testing and modeling multivariate threshold models abstract threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years in this article i use predictive residuals to construct a test statistic for detecting threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model the thresholds and the model are selected jointly based on the akaike information criterion the finite sample performance of the proposed test is studied by simulation the modeling procedure is then used to study arbitrage in security markets and results in a threshold cointegration between logarithms of future contracts and spot prices of a security after adjusting for the cost of carrying the contracts in this particular application thresholds are determined in part by the transaction costs i also apply the proposed procedure to u s monthly interest rates and two river flow series of iceland

a mass redistributed finite element method mr fem for acoustic problems using triangular mesh the accuracy of numerical results using standard finite element method fem in acoustic problems will deteriorate with increasing frequency due to the dispersion error such dispersion error depends on the balance between the stiffness and mass of discretization equation systems this paper reports an improved finite element method fem for solving acoustic problems by re distributing the mass in the mass matrix to tune the balance aiming to minimize the dispersion errors this is done by shifting the integration point locations when computing the entries of the mass matrix while ensuring the mass conservation the new method is verified through the detailed numerical error analysis and a strategy is also proposed for the best mass redistribution in terms of minimizing dispersion error the relative dispersion error of present mass redistributed finite element method mr fem is found to be much smaller than the fem solution in both theoretical prediction and numerical examination the present mr fem works well by using the linear triangular elements that can be generated automatically which enables automation in computation and saving computational cost in mesh generation numerical examples demonstrate the advantages of mr fem in comparison with the standard fem using the same triangular meshes and quadrilateral meshes

a novel multigrid based preconditioner for heterogeneous helmholtz problems an iterative solution method in the form of a preconditioner for a krylov subspace method is presented for the helmholtz equation the preconditioner is based on a helmholtz type differential operator with a complex term a multigrid iteration is used for approximately inverting the preconditioner the choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with fourier analysis multigrid analysis results are verified by numerical experiments high wavenumber helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner

double sweep preconditioner for optimized schwarz methods applied to the helmholtz problem this paper presents a preconditioner for non overlapping schwarz methods applied to the helmholtz problem starting from a simple analytic example we show how such a preconditioner can be designed by approximating the inverse of the iteration operator for a layered partitioning of the domain the preconditioner works by propagating information globally by concurrently sweeping in both directions over the subdomains and can be interpreted as a coarse grid for the domain decomposition method the resulting algorithm is shown to converge very fast independently of the number of subdomains and frequency the preconditioner has the advantage that like the original schwarz algorithm it can be implemented as a matrix free routine with no additional preprocessing

a hybrid discontinuous galerkin method for computing the ground state solution of bose einstein condensates a numerical method for computing the ground state solution of bose einstein condensates modeled by the gross pitaevskii equation is presented in this method the three dimensional computational domain is divided into hexahedral elements in which the solution is approximated by a sum of basis functions both polynomial and plane wave bases are considered for this purpose and lagrange multipliers are introduced to weakly enforce the interelement continuity of the solution the ground state is computed by an iterative procedure for minimizing the energy the performance results obtained for several numerical experiments demonstrate that the proposed method is more computationally efficient than similar solution approaches based on the standard higher order finite element method

on a mixture autoregressive conditional heteroscedastic model we propose a mixture autoregressive conditional heteroscedastic mar arch model for modeling nonlinear time series the models consist of a mixture of k autoregressive components with autoregressive conditional heteroscedasticity that is the conditional mean of the process variable follows a mixture ar mar process whereas the conditional variance of the process variable follows a mixture arch process in addition to the advantage of better description of the conditional distributions from the mar model the mararch model allows a more flexible squared autocorrelation structure the stationarity conditions autocorrelation function and squared autocorrelation function are derived construction of multiple step predictive distributions is discussed the estimation can be easily done through a simple em algorithm and the model selection problem is addressed the shape changing feature of the conditional distributions makes these models capable of modeling time series with multimodal conditional distr

a relaxation procedure for domain decomposition methods using finite elements we present the convergence analysis of a new domain decomposition technique for finite element approximations this technique was introduced in 11 and is based on an iterative procedure among subdomains in which transmission conditions at interfaces are taken into account partly in one subdomain and partly in its adjacent no global preconditioner is needed in the practice but simply single domain finite element solvers are required an optimal strategy for an automatic selection of a relaxation parameter to be used at interface subdomains is indicated applications are given to both elliptic equations and incompressible stokes equations

on a mixture autoregressive model we generalize the gaussian mixture transition distribution gmtd model introduced by le and co workers to the mixture autoregressive mar model for the modelling of non linear time series the models consist of a mixture of k stationary or non stationary ar components the advantages of the mar model over the gmtd model include a more full range of shape changing predictive distributions and the ability to handle cycles and conditional heteroscedasticity in the time series the stationarity conditions and autocorrelation function are derived the estimation is easily done via a simple em algorithm and the model selection problem is addressed the shape changing feature of the conditional distributions makes these models capable of modelling time series with multimodal conditional distributions and with heteroscedasticity the models are applied to two real data sets and compared with other competing models the mar models appear to capture features of the data better than other competing models do

