a critical evaluation of the resolution properties of b spline and compact finite difference methods resolution properties of b spline and compact finite difference schemes are compared using fourier analysis in periodic domains and tests based on solution of the wave and heat equations in finite domains with uniform and nonuniform grids results show that compact finite difference schemes have a higher convergence rate and in some cases better resolution however b spline schemes have a more straightforward and robust formulation particularly near boundaries on nonuniform meshes

reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics abstract galerkin and stabilized galerkin least squares and galerkin gradient least squares finite element methods for solving problems of time harmonic acoustics are presented and analyzed the error of discretization is related to spurious representation of physical phenomena namely dispersion anisotropy and reflection all of which decrease with mesh refinement the performance of the stabilized methods in terms of dispersion and anisotropy is identical both are superior to the galerkin method relaxing wave resolution requirements further insight into the design of these methods is provided by the analyses the stabilized methods differ in the degree of spurious reflection that is engendered by transitions in mesh size the performance of galerkin gradient least squares deteriorates on non uniform meshes however galerkin least squares maintains its enhanced performance exhibiting low sensitivity to transitions in mesh size thereby reducing spurious dispersion anisotropy and reflection in finite element analysis of time harmonic acoustics guidelines for discretization pertaining to mesh orientation and wave resolution are presented

precursors of extreme increments we investigate precursors and the predictability of extreme increments in a time series the events we are focusing on consist in large increments within successive time steps we are especially interested in understanding how the quality of the predictions depends on the strategy to choose precursors on the size of the event and on the correlation strength we study the prediction of extreme increments analytically in an autoregressive process of order 1 and numerically in wind speed recordings and long range correlated autoregressive moving average processes data we evaluate the success of predictions via receiver operator characteristics roc curves furthermore we observe an increase of the quality of predictions with increasing event size and with decreasing correlation in all examples both effects can be understood by using the likelihood ratio as a summary index for smooth roc curves

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

enumeration of classes of linear systems via equations and via partitions in an ordered abelian monoid abstract we prove that the feedback classes of locally brunovsky linear systems are given by the decomposition of state space into direct summands hence the problem of enumerating feedback classes of systems is equivalent to the problem of enumerating all solutions of a linear equation over a commutative zerosumfree monoid if this monoid is also cancelative then the problem is solved by all the partitions

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

influence of the event magnitude on the predictability of an extreme event we investigate the predictability of extreme events in time series the focus of this work is to understand under which circumstances large events are better predictable than smaller events therefore we use a simple prediction algorithm based on precursory structures which are identified using the maximum likelihood principle using the receiver operator characteristic curve as a measure for the quality of predictions we find that the dependence on the event size is closely linked to the probability distribution function of the underlying stochastic process we evaluate this dependence on the probability distribution function analytically and numerically if we assume that the optimal precursory structures are used to make the predictions we find that large increments are better predictable if the underlying stochastic process has a gaussian probability distribution function whereas larger increments are harder to predict if the underlying probability distribution function has a power law tail in the case of an exponential distribution function we find no significant dependence on the event size furthermore we compare these results with predictions of increments in correlated data namely velocity increments of a free jet flow the velocity increments in the free jet flow are in dependence on the time scale either asymptotically gaussian or asymptotically exponential distributed the numerical results for predictions within free jet data are in good agreement with the previous analytical considerations for random numbers

assignable polynomials to linear systems over von neumann regular rings abstract given a system a b over a commutative von neumann regular ring r it is proved that there exist a matrix f and a vector u such that the single input system a b f b u and the original system a b have the same module of reachable states and the same set of polynomials assignable by state feedback moreover there is a bijection between reachable states and assignable polynomials in the form of a certain isomorphism of r modules and the existence of this isomorphism for all systems actually characterizes von neumann regular rings finally the set of assignable polynomials to a single input system is completely described for arbitrary commutative rings which in the case of von neumann regular rings completes the study of assignable polynomials to multi input systems

the solution of elastostatic and elastodynamic problems with chebyshev spectral finite elements chebyshev spectral finite elements are applied to the solution of elastostatic and elastodynamic problems in two dimensions the accuracy of the spectral approach is judged by examining the dispersion of the solutions it is shown that the spectral approach can achieve nearly zero dispersion for a wide range of spatial and temporal discretizations even coarse mesh solutions using the explicit lumped capacitance approach demonstrate exceptional accuracy a brief description of the development of the chebyshev spectral elements is included

