a probabilistic collocation eulerian lagrangian localized adjoint method on sparse grids for assessing co2 leakage through wells in randomly heterogeneous porous media abstract we develop a probabilistic collocation eulerian lagrangian localized adjoint method on sparse grids for assessing co2 leakage through wells in randomly heterogeneous porous media by utilizing the intrinsic mathematical numerical and physical properties of the mathematical model we model the process in which co2 is injected into a deep aquifer spreads within the aquifer and upon reaching a leaky well rises up to a shallower aquifer to quantify the leakage rate which depends on the pressure build up in the aquifer due to injection and the buoyancy of co2 the underlying eulerian lagrangian framework has high potential to improve the efficiency and accuracy for the numerical simulation of complex flow and transport processes in co2 sequestration the sparse grid probabilistic collocation framework adds computationally efficient uncertainty quantification functionality onto pre existing eulerian lagrangian methods in a nonintrusive manner it also provides a scalable framework to consider uncertainty in a straightforward parallel manner preliminary numerical experiments show the feasibility and potential of the method

an optimal order error estimate for the mass conservative characteristic finite element scheme abstract the mass conservative characteristic mcc finite element scheme preserves the mass balance which is an important property in the numerical simulation of the convection diffusion problems in this paper an optimal order error estimate is obtained for the model problem in one space dimension the convergence rate is o h 2 t in the l l 2 norm for the linear finite element some numerical examples are given to confirm the conclusion

an unsplit higher order godunov method for scalar conservation laws in multiple dimensions abstract in this paper we develop an unsplit higher order godunov method for scalar conservation laws in two dimensions the method represents an extension for the special case being considered of methods developed by colella and by van leer in our method we begin with a piecewise bilinear representation of the solution on each grid cell a new piecewise bilinear representation at the next time level is then obtained from a two step procedure in the first step a conservative predictor corrector scheme derived from the integral form of the differential equation and characteristic considerations is used to obtain average values of the solution over grid cells at the new time level next these new average values are then used to construct a limited piecewise bilinear profile for each cell at the new time level the resulting method is shown to satisfy a maximum principle for constant coefficient linear advection computational results are presented comparing the new method to colella s method for linear advection the method is also applied to two model problems from porous media flow miscible and immiscible displacement the new scheme provides accurate resolution of sharp fronts without any significant distortion

time stepping along characteristics with incomplete iteration for a galerkin approximation of miscible displacement in porous media miscible displacement of one incompressible fluid by another in a porous medium is modeled by a nonlinear coupled system of two partial differential equations the pressure equation is elliptic while the concentration equation is parabolic but normally convection dominated a sequential backward difference time stepping scheme is defined it approximates the pressure by a standard galerkin procedure and the concentration by a combination of a galerkin method and the method of characteristics optimal convergence rates in l 2 and h 1 are demonstrated for this scheme and for a modified version in which the algebraic equations at each time step are solved approximately by a limited number of preconditioned conjugate gradient iterations time stepping along the characteristics of the hyperbolic part of the concentration equation is shown to result in smaller time truncation errors than those of standard methods numerical results published elsewhere have confirmed that larger time steps are appropriate

a new formula for the analytical solution of the radial dispersion problem a new formula is presented for the analytical solution of the radial dispersion problem which analyzes the dispersive transport of a tracer in radial flow from a recharge well this formula is simpler than a solution presented by previous investigators but the two solutions are shown to be equivalent because the analytical solution consists of an integral of an oscillatory function it is evaluated as an alternating series the terms of which are the integrals over successive half cycles of the integrand an efficient algorithm is used to accelerate convergence of the series the accuracies of previous solutions obtained by finite difference numerical laplace transform and perturbation methods are examined by comparison with the analytical solution numerical values of the solution are tabulated for readers interested in checking the accuracies of solute transport codes