optimal discrete transmission conditions for a nonoverlapping domain decomposition method for the helmholtz equation this paper is dedicated to recent developments of a two lagrange multipliers domain decomposition method for the helmholtz equation c farhat et al comput methods appl mech engrg 184 2000 pp 213 240 m j gander f magoules and f nataf siam j sci comput 24 2002 pp 38 60 involving an additional augmented operator along the interface between the subdomains most methods for optimizing the augmented interface operator are based on the discretization of approximations of the continuous transparent operator b despres proceedings of the second international conference on mathematical and numerical aspects of wave propagation r kleinman et al eds siam philadelphia 1993 pp 197 206 j d benamou and b despres j comput phys 136 1997 pp 68 82 p chevalier and f nataf domain decomposition methods 10 ams providence ri 1998 pp 400 407 m j gander proceedings of the 12th international conference on domain decomposition methods chiba japan ddm org 2000 pp 247 254 m j gander f magoules and f nataf siam j sci comput 24 2002 pp 38 60 at the discrete level the optimal operator can be proved to be equal to the schur complement of the outer domain this schur complement can be directly approximated using purely algebraic techniques like sparse approximate inverse methods or incomplete factorization the main advantage of such an algebraic approach is that it is much easier to implement in existing code without any information on the geometry of the interface and the finite element formulation used convergence results and parallel efficiency of several algebraic optimization techniques of an interface operator for acoustic analysis applications will be presented

optimized schwarz methods without overlap for the helmholtz equation the classical schwarz method is a domain decomposition method to solve elliptic partial differential equations in parallel convergence is achieved through overlap of the subdomains we study in this paper a variant of the schwarz method which converges without overlap for the helmholtz equation we show that the key ingredients for such an algorithm are the transmission conditions we derive optimal transmission conditions which lead to convergence of the algorithm in a finite number of steps these conditions are however nonlocal in nature and we introduce local approximations which we optimize for performance of the schwarz method this leads to an algorithm in the class of optimized schwarz methods we present an asymptotic analysis of the optimized schwarz method for two types of transmission conditions robin conditions and transmission conditions with second order tangential derivatives numerical results illustrate the effectiveness of the optimized schwarz method on a model problem and on a problem from industry

a phase based interior penalty discontinuous galerkin method for the helmholtz equation with spatially varying wavenumber this paper is concerned with an interior penalty discontinuous galerkin ipdg method based on a flexible type of non polynomial local approximation space for the helmholtz equation with varying wavenumber the local approximation space consists of multiple polynomial modulated phase functions which can be chosen according to the phase information of the solution we obtain some approximation properties for this space and a priori l2l2 error estimates for the h convergence of the ipdg method using duality argument we also provide ample numerical examples to show that building phase information into the local spaces often gives more accurate results comparing to using the standard polynomial spaces

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

on trefftz and weak trefftz discontinuous galerkin approaches for medium frequency acoustics in this paper the wave approach called the variational theory of complex rays vtcr which was developed for medium frequency acoustics and vibrations is revisited as a discontinuous galerkin method extensions leading to a weak trefftz constraint are introduced this weak trefftz discontinuous galerkin approach enables hybrid fem vtcr strategies to be developed easily and paves the way for new computational techniques for the resolution of engineering problems this paper presents some of the fundamental properties of the approach which is illustrated by several numerical examples

contemporaneous threshold autoregressive models estimation testing and forecasting this paper proposes a contemporaneous smooth transition threshold autoregressive model c star as a modification of the smooth transition threshold autoregressive model surveyed in terasvirta 1998 modelling economic relationships with smooth transition regressions in ullah a giles d e a eds handbook of applied economic statistics marcel dekker new york pp 507 552 in which the regime weights depend on the ex ante probability that a latent regime specific variable will exceed a threshold value we argue that the contemporaneous model is well suited to rational expectations applications and pricing exercises in that it does not require the initial regimes to be predetermined we investigate the properties of the model and evaluate its finite sample maximum likelihood performance we also propose a method to determine the number of regimes based on a modified hansen 1992 the likelihood ratio test under nonstandard conditions testing the markov switching model of gnp journal of applied econometrics 7 s61 s82 procedure furthermore we construct multiple step ahead forecasts and evaluate the forecasting performance of the model finally an empirical application of the short term interest rate yield is presented and discussed

the ultra weak variational formulation for elastic wave problems the ultra weak variational formulation has been used effectively to solve time harmonic acoustic and electromagnetic wave propagation in inhomogeneous media we develop the ultra weak variational formulation for elastic wave propagation in two space dimensions in order to improve the accuracy and stability of the method we find it necessary to approximate the s and p wave components of the solution in a balanced way some preliminary analysis is provided and numerical evidence is presented for the efficiency of the scheme in comparison to piecewise linear finite elements