dispersive and dissipative behaviour of high order discontinuous galerkin finite element methods the dispersive and dissipative properties of hp version discontinuous galerkin finite element approximation are studied in three different limits for the small wave number limit hk 0 we show the discontinuous galerkin gives a higher order of accuracy than the standard galerkin procedure thereby confirming the conjectures of hu and atkins j comput phys 182 2 2002 516 if the mesh is fixed and the order p is increased it is shown that the dissipation and dispersion errors decay at a super exponential rate when the order p is much larger than hk finally if the order is chosen so that 2p 1 hk for some fixed constant 1 then it is shown that an exponential rate of decay is obtained

consistent treatment of boundaries with mortar contact formulations using dual lagrange multipliers abstract computational modelling of contact problems raises two basic questions which method should be used to enforce the contact conditions and how should this method be discretised the most popular enforcement methods are the lagrange multiplier method the penalty method and combinations of these two a frequently used discretisation method is the so called node to segment approach however this approach might lead to problems like jumps in contact forces loss of convergence or failure to pass the patch test thus in the last few years several segment to segment contact algorithms based on the mortar method were proposed combination of a mortar discretisation with a penalty based enforcement of the contact conditions leads to unphysical penetrations on the other hand a lagrange multiplier mortar method requires additional unknowns hence condensation of the lagrange multipliers is desirable to preserve the initial size of the system of equations this can be achieved by interpolating the lagrange multipliers with so called dual shape functions discretising two contacting bodies leads to opposed contact surface representations of finite element edges called slave and master elements respectively in current versions of dual lagrange multiplier mortar formulations an inconsistency at the boundary appears when only a part of a slave element instead of the entire element belongs to the contact area we present a modified definition of the dual shape functions in such slave elements the basic idea is to construct dual shape functions that fulfill the so called biorthogonality condition within the contact area this leads to consistent mortar matrices also in the boundary region to avoid ill conditioning of the stiffness matrix the modified mortar matrices are weighted with appropriate weighting factors in doing so the corresponding modified lagrange multiplier nodal values are of the same order as the unmodified ones various examples demonstrate the performance of the modified mortar contact algorithm

two dimensional mortar contact methods for large deformation frictional sliding this paper presents a mortar based formulation for the solution of two dimensional frictional contact problems involving finite deformation and large sliding as is widely recognized traditional node to surface contact formulations have several drawbacks in solution of deformable to deformable contact problems including lack of general patch test passage degradation of spatial convergence rates and robustness issues associated with the faceted representation of contacting surfaces the mortar finite element method initially proposed as a technique to join dissimilarly meshed domains has been shown to preserve optimal convergence rates in tied contact problems see discretization methods and iterative solvers based on domain decomposition springer verlag heidelberg 2001 for a recent review and is examined here as an alternative spatial discretization method for large sliding contact in particular a novel description for frictional sliding conditions in large deformation mortar formulations is proposed in this work in recent years the mortar element method has already been successfully implemented to solve frictional contact problems with linearized kinematics see int j numer meth engng 1993 36 3451 however in the presence of large deformations and finite sliding one must face difficulties associated with the definition and linearization of contact virtual work in the case where the mortar projection has a direct dependence on the tangential relative motion along the interface in this paper such a formulation is presented with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics some novel techniques are proposed to treat the non smoothness in the contact geometry and the searching required to define mortar segments a number of numerical examples illustrate the performance and accuracy of the proposed formulation copyright 2004 john wiley sons ltd

grid dispersion and stability criteria of some common finite element methods for acoustic and elastic wave equations purely numerical methods based on finite element approximation of the acoustic or elastic wave equation are becoming increasingly popular for the generation of synthetic seismograms we present formulas for the grid dispersion and stability criteria for some popular finite element methods fem for wave propagation namely classical and spectral fem we develop an approach based on a generalized eigenvalue formulation to analyze the dispersive behavior of these fems for acoustic or elastic wave propagation that overcomes difficulties caused by irregular node spacing within the element and the use of high order polynomials as is the case for spectral fem analysis reveals that for spectral fem of order four or greater dispersion is less than 0 2 at four to five nodes per wavelength and dispersion is not angle dependent new results can be compared with grid dispersion results of some classical finite difference methods fdm used for acoustic or elastic wave propagation analysis reveals that fdm and classical fem require a larger sampling ratio than a spectral fem to obtain results with the same degree of accuracy the staggered grid fdm is an efficient scheme but the dispersion is angle dependent with larger values along the grid axes on the other hand spectral fem of order four or greater is isotropic with small dispersion making it attractive for simulations with long propagation times