identification of non linear systems using multi scale ridges and skeletons of the wavelet transform abstract a new procedure of non linear system identification is presented the procedure employs the slowly varying time dependent amplitude and phase functions of the impulse response of the system these instantaneous characteristics are obtained from the ridges and skeletons of the wavelet transform the ridge extraction procedure uses the modulus of the transform and involves a combinatorial optimization algorithm based on simulated annealing the method is illustrated using two simple simulated examples it is shown that the procedure can be used for multi degree of freedom systems due to the frequency localization property of the continuous grossman morlet wavelets

damage size estimation by the continuous wavelet ridge analysis of dispersive bending waves in a beam the damage assessment in a structure consists of the estimation of its location and extent the objective of this work is to assess the damage size using the ratio of the incident wave toward and the reflected wave from the damage since waves to be analyzed are of the bending type the measured signals are highly dispersive it is almost impossible to estimate the magnitude ratio alone in the time domain so we propose to use the continuous wavelet transform of the measured signal and perform the ridge analysis in order to extract accurately the magnitudes of the incident and the reflected waves for a range of frequencies of interest from the measured wave signal wave experiments are conduced in a slender cylindrical beam and the magnetostrictive sensors are used to capture the bending waves in the beam to correlate the magnitude ratio with the damage size we employ the timoshenko beam theory several experiments are conducted to check the effectiveness of the proposed wavelet based method

ridges reconstruction based on inverse wavelet transform ridges always carry important physical information in practice ridge reconstruction based on inverse wavelet transform is studied in this article it is emphasized that the points within the neighbor area have to be added in the reconstruction to avoid energy lost however no discussion has been proposed about how to choose the neighbor area up to now although it is the key to achieve good performance a formula is given in this article to calculate the width of the neighbor area which varies with scale and the signal itself some examples are given in this article to show the performance of the proposed method which manifests that the method works very well for signals with multiple components as long as there is no cross section between them it also works well when the signal to noise ratio is not very low

convergence of a fully conservative volume corrected characteristic method for transport problems we consider the convergence of a volume corrected characteristics mixed method vccmm for advection diffusion systems it is known that without volume correction the method is first order convergent provided there is a nondegenerate diffusion term we consider the advective part of the system and give some properties of the weak solution with these properties we prove that the volume corrected method with no diffusion term gives a lower order l 1 convergence rate of mathcal o h sqrt delta t h delta t r where r is related to the accuracy of the characteristic tracing this result compares favorably to godunov s method but avoids the cfl constraint so large time steps can be taken in practice in fact godunov s method converges at mathcal o h 1 2 which is our result for delta t ch where now c is not limited however the optimal choice delta t ch 2 2r 1 gives a better rate mathcal o h 2r 2r 1 than godunov s method e g mathcal o h 2 3 if r 1 with a nondegenerate diffusion term we obtain an l 2 error estimate for the problem we also prove the existence of and give an error estimate for a perturbed velocity field for which the volume is locally conserved finally some convergence tests are given to verify the optimal convergence rate for r 1

hilbert transform and its engineering applications the hilbert transform is useful in calculating instantaneous attributes of a time series especially the envelope amplitude and instantaneous frequency the instantaneous envelope is the amplitude of the complex hilbert transform the instantaneous frequency is the time rate of change of the instantaneous phase angle these properties can be applied to identify dynamic characteristics of a linear as well as a nonlinear system however the conventional discrete hilbert transform which is based on fast fourier transform and inverse fourier transform has shown the lack of accuracy for time derivative calculations in this paper we first introduce the hilbert transform and its applications to the nonlinear system parameter identification then we address the practical issues in applying the hilbert transform to engineering applications to increase the accuracy of the envelope detection we propose a hilbert transform technique based on local maxima interpolation analyses and simulations are carried out to demonstrate the advantages of the proposed technique finally we employ the proposed local maxima interpolation technique in identifying the nonlinear dynamic characteristics of industrial examples

