnel junctions. An optional germanium (Ge) p-n junction can be formed in the substrate upon which the other p-n junctions are grown. The bandgap energies for each p-n junction are tailored to provide substantially equal short-circuit currents for each p-n junction, thereby eliminating current bottlenecks and improving the overall energy conversion efficiency of the solar cell. Additionally, the use of an InGaAsN p-n junction overcomes super-bandgap energy losses that are present in conventional multi-junction solar cells. A method is also disclosed for fabricating the high-efficiency 3- or 4-junction solar cell by metal-organic chemical vapor deposition (MOCVD).
NASA Astrophysics Data System (ADS)
Wu, Y. S.; Huang, Z.; Winterfeld, P. H.
2014-12-01
The safety of CO2 sequestration in geological formations relies on the integrity of the caprock. However, the elevated fluid pressure during CO2 injection changes the stress states in the caprock, and may lead to reactivate pre-existing fractures or even fracture the caprock. It is necessary to develop an efficient and practical monitor technology to detect and identify CO2 leakage pathways. To this end, we should understand the transport behavior of CO2 coupled with geomechanical effects during injection. In this work, we first developed an efficient parallel fully-coupled thermal-hydro-mechanical simulator to model CO2 transport in geological formations. The numerical model was verified through classical problems with analytical solutions. Then, based on this simulator, we investigated the fluid flow behavior when CO2 leakage occurs through fluid-driven fracturing zones. We proposed an implicit, physics-based model to simulate the fluid-driven fracturing process by using several practical correlations, including fracturing pressure functions, porosity/permeability-stress relationships, which can be obtained by lab experiments. A set of numerical simulations have been conducted by considering various scenarios, such as different injection rates, locations and distributions of fracture zones, and initial fracture permeability. The numerical results show that there are several characteristics can be used to detect CO2 leakage pathways, and it is possible to develop an advanced inverse modeling and monitoring technology to identify leakage locations, times and rates using measured pressure data of permanent downhole gauges and our simulator.
NASA Technical Reports Server (NTRS)
Tuccillo, J. J.
1984-01-01
Numerical Weather Prediction (NWP), for both operational and research purposes, requires only fast computational speed but also large memory. A technique for solving the Primitive Equations for atmospheric motion on the CYBER 205, as implemented in the Mesoscale Atmospheric Simulation System, which is fully vectorized and requires substantially less memory than other techniques such as the Leapfrog or Adams-Bashforth Schemes is discussed. The technique presented uses the Euler-Backard time marching scheme. Also discussed are several techniques for reducing computational time of the model by replacing slow intrinsic routines by faster algorithms which use only hardware vector instructions.
Wang, Peng; Zhu, Zhouquan; Huang, Shuai
2013-01-01
This paper presents a novel biologically inspired metaheuristic algorithm called seven-spot ladybird optimization (SLO). The SLO is inspired by recent discoveries on the foraging behavior of a seven-spot ladybird. In this paper, the performance of the SLO is compared with that of the genetic algorithm, particle swarm optimization, and artificial bee colony algorithms by using five numerical benchmark functions with multimodality. The results show that SLO has the ability to find the best solution with a comparatively small population size and is suitable for solving optimization problems with lower dimensions. PMID:24385879
NASA Technical Reports Server (NTRS)
Coppolino, R. N.
1974-01-01
Details are presented of the implementation of the new formulation into NASTRAN including descriptions of the DMAP statements required for conversion of the program and details pertaining to problem definition and bulk data considerations. Details of the current 1/8-scale space shuttle external tank mathematical model, numerical results and analysis/test comparisons are also presented. The appendices include a description and listing of a FORTRAN program used to develop harmonic transformation bulk data (multipoint constraint statements) and sample bulk data information for a number of hydroelastic problems.