hypothesis testing and earthquake prediction abstract requirements for testing include advance specification of the conditional rate density probability per unit time area and magnitude or alternatively probabilities for specified intervals of time space and magnitude here i consider testing fully specified hypotheses with no parameter adjustments or arbitrary decisions allowed during the test period because it may take decades to validate prediction methods it is worthwhile to formulate testable hypotheses carefully in advance earthquake prediction generally implies that the probability will be temporarily higher than normal such a statement requires knowledge of normal behavior that is it requires a null hypothesis hypotheses can be tested in three ways i by comparing the number of actual earth quakes to the number predicted ii by comparing the likelihood score of actual earthquakes to the predicted distribution and iii by comparing the likelihood ratio to that of a null hypothesis the first two tests are purely self consistency tests while the third is a direct comparison of two hypotheses predictions made without a statement of probability are very difficult to test and any test must be based on the ratio of earthquakes in and out of the forecast regions

on the solvability of closest point projection procedures in contact analysis analysis and solution strategy for surfaces of arbitrary geometry abstract the uniqueness and existence of the closest point projection procedure widely used in contact mechanics are analyzed in the current article first a projection domain for c 2 continuous surfaces is created based on the geometrical properties of surfaces then any point from the projection domain has a unique projection onto the given surface it is shown that in order to construct a continuous projection domain for arbitrary globally c 1 or c 0 continuous surfaces a projection routine should be generalized and also include a projection onto a curved edge and onto corner points criteria of uniqueness and existence of the corresponding projection routine are given and discussed from the geometrical point of view some examples showing the construction of the projection domain as well as the necessity of a generalized projection routine are given

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

assessment of methods for computing the closest point projection penetration and gap functions in contact searching problems summary in computational contact mechanics problems local searching requires calculation of the closest point projection of a contactor point onto a given target segment it is generally supposed that the contact boundary is locally described by a convex region however because this assumption is not valid for a general curved segment of a three dimensional quadratic serendipity element an iterative numerical procedure may not converge to the nearest local minimum to this end several unconstrained optimization methods are tested the newton raphson method the least square projection the sphere and torus approximation method the steepest descent method the broyden method the broyden fletcher goldfarb shanno method and the simplex method the effectiveness and robustness of these methods are tested by means of a proposed benchmark problem it is concluded that the newton raphson method in conjunction with the simplex method significantly increases the robustness of the local contact search procedure of pure penalty contact methods whereas the torus approximation method can be recommended for contact searching algorithms which employ the lagrange method or the augmented lagrangian method copyright 2015 john wiley sons ltd

discrete chaotic maps obtained by symmetric integration abstract chaotic return maps are widely used to model various dynamical systems such as charged particle movement laser beam dynamic celestial body orbiting and many others return maps are commonly obtained by discretization of continuous equations using the euler cromer operator with the only motivation that it is the simplest symplectic operator recent progress in geometric integration raised considerable interest to symmetric operators due to their ability to preserve some geometric properties of continuous flows this way yielding better agreement between discrete and continuous dynamical systems here we compare symmetric and asymmetric discretization approaches applied to several examples of hamiltonian systems in particular we suggest symmetric modifications of chirikov and henon maps and show explicitly that the implied symmetric integration procedure yields reflectional symmetry in the phase space for verification we show that a smooth even perturbation function used instead of a discontinuous delta pulse provides asymptotically similar results numerical experiments using several statistical methods show that symmetric and asymmetric maps while yielding similar asymptotic behavior often exhibit considerably different statistical properties for intermediate regimes providing smoother transitions that are more reminiscent to those observed in various natural phenomena we believe that the proposed approach may be useful for modeling empirical systems by preserving their keynote physical properties

predictability of critical transitions critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socioeconomic changes and climate transitions between ice ages and warm ages from bifurcation theory we can expect certain critical transitions to be preceded by a decreased recovery from external perturbations the consequences of this critical slowing down have been observed as an increase in variance and autocorrelation prior to the transition however especially in the presence of noise it is not clear whether these changes in observation variables are statistically relevant such that they could be used as indicators for critical transitions in this contribution we investigate the predictability of critical transitions in conceptual models we study the quadratic integrate and fire model and the van der pol model under the influence of external noise we focus especially on the statistical analysis of the success of predictions and the overall predictability of the system the performance of different indicator variables turns out to be dependent on the specific model under study and the conditions of accessing it furthermore we study the influence of the magnitude of transitions on the predictive performance