numerical analysis of a second order pure lagrange galerkin method for convection diffusion problems part ii fully discretized scheme and numerical results we analyze a second order pure lagrange galerkin method for variable coefficient convection diffusion possibly degenerate diffusion equations with mixed dirichlet robin boundary conditions in a previous paper the proposed second order pure lagrangian time discretization scheme was introduced and analyzed for the same problem more precisely the l infty h 1 stability and l infty h 1 error estimates of order o delta t 2 had been obtained moreover for the particular case of incompressible flows stability inequalities with constants independent of the final time have been stated in the present paper l infty h 1 error estimates of order o delta t 2 o h k are obtained for the fully discretized pure lagrange galerkin method to prove these results we use some properties obtained in the previous paper finally numerical tests are presented that confirm the theoretical results

mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences we present an expanded mixed finite element approximation of second order elliptic problems containing a tensor coefficient the mixed method is expanded in the sense that three variables are explicitly approximated namely the scalar unknown the negative of its gradient and its flux the tensor coefficient times the negative gradient the resulting linear system is a saddle point problem in the case of the lowest order raviart thomas elements on rectangular parallelepipeds we approximate this expanded mixed method by incorporating certain quadrature rules this enables us to write the system as a simple cell centered finite difference method requiring the solution of a sparse positive semidefinite linear system for the scalar unknown for a general tensor coefficient the sparsity pattern for the scalar unknown is a 9 point stencil in two dimensions and 19 points in three dimensions existing theory shows that the expanded mixed method gives optimal order approximations in the l 2 and h s norms and superconvergence is obtained between the l 2 projection of the scalar variable and its approximation we show that these rates of convergence are retained for the finite difference method if h denotes the maximal mesh spacing then the optimal rate is o h the superconvergence rate o h 2 is obtained for the scalar unknown and rate o h 3 2 for its gradient and flux in certain discrete norms moreover the full o h 2 is obtained in the strict interior of the domain computational results illustrate these theoretical results

identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform we consider the free response of a nonlinear vibrating system using the ridges and skeletons of the continuous wavelet transform we identify weak nonlinearities on damping and stiffness and estimate their physical parameters the crucial choice of the son wavelet function is obtained using an optimization technique based on the entropy of the continuous wavelet transform the method is applied to simulated single degree of freedom systems and multi degree of freedom systems with nonlinearities on damping and stiffness experimental validation of the nonlinear identification and parameter estimation method is presented the experimental system is a clamped beam with nonlinearities on damping and stiffness and these nonlinearities are identified and quantified from a displacement sensor

a fully mass and volume conserving implementation of a characteristic method for transport problems the characteristics mixed method considers the transport not of a single point or fluid particle but rather the mass in an entire region of fluid this mass is transported along the characteristic curves of the hyperbolic part of the transport equation and the scheme thereby produces very little numerical dispersion conserves mass locally and can use long time steps however since the shape of a characteristic trace back region must be approximated in numerical implementation its volume may be incorrect resulting in inaccurate concentration densities and further inaccurate reaction dynamics we present a simple modification to the characteristics mixed method that conserves both mass and volume of the transported fluid regions our algorithm also handles boundary conditions through a space time change of variables in the trace back routines which allows the boundary to be treated as if it were interior to the domain nearly point sources such as wells present special difficulties since characteristic trace back curves converge in their vicinity we also present techniques that allow one to conservatively implement wells the techniques are illustrated in five numerical examples

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

godunov mixed methods for advection diffusion equations in multidimensions time split methods for multidimensional advection diffusion equations are considered in these methods advection is approximated by a godunov type procedure and diffusion is approximated by a low

good invariants for bad ideals abstract we generalize the notion of the segre class of ideals defined by murthy and obtain various analogous results using the theory of the euler class groups