a domain decomposition method for discontinuous galerkin discretizations of helmholtz problems with plane waves and lagrange multipliers a nonoverlapping domain decomposition dd method is proposed for the iterative solution of systems of equations arising from the discretization of helmholtz problems by the discontinuous enrichment method this discretization method is a discontinuous galerkin finite element method with plane wave basis functions for approximating locally the solution and dual lagrange multipliers for weakly enforcing its continuity over the element interfaces the primal subdomain degrees of freedom are eliminated by local static condensations to obtain an algebraic system of equations formulated in terms of the interface lagrange multipliers only as in the feti h and feti dph dd methods for continuous galerkin discretizations this system of lagrange multipliers is iteratively solved by a krylov method equipped with both a local preconditioner based on subdomain data and a global one using a coarse space numerical experiments performed for two and three dimensional acoustic scattering problems suggest that the proposed dd based iterative solver is scalable with respect to both the size of the global problem and the number of subdomains copyright 2009 john wiley sons ltd

deflation accelerated preconditioning of the poisson neumann schur problem on long domains with a high order discontinuous element based collocation method a combination of block jacobi and deflation preconditioning is used to solve a high order discontinuous element based collocation discretization of the schur complement of the poisson neumann system as arises in the operator splitting of the incompressible navier stokes equations the preconditioners and deflation vectors are chosen to mitigate the effects of ill conditioning due to highly elongated domains typical of simulations of strongly non hydrostatic environmental flows and to achieve generalized minimum residual method gmres convergence independent of the size of the number of elements in the long direction the ill posedness of the poisson neumann system manifests as an inconsistency of the schur complement problem but it is shown that this can be accounted for with appropriate projections out of the null space of the schur complement matrix without affecting the accuracy of the solution the block jacobi preconditioner is shown to yield gmres convergence independent of the polynomial order and only weakly dependent on the number of elements within a subdomain in the decomposition the combined deflation and block jacobi preconditioning is compared with two level non overlapping block jacobi preconditioning of the schur problem and while both methods achieve convergence independent of the grid size deflation is shown to require half as many gmres iterations and 25 less wall clock time for a variety of grid sizes and domain aspect ratios the deflation methods shown to be effective for the two dimensional poisson neumann problem are extensible to the three dimensional problem assuming a fourier discretization in the third dimension a fourier discretization results in a two dimensional helmholtz problem for each fourier component that is solved using deflated block jacobi preconditioning on its schur complement here again deflation is shown to be superior to two level non overlapping block jacobi preconditioning requiring about half as many gmres iterations and 15 less time

gaussian mixture vector autoregression this paper proposes a new nonlinear vector autoregressive var model referred to as the gaussian mixture vector autoregressive gmvar model the gmvar model belongs to the family of mixture vector autoregressive models and is designed for analyzing time series that exhibit regime switching behavior the main difference between the gmvar model and previous mixture var models lies in the definition of the mixing weights that govern the regime probabilities in the gmvar model the mixing weights depend on past values of the series in a specific way that has very advantageous properties from both theoretical and practical point of view a practical advantage is that there is a wide diversity of ways in which a researcher can associate different regimes with specific economically meaningful characteristics of the phenomenon modeled a theoretical advantage is that stationarity and ergodicity of the underlying stochastic process are straightforward to establish and contrary to most other nonlinear autoregressive models explicit expressions of low order stationary marginal distributions are known these theoretical properties are used to develop an asymptotic theory of maximum likelihood estimation for the gmvar model whose practical usefulness is illustrated in a bivariate setting by examining the relationship between the eur usd exchange rate and a related interest rate data

global attractivity of cohen grossberg model with finite and infinite delays in this paper we have studied the global attractivity of the equilibrium of cohen grossberg model with both finite and infinite delays criteria for global attractivity are also derived by means of lyapunov functionals as a corollary we show that if the delayed system is dissipative and the coefficient matrix is vl stable then the global attractivity of the unique equilibrium is maintained provided the delays are small estimates on the allowable sizes of delays are also given applications to the hopfield neural networks with discrete delays are included

dynamical analysis of cohen grossberg neural networks with finite and infinite delays a model describing dynamics of cohen grossberg neural networks with finite and infinite delays is considered by means of lyapunov functionals and differential inequality techniques criteria on global asymptotic stability of this model are derived the results of this paper are new and they supplement previously known results

a least squares method for the helmholtz equation abstract we investigate the use of least squares methods to approximate the helmholtz equation the basis used in the discrete method consists of solutions of the helmholtz equation either consisting of plane waves or bessel functions on each element of a finite element grid unlike previous methods of this type we do not use polynomial based finite elements the use of small elements and relatively few basis functions per element allows us to prove convergence theorems for the method and to some extent control the conditioning of the resulting linear sy stem numerical results show the efficiency of the new method and suggest that it may be possible to obtain accurate results with a coarser grid than is usual for standard finite element methods

a quasi optimal non overlapping domain decomposition algorithm for the helmholtz equation this paper presents a new non overlapping domain decomposition method for the helmholtz equation whose effective convergence is quasi optimal these improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the dirichlet to neumann operator a convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions

a fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems part 2 neumann boundary conditions we present a fictitious domain decomposition method for the fast solution of acoustic scattering problems characterized by a partially axisymmetric sound hard scatterer we apply this method to the solution of a mock up submarine problem and highlight its computational advantages and intrinsic parallelism a key component of our method is an original idea for addressing a neumann boundary condition in the general framework of a fictitious domain method this idea is applicable to many other linear partial differential equations besides the helmholtz equation copyright 2003 john wiley sons ltd