isogeometric analysis of free vibration of simple shaped elastic samples the paper is devoted to numerical solution of free vibration problems for elastic bodies of canonical shapes by means of a spline based finite element method fem called isogeometric analysis iga it has an advantage that the geometry is described exactly and the approximation of unknown quantities is smooth due to higher order continuous shape functions iga exhibits very convenient convergence rates and small frequency errors for higher frequency spectrum in this paper the iga strategy is used in computation of eigen frequencies of a block and cylinder as benchmark tests results are compared with the standard fem the rayleigh ritz method and available experimental data the main attention is paid to the comparison of convergence rate accuracy and time consumption of iga against fem and also to show a spline order and parameterization effects in addition the potential of iga in resonant ultrasound spectroscopy measurements of elastic properties of general anisotropy solids is discussed

a galerkin least squares finite element method for the two dimensional helmholtz equation in this paper a galerkin least squares gls finite element method in which residuals in least squares form are added to the standard galerkin variational equation is developed to solve the helmholtz equation in two dimensions an important feature of gls methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes previous work has accomplished this for the one dimensional helmholtz equation using dispersion analysis in this paper the selection of the gls mesh parameter for two dimensions is considered and leads to elements that exhibit improved phase accuracy for any given direction of wave propagation an optimal gls mesh parameter is determined using two dimensional fourier analysis in general problems the direction of wave propagation will not be known a priori in this case an optimal gls parameter is found which reduces phase error for all possible wave vector orientations over elements the optimal gls parameters are derived for both consistent and lumped mass approximations several numerical examples are given and the results compared with those obtained from the galerkin method the extension of gls to higher order quadratic interpolations is also presented

the pointwise feedback relation for linear dynamical systems abstract let and be two m input n dimensional linear dynamical systems over a commutative ring r if is feedback equivalent to then is pointwise feedback equivalent to i e for all prime ideal p of r the systems p and p are feedback equivalent over the residue field k p where p is the natural extension of to k p this paper is devoted to the study of the pointwise feedback relation we characterize when two systems and are pointwise equivalent we show that r is an absolutely flat ring if and only if the feedback relation and the pointwise feedback relation are equivalent the particular case of rings of real valued continuous functions is specially treated

rosenbrock s theorem for systems over von neumann regular rings abstract if a b is a finite system over a commutative von neumann regular ring r the problem of searching for a matrix f such that the pencil s i a b f has some prescribed smith normal form is reduced to the case where r is a field a problem which for controllable systems is described by a well known theorem of rosenbrock on pole assignment 12 and was then generalized to noncontrollable pairs 14 it this paper von neumann regular rings are characterized as the class of commutative rings for which the solution of the above problem over the ring is equivalent to its solution in each residue field

grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics summary the spatial discretisation of a continuum by the fem introduces dispersion errors to the numerical solution of stress wave propagation errors of phase and group velocities and the scatter of wave propagation are induced when these propagating phenomena are modelled by the fem the speed of a single harmonic wave depends on its frequency parasitic effects do not exist in an ideal unbounded continuum with higher order finite elements there are optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefronts in principle the dispersion errors and the spurious oscillations cannot be removed from these solutions but can be suppressed to a certain extent for reliable numerical solutions by the fem the dispersion errors should be analysed and determined the dispersion properties of a plane square biquadratic serendipity finite element are examined and compared with a bilinear one dispersion analysis is carried out for the consistent and lumped mass matrices a dispersive improved lumped mass matrix for biquadratic serendipity elements is proposed the paper closes with the recommendation of a choice of permissible dimensionless wavelengths for bilinear and biquadratic serendipity finite element meshes copyright 2013 john wiley sons ltd

improved risk estimation in multifractal records application to the value at risk in finance we suggest a risk estimation method for financial records that is based on the statistics of return intervals between events above below a certain threshold q and is particularly suited for multifractal records the method is based on the knowledge of the probability w q t ensuremath delta t that within the next ensuremath delta t units of time at least one event above q occurs if the last event occurred t time units ago we propose an analytical estimate of w q and show explicitly that the proposed method is superior to the conventional precursory pattern recognition technique widely used in signal analysis which requires considerable fine tuning and is difficult to implement we also show that the estimation of the value at risk which is a standard tool in finances can be improved considerably by the method

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

modified integration rules for reducing dispersion error in finite element methods abstract this paper describes a simple but effective technique for reducing dispersion errors in finite element solutions of time harmonic wave propagation problems the method involves a simple shift of the integration points to locations away from conventional gauss or gauss lobatto integration points for bilinear rectangular elements such a shift results in fourth order accuracy with respect to dispersion error error in wavelength as opposed to the second order accuracy resulting from conventional integration numerical experiments involving distorted meshes indicate that the method has superior performance in comparison with other dispersion reducing finite elements