dynamic testing of nonlinear vibrating structures using nonlinear normal modes modal testing and analysis is well established for linear systems the objective of this paper is to progress toward a practical experimental modal analysis ema methodology of nonlinear mechanical structures in this context nonlinear normal modes nnms offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena yet they have a clear and simple conceptual relation to the classical linear normal modes lnms a nonlinear extension of force appropriation techniques is developed in this study in order to isolate one single nnm during the experiments with the help of time frequency analysis the energy dependence of nnm modal curves and their frequencies of oscillation are then extracted from the time series the proposed methodology is demonstrated using two numerical benchmarks a two degree of freedom system and a planar cantilever beam with a cubic spring at its free end

a finite element semi lagrangian method with l2 interpolation summary high order accurate methods for convection dominated problems have the potential to reduce the computational effort required for a given order of solution accuracy the state of the art in this field is more advanced for eulerian methods than for semi lagrangian slag methods in this paper we introduce a new slag method that is based on combining the modified method of characteristics with a high order interpolating procedure the method employs the finite element method on triangular meshes for the spatial discretization an l2 interpolation procedure is developed by tracking the feet of the characteristic lines from the integration nodes numerical results are illustrated for a linear advection diffusion equation with known analytical solution and for the viscous burgers equation the computed results support our expectations for a robust and highly accurate finite element slag method copyright 2012 john wiley sons ltd

a mass conservative characteristic fe scheme for optimal control problems governed by convection diffusion equations abstract in this paper we develop a mass conservative characteristic finite element scheme for optimal control problems governed by linear singularly perturbed convection diffusion equations we discuss the case that the velocity fields are non divergence free the space discretization of the state variable is done by piecewise linear continuous functions whereas the control variable is approximated by piecewise constant functions due to the limitation of the regularity the scheme preserves the mass balance for the original state equation we derive a priori error estimates for both the control and state approximations some numerical examples are presented to show the efficiency of the proposed scheme

conservative multimoment transport along characteristics for discontinuous galerkin methods a set of algorithms based on characteristic discontinuous galerkin methods is presented for tracer transport on the sphere the algorithms are designed to reduce message passing interface communica

a fully conservative eulerian lagrangian method for a convection diffusion problem in a solenoidal field tracer transport is governed by a convection diffusion problem modeling mass conservation of both tracer and ambient fluids numerical methods should be fully conservative enforcing both conservation principles on the discrete level locally conservative characteristics methods conserve the mass of tracer but may not conserve the mass of the ambient fluid in a recent paper by the authors t arbogast c huang a fully mass and volume conserving implementation of a characteristic method for transport problems siam j sci comput 28 2006 2001 2022 a fully conservative characteristic method the volume corrected characteristics mixed method vccmm was introduced for potential flows here we extend and apply the method to problems with a solenoidal i e divergence free flow field the modification is a computationally inexpensive simplification of the original vccmm requiring a simple adjustment of trace back regions in an element by element traversal of the domain our numerical results show that the method works well in practice is less numerically diffuse than uncorrected characteristic methods and can use up to at least about eight times the cfl limited time step

continuous wavelet transform for modal identification using free decay response abstract this paper deals with the use of the continuous wavelet transform for system identification purposes the wavelet analysis of the free responses of a linear mechanical system allows the estimation of its natural frequencies viscous damping ratios and mode shapes using either the modulus or the phase of the wavelet transform a complete procedure for modal identification from free responses based on the continuous wavelet transform is presented two difficulties during the implementation of this technique are highlighted the edge effect and the choice of the time frequency localization of the wavelet transform some upper and lower bounds for the mother wavelet s parameters are given in order to improve the numerical computation three complex valued mother wavelets are studied and the full procedure is applied to a damped discrete system the correct choice of the mother wavelet s parameters leads to an accurate identification of the modal parameters