a parallel fictitious domain method for the three dimensional helmholtz equation the application of a fictitious domain domain embedding method to the three dimensional helmholtz equation with absorbing boundary conditions is considered the finite element discretization is performed by using locally fitted meshes and an algebraic fictitious domain method with a separable preconditioner is used in the iterative solution of the resultant linear systems such a method is based on embedding the original domain into a larger one with a simple geometry with this approach it is possible to realize the gmres iterations in a low dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner an efficient parallel implementation of the iterative algorithm is introduced results of numerical experiments demonstrate good scalability properties on distributed memory parallel computers and the ability to solve high frequency acoustic scattering problems

higher order extensions of a discontinuous galerkin method for mid frequency helmholtz problems recently a discontinuous galerkin method with plane wave basis functions and lagrange multiplier degrees of freedom was proposed for the efficient solution of helmholtz problems in the mid frequency regime in this paper this method is extended to higher order elements performance results obtained for various two dimensional problems highlight the advantages of these elements over classical higher order galerkin elements such as q2 and q4 for the discretization of interior and exterior helmholtz problems copyright 2004 john wiley sons ltd

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

global exponential stability of nonautonomous neural networks with time varying delays and reaction diffusion terms a class of nonautonomous neural networks with time varying delays and reaction diffusion terms is considered by means of lyapunov functionals and differential inequality techniques criteria on global exponential stability of this model with the neumann boundary conditions and the dirichlet boundary conditions are derived respectively the results of this paper are new and they improve and generalize previously known results

an ultra weak method for acoustic fluid solid interaction we introduce the ultra weak variational formulation uwvf for fluid solid vibration problems in particular we consider the scattering of time harmonic acoustic pressure waves from solid elastic objects the problem is modeled using a coupled system of the helmholtz and navier equations the transmission conditions on the fluid solid interface are represented in an impedance type form after which we can employ the well known ultra weak formulations for the helmholtz and navier equations the uwvf approximation for both equations is computed using a superposition of propagating plane waves a condition number based criterion is used to define the plane wave basis dimension for each element as a model problem we investigate the scattering of sound from an infinite elastic cylinder immersed in a fluid a comparison of the uwvf approximation with the analytical solution shows that the method provides a means for solving wave problems on relatively coarse meshes however particular care is needed when the method is used for problems at frequencies near the resonance frequencies of the fluid solid system

application of an ultra weak variational formulation of elliptic pdes to the two dimensional helmholtz problem a new technique to solve elliptic linear pdes called ultra weak variational formulation uwvf in this paper is introduced in b despres c r acad sci paris 318 1994 pp 939 944 this paper is devoted to an evaluation of the potentialities of this technique it is applied to a model wave problem the two dimensional helmholtz problem the new method is presented in three parts following the same style of presentation as the classical one of the finite elements method even though they are definitely conceptually different methods the first part is committed to the variational formulation and to the continuous problem the second part defines the discretization process using a galerkin procedure the third part actually studies the efficiency of the technique from the order of convergence point of view this is achieved using theoretical proofs and a series of numerical experiments in particular it is proven and shown the order of convergence is lower bounded by a linear function of the number of degrees of freedom an application to scattering problems is presented in a fourth part

richardson s iteration for nonsymmetric matrices abstract to solve the linear n n system 1 ax a for any nonsingular matrix a richardson s iteration 2 x j 1 x j j ax j a j 1 2 n which is applied in a cyclic manner with cycle length n is investigated where the j are free parameters the objective is to minimize the error x n 1 x where x is the solution of 1 if the spectrum of a is known to lie in a compact set s one is led to the chebyshev type approximation problem 3 min p 1 v n max z s p z where v n is the linear span of z z 2 z n if p solves 3 then the reciprocals of the zeros of p are optimal iteration parameters j it is shown that for a real problem 1 the iteration 2 can be carried out with real arithmetic alone even when there are complex j the stationary case n 1 is solved completely i e for all compact sets s the problem 3 is solved explicitly as a consequence the converging stationary iteration processes can be characterized for arbitrary closed disks s the problem 3 can be solved for all n n and a simple proof is provided the lemniscates associated with s are introduced they appear as an important tool for studying the stability of the iteration 2

global attractivity in delayed hopfield neural network models two different approaches are employed to investigate the global attractivity of delayed hopfield neural network models without assuming the monotonicity and differentiability of the activation functions liapunov functionals and functions combined with the razumikhin technique are constructed and employed to establish sufficient conditions for global asymptotic stability independent of the delays in the case of monotone and smooth activation functions the theory of monotone dynamical systems is applied to obtain criteria for global attractivity of the delayed model such criteria depend on the magnitude of delays and show that self inhibitory connections can contribute to the global convergence

