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Numerical Stability (numerical + stability)

Distribution by Scientific Domains

Engineering	75%
Chemistry	12%
Mathematics and Statistics	6%
2 Other Domains	7%

Selected Abstracts

Some numerical issues using element-free Galerkin mesh-less method for coupled hydro-mechanical problems

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2009
Mohammad Norouz Oliaei
Abstract A new formulation of the element-free Galerkin (EFG) method is developed for solving coupled hydro-mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro-mechanical problems. Examples are studied and compared with closed-form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro-mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Numerical stability of unsteady stream-function vorticity calculations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2003
E. Sousa
Abstract The stability of a numerical solution of the Navier,Stokes equations is usually approached by con- sidering the numerical stability of a discretized advection,diffusion equation for either a velocity component, or in the case of two-dimensional flow, the vorticity. Stability restrictions for discretized advection,diffusion equations are a very serious constraint, particularly when a mesh is refined in an explicit scheme, so an accurate understanding of the numerical stability of a discretization procedure is often of equal or greater practical importance than concerns with accuracy. The stream-function vorticity formulation provides two equations, one an advection,diffusion equation for vorticity and the other a Poisson equation between the vorticity and the stream-function. These two equations are usually not coupled when considering numerical stability. The relation between the stream-function and the vorticity is linear and so has, in principle, an exact inverse. This allows an algebraic method to link the interior and the boundary vorticity into a single iteration scheme. In this work, we derive a global time-iteration matrix for the combined system. When applied to a model problem, this matrix formulation shows differences between the numerical stability of the full system equations and that of the discretized advection,diffusion equation alone. It also gives an indication of how the wall vorticity discretization affects stability. Despite the added algebraic complexity, it is straightforward to use MATLAB to carry out all the matrix operations. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Numerical stability and error analysis for the incompressible Navier,Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2002
S. Prudhomme
Abstract This paper describes a strategy to control errors in finite element approximations of the time-dependent incompressible Navier,Stokes equations. The approach involves estimating the errors due to the discretization in space, using information from the residuals in the momentum and continuity equations. Following a numerical stability analysis of channel flows past a cylinder, it is concluded that the errors due to the residual in the continuity equation should be carefully controlled since it appears to be the source of unphysical perturbations artificially created by the spatial discretization. The performance of the adaptive strategy is then tested for lid-driven oblique cavity flows. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A Petrov,Galerkin finite element model for one-dimensional fully non-linear and weakly dispersive wave propagation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2001
Seung-Buhm Woo
Abstract A new finite element method is presented to solve one-dimensional depth-integrated equations for fully non-linear and weakly dispersive waves. For spatial integration, the Petrov,Galerkin weighted residual method is used. The weak forms of the governing equations are arranged in such a way that the shape functions can be piecewise linear, while the weighting functions are piecewise cubic with C2 -continuity. For the time integration an implicit predictor,corrector iterative scheme is employed. Within the framework of linear theory, the accuracy of the scheme is discussed by considering the truncation error at a node. The leading truncation error is fourth-order in terms of element size. Numerical stability of the scheme is also investigated. If the Courant number is less than 0.5, the scheme is unconditionally stable. By increasing the number of iterations and/or decreasing the element size, the stability characteristics are improved significantly. Both Dirichlet boundary condition (for incident waves) and Neumann boundary condition (for a reflecting wall) are implemented. Several examples are presented to demonstrate the range of applicabilities and the accuracy of the model. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Numerical stability of the BEM for advection-diffusion problems

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2004
Andrés Peratta
Abstract A boundary element method (BEM) approach has been developed to solve the time-dependent 1D advection-diffusion equation. The 1D solution is part of a 3D numerical scheme for solving advection-diffusion (AD) problems in fractured porous media. The full 3D scheme includes a 3D solution for the porous matrix, which is coupled with a 2D solution for fractures and a 1D solution for fracture intersections. As the hydraulic conductivity of the fracture intersections is usually higher than the hydraulic conductivity of the fractures and by at least one order of magnitude higher than the hydraulic conductivity of the porous matrix, the fastest flow and solute transport occurs in the fracture intersections. Therefore it is important to have an accurate and stable 1D solution of the transient AD problems. This article presents two different 1D BEM formulations for solution of the AD problems. The particular advantage of these formulations is that they provide one of the most straightforward and simplest ways to couple multiple intersecting 2D Boundary Element problems discretized with linear discontinuous elements. Both formulations are tested and compared for accuracy, stability, and consistency. The analysis helps to select the more suitable formulations according to the properties of the problem under consideration. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 [source]