uniform error analysis for lagrange galerkin approximations of convection dominated problems in this paper we present a rigorous error analysis for the lagrange galerkin method applied to convection dominated diffusion problems we prove new error estimates in which the constants depend on norms of the data and not of the solution and do not tend to infinity in the hyperbolic limit this is in contrast to other results in this field for the time discretization uniform convergence with respect to the diffusion parameter of order o k tn is shown for initial values in l2 and o k for initial values in h2 for the spatial discretization with linear finite elements we verify uniform convergence of order o h2 min h h2 k for data in h2 by interpolation of banach spaces suboptimal convergence rates are derived under less restrictive assumptions the analysis is heavily based on a priori estimates uniform in the diffusion parameter for the solution of the continuous and the semidiscrete problem they are derived in a lagrangian framework by transforming the eulerian coordinates completely into subcharacteristic coordinates finally we illustrate the error estimates by some numerical results

the modified method of characteristics with adjusted advection the mmoc procedure for approximating the solutions of transport dominated diffusion problems does not automatically preserve integral conservation laws leading to mass balance errors in many kinds of flow problems the variant called the mmocaa discussed herein preserves the conservation law at a minor additional computational cost it is shown that its solution in either galerkin or finite difference form converges at the same rates as were proved earlier by dougl as and russell for the standard mmoc procedure

highly accurate lagrangian flux calculation via algebraic quadratures on spline approximated donating regions abstract lagrangian flux through a fixed curve segment within a time interval t n t n k can be formulated as an integral at the initial time t n over a compact point set called donating region in which each particle will pass through the curve during the time interval and contribute to the flux based an explicit constructive and analytical solution of the donating region the author proposes algorithms of lagrangian flux calculation lfc as algebraic quadratures over the spline approximated donating regions this generic formulation yields high accuracies up to the 8th order both in time and space as another benefit lfc leads to a conservative semi lagrangian method whose time step size is free of the eulerian stability constraint c r 1 the high accuracy and robustness of the proposed lfc algorithms are demonstrated by various numerical tests with courant numbers ranging from 1 to 10 000 and with accuracies from the 2nd order to the 8th order lfc might also be useful in designing hybrid eulerian methods for complex geometries

solution of nonlinear convection diffusion problems by a conservative galerkin characteristics method we consider a scheme for nonlinear degenerate convection dominant diffusion problems that arise in contaminant transport in porous media with equilibrium adsorption isotherm this scheme is based on a regularization relaxation scheme that has been introduced by jager and kacur numer math 60 407 427 1991 m2an math model numer anal 29 n5 605 627 1995 with a type of numerical integration by bermejo siam j numer anal 32 425 455 1995 to the modified method of characteristics with adjusted advection mmocaa that was recently developed by douglas et al numer math 83 3 353 369 1999 comput geosci 1 155 190 1997 we present another variant of adjusting advection method the convergence of the scheme is proved an error estimate of the approximated scheme is derived computational experiments are carried out to illustrate the capability of the scheme to conserve the mass

optimization based mesh correction with volume and convexity constraints we consider the problem of finding a mesh such that 1 it is the closest with respect to a suitable metric to a given source mesh having the same connectivity and 2 the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh this volume correction problem arises in important simulation contexts such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi lagrangian transport schemes in this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective while the prescribed cell volumes mesh validity and or cell convexity specify the constraints we solve this problem numerically using a sequential quadratic programming sqp method whose performance scales with the mesh size to achieve scalable performance we develop a specialized multigrid based preconditioner for optimality systems that arise in the application of the sqp method to the volume correction problem numerical examples illustrate the importance of volume correction and showcase the accuracy robustness and scalability of our approach

analytical and variational numerical methods for unstable miscible displacement flows in porous media the miscible displacement of one fluid by another in a porous medium has received considerable attention in sub surface environmental and petroleum engineering applications when a fluid of higher mobility displaces another of lower mobility unstable patterns referred to as viscous fingering may arise their physical and mathematical study has been the object of numerous investigations over the past century the objective of this paper is to present a review of these contributions with particular emphasis on variational methods these algorithms are tailored to real field applications thanks to their advanced features handling of general complex geometries robustness in the presence of rough tensor coefficients low sensitivity to mesh orientation in advection dominated scenarios and provable convergence with fully unstructured grids this paper is dedicated to the memory of dr jim douglas jr for his seminal contributions to miscible displacement and variational numerical methods