testing for observation dependent regime switching in mixture autoregressive models abstract testing for regime switching when the regime switching probabilities are specified either as constants mixture models or are governed by a finite state markov chain markov switching models are long standing problems that have also attracted recent interest this paper considers testing for regime switching when the regime switching probabilities are time varying and depend on observed data observation dependent regime switching specifically we consider the likelihood ratio test for observation dependent regime switching in mixture autoregressive models the testing problem is highly nonstandard involving unidentified nuisance parameters under the null parameters on the boundary singular information matrices and higher order approximations of the log likelihood we derive the asymptotic null distribution of the likelihood ratio test statistic in a general mixture autoregressive setting using high level conditions that allow for various forms of dependence of the regime switching probabilities on past observations and we illustrate the theory using two particular mixture autoregressive models the likelihood ratio test has a nonstandard asymptotic distribution that can easily be simulated and monte carlo studies show the test to have good finite sample size and power properties

the two level feti method for static and dynamic plate problems part i an optimal iterative solver for biharmonic systems abstract we present a lagrange multiplier based substructuring method for solving iteratively large scale systems of equations arising from the finite element discretization of static and dynamic plate bending problems the proposed method is essentially an extension of the feti domain decomposition algorithm to fourth order problems the main idea is to enforce exactly the continuity of the transverse displacement field at the substructure corners throughout the preconditioned conjugate projected gradient iterations this results in a two level feti substructuring method where the condition number of the preconditioned interface problem does not grow with the number of substructures and grows at most polylogarithmically with the number of elements per substructure these theoretically proven optimal convergence properties of the new feti method are numerically demonstrated for several finite element plate bending static and transient problems the two level iterative solver presented in this paper is applicable to a large family of biharmonic time independent as well as time dependent systems it is also extendible to shell problems

three dimensional discontinuous galerkin elements with plane waves and lagrange multipliers for the solution of mid frequency helmholtz problems recently a discontinuous galerkin finite element method with plane wave basis functions and lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of helmholtz problems in the mid frequency regime in this paper this method is extended to three dimensions and several new elements are proposed computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher order galerkin method

regression density estimation using smooth adaptive gaussian mixtures we model a regression density flexibly so that at each value of the covariates the density is a mixture of normals with the means variances and mixture probabilities of the components changing smo

stability in delayed cohen grossberg neural networks lmi optimization approach in this paper stability problems are further discussed for a class of delayed cohen grossberg neural networks on the basis of the linear matrix inequality lmi optimization approach and also the lyapunov krasovskii functional method combined with the halanay inequality technique several new sufficient criteria are given for ascertaining the global asymptotic stability and exponential stability of the equilibrium point for this system the proposed results are less restrictive than those given in the earlier literature and are easier to verify in practice in addition four examples and their numerical simulations are given two of them are used to demonstrate the effectiveness of the proposed results and another two show that there exist stable bifurcating periodic solutions if the given conditions do not hold

an algebraic multigrid based shifted laplacian preconditioner for the helmholtz equation a preconditioner defined by an algebraic multigrid cycle for a damped helmholtz operator is proposed for the helmholtz equation this approach is well suited for acoustic scattering problems in complicated computational domains and with varying material properties the spectral properties of the preconditioned systems and the convergence of the gmres method are studied with linear quadratic and cubic finite element discretizations numerical experiments are performed with two dimensional problems describing acoustic scattering in a cross section of a car cabin and in a layered medium asymptotically the number of iterations grows linearly with respect to the frequency while for lower frequencies the growth is milder the proposed preconditioner is particularly effective for low frequency and mid frequency problems

on wave based weak trefftz discontinuous galerkin approach for medium frequency heterogeneous helmholtz problem abstract medium frequency heterogeneous helmholtz problem gives rise to severe numerical challenge to finite element method fem an extended variational theory of complex rays vtcr is developed for solving this problem since vtcr is kind of trefftz method analytic solutions of governing equation need to be known a priori but this requirement limits the application of vtcr to some specific forms of governing equations recently a new computational method named weak trefftz discontinuous galerkin method wtdg is proposed to enable hybrid finite element method fem variational theory of complex rays vtcr strategies to be developed easily in acoustics and vibrations this hybrid method combines the advantages of fem and vtcr to solve efficiently low frequency and medium frequency problems this paper proposes a wave based wtdg for heterogeneous helmholtz problem without knowing analytic solution of governing equation wtdg method provides a simple and general resolution strategy for medium frequency heterogeneous helmholtz problem

a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime we present a discontinuous galerkin method dgm for the solution of the helmholtz equation in the mid frequency regime our approach is based on the discontinuous enrichment method in which the standard polynomial field is enriched within each finite element by a non conforming field that contains free space solutions of the homogeneous partial differential equation to be solved hence for the helmholtz equation the enrichment field is chosen here as the superposition of plane waves we enforce a weak continuity of these plane waves across the element interfaces by suitable lagrange multipliers preliminary results obtained for two dimensional model problems discretized by uniform meshes reveal that the proposed dgm enables the development of elements that are far more competitive than both the standard linear and the standard quadratic galerkin elements for the discretization of helmholtz problems