Zhu, Zhouquan
2013-01-01
This paper presents a novel biologically inspired metaheuristic algorithm called seven-spot ladybird optimization (SLO). The SLO is inspired by recent discoveries on the foraging behavior of a seven-spot ladybird. In this paper, the performance of the SLO is compared with that of the genetic algorithm, particle swarm optimization, and artificial bee colony algorithms by using five numerical benchmark functions with multimodality. The results show that SLO has the ability to find the best solution with a comparatively small population size and is suitable for solving optimization problems with lower dimensions. PMID:24385879
Direct Numerical Simulation of Interfacial Flows: Implicit Sharp-Interface Method (I-SIM)
Robert Nourgaliev; Theo Theofanous; HyeongKae Park; Vincent Mousseau; Dana Knoll
2008-01-01
In recent work (Nourgaliev, Liou, Theofanous, JCP in press) we demonstrated that numerical simulations of interfacial flows in the presence of strong shear must be cast in dynamically sharp terms (sharp interface treatment or SIM), and that moreover they must meet stringent resolution requirements (i.e., resolving the critical layer). The present work is an outgrowth of that work aiming to overcome consequent limitations on the temporal treatment, which become still more severe in the presence of phase change. The key is to avoid operator splitting between interface motion, fluid convection, viscous/heat diffusion and reactions; instead treating all these non-linear operators fully-coupled within a Newton iteration scheme. To this end, the SIM’s cut-cell meshing is combined with the high-orderaccurate implicit Runge-Kutta and the “recovery” Discontinuous Galerkin methods along with a Jacobian-free, Krylov subspace iteration algorithm and its physics-based preconditioning. In particular, the interfacial geometry (i.e., marker’s positions and volumes of cut cells) is a part of the Newton-Krylov solution vector, so that the interface dynamics and fluid motions are fully-(non-linearly)-coupled. We show that our method is: (a) robust (L-stable) and efficient, allowing to step over stability time steps at will while maintaining high-(up to the 5th)-order temporal accuracy; (b) fully conservative, even near multimaterial contacts, without any adverse consequences (pressure/velocity oscillations); and (c) highorder-accurate in spatial discretization (demonstrated here up to the 12th-order for smoothin-the-bulk-fluid flows), capturing interfacial jumps sharply, within one cell. Performance is illustrated with a variety of test problems, including low-Mach-number “manufactured” solutions, shock dynamics/tracking with slow dynamic time scales, and multi-fluid, highspeed shock-tube problems. We briefly discuss preconditioning, and we introduce two physics
Earthquake Source Simulations: A Coupled Numerical Method and Large Scale Simulations
NASA Astrophysics Data System (ADS)
Ely, G. P.; Xin, Q.; Faerman, M.; Day, S.; Minster, B.; Kremenek, G.; Moore, R.
2003-12-01
We investigate a scheme for interfacing Finite-Difference (FD) and Finite-Element (FE) models in order to simulate dynamic earthquake rupture. The more powerful but slower FE method allows for (1) unusual geometries (e.g. dipping and curved faults), (2) nonlinear physics, and (3) finite displacements. These capabilities are computationally expensive and limit the useful size of the problem that can be solved. Large efficiencies are gained by employing FE only where necessary in the near source region and coupling this with an efficient FD solution for the surrounding medium. Coupling is achieved through setting up and an overlapping buffer zone between the domains modeled by the two methods. The buffer zone is handled numerically as a set of mutual offset boundary conditions. This scheme eliminates the effect of the artificial boundaries at the interface and allows energy to propagate in both directions across the boundary. In general it is necessary to interpolate variables between the meshes and time discretizations used for each model, and this can create artifacts that must be controlled. A modular approach has been used in which either of the two component codes can be substituted with another code. We have successfully demonstrated coupling for a simulation between a second-order FD rupture dynamics code and fourth-order staggered-grid FD code. To be useful earthquake source models must capture a large range of length and time scales, which is very computationally demanding. This requires that (for current computer technology) codes must utilize parallel processing. Additionally, if larges quantities of output data are to be saved, a high performance data management system is desirable. We show results from a large scale rupture dynamics simulation designed to test these capabilities. We use second-order FD with dimensions of 400 x 800 x 800 nodes, run for 3000 time steps. Data were saved for the entire volume for three components of velocity at every time
A numerical method of tracing a vortical axis along local topological axis line
NASA Astrophysics Data System (ADS)
Nakayama, Katsuyuki; Hasegawa, Hideki
2016-06-01
A new numerical method is presented to trace or identify a vortical axis in flow, which is based on Galilean invariant flow topology. We focus on the local flow topology specified by the eigenvalues and eigenvectors of the velocity gradient tensor, and extract the axis component from its flow trajectory. Eigen-vortical-axis line is defined from the eigenvector of the real eigenvalue of the velocity gradient tensor where the tensor has the conjugate complex eigenvalues. This numerical method integrates the eigen-vortical-axis line and traces a vortical axis in terms of the invariant flow topology, which enables to investigate the feature of the topology-based vortical axis.