a method for detecting damage induced nonlinearities in structures using information theory abstract in this work a new approach is presented for detecting the presence of damage induced nonlinearities in structures from measurements of structural dynamics two different information theoretic it measures the time delayed mutual information and the time delayed transfer entropy are used to provide a probabilistic measure of the coupling between structural components these measures may be used to capture both linear and nonlinear relationships among time series data the formula for both quantities is derived for a linear five degree of freedom system subject to gaussian excitation an algorithm is then described for computing the it metrics from time series data and results are shown to agree with theory we then show that as the coupling between the structure s components changes from linear to nonlinear the information flow can be used to indicate the degree of nonlinearity deviations from a linear model are quantified statistically by generating surrogate data sets that by construction possess only linear second order correlations we then apply the proposed algorithms to both the original data and the surrogates differences in the results are shown to be proportional to the degree of nonlinearity this result is shown to be independent of global changes in stiffness and is therefore unaffected by certain models of environmental variability furthermore the method provides an absolute measure of nonlinearity and therefore does not require a baseline data set for making comparisons this approach is discussed in the context of structural health monitoring where damage is often associated with structural nonlinearity

a characteristics mixed finite element method for advection dominated transport problems we define a new finite element method called the characteristics mixed method for approximating the solution to an advection dominated transport problem the method is based on a space time variational form of the advection diffusion equation our test functions are piecewise constant in space and in time they approximately follow the characteristics of the advective i e hyperbolic part of the equation thus the scheme uses a characteristic approximation to handle advection in time this is combined with a low order mixed finite element spatial approximation of the equation boundary conditions are incorporated in a natural and mass conservative fashion the scheme is completely locally conservative in fact on the discrete level fluid is transported along the approximate characteristics a postprocessing step is included in the scheme in which the approximation to the scalar unknown is improved by utilizing the approximate vector flux this has the effect of improving the rate of convergence of

identification of coupled non linear modes from free vibration using time frequency representations abstract a new method based on time frequency representations is presented for identifying the non linear modal parameters of a multi degree of freedom non linear lightly damped mechanical system the coupled non linear modes are first introduced it is shown that by using the coupled non linear modes the free response can be expressed as a linear combination of frequency and amplitude modulated components this suggests the use of time frequency methods to characterize these modulation laws and then identify the coupled non linear modes these modulation laws are extracted by using an extended definition of the so called ridges of the continuous gabor transform which enables a more accurate estimation an identification procedure of the coupled non linear modes is proposed and the validity of the whole process is confirmed by performing computer simulations of different types of non linear elastic dynamic systems

mixed methods using standard conforming finite elements abstract we investigate the mixed finite element method mfem for solving a second order elliptic problem with a lowest order term as might arise in the simulation of single phase flow in porous media we find that traditional mixed finite element spaces are not necessary when a positive lowest order i e reaction term is present hence we propose to use standard conforming finite elements q k q k d on rectangles or p k p k d on simplices to solve for both the pressure and velocity field in d dimensions the price we pay is that we have only sub optimal order error estimates with a delicate superconvergence analysis we find some improvement for the simplest pair q k q k d with any k 1 or for p 1 p 1 d when the mesh is uniform and the solution has one extra order of regularity we also prove similar results for both parabolic and second order hyperbolic problems numerical results using q 1 q 1 2 and p 1 p 1 2 are presented in support of our analysis these observations allow us to simplify the implementation of the mfem especially for higher order approximations as might arise in an hp adaptive procedure

numerical simulations for the chemotaxis models on surfaces via a novel characteristic finite element method abstract in this paper the chemotaxis partial differential equations models which describe the movement by one community in reaction to one chemical or biological signal are given and solved numerically on surfaces the models and the numerical method concerned are in terms of a generic form of chemotaxis models we develop a new semi implicit finite element scheme based on the gradient and laplacian recoveries to linearize the equations meanwhile we modify the proposed semi implicit scheme as a characteristic form and present a novel strategy for the discretization of characteristic derivative on surface the lumped mass modification is employed for positivity preservation and the related analysis results are provided we investigate the accuracy and convergence of the proposed method by numerical tests and the simulations of blowing up solution pattern formulations and aggregations of bacteria demonstrate the applicability of the proposed methods