the inside outside contact search algorithm for finite element analysis a new contact search algorithm inside outside algorithm for the sheet forming simulation has been developed and implemented in the dynamic explicit fe code dynamic the inside outside algorithm is derived based on the feature of the inside outside status of a nodal mesh normal vector in respect to a surface segment for the judgment of the contact of fe nodes with the tool surface this new algorithm includes local search local track and penetration calculation processes almost no additional cpu time is required for the local search process because the calculations for both global and local search are combined moreover the problems of conventional contact searching algorithms such as iterations for local search and the deadzone problem are resolved therefore the quick robust contact searching and accurate evaluation of penetration have been achieved the numerical results show that the new contact searching algorithm is more cost effective and robust than conventional ones 1997 john wiley sons ltd

feedback invariants for linear dynamical systems over a principal ideal domain abstract this paper studies the action of the feedback group f n m on m input n dimensional reachable linear dynamical systems over a principal ideal domain r for such a 2 dimensional system a complete set of invariants is given which characterizes the feedback class of in particular it is characterized in terms of these invariants when has the feedback cyclization property the particular cases r z and r r x are studied in some detail finally when n is arbitrary the feedback classification is given for the class of reachable systems f g such that g is a matrix with at least n 1 invariant factors equal to one

discrete dispersion relation for hp version finite element approximation at high wave number the dispersive properties of high order finite element schemes are analyzed in the setting of the helmholtz equation and an explicit form of the discrete dispersion relation is obtained for elements of arbitrary order it is shown that the numerical dispersion displays three different types of behavior depending on the size of the order of the method relative to the mesh size and the wave number quantitative estimates are obtained for the behavior and rates of decay of the dispersion error in the differing regimes all estimates are fully explicit and are shown to be sharp limits are obtained where transitions between the different regimes occur and used to provide guidelines for the selection of the mesh size and the polynomial order in terms of the wave number so that the dispersion error is controlled

accuracy of finite difference and finite element modeling of the scalar and elastic wave equations numerical solutions of the scalar and elastic wave equations have greatly aided geophysicists in both forward modeling and migration of seismic wave fields in complicated geologic media and they promise to be invaluable in solving the full inverse problem this paper quantitatively compares finite difference and finite element solutions of the scalar and elastic hyperbolic wave equations for the most popular implicit and explicit time domain and frequency domain techniques in addition to versatility and ease of implementation it is imperative that one choose the most cost effective solution technique for a fixed degree of accuracy to be of value a solution technique must be able to minimize 1 numerical attenuation or amplification 2 polarization errors 3 numerical anisotropy 4 errors in phase and group velocities 5 extraneous numerical parasitic modes 6 numerical diffraction and scattering and 7 errors and transmission coefficients this paper shows that in homogeneous media the

a mortar based frictional contact formulation for large deformations using lagrange multipliers abstract in this work a lagrange multiplier method is proposed to solve 2d coulomb frictional contact problems in the context of large deformations as the proposed formulation is based on the mortar method the constraints are imposed in a weak integral sense along the contact surface in order to compute the contact integrals we use a numerical integration based on the definition of the kinematical variables gap slip and their variations at the quadrature points the linearization of non linear equations virtual work and contact constraints is developed in order to apply a newton s method the examples show that the numerical integration still preserves the optimal rate of convergence of the finite element solution

dispersion corrected explicit integration of the wave equation a simple dispersion correction is introduced into the centered difference explicit time integration scheme for wave propagation problems the extra term introduces a change of the wave speed depending on local wave characteristics a rigorous theoretical analysis is provided for the scalar wave equation on a regular mesh and a notable improvement in the ability to conserve wave fronts is demonstrated by two numerical examples the correction is reinterpreted to apply to a typical finite element formulation in terms of mass and stiffness matrices resulting in a general dispersion correction of the explicit centered difference time integration algorithm for acoustic and elastic wave propagation problems

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

recurrence time analysis long term correlations and extreme events the recurrence times between extreme events have been the central point of statistical analyses in many different areas of science simultaneously the poincar e recurrence time has been extensively used to characterize nonlinear dynamical systems we compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series in particular we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function on the interval whereto the recurrences are observed and on the temporal correlations of time series in the case of long term correlations we verify the validity of the stretched exponential distribution which is uniquely defined by the exponent ensuremath gamma at the same time showing that it is restricted to the class of linear long term correlated processes simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different ensuremath gamma which shows a lack of invariance under the change of observables

pole shifting for linear systems over commutative rings abstract this paper deals with the pole shifting problem for non necessarily reachable linear systems the notion of ps ring is introduced in the same way as the notion of pole assignable ring is given for reachable systems we prove that a bcs ring is a ps ring and that over a prufer domain these properties are equivalent finally we study when the converse of the pole shifting theorem is verified