testing for regime switching we analyze use of a quasi likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a markov regime switching context this test exploits mixture properties implied by the regime switching process but ignores certain implied serial correlation properties when formulated in the natural way the setting is nonstandard involving nuisance parameters on the boundary of the parameter space nuisance parameters identified only under the alternative or approximations using derivatives higher than second order we exploit recent advances by andrews 2001 and contribute to the literature by extending the scope of mixture models obtaining asymptotic null distributions different from those in the literature we further provide critical values for popular models or bounds for tail probabilities that are useful in constructing conservative critical values for regime switching tests we compare the size and power of our statistics to other useful tests for regime switching via monte carlo methods and find relatively good performance we apply our methods to reexamine the classic cartel study of porter 1983 and reaffirm porter s findings

a discontinuous enrichment method for capturing evanescent waves in multiscale fluid and fluid solid problems abstract an evanescent wave is produced when a propagating incident wave impinges on an interface between two media or materials at a sub critical angle the sub scale nature of such a wave makes it difficult to be captured computationally in this paper the discontinuous enrichment method dem developed in c farhat i harari l p franca the discontinuous enrichment method comput methods appl mech engrg 190 2001 6455 6479 c farhat i harari u hetmaniuk a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime comput methods appl mech engrg 192 2003 1389 1419 c farhat i harari u hetmaniuk the discontinuous enrichment method for multiscale analysis comput methods appl mech engrg 192 2003 3195 3210 c farhat r tezaur p weidemann goiran higher order extensions of a discontinuous galerkin method for mid frequency helmholtz problems int j numer methods engrg 61 2004 1938 1956 c farhat p wiedemann goiran r tezaur a discontinuous galerkin method with plane waves and lagrange multipliers for the solution of short wave exterior helmholtz problems on unstructured meshes new computational methods for wave propagation wave motion 39 4 2004 307 317 l zhang r tezaur c farhat the discontinuous enrichment method for elastic wave propagation in the medium frequency regime int j numer methods engrg 66 2006 2086 2114 r tezaur c farhat three dimensional discontinuous galerkin elements with plane waves and lagrange multipliers for the solution of mid frequency helmholtz problems int j numer methods engrg 66 2006 796 815 is extended to a class of evanescent wave problems new dem elements are constructed by enriching polynomial approximations with free space evanescent solutions in order to achieve high accuracy for problems with fluid fluid or fluid solid interfaces on which evanescent waves may occur the new dem elements are applied to the solution of various two dimensional model problems with evanescent waves their performance is observed to be better than that of the basic helmholtz type dem elements and superior to that of the classical higher order polynomial finite element method

the discontinuous enrichment method for elastic wave propagation in the medium frequency regime the discontinuous enrichment method dem is specified and developed for the solution of two dimensional elastic wave propagation problems in the frequency domain the classical finite element polynomial approximation of the displacement field is enriched by the superposition of discontinuous pressure and shear wave functions the continuity of the solution across the element interfaces is weakly enforced by suitable lagrange multipliers higher order rectangular dem elements are constructed and benchmarked against the standard higher order polynomial galerkin elements for two dimensional problems in the medium frequency regime in general it is found that for such applications dem can achieve the same accuracy as the p finite element method using a similar computational complexity but with about 10 times fewer degrees of freedom this highlights the potential of this hybrid method for problems where the scale of vibrations is very small compared to the characteristic dimension of the physical medium copyright 2006 john wiley sons ltd

two level domain decomposition methods with lagrange multipliers for the fast iterative solution of acoustic scattering problems we present two different but related lagrange multiplier based domain decomposition dd methods for solving iteratively large scale systems of equations arising from the finite element discretization of high frequency exterior helmholtz problems the proposed methods are essentially two distinct extensions of the regularized finite element tearing and interconnecting feti method to indefinite or complex problems the first method employs a single lagrange multiplier field to glue the local solutions at the subdomain interface boundaries the second method employs two lagrange multiplier fields for that purpose the key ingredients of both of these feti methods are the regularization of each subdomain matrix by a complex lumped mass matrix defined on the subdomain interface boundary and the preconditioning of the global interface problem by a coarse second level problem constructed with planar waves we show numerically that both methods are scalable with respect to the mesh size the subdomain size and the wavenumber but that the feti method with a single lagrange multiplier field labeled feti h h for helmholtz in this paper delivers superior computational performances we apply the feti h method to the parallel solution on a 24 processor origin 2000 of an acoustic scattering problem with a submarine shaped obstacle and report performance results that highlight the unique efficiency of this dd method for the solution of high frequency acoustic scattering problems

overview of the discontinuous enrichment method the ultra weak variational formulation and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons

on the homogenization of multiple integrals in the strong lp topology or equivalently w h j j in case of equicoercive functionals and l topology with f f x vv periodic in x and quasiconvex in w this is a problem of homogenization in the sense of bensoussan lions papanicolaou l we refer to marcellini s and carbone sbordone 2 for a detailed discussion of the relation between the i convergence and the homogenization in the scalar case indeed the i convergence of 1 1 is one of the two main particular cases of i convergence of variational integrals