NASA Astrophysics Data System (ADS)
Wang, Xiaoqiang; Ju, Lili; Du, Qiang
2016-07-01
The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.
Numerical methods for large-scale, time-dependent partial differential equations
NASA Technical Reports Server (NTRS)
Turkel, E.
1979-01-01
A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.
Ritter, André
2014-10-20
The shifted angular spectrum method allows a reduction of the number of samples required for numerical off-axis propagation of scalar wave fields. In this work, a modification of the shifted angular spectrum method is presented. It allows a further reduction of the spatial sampling rate for certain wave fields. We calculate the benefit of this method for spherical waves. Additionally, a working implementation is presented showing the example of a spherical wave propagating through a circular aperture. PMID:25401659
NASA Technical Reports Server (NTRS)
Heldenfels, Richard R
1951-01-01
A numerical method is presented for the stress analysis of stiffened-shell structures of arbitrary cross section under nonuniform temperature distributions. The method is based on a previously published procedure that is extended to include temperature effects and multicell construction. The application of the method to practical problems is discussed and an illustrative analysis is presented of a two-cell box beam under the combined action of vertical loads and a nonuniform temperature distribution.
A numerical study of the Regge calculus and smooth lattice methods on a Kasner cosmology
NASA Astrophysics Data System (ADS)
Brewin, Leo
2015-10-01
Two lattice based methods for numerical relativity, the Regge calculus and the smooth lattice relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge calculus is of the order of 110 times slower than the smooth lattice method.
Feeding methods and efficiencies of selected frugivorous birds
Foster, M.S.
1987-01-01
I report on handling methods and efficiencies of 26 species of Paraguayan birds freeding on fruits of Allophyllus edulis (Sapindaceae). A bird may swallow fruits whole (Type I: pluck and swallow feeders), hold a fruit and cut the pulp from the seed with the edge of the bill, swallowing the pulp but not the seed (Type II: cut or mash feeders), or take bites of pulp from a fruit that hangs from the tree or that is held and manipulated against a branch (Type III: push and bite feeders). In terms of absolute amount of pulp obtained from a fruit, and amount obtained per unit time. Type I species are far more efficient than Type II and III species. Bill morphology influences feeding methods but is not the only important factor. Diet breadth does not appear to be significant. Consideration of feeding efficiency relative to the needs of the birds indicates that these species need to spend relatively little time feeding to meet their estimated energetic needs, and that handling time has a relatively trivial effect on the time/energy budges of the bird species observed.
NASA Technical Reports Server (NTRS)
Bi, Lei; Yang, Ping; Kattawar, George W.; Mishchenko, Michael I.
2013-01-01
The extended boundary condition method (EBCM) and invariant imbedding method (IIM) are two fundamentally different T-matrix methods for the solution of light scattering by nonspherical particles. The standard EBCM is very efficient but encounters a loss of precision when the particle size is large, the maximum size being sensitive to the particle aspect ratio. The IIM can be applied to particles in a relatively large size parameter range but requires extensive computational time due to the number of spherical layers in the particle volume discretization. A numerical combination of the EBCM and the IIM (hereafter, the EBCM+IIM) is proposed to overcome the aforementioned disadvantages of each method. Even though the EBCM can fail to obtain the T-matrix of a considered particle, it is valuable for decreasing the computational domain (i.e., the number of spherical layers) of the IIM by providing the initial T-matrix associated with an iterative procedure in the IIM. The EBCM+IIM is demonstrated to be more efficient than the IIM in obtaining the optical properties of large size parameter particles beyond the convergence limit of the EBCM. The numerical performance of the EBCM+IIM is illustrated through representative calculations in spheroidal and cylindrical particle cases.