convergence analysis of a family of ellam schemes for a fully coupled model of miscible displacement in porous media we analyse the convergence of numerical schemes in the gdm ellam gradient discretisation method eulerian lagrangian localised adjoint method framework for a strongly coupled elliptic parabolic pde which models miscible displacement in porous media these schemes include but are not limited to mixed finite element ellam and hybrid mimetic mixed ellam schemes a complete convergence analysis is presented on the coupled model using only weak regularity assumptions on the solution which are satisfied in practical applications and not relying on l infty bounds which are impossible to ensure at the discrete level given the anisotropic diffusion tensors and the general grids used in applications

system identification in frequency domain using wavelets conceptual remarks abstract model identification plays a central role in any activity associated with process operations with control being done on different levels different models are required for the same plant each for a different range of dynamics besides that most identification methods apply to the linear models they also do not allow for selecting a frequency range wavelet based methods have the intrinsic ability to select time and frequency windows and to some extent are also applicable to non linear processes the paper presents an approach in which the wavelet transform is employed for system identification enabling the selection of the particular frequency range of interest we will show the use of some wavelet filters with a property of superior selectivity in the frequency domain and having compact support in the time domain which in turn influences an accurate implementation these properties provide us with a possibility of the measured data analysis in the frequency domain without any loss of information selection of a proper filter allows us to identify the system on a desired frequency range or to identify a number of systems for distinct frequency ranges this is specifically convenient for the systems with dominant modes such as singularly perturbed systems the possibility of selection of the specific frequency range can be utilized for application based identification such as control when only a limited frequency range is required we conclude with a case study where the proposed algorithms are tested and results are presented

a characteristics mixed covolume method for a convection dominated transport problem in this paper we propose a characteristics mixed covolume method for approximating the solution to a convection dominated transport problem the method is a combination of characteristic approximation to handle the convection term in time and mixed covolume method spatial approximation to deal with the diffusion term the velocity and press are approximated by the lowest order raviart thomas mixed finite element space on rectangles the projection of a mixed covolume element is introduced we prove its first order optimal rate of convergence for the approximate velocities in the l 2 norm as well as for the approximate pressures in the l 2 norm

addition and subtraction of ideals abstract letabe a noetherian ring andibe comaximal ideals ofa andpbe a projectivea module addition refers to being given a surjectionp and producing a surjectionp i this is useful for example whenpis free to determine how many elements it takes to generate the ideal i subtraction refers to being givenp iand producing somep a major use of this is when a to show a projective module has a unimodular element here we extend certain addition and subtraction results of r sridharan 1995 j algebra176 947 958 and s mandal and r sridharan 1996 j math kyoto univ 36 no 3 453 470 in both addition and subtraction we weaken the hypotheses imposed on and in a suitable fashion remove the hypothesis thatpmust have trivial determinant with certain restrictions we also now allow dim a i 1 rather than ht i dim a whenais an affine algebra over a fieldf mandal and sridharan had subtraction results for wheniis the intersection of finitely many maximal ideals whose residue fields are quadratically closed when i has this form if char f 2 or wheniis the maximal ideal of anf rational point in our generalization we allowito be the intersection of finitely many maximal ideals all of whose residue fields are quadratically closed except possibly one which instead defines anf rational point when char f 2 we only need to require i to have this form in particular we can subtract an ideal whose radical is the maximal ideal of anf rational point this has been used by s m bhatwadekar and r sridharan 1998 invent math 133 no 1 161 192 to construct a certain local complete intersection ideal which is not a complete intersection ideal