On coupling the Reynolds-averaged Navier,Stokes equations with two-equation turbulence model equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2006
Seungsoo Lee
Abstract Two methods for coupling the Reynolds-averaged Navier,Stokes equations with the q,, turbulence model equations on structured grid systems have been studied; namely a loosely coupled method and a strongly coupled method. The loosely coupled method first solves the Navier,Stokes equations with the turbulent viscosity fixed. In a subsequent step, the turbulence model equations are solved with all flow quantities fixed. On the other hand, the strongly coupled method solves the Reynolds-averaged Navier,Stokes equations and the turbulence model equations simultaneously. In this paper, numerical stabilities of both methods in conjunction with the approximated factorization-alternative direction implicit method are analysed. The effect of the turbulent kinetic energy terms in the governing equations on the convergence characteristics is also studied. The performance of the two methods is compared for several two- and three-dimensional problems. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 1 2009
Cheng Chen
Abstract Real-time hybrid testing combines experimental testing and numerical simulation, and provides a viable alternative for the dynamic testing of structural systems. An integration algorithm is used in real-time hybrid testing to compute the structural response based on feedback restoring forces from experimental and analytical substructures. Explicit integration algorithms are usually preferred over implicit algorithms as they do not require iteration and are therefore computationally efficient. The time step size for explicit integration algorithms, which are typically conditionally stable, can be extremely small in order to avoid numerical stability when the number of degree-of-freedom of the structure becomes large. This paper presents the implementation and application of a newly developed unconditionally stable explicit integration algorithm for real-time hybrid testing. The development of the integration algorithm is briefly reviewed. An extrapolation procedure is introduced in the implementation of the algorithm for real-time testing to ensure the continuous movement of the servo-hydraulic actuator. The stability of the implemented integration algorithm is investigated using control theory. Real-time hybrid test results of single-degree-of-freedom and multi-degree-of-freedom structures with a passive elastomeric damper subjected to earthquake ground motion are presented. The explicit integration algorithm is shown to enable the exceptional real-time hybrid test results to be achieved. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Displacement-controlled method and its applications to material non-linearity

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2005
H. Zheng
Abstract For the analysis of non-linear problems, the displacement-controlled method (DCM) has a more extensive application scope and more powerful abilities than the load-controlled method (LCM). However, difficulties of the DCM's procedure not amenable to most finite element implementations of the conventional LCM have restricted its applications in geomechanics. By means of Sherman,Morrison's theorem, the solution of DCM is improved. The improved procedure is characterized by high efficiency, good numerical stability and a programme structure similar to LCM. Two aspects of applications of DCM are illustrated. The first application is to compute the response of a structure under a given load level like the conventional finite element analysis. The second application is to trace the equilibrium path of a structure under a given load distribution type. A simple but effective algorithm is presented for automatically adjusting the step length in tracing the equilibrium path. Examples illustrate that the proposed procedures are suited for modelling complicated non-linear problems in geomechanics. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Numerical stability of unsteady stream-function vorticity calculations

PC cluster parallel finite element analysis of sloshing problem by earthquake using different network environments

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002
Kazuo Kashiyama
Abstract This paper presents a parallel finite element method for the analysis of the sloshing problem caused by earthquakes. The incompressible Navier,Stokes equation based on Arbitrary Lagrangian,Eulerian description is used as the governing equation. The SUPG/PSPG formulation is employed to improve the numerical stability and the accuracy. Parallel implementation of the unstructured grid based formulation was carried out on a PC cluster. The present method was applied to analyse the sloshing problem of a rectangular tank and an actual reservoir. The effect of parallelization on the efficiency of the computations was examined using a number of different network environments. Copyright © 2002 John Wiley & Sons, Ltd. [source]