symmetry preserving algorithm for large displacement frictionless contact by the pre discretization penalty method a three dimensional contact algorithm based on the pre discretization penalty method is presented using the pre discretization formulation gives rise to contact searching performed at the surface gaussian integration points it is shown that the proposed method is consistent with the continuum formulation of the problem and allows an easy incorporation of higher order elements with midside nodes to the analysis moreover a symmetric treatment of mutually contacting surfaces is preserved even under large displacement increments the proposed algorithm utilizes the bfgs method modified for constrained non linear systems the effectiveness of quadratic isoparametric elements in contact analysis is tested in terms of numerical examples verified by analytical solutions and experimental measurements the symmetry of the algorithm is clearly manifested in the problem of impact of two elastic cylinders copyright 2004 john wiley sons ltd

spurious reflection of elastic waves due to gradually changing finite element size summary when a homogeneous elastic continuum is modelled by a non uniform finite element grid the differences in the size of adjacent finite elements can cause a spurious wave reflection which does not exist in the continuum extending previous studies in which the spurious wave reflection was investigated for the case of two uniform grids with a sudden element size change from one grid to the other the present study deals with the case when the two uniform grids of different element sizes are separated by a transition zone through which the element size varies gradually either by a geometric progression or by an arithmetic progression the solution is carried out in complex variables and numerical plots of the results are given when the ratio of wavelength to the largest element size is as low as 4 1 the spurious wave reflection is very significant while for the ratios over 10 1 it is insignificant inserting a transition zone with gradually varying element size between the two uniform parts of the grid somewhat mitigates the phenomenon of spurious reflection but this is significant only when the ratio of element sizes in the uniform grids is small less than about 1 5 1 varying the element size throughout the transition zone in an arithmetic progression seems slightly better than in a geometric progression the spurious wave reflection is less pronounced for higher order elements in particular for linear strain elements as compared to constant strain elements the spurious reflection is also less severe for consistent mass than for lumped mass

a finite deformation mortar contact formulation using a primal dual active set strategy in recent years nonconforming domain decomposition techniques and in particular the mortar method have become popular in developing new contact algorithms here we present an approach for two dimensional frictionless multibody contact based on a mortar formulation and using a primal dual active set strategy for contact constraint enforcement we consider linear and higher order quadratic interpolations throughout this work so called dual lagrange multipliers are introduced for the contact pressure but can be eliminated from the global system of equations by static condensation thus avoiding an increase in system size for this type of contact formulation we provide a full linearization of both contact forces and normal non penetration and tangential frictionless sliding contact constraints in the finite deformation frame the necessity of such a linearization in order to obtain a consistent newton scheme is demonstrated by further interpreting the active set search as a semi smooth newton method contact nonlinearity and geometrical and material nonlinearity can be resolved within one single iterative scheme this yields a robust and highly efficient algorithm for frictionless finite deformation contact problems numerical examples illustrate the efficiency of our method and the high quality of results

the influence of the mass matrix on the dispersive nature of the semi discrete second order wave equation abstract the application of discrete solution methods to the second order wave equation can yield a dispersive representation of the non dispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction of propagation in this work the dependence of the dispersive errors on the wave propagation direction mesh aspect ratio and wave number is investigated with the goal of understanding and hopefully reducing the phase and group errors associated with the two dimensional bilinear finite element an analysis of the dispersive effects associated with the consistent row sum lumped and higher order mass matrices has led to a reduced coupling penta diagonal mass matrix that yields improved phase and group errors with respect to wavelength and propagation direction the influence of row sum lumping the finite element mass matrix is demonstrated to always introduce lagging phase and group error while a linear combination of the lumped and consistent mass matrices i e a higher order mass matrix is shown to improve the dispersion characteristics of both the reduced and full integration element using a 2 5 phase error metric the higher order mass matrix can reduce the mesh resolution requirements relative to the lumped mass matrix by nearly a factor of two in one dimension a factor of 4 in two dimensions similarly the reduced coupling mass matrix can reduce the grid requirements by a factor of approximately four relative to the lumped mass matrix a factor of 16 in two dimensions although the reduced coupling mass matrix requires additional storage relative to the lumped mass the factor of 16 reduction in grid requirements promises tremendous overall savings for computing a fixed wavelength spectrum or alternatively for resolving shorter wavelengths with a fixed grid resolution