optimal test for markov switching parameters this paper proposes a class of optimal tests for the constancy of parameters in random coefficients models our testing procedure covers the class of hamilton s models where the parameters vary according to an unobservable markov chain but also applies to nonlinear models where the random coefficients need not be markov we show that the contiguous alternatives converge to the null hypothesis at a rate that is slower than the standard rate therefore standard approaches do not apply we use bartlett type identities for the construction of the test statistics this has several desirable properties first it only requires estimating the model under the null hypothesis where the parameters are constant second the proposed test is asymptotically optimal in the sense that it maximizes a weighted power function we derive the asymptotic distribution of our test under the null and local alternatives asymptotically valid bootstrap critical values are also proposed

modeling flat stretches bursts and outliers in time series using mixture transition distribution models abstract the class of mixture transition distribution mtd time series models is extended to general non gaussian time series in these models the conditional distribution of the current observation given the past is a mixture of conditional distributions given each one of the last p observations they can capture non gaussian and nonlinear features such as flat stretches bursts of activity outliers changepoints in a single unified model class they can also represent time series defined on arbitrary state spaces univariate or multivariate continuous discrete or mixed which need not even be euclidean they perform well in the usual case of gaussian time series without obvious nonstandard behaviors the models are simple analytically tractable easy to simulate readily estimated the stationarity and autocorrelation properties of the models are derived a simple em algorithm is given and shown to work well for estimation the models are applied to several real and simulated datasets with satisfacto

computational aspects of the ultra weak variational formulation the ultra weak variational formulation uwvf approach has been proposed as an effective method for solving helmholtz problems with high wave numbers however for coarse meshes the method can suffer from instability in this paper we consider computational aspects of the ultra weak variational formulation for the inhomogeneous helmholtz problem we introduce a method to improve the uwvf scheme and we compare iterative solvers for the resulting linear system computations for the acoustic transmission problem in 2d show that the new approach enables helmholtz problems to be solved on a relatively coarse mesh for a wide range of wave numbers

global asymptotic stability of nonautonomous cohen grossberg neural network models with infinite delays for a general cohen grossberg neural network model with potentially unbounded time varying coefficients and infinite distributed delays we give sufficient conditions for its global asymptotic stability the model studied is general enough to include as subclass the most of famous neural network models such as cohen grossberg hopfield and bidirectional associative memory contrary to usual in the literature in the proofs we do not use lyapunov functionals as illustrated the results are applied to several concrete models studied in the literature and a comparison of results shows that our results give new global stability criteria for several neural network models and improve some earlier publications

multivariate contemporaneous threshold autoregressive models this paper proposes a contemporaneous threshold multivariate smooth transition autoregressive c mstar model in which the regime weights depend on the ex ante probabilities that latent regime specific variables exceed certain threshold values a key feature of the model is that the transition function depends on all the parameters of the model as well as on the data since the mixing weights are also a function of the regime specific noise covariance matrix the model can account for contemporaneous regime specific co movements of the variables the stability and distributional properties of the proposed model are discussed as well as issues of estimation testing and forecasting the practical usefulness of the c mstar model is illustrated by examining the relationship between us stock prices and interest rates

trefftz approximations in complex media accuracy and applications abstract approximations by trefftz functions are rapidly gaining popularity in the numerical solution of boundary value problems of mathematical physics by definition these functions satisfy locally in weak form the underlying differential equations of the problem which often results in high order or even exponential accuracy with respect to the size of the basis set we highlight two separate examples in applied electromagnetics and photonics i homogenization of periodic structures and ii numerical simulation of electromagnetic waves in slab geometries extensive numerical evidence and theoretical considerations show that trefftz approximations can be applied much more broadly than is traditionally done they are effective not only in physically homogeneous regions but also in complex inhomogeneous ones two mechanisms underlying the high accuracy of trefftz approximations in such complex cases are pointed out the first one is related to trigonometric interpolation and the second one somewhat surprisingly to well posedness of random matrices

dpg method with optimal test functions for a transmission problem we propose and analyze a numerical method to solve an elliptic transmission problem in full space the method consists of a variational formulation involving standard boundary integral operators on the coupling interface and an ultra weak formulation in the interior to guarantee the discrete inf sup condition the system is discretized by the dpg method with optimal test functions we prove that the principal unknowns are approximated quasi optimally numerical experiments for problems with smooth and singular solutions confirm optimal convergence orders

a multigrid method enhanced by krylov subspace iteration for discrete helmholtz equations standard multigrid algorithms have proven ineffective for the solution of discretizations of helmholtz equations in this work we modify the standard algorithm by adding gmres iterations at coarse levels and as an outer iteration we demonstrate the algorithm s effectiveness through theoretical analysis of a model problem and experimental results in particular we show that the combined use of gmres as a smoother and outer iteration produces an algorithm whose performance depends relatively mildly on wave number and is robust for normalized wave numbers as large as 200 for fixed wave numbers it displays grid independent convergence rates and has costs proportional to the number of unknowns

a two level domain decomposition method for the iterative solution of high frequency exterior helmholtz problems summary we present a lagrange multiplier based two level domain decomposition method for solving iteratively large scale systems of equations arising from the finite element discretization of high frequency exterior helmholtz problems the proposed method is essentially an extension of the regularized feti finite element tearing and interconnecting method to indefinite problems its two key ingredients are the regularization of each subdomain matrix by a complex interface lumped mass matrix and the preconditioning of the interface problem by an auxiliary coarse problem constructed to enforce at each iteration the orthogonality of the residual to a set of carefully chosen planar waves we show numerically that the proposed method is scalable with respect to the mesh size the subdomain size and the wavenumber we report performance results for a submarine application that highlight the efficiency of the proposed method for the solution of high frequency acoustic scattering problems discretized by finite elements