On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010
I. Kalashnikova
Abstract A reduced order model (ROM) based on the proper orthogonal decomposition (POD)/Galerkin projection method is proposed as an alternative discretization of the linearized compressible Euler equations. It is shown that the numerical stability of the ROM is intimately tied to the choice of inner product used to define the Galerkin projection. For the linearized compressible Euler equations, a symmetry transformation motivates the construction of a weighted L2 inner product that guarantees certain stability bounds satisfied by the ROM. Sufficient conditions for well-posedness and stability of the present Galerkin projection method applied to a general linear hyperbolic initial boundary value problem (IBVP) are stated and proven. Well-posed and stable far-field and solid wall boundary conditions are formulated for the linearized compressible Euler ROM using these more general results. A convergence analysis employing a stable penalty-like formulation of the boundary conditions reveals that the ROM solution converges to the exact solution with refinement of both the numerical solution used to generate the ROM and of the POD basis. An a priori error estimate for the computed ROM solution is derived, and examined using a numerical test case. Published in 2010 by John Wiley & Sons, Ltd. [source]

Transient three-dimensional domain decomposition problems: Frame-indifferent mortar constraints and conserving integration

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2010
Christian Hesch
Abstract The present work deals with transient large-deformation domain decomposition problems. The tying of dissimilar meshed grids is performed by applying the mortar method. In this connection, a reformulation of the original linear mortar constraints is proposed, which retains frame-indifference for arbitrary discretizations of the interface. Furthermore, a specific coordinate augmentation technique is proposed to make possible the design of an energy,momentum scheme. Numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energy,momentum scheme for three-dimensional problems. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Discrete element method for modelling solid and particulate materials

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2007
Federico A. Tavarez
Abstract The discrete element method (DEM) is developed in this study as a general and robust technique for unified two-dimensional modelling of the mechanical behaviour of solid and particulate materials, including the transition from solid phase to particulate phase. Inter-element parameters (contact stiffnesses and failure criteria) are theoretically established as functions of element size and commonly accepted material parameters including Young's modulus, Poisson's ratio, ultimate tensile strength, and fracture toughness. A main feature of such an approach is that it promises to provide convergence with refinement of a DEM discretization. Regarding contact failure, an energy criterion based on the material's ultimate tensile strength and fracture toughness is developed to limit the maximum contact forces and inter-element relative displacement. This paper also addresses the issue of numerical stability in DEM computations and provides a theoretical method for the determination of a stable time-step. The method developed herein is validated by modelling several test problems having analytic solutions and results show that indeed convergence is obtained. Moreover, a very good agreement with the theoretical results is obtained in both elastic behaviour and fracture. An example application of the method to high-speed penetration of a concrete beam is also given. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A new formulation of Signorini's type for seepage problems with free surfaces

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005
H. Zheng
Abstract A new variational inequality formulation for seepage problems with free surfaces is presented, in which a boundary condition of Signorini's type is prescribed over the potential seepage surfaces. This makes the singularity of seepage points eliminated and the location of seepage points determined easily. Compared to other variational formulations, the proposed formulation can effectively overcome the mesh dependency and significantly improve the numerical stability. A very challenging engineering example with complicated geometry and strong inhomogeneity is investigated in detail. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Non-hydrostatic 3D free surface layer-structured finite volume model for short wave propagation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009
L. Cea
Abstract In this paper a layer-structured finite volume model for non-hydrostatic 3D environmental free surface flow is presented and applied to several test cases, which involve the computation of gravity waves. The 3D unsteady momentum and mass conservation equations are solved in a collocated grid made of polyhedrons, which are built from a 2D horizontal unstructured mesh, by just adding several horizontal layers. The mesh built in such a way is unstructured in the horizontal plane, but structured in the vertical direction. This procedure simplifies the mesh generation and at the same time it produces a well-oriented mesh for stratified flows, which are common in environmental problems. The model reduces to a 2D depth-averaged shallow water model when one single layer is defined in the mesh. Pressure,velocity coupling is achieved by the Semi-Implicit Method for Pressure-Linked Equations algorithm, using Rhie,Chow interpolation to stabilize the pressure field. An attractive property of the model proposed is the ability to compute the propagation of short waves with a rather coarse vertical discretization. Several test cases are solved in order to show the capabilities and numerical stability of the model, including a rectangular free oscillating basin, a radially symmetric wave, short wave propagation over a 1D bar, solitary wave runup on a vertical wall, and short wave refraction over a 2D shoal. In all the cases the numerical results are compared either with analytical or with experimental data. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Friction term discretization and limitation to preserve stability and conservation in the 1D shallow-water model: Application to unsteady irrigation and river flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008
J. Burguete
Abstract Friction is one of the relevant forces included in the momentum equation of the 1D shallow-water model. This work shows that a pointwise discretization of the friction term unbalances this term with the rest of the terms in the equation in steady state. On the other hand, an upwind discretization of the friction term ensures the correct discrete balance. Furthermore, a conservative technique based on the limitation of the friction value is proposed in order to avoid unbounded values of the friction term in unsteady cases of advancing front over dry and rough surfaces. This limitation improves the quality of unsteady solutions in wet/dry fronts and guarantees the numerical stability in cases with dominant friction terms. The proposed discretization is validated in some test cases with analytical solution or with measured data and used in some practical cases. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Extension of an explicit finite volume method to large time steps (CFL>1): application to shallow water flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2006
J. Murillo
Abstract In this work, the explicit first order upwind scheme is presented under a formalism that enables the extension of the methodology to large time steps. The number of cells in the stencil of the numerical scheme is related to the allowable size of the CFL number for numerical stability. It is shown how to increase both at the same time. The basic idea is proposed for a 1D scalar equation and extended to 1D and 2D non-linear systems with source terms. The importance of the kind of grid used is highlighted and the method is outlined for irregular grids. The good quality of the results is illustrated by means of several examples including shallow water flow test cases. The bed slope source terms are involved in the method through an upwind discretization. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Computing non-Newtonian fluid flow with radial basis function networks