NASA Astrophysics Data System (ADS)
Chen, Peng; Liu, Jin-Yang; Hong, Jia-Zhen
2016-04-01
In this paper, an efficient formulation based on the Lagrangian method is presented to investigate the contact-impact problems of flexible multi-body systems. Generally, the penalty method and the Hertz contact law are the most commonly used methods in engineering applications. However, these methods are highly dependent on various non-physical parameters, which have great effects on the simulation results. Moreover, a tremendous number of degrees of freedom in the contact-impact problems will influence the numerical efficiency significantly. With the consideration of these two problems, a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact-impact problems in flexible multi-body system numerically. Meanwhile, the finite element meshing laws of the contact bodies will be studied preliminarily. A numerical example with experimental verification will certify the reliability of the presented formulation in contact-impact analysis. Furthermore, a series of numerical investigations explain how great the influence of the finite element meshing has on the simulation results. Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficiency.
An Efficient Method to Obtain Dedifferentiated Fat Cells.
Taniguchi, Hiroaki; Kazama, Tomohiko; Hagikura, Kazuhiro; Yamamoto, Chii; Kazama, Minako; Nagaoka, Yuki; Matsumoto, Taro
2016-01-01
Tissue engineering and cell therapy hold great promise clinically. In this regard, multipotent cells, such as mesenchymal stem cells (MSCs), may be used therapeutically, in the near future, to restore function to damaged organs. Nevertheless, several technical issues, including the highly invasive procedure of isolating MSCs and the inefficiency surrounding their amplification, currently hamper the potential clinical use of these therapeutic modalities. Herein, we introduce a highly efficient method for the generation of dedifferentiated fat cells (DFAT), MSC-like cells. Interestingly, DFAT cells can be differentiated into several cell types including adipogenic, osteogenic, and chondrogenic cells. Although other groups have previously presented various methods for generating DFAT cells from mature adipose tissue, our method allows us to produce DFAT cells more efficiently. In this regard, we demonstrate that DFAT culture medium (DCM), supplemented with 20% FBS, is more effective in generating DFAT cells than DMEM, supplemented with 20% FBS. Additionally, the DFAT cells produced by our cell culture method can be redifferentiated into several tissue types. As such, a very interesting and useful model for the study of tissue dedifferentiation is presented. PMID:27500409
NASA Astrophysics Data System (ADS)
Furzeland, R. M.; Verwer, J. G.; Zegeling, P. A.
1990-08-01
In recent years, several sophisticated packages based on the method of lines (MOL) have been developed for the automatic numerical integration of time-dependent problems in partial differential equations (PDEs), notably for problems in one space dimension. These packages greatly benefit from the very successful developments of automatic stiff ordinary differential equation solvers. However, from the PDE point of view, they integrate only in a semiautomatic way in the sense that they automatically adjust the time step sizes, but use just a fixed space grid, chosen a priori, for the entire calculation. For solutions possessing sharp spatial transitions that move, e.g., travelling wave fronts or emerging boundary and interior layers, a grid held fixed for the entire calculation is computationally inefficient, since for a good solution this grid often must contain a very large number of nodes. In such cases methods which attempt automatically to adjust the sizes of both the space and the time steps are likely to be more successful in efficiently resolving critical regions of high spatial and temporal activity. Methods and codes that operate this way belong to the realm of adaptive or moving-grid methods. Following the MOL approach, this paper is devoted to an evaluation and comparison, mainly based on extensive numerical tests, of three moving-grid methods for 1D problems, viz., the finite-element method of Miller and co-workers, the method published by Petzold, and a method based on ideas adopted from Dorfi and Drury. Our examination of these three methods is aimed at assessing which is the most suitable from the point of view of retaining the acknowledged features of reliability, robustness, and efficiency of the conventional MOL approach. Therefore, considerable attention is paid to the temporal performance of the methods.
System and method to determine electric motor efficiency nonintrusively
Lu, Bin; Habetler, Thomas G.; Harley, Ronald G.
2011-08-30
A system and method for nonintrusively determining electric motor efficiency includes a processor programed to, while the motor is in operation, determine a plurality of stator input currents, electrical input data, a rotor speed, a value of stator resistance, and an efficiency of the motor based on the determined rotor speed, the value of stator resistance, the plurality of stator input currents, and the electrical input data. The determination of the rotor speed is based on one of the input power and the plurality of stator input currents. The determination of the value of the stator resistance is based on at least one of a horsepower rating and a combination of the plurality of stator input currents and the electrical input data. The electrical input data includes at least one of an input power and a plurality of stator input voltages.