dispersion analysis of a non conforming finite element method for the helmholtz and elastodynamic equations summary we investigate the dispersive properties of a non conformingnite element method to solve the two dimensional helmholtz and elastodynamics equations the study is performed by deriving and analysing the dispersion relations and by evaluating the derived quantities such as the dimensionless phase and group velocities also the phase dierence between exact and numerical solutions is investigated the studied method which yields a linear spatial approximation is shown to be less dispersive than a conforming bilinearnite element method in the two cases shown herein moreover it almost halves the number of points per wavelength necessary to reach a given accuracy when calculating the mentioned velocities in both cases here presented copyright 2003 john wiley sons ltd

a characterization of von neumann rings in terms of linear systems abstract a new characterization of commutative von neumann regular rings is given in terms of linear control systems having locally a brunovsky canonical form the problem of enumerating reachable systems over certain von neumann regular ring is solved extending classical results over fields

variationally consistent inertia templates for b spline and nurbs based fem inertia scaling and customization abstract in this contribution variationally consistent inertia templates for b spline and nurbs based finite elements are proposed as a unified concept for two different purposes customization of the template allows construction of masses and reciprocal masses with desired properties like higher order accuracy or improved dispersion behavior inertia scaling allows substantial speed up for explicit dynamics by increased critical time steps the derivation of the template is based on a three field parametrized functional as in previous works of the authors group but with modified primary variables namely displacement velocity and mass specific linear momentum the latter allows for mass preservation for non constant density throughout the domain and is therefore an enhancement to the formulation proposed in tkachuk and bischoff 2015 with the focus on b spline and nurbs based finite elements the proposed template provides alternatives to the row sum lumped mass matrix which is only 2nd order accurate independent of the polynomial order earlier proposed algebraically constructed higher order masses from the literature can be reconstructed in the variational setting described here as special instances furthermore higher order reciprocal masses can be constructed from the template they are especially attractive for explicit dynamics as there is no extra expense per time step compared with lumped mass for linear problems for non linear problems only small overhead is expected but this paper focuses on linear problems only and mainly undistorted meshes tuning the method towards inertia scaling a reduction of the maximum eigenfrequency by 25 40 is obtained in the examples herein whereas the accuracy is higher than for lumped or consistent mass

modelling wave propagation in two dimensional structures using finite element analysis a method is described by which the dispersion relations for a two dimensional structural component can be predicted from a finite element fe model the structure is homogeneous in two dimensions but the properties might vary through the thickness this wave finite element wfe method involves post processing the mass and stiffness matrices found using conventional fe methods of a segment of the structure this is typically a 4 noded rectangular segment although other elements can be used periodicity conditions are applied to relate the nodal degrees of freedom and forces the wavenumbers real imaginary or complex and the frequencies then follow from various resulting eigenproblems the form of the eigenproblem depends on the nature of the solution sought and may be a linear quadratic polynomial or transcendental eigenproblem numerical issues are discussed examples of a thin plate an asymmetric laminated plate and a laminated foam cored sandwich panel are presented for the last two examples developing an analytical model is a formidable task at best the method is seen to give accurate predictions at very little computational cost furthermore since the element matrices are typically found using a commercial fe package the meshing capabilities and the wealth of existing element libraries can be exploited

compatible description of tool surfaces and fem meshes for analysing sheet forming operations implementation of the 3 d finite element method fem of sheet forming operations has proceeded slowly in particular describing the arbitrary tool surfaces in an accurate and smooth manner with well behaved first and second derivatives has been a major obstacle a new geometric method suitable for representing any rigid tool surface has been developed and shown to be superior to the usual schemes the new method relies on the described tool surface for position data only the spatial derivatives are obtained by considering only the sheet mesh nodal positions this new scheme has been implemented with a rigid viscoplastic fem program using general surface descriptions based on b splines and linear inter polation analytic representations of a hemispherical and rounded square punch were also compared the comparisons show that the proposed method offers several advantages over other general formulations 1 the new representation is the proper one for formulating the equilibrium condition alternate forms can produce spurious results 2 the proposed method introduces inherently smooth surface derivatives that improve numerical stability even with crude surface resolution suitable test problems show covergence with the new method far past the divergence points of the simulations using the standard general surface description 3 the method is reasonably efficient with a time penalty of approximately 30 50 per cent unoptimized with respect to analytic surface descriptions