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2005
N. Mai-Duy
Abstract This paper is concerned with the application of radial basis function networks (RBFNs) for solving non-Newtonian fluid flow problems. Indirect RBFNs, which are based on an integration process, are employed to represent the solution variables; the governing differential equations are discretized by means of point collocation. To enhance numerical stability, stress-splitting techniques are utilized. The proposed method is verified through the computation of the rectilinear and non-rectilinear flows in a straight duct and the axisymmetric flow in an undulating tube using Newtonian, power-law, Criminale,Ericksen,Filbey (CEF) and Oldroyd-B models. The obtained results are in good agreement with the analytic and benchmark solutions. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Performance of finite volume solutions to the shallow water equations with shock-capturing schemes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2002
K. S. Erduran
Abstract Numerical methods have become well established as tools for solving problems in hydraulic engineering. In recent years the finite volume method (FVM) with shock capturing capabilities has come to the fore because of its suitability for modelling a variety of types of flow; subcritical and supercritical; steady and unsteady; continuous and discontinuous and its ability to handle complex topography easily. This paper is an assessment and comparison of the performance of finite volume solutions to the shallow water equations with the Riemann solvers; the Osher, HLL, HLLC, flux difference splitting (Roe) and flux vector splitting. In this paper implementation of the FVM including the Riemann solvers, slope limiters and methods used for achieving second order accuracy are described explicitly step by step. The performance of the numerical methods has been investigated by applying them to a number of examples from the literature, providing both comparison of the schemes with each other and with published results. The assessment of each method is based on five criteria; ease of implementation, accuracy, applicability, numerical stability and simulation time. Finally, results, discussion, conclusions and recommendations for further work are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Spectral analysis of flux vector splitting finite volume methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2001
Tapan K. Sengupta
Abstract New results are presented here for finite volume (FV) methods that use flux vector splitting (FVS) along with higher-order reconstruction schemes. Apart from spectral accuracy of the resultant methods, the numerical stability is investigated which restricts the allowable time step or the Courant,Friedrich,Lewy (CFL) number. Also the dispersion relation preservation (DRP) property of various spatial and temporal discretization schemes is investigated. The DRP property simultaneously fixes space and time steps. This aspect of numerical schemes is important for simulation of high-Reynolds number flows, compressible flows with shock(s) and computational aero-acoustics. It is shown here that for direct numerical simulation applications, the DRP property is more restrictive than stability criteria. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Improved adaptive control for the discrete-time parametric-strict-feedback form

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 12 2009
Graciela Adriana González
Abstract Adaptive control design for a class of single-input single-output nonlinear discrete-time systems in parametric-strict-feedback form is re-visited. No growth restrictions are assumed on the nonlinearities. The control objective is to achieve tracking of a reference signal. As usual, the algorithm derives from the combination of a control law and a parameter estimator (certainty equivalence principle). The parameter estimator strongly lies on the regressor subspace identification by means of an orthogonalization process. Certain drawbacks of previous schemes are analyzed. Several modifications on them are considered to improve the algorithm complexity, control performance and numerical stability. As a result, an alternative control scheme is proposed. When applied to the proposed class of systems, global boundedness and convergence remain as achieved objectives while improving the performance issues of previous schemes. Copyright © 2009 John Wiley & Sons, Ltd. [source]