stability monotonicity maximum and minimum principles and implementation of the volume corrected characteristic method we consider the volume corrected characteristics mixed method vccmm for tracer transport problems the volume correction adjustment maintains the local volume conservation of bulk fluids and the numerical convergence of the method we discuss some details of implementation by considering the scheme from an algebraic point of view we show that the volume correction adjustment is important for stability and necessary for the monotonicity and the maximum and minimum principles of the method we also derive a relatively weaker stability property for the uncorrected characteristic mixed method cmm some numerical experiments of a quarter five spot pattern of wells are given to verify our theoretical results and compare the concentration errors of vccmm and cmm due to random perturbations set up in the computation of the algorithm more numerical tests including one related to long time nuclear waste storage are given to compare vccmm with cmm and godunov s method showing that vccmm exhibits no overshoots or undershoots and less numerical diffusion

spatial filter averaging approach of probabilistic method to linear second order partial differential equations of the parabolic type a backward in time probabilistic method with spatial filter averaging is presented to solve linear second order partial differential equations of the parabolic type an advantage of this methodology is that while forward methods are subject to region with loss of density of particles and hence loss of spatial resolution of the solution the solution given by backward methods is given on any desired grid however traditional backward time probabilistic method using monte carlo averaging are computationally expensive we prove a convergence result and present several examples the method leads to important improvement in computational efficiency and is expected to perform well to solve high dimensional problems where a solution is needed on a large grid

mathbb p 1 p 1 gluing for local complete intersections we prove an analogue of the affine horrocks theorem for local complete intersection ideals of height n in r t where r is a regular domain of dimension d which is essentially of finite type over an infinite perfect field of characteristic unequal to 2 and 2n ge d 3

a two grid mmoc finite element method for nonlinear variable order time fractional mobile immobile advection diffusion equations abstract a fully discrete two grid modified method of characteristics mmoc scheme is proposed for nonlinear variable order time fractional advection diffusion equations in two space dimensions the mmoc is used to handle the advection dominated transport and the two grid method is designed for efficiently solving the resulting nonlinear system optimal l 2 error estimates are derived for both the mmoc scheme and the corresponding two grid mmoc scheme numerical experiments are presented to demonstrate the accuracy and the efficiency of the proposed method

an approach to parameter identification for a single degree of freedom dynamical system based on short free acceleration response an approach to parameter identification for the single degree of freedom s d o f system is presented it fits into the group of parametric system identification methods that use a structured mathematical model it uses the free acceleration response of the system in order to estimate the parameters of the equation of motion for the model under consideration the approach has been numerically tested on duffing s oscillator with dry friction at different sampling rates of the acceleration time history and at different signal to noise ratios snr the experiment has been carried out on an experimental device with the features of duffing s oscillator the validity and advantages of the approach are presented the results show that this approach offers parameter identification with good quality for short time series using only a modest number of data points for a wide range of s d o f systems

the mmoc and mmocaa schemes for the finite volume element method of convection diffusion problems we present and analyze the modified method of characteristics mmoc and the modified method of characteristics with adjusted advection mmocaa for the finite volume element fve method of convection diffusion problems these two schemes maintain the advantages of both the mmoc and the fve method and the mmocaa scheme discussed herein conserves the conservation law globally at a minor additional computational cost optimal order error estimates in the h 1 norm are proved for these schemes a numerical example is presented to confirm the estimates

the euler class group of a polynomial algebra in this paper we continue our study on the theory of the euler class group of a polynomial algebra a t where a is a commutative noetherian ring containing q of dimension n for such a ring a in 9 we defined the notion of the nth euler class group en a t of a t for simplicity let us call it e a t in 9 we also studied the relations between e a t and e a where e a is the nth euler class group of a for example there is canonical map e a e a t which is an injective group homomorphism and it is an isomorphism when a is a smooth affine domain 9 proposition 5 7 in general these two groups are not isomorphic see discussion preceding 9 proposition 5 7 in this context the following question is natural