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

predictability of extreme events in a nonlinear stochastic dynamical model the objective of this work is to evaluate the potential of reduced order models to reproduce the extreme event and predictability characteristics of higher dimensional dynamical systems a nonlinear toy model is used which contains key features of comprehensive climate models first we demonstrate that the systematic stochastic mode reduction strategy leads to a reduced order model with the same extreme value characteristics as the full dynamical models for a wide range of time scale separations second we find that extreme events in this model follow a generalized pareto distribution with a negative shape parameter thus extreme events are bounded in this model third we show that a precursor approach has good forecast skill for extreme events we then find that the reduced stochastic models capture the predictive skill of extreme events of the full dynamical models well consistent with previous studies we also find that the larger the extreme events the better predictable they are our results suggest that systematically derived reduced order models have the potential to be used for the modeling and statistical prediction of weather and climate related extreme events and possibly in other areas of science and engineering too

a fourier analysis of spurious mechanisms and locking in the finite element method a fourier analysis technique is used to examine spurious mechanisms and the element locking phenomena engendered by different finite element discretizations it is shown that these phenomena can be identified by examining the uncoupled discrete fourier operators and corresponding characteristic equations and are caused in terms of discrete filter concepts by either a spurious mode carrier or by violating the unlocking condition specified in the paper the analysis is performed for two simple problems wave propagation in a bar and vibration of a timoshenko beam which when discretized by linear shape functions succinctly manifest the two phenomena as being directly traceable to specific components of the finite element discretizations

a dual mortar approach for 3d finite deformation contact with consistent linearization in this paper an approach for three dimensional frictionless contact based on a dual mortar formulation and using a primal dual active set strategy for direct constraint enforcement is presented we focus on linear shape functions but briefly address higher order interpolation as well the study builds on previous work by the authors for two dimensional problems first and foremost the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi smooth newton method are extended to the 3d case this allows for solving all types of nonlinearities i e geometrical material and contact within one single newton scheme owing to the dual lagrange multiplier approach employed this advantage is not accompanied by an undesirable increase in system size as the lagrange multipliers can be condensed from the global system of equations moreover it is pointed out that the presented method does not make use of any regularization of contact constraints numerical examples illustrate the efficiency of our method and the high quality of results in 3d finite deformation contact analysis

dynamic feedback over principal ideal domains and quotient rings let r be a principal ideal domain in this paper we prove that for a large class of linear systems dynamic feedback over r is equivalent to static feedback over a quotient ring of r in particular when r is the ring of integers z one has that the static feedback classification problem over finite rings is equivalent to the dynamic feedback classification problem over z restricted to a special type of system

feedback classification of linear systems over von neumann regular rings abstract it is proved that feedback classification of a linear system over a commutative von neumann regular ring r can be reduced to the classification of a finite family of systems each of which is properly split into a reachable and a non reachable part where the reachable part is in a brunovski type canonical form while the non reachable part can only be altered by similarity if a canonical form is known for similarity of matrices over r then it can be used to construct a canonical form for feedback equivalence an explicit algorithm is given to obtain the canonical form in a computable context together with an example over a finite ring

brunovsky s canonical form for linear dynamical systems over commutative rings abstract this paper is devoted to studying the action of the feedback group on linear dynamical systems over a commutative ring r with unit we characterize the class of m input n dimensional reachable linear dynamical systems f g over r that are feedback equivalent to a system c fc gc with brunovsky s canonical form this characterization is obtained in terms of the minors of the matrices g i g fg f i 1 g for 1 i n

dispersion of elastic waves in the contact impact problem of a long cylinder numerical dispersion of two dimensional finite elements was studied the outcome of the dispersion study was verified by the numerical and analytical solutions to the longitudinal impact of two long cylindrical bars in accordance with the results of the dispersion analysis it was demonstrated that the quadratic elements showed better accuracy than the linear ones

a constrained optimization methodology for the detection phase in contact mechanics simulations the detection phase in computational contact mechanics can be subdivided into a global search and a local detection when potential contact is detected by the former a rigorous local detection determines which surface elements come or may come in contact in the current increment we first introduce a rigorous definition of the closest point for non differentiable lower dimensional manifolds we then simplify the detection by formulating an optimization problem subject to inequality constraints the formulation is then solved using different techniques from the field of mathematical optimization for both linear and quadratic finite element meshes the resulting general and robust detection scheme is tested on a set of problems and compared with other techniques commonly used in computational geometry

effects of spatial discretization on dispersion and spurious oscillations in elastic wave propagation the dispersive and spurious oscillation properties of one dimensional uniform finite element meshes are investigated using the information provided by the frequency response functions of the finite element meshes the modal superposition method in which the effects of temporal discretization are eliminated is employed to integrate the discretized equations of motion

on higher order linear systems reachability and feedback invariants we consider l order linear control systems with coefficients in a commutative ring r the notion of reachability is studied for such systems and it is related to the reachability of the associated linearized system lin we prove that reachability is a pointwise property just as in the case of first order systems the feedback equivalence of l order linear control systems over a commutative ring is also studied we introduce some feedback invariants that generalize the hermida perez sanchezgiralda invariant modules mi to conclude we apply results in order to give classification results in low dimension