iterative solution of helmholtz problem with high order isogeometric analysis and finite element method at mid range frequencies abstract solving wave problems with isogeometric analysis has attracted a significant attention in the past few years it is well known that keeping a fixed number of degrees of freedom per wavelength leads to an increased error as higher wavenumbers are considered this behaviour often cited as the pollution error improves significantly with isogeometric analysis when compared to the conventional finite element method the improvement in handling pollution along with the ability to represent exact geometries has been the main reasons behind the attention that isogeometric analysis has received furthermore using high order elements also presents major advantages over low order elements for this range of frequencies however it remains to be studied how iterative linear solvers often necessary for solving high frequency wave problems perform when using isogeometric analysis compared to the finite element method especially at high polynomial orders this paper is one of the first studies in this direction in this work we investigate the generalised minimal residual method a standard krylov subspace iterative technique for solving the linear system resulting form isogeometric analysis furthermore we look into the use of some recently proposed preconditioners for helmholtz problem such as shifted laplace or ilu with a complex shift preconditioners and how they perform with high order isogeometric analysis and finite element method in general the results show improvement when using isogeometric analysis in terms of the number of iterations required for convergence compared to the finite element method for both preconditioned and non preconditioned linear systems we use eigenvalue spectra to understand this improvement

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

stability analysis of cohen grossberg neural network with both time varying and continuously distributed delays in this paper the cohen grossberg neural network model with both time varying and continuously distributed delays is considered without assuming both global lipschitz conditions on these activation functions and the differentiability on these time varying delays applying the idea of vector lyapunov function m matrix theory and inequality technique several new sufficient conditions are obtained to ensure the existence uniqueness and global exponential stability of equilibrium point for cohen grossberg neural network with both time varying and continuously distributed delays these results generalize and improve the earlier publications two numerical examples are given to show the effectiveness of the obtained results it is believed that these results are significant and useful for the design and applications of the cohen grossberg neural networks

on a logistic mixture autoregressive model summary we generalise the mixture autoregressive mar model to the logistic mixture autoregressive with exogenous variables lmarx model for the modelling of nonlinear time series the models consist of a mixture of two gaussian transfer function models with the mixing proportions changing over time the model can also be considered as a generalisation of the self exciting threshold autoregressive setar model and the open loop threshold autoregressive tarso model the advantages of the lmarx model over other nonlinear time series models include a wider range of shape changing predictive distributions the ability to handle cycles and conditional heteroscedasticity in the time series and better point prediction estimation is easily done via a simple em algorithm and the model selection problem is addressed the models are applied to two real datasets and compared with other competing models

iterative solution applied to the helmholtz equation complex deflation on unstructured grids abstract extensions of deflation techniques developed for the poisson and navier equations aubry et al 2008 mut et al 2010 lohner et al 2011 aubry et al 2011 1 2 3 4 are presented for the helmholtz equation numerous difficulties arise compared to the previous case after discretization the matrix is now indefinite without sommerfeld boundary conditions or complex with them it is generally symmetric complex but not hermitian discarding optimal short recurrences from an iterative solver viewpoint saad 2003 5 furthermore the kernel of the operator in an infinite space typically does not belong to the discrete space the choice of the deflation space is discussed as well as the relationship between dispersion error and solver convergence similarly to the symmetric definite positive spd case subdomain deflation accelerates convergence if the low frequency eigenmodes are well described however the analytic eigenvectors are well represented only if the dispersion error is low cpu savings are therefore restricted to a low to mid frequency regime compared to the mesh size which could be still relevant from an application viewpoint given the ease of implementation

comparisons of three kinds of plane wave methods for the helmholtz equation and time harmonic maxwell equations with complex wave numbers abstract in this paper we are concerned with some plane wave discretization methods of the helmholtz equation and time harmonic maxwell equations with complex wave numbers we design two new variants of the variational theory of complex rays and the ultra weak variational formulation for the discretization of these types of equations respectively the well posedness of the approximate solutions generated by the two methods is derived moreover based on the pwls lsfe method introduced in hu and yuan 2018 we extend these two methods vtcr method and uwvf method combined with local spectral element to discretize nonhomogeneous helmholtz equation and maxwell s equations the numerical results show that the resulting approximate solution generated by the uwvf method is clearly more accurate than that generated by the vtcr method

non overlapping domain decomposition algorithm based on modified transmission conditions for the helmholtz equation abstract a square root based transmission conditions domain decomposition method was recently introduced for the helmholtz equation it produces an effective algorithm where the convergence is independent of the wavenumber and the mesh discretization we modify here these conditions in order to guarantee well posedness of local problems and further improve the efficiency of the whole method numerical results in particular in the three dimensional case show significant reduction of the computational time needed in the iterative procedure while preserving the iteration number when compared with the original algorithm