Filtration method efficiently desalts crude in commercial test
Not Available
1993-05-17
During 3 months of industrial testing of a filtration crude oil desalting method, a total of 120,500 metric tons (mt), or 1,475 mt/d (almost 11,000 b/d) of crude was processed. Rongxi Du, Kai Peng, and Li Wang, engineers at Wuhan Petrochemical Works, Wuhan, China, in an unpublished report, indicate that they determined unit operating parameters and performed statistical analyses of desalting-efficiency data from the test run. The engineers also determined relationships between desalting efficiency and flow velocity, relative density, mixing pressure drop (MPD), filtration-tank pressure drop, and temperature. The desalting and dewatering level of single-stage filtrations desalting was found to be equal to that of two-stage electrostatic desalting with remarkable benefits resulting from reduced power, water, and demulsifier requirements. This paper describes the filtration desalting, test parameters, performance results, and filter revivification.
Implementing efficient dynamic formal verification methods for MPI programs.
Vakkalanka, S.; DeLisi, M.; Gopalakrishnan, G.; Kirby, R. M.; Thakur, R.; Gropp, W.; Mathematics and Computer Science; Univ. of Utah; Univ. of Illinois
2008-01-01
We examine the problem of formally verifying MPI programs for safety properties through an efficient dynamic (runtime) method in which the processes of a given MPI program are executed under the control of an interleaving scheduler. To ensure full coverage for given input test data, the algorithm must take into consideration MPI's out-of-order completion semantics. The algorithm must also ensure that nondeterministic constructs (e.g., MPI wildcard receive matches) are executed in all possible ways. Our new algorithm rewrites wildcard receives to specific receives, one for each sender that can potentially match with the receive. It then recursively explores each case of the specific receives. The list of potential senders matching a receive is determined through a runtime algorithm that exploits MPI's operation ordering semantics. Our verification tool ISP that incorporates this algorithm efficiently verifies several programs and finds bugs missed by existing informal verification tools.
NASA Astrophysics Data System (ADS)
Nardi, Albert; Idiart, Andrés; Trinchero, Paolo; de Vries, Luis Manuel; Molinero, Jorge
2014-08-01
This paper presents the development, verification and application of an efficient interface, denoted as iCP, which couples two standalone simulation programs: the general purpose Finite Element framework COMSOL Multiphysics® and the geochemical simulator PHREEQC. The main goal of the interface is to maximize the synergies between the aforementioned codes, providing a numerical platform that can efficiently simulate a wide number of multiphysics problems coupled with geochemistry. iCP is written in Java and uses the IPhreeqc C++ dynamic library and the COMSOL Java-API. Given the large computational requirements of the aforementioned coupled models, special emphasis has been placed on numerical robustness and efficiency. To this end, the geochemical reactions are solved in parallel by balancing the computational load over multiple threads. First, a benchmark exercise is used to test the reliability of iCP regarding flow and reactive transport. Then, a large scale thermo-hydro-chemical (THC) problem is solved to show the code capabilities. The results of the verification exercise are successfully compared with those obtained using PHREEQC and the application case demonstrates the scalability of a large scale model, at least up to 32 threads.
NASA Astrophysics Data System (ADS)
Takahashi, Ryohei; Mamori, Hiroya; Yamamoto, Makoto
2016-02-01
A numerical method for simulating gas-liquid-solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas-liquid two-phase problem, and the latter is a gas-liquid-solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.