The Gauss-Seidel fast affine projection algorithm for multichannel active noise control and sound reproduction systems

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2-3 2005
Martin Bouchard
Abstract In the field of adaptive filtering, the fast implementations of affine projection algorithms are known to provide a good tradeoff between convergence speed and computational complexity. Such algorithms have recently been published for multichannel active noise control systems. Previous work reported that these algorithms can outperform more complex recursive least-squares algorithms when noisy plant models are used in active noise control systems. This paper proposes a new fast affine projection algorithm for multichannel active noise control or sound reproduction systems, based on the Gauss,Seidel solving scheme. The proposed algorithm has a lower complexity than the previously published algorithms, with the same convergence speed and the same good performance with noisy plant models, and a potential for better numerical stability. It provides the best performance/cost ratio. Details of the algorithm and its complexity are presented in the paper, with simulation results to validate its performance. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Split-component PML absorbing conditions for SS-TLM

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 3 2004
S. Le Maguer
Abstract Known as alternate direct implicit (ADI) or split-step (SS) schemes, a new class of time-domain algorithms has recently been proposed. Their salient feature concerns their numerical stability, regardless the time-step used. Thus, significant computational advantages can be obtained when non-uniform mesh is used. To study open structures or determine S-parameters, absorbing boundary conditions (ABC) have to be used. The perfectly matched layers (PML) technique based on split field component is implemented for the SS-TLM algorithm. The complete set of updating equations is provided and the new PML is validated. It is shown to provide high accuracy even better than that of classical PML-TLM scheme. In addition, it is found that using a high time-step does not seem to degrade significantly the accuracy of PML. Thus, the PML technique is very well adapted to SS-TLM as confirmed by various applications. Finally, unlike all classical TLM-PML schemes, the technique is found to be stable. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A comparison of nine PLS1 algorithms

JOURNAL OF CHEMOMETRICS, Issue 10 2009
Martin Andersson
Abstract Nine PLS1 algorithms were evaluated, primarily in terms of their numerical stability, and secondarily their speed. There were six existing algorithms: (a) NIPALS by Wold; (b) the non-orthogonalized scores algorithm by Martens; (c) Bidiag2 by Golub and Kahan; (d) SIMPLS by de Jong; (e) improved kernel PLS by Dayal; and (f) PLSF by Manne. Three new algorithms were created: (g) direct-scores PLS1 based on a new recurrent formula for the calculation of basis vectors yielding scores directly from X and y; (h) Krylov PLS1 with its regression vector defined explicitly, using only the original X and y; (i) PLSPLS1 with its regression vector recursively defined from X and the regression vectors of its previous recursions. Data from IR and NIR spectrometers applied to food, agricultural, and pharmaceutical products were used to demonstrate the numerical stability. It was found that three methods (c, f, h) create regression vectors that do not well resemble the corresponding precise PLS1 regression vectors. Because of this, their loading and score vectors were also concluded to be deviating, and their models of X and the corresponding residuals could be shown to be numerically suboptimal in a least squares sense. Methods (a, b, e, g) were the most stable. Two of them (e, g) were not only numerically stable but also much faster than methods (a, b). The fast method (d) and the moderately fast method (i) showed a tendency to become unstable at high numbers of PLS factors. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Erratum: On the numerical stability of two widely used PLS algorithms

JOURNAL OF CHEMOMETRICS, Issue 6 2008
Nicolaas (Klaas) M. Faber
The above article (DOI: 10.1002/cem.1112) was published online on 14 February 2008. An error was subsequently identified: the captions for Figures 1 and 2 were omitted; they should read as follows: Figure 1. Orthogonality criterion (,A) for the octane data as a function of number of components (A) calculated using the standard PLS algorithm and SIMPLS. Figure 2. Orthogonality criterion (,A) for the wines data as a function of number of components (A) calculated using the standard PLS algorithm and SIMPLS. [source]

Comparison of the numerical stability of methods for anharmonic calculations of vibrational molecular energies