NASA Astrophysics Data System (ADS)
Guo, Nailong
Our research is motivated by the concept of Coupled Resonator Optical Waveguides (CROWs) [Aya99, Nst98, Bel97] emerged only a few years ago as a new way of integrating coupled cavities onto a single chip. This concept can be used to manipulate light paths and photonic dispersions [Tmu99, Bmm04] on a microscopic scale. Due to the weak evanescent coupling between adjacent high quality resonators, the group velocity of light can be significantly reduced in such structures leading to applications in optical buffering and controllable delay lines. CROWs are not limited to coupled defects in photonic crystals and can be realized in a coherent coupling of whispering gallery modes (WGMs) in microrings [Bel97], microdisks, dielectric bispheres [Tmu99, Bmm04] and long chains [Vna04] of microspheres. To numerically study the optical coupling by evanescent WGMs between two microspheres, the building blocks of coupled resonator optical waveguide devices, we introduce a high-order time-domain discontinuous spectral element method to the 3-D Maxwell's equations, and propose a mesh generation method for optical coupled spherical resonators with well conditioned mass matrices. A Legendre orthogonal polynomial basis is used on cubes, cuboids, and truncated square pyramids with a spherical surface. A general multidomain scheme is developed to simulate scattering of plane wave by a dielectric sphere, and the corresponding numerical results demonstrate the exponential convergence of the discontinuous spectral element method (DSEM) with increasing expansion order. The numerical results of WGMs show the successful optical coupling of WGMs between two microspheres, and validate our numerical method and algorithms. Finally, an algorithm for improving the efficiency of DSEM is proposed, and a theorem to estimate the maximum error, introduced by this algorithm, is proved.
Numerical simulation: Toward the design of high-efficiency planar perovskite solar cells
Liu, Feng; Zhu, Jun E-mail: sydai@ipp.ac.cn; Wei, Junfeng; Li, Yi; Lv, Mei; Yang, Shangfeng; Zhang, Bing; Yao, Jianxi; Dai, Songyuan E-mail: sydai@ipp.ac.cn
2014-06-23
Organo-metal halide perovskite solar cells based on planar architecture have been reported to achieve remarkably high power conversion efficiency (PCE, >16%), rendering them highly competitive to the conventional silicon based solar cells. A thorough understanding of the role of each component in solar cells and their effects as a whole is still required for further improvement in PCE. In this work, the planar heterojunction-based perovskite solar cells were simulated with the program AMPS (analysis of microelectronic and photonic structures)-1D. Simulation results revealed a great dependence of PCE on the thickness and defect density of the perovskite layer. Meanwhile, parameters including the work function of the back contact as well as the hole mobility and acceptor density in hole transport materials were identified to significantly influence the performance of the device. Strikingly, an efficiency over 20% was obtained under the moderate simulation conditions.
NASA Astrophysics Data System (ADS)
Mishchenko, Michael I.; Dlugach, Janna M.; Chowdhary, Jacek; Zakharova, Nadezhda T.
2015-05-01
We describe a simple yet efficient numerical algorithm for computing polarized bidirectional reflectance of an optically thick (semi-infinite), macroscopically flat layer composed of statistically isotropic and mirror symmetric random particles. The spatial distribution of the particles is assumed to be sparse, random, and statistically uniform. The 4×4 Stokes reflection matrix is calculated by iterating the Ambartsumian's vector nonlinear integral equation. The result is a numerically exact solution of the vector radiative transfer equation and as such fully satisfies the energy conservation law and the fundamental reciprocity relation. Since this technique bypasses the computation of the internal radiation field, it is very fast and highly accurate. The FORTRAN implementation of the technique is publicly available on the World Wide Web at
NASA Technical Reports Server (NTRS)
Cook, C. H.
1977-01-01
The results of a comprehensive numerical investigation of the basic capabilities of the finite element method (FEM) for numerical solution of compressible flow problems governed by the two-dimensional and axis-symmetric Navier-Stokes equations in primitive variables are presented. The strong and weak points of the method as a tool for computational fluid dynamics are considered. The relation of the linear element finite element method to finite difference methods (FDM) is explored. The calculation of free shear layer and separated flows over aircraft boattail afterbodies with plume simulators indicate the strongest assets of the method are its capabilities for reliable and accurate calculation employing variable grids which readily approximate complex geometry and capably adapt to the presence of diverse regions of large solution gradients without the necessity of domain transformation.
The stability of numerical methods for second order ordinary differential equations
NASA Technical Reports Server (NTRS)
Gear, C. W.
1978-01-01
An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem dy/dt = Ay are inside this region, the numerical method is stable. If the second order system d/dt(dy/dt) = 2Ady/dt - By is solved as a first order system, the same result applies to the eigenvalues of the generalized eigenvalue problem (lambda-squared)I 2(lambda)A + B. No such region exists for general methods for second order equations, but in some cases a region of absolute stability can be defined for methods for the single second order equation d/dt(dy/dt) = 2ady/dt - by. The absence of a region of absolute stability can occur when different members of a system of first order equations are solved by different methods.