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2007
Petr Dan
Abstract On model examples, we compare the performance of the vibrational self-consistent field, variational, and four perturbational schemes used for computations of vibrational energies of semi-rigid molecules, with emphasis on the numerical stability. Although the accuracy of the energies is primarily dependent on the quality of the potential energy surface, approximate approaches to the anharmonic vibrational problem often do not converge to the same results due to the approximations involved. For furan, the sensitivity to variations of the anharmonic potential was systematically investigated by adding random noise to the cubic and quartic constants. The self-consistent field methods proved to be the most resistant to the potential variations. The second order perturbational techniques are sensitive to random degeneracies and provided the least stable results. However, their stability could be significantly improved by a simple generalization of the perturbational formula. The variational configuration interaction is practically limited by the size of the matrix that can be diagonalized for larger molecules; however, relatively fewer states need to be involved than for smaller ones, in favor of the computing. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [source]

A Discrete, Space Variation Model for Studying the Kinetics of Shape Deformation of Vesicles Coupled with Phase Separation

MACROMOLECULAR THEORY AND SIMULATIONS, Issue 5 2006
Jianfeng Li
Abstract Summary: The evolution dynamics of phase separation, coupled with shape deformation of vesicles is described by using dissipative dynamic equations, specifically the time-dependent Ginzburg-Landau (TDGL) equations. In order to improve the numerical stability and thus to efficiently deal with a large deformation of vesicles, a new algorithm, namely the discrete space variation model (DSVM) has been developed for the first time. The algorithm is based on the variation of the discretized free-energy functional, which is constructed in discrete membrane space, in contrast to the commonly used continuous free-energy functional. For the sake of numerical tractability, only the cylindrical vesicles (2D), with two components, are taken into consideration to illustrate the efficiency and validity of new algorithm. The simulation results, based on the DSVM algorithm have been compared with those from both linear analysis and strong segregation theory using the continuous space free-energy functional. It is found that the DSVM algorithm can correctly describe the coupling between the lateral phase-separation on the vesicle membrane and the vesicle shape deformation, both for early and late stages. A flower-like vesicle obtained by DSVM simulation. [source]

ADI-FDTD method perturbed by the second order cross derivative terms

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 7 2008
Ki-Bok Kong
Abstract A two-step FDTD method as a compromise of conditional stability and reduced splitting error is formulated and its numerical stability is investigated. It is the perturbed form to the ADI-FDTD method by the addition of second order cross derivative term. It is validated from the comparison of numerical anisotropy and numerical error over the ADI-FDTD that numerical performances can be improved by controlling the perturbed term within the stable region of the cross derivative term. © Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1822,1826, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23479 [source]

Application of the high-order symplectic FDTD scheme to the curved three-dimensional perfectly conducting objects

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 4 2007
Wei Sha
Abstract A high-order symplectic finite-difference time-domain (SFDTD) scheme using the diagonal split-cell model is presented to analyze electromagnetic scattering of the curved three-dimensional perfectly conducting objects. On the one hand, for the undistorted cells, the fourth-order accurate spatial difference is employed. On the other hand, for the completely distorted cells, the treatment of the curved surfaces is based on the diagonal split-cell model. Finally, for the partially distorted cells, the interpolation strategy is proposed to keep the field components continuous. The numerical experiments suggest that the diagonal SFDTD scheme can obtain more accurate results than both the staircased SFDTD scheme and the traditional diagonal FDTD method. Furthermore, in view of the high numerical stability, the improved symplectic scheme does not need to decrease time increment to comply with the stability criterion. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 931,934, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22306 [source]

Some numerical properties of approaches to physics,dynamics coupling for NWP

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 614 2006
Mark Dubal
Abstract At the present time there exist a number of different approaches to the problem of coupling parametrized physical processes to the dynamical core in operational numerical weather-prediction (NWP) and climate models. Motivated by the various strategies in use, some idealized representative coupling schemes are constructed and subsequently analysed using a methodology in which the physics and dynamics terms are represented in a simplified way. Particular numerical properties of the idealized schemes which are of interest are the ability to capture correct steady-state solutions and to be second-order accurate in time. In general, the schemes require specific choices for the time-differencing of certain coupled processes if correct steady-state solutions are to be obtained. This has implications for the overall numerical stability of a coupling strategy. An alternative physics,dynamics coupling approach is then described and analysed. A multiple-sweep predictor,corrector coupling scheme is shown to capture the correct steady-state solution and to allow for second-order accuracy, provided that the convective process is coupled explicitly. This approach has a number of advantages over those currently used in operational NWP models. Copyright © 2006 Crown copyright [source]