an extension of slow feature analysis for nonlinear blind source separation we present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation the algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a high reliability the algorithm is based on a mathematical analysis of slow feature analysis for the case of input data that are generated from statistically independent sources

shape optimization of piezoelectric devices using an enriched meshfree method we present an enriched reproducing kernel particle method for shape sensitivity analysis and shape optimization of two dimensional electromechanical domains this meshfree method incorporates enrichment functions for better representation of discontinuous electromechanical fields across internal boundaries we use cubic splines for delineating the geometry of internal external domain boundaries and the nodal coordinates and slopes of these splines at their control points become the design parameters this approach enables smooth manipulations of bi material interfaces and external boundaries during the optimization process it also enables the calculation of displacement and electric potential field sensitivities with respect to the design parameters through direct differentiation for which we adopt the classical material derivative approach we verify this implementation of sensitivity calculations against an exact solution to a variant of lame s problem and also finite difference approximations we follow a sequential quadratic programming approach to minimize the cost function and demonstrate the utility of the overall technique through a model problem that involves the shape optimization of a piezoelectric fan copyright 2008 john wiley sons ltd

learning overcomplete representations in an overcomplete basis the number of basis vectors is greater than the dimensionality of the input and the representation of an input is not a unique combination of basis vectors overcomplete representations have been advocated because they have greater robustness in the presence of noise can be sparser and can have greater flexibility in matching structure in the data overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex previous work has focused on finding the best representation of a signal using a fixed overcomplete basis or dictionary we present an algorithm for learning an overcomplete basis by viewing it as probabilistic model of the observed data we show that overcomplete bases can yield a better approximation of the underlying statistical distribution of the data and can thus lead to greater coding efficiency this can be viewed as a generalization of the technique of independent component analysis and provides a method for bayesian reconstruction of signals in the presence of noise and for blind source separation when there are more sources than mixtures

static fundamental solutions for a bi material full space in this paper the complete static response of two joined dissimilar half spaces due to an arbitrary interior point load is derived by means of a method of displacement potentials and integral transforms a dual format of the solution in the form of a hankel integral representation and algebraic closed form expressions is presented as illustrations its analytical degeneration to benchmark solutions for a homogeneous medium as well as its variation under general geometric and material conditions are shown the importance of the dual format of the bi material solution in connection with the method of asymptotic decomposition to the development of a rigorous treatment of its dynamic counterpart is also demonstrated

slow feature analysis a theoretical analysis of optimal free responses temporal slowness is a learning principle that allows learning of invariant representations by extracting slowly varying features from quickly varying input signals slow feature analysis sfa is an efficient algorithm based on this principle and has been applied to the learning of translation scale and other invariances in a simple model of the visual system here a theoretical analysis of the optimization problem solved by sfa is presented which provides a deeper understanding of the simulation results obtained in previous studies

a spectral super element for modelling of plate vibration part 1 general theory the dynamic response of vibrating structures is studied with a proposed merger of the standard finite element method with the more computationally efficient spectral finite element method first a plate structure is modelled with a newly developed spectral super element then this element is coupled to other parts that can have a more complex geometry and are modelled entirely with conventional finite elements some numerical examples are given to illustrate and validate the developed method and studies of numerical stability are also presented in an accompanying paper the predicted and measured response of a turbulence excited aircraft panel are compared

a boundary element method for anisotropic inhomogeneous elasticity this paper is concerned with obtaining boundary integral equations for the numerical solution of the partial differential equations governing static deformations of inhomogeneous anisotropic elastic materials the elastic parameters for the inhomogeneous materials are assumed to vary continuously with the spatial variables

the non homogeneous biharmonic plate equation fundamental solutions abstract real materials and structural components are often non homogeneous either by design or because of the physical composition and imperfections in the underlying material thus analytical solutions for non homogeneous materials under mechanical loads are of considerable interest to engineers and have widespread applications given the prevalence of these materials in fields as diverse as aerospace construction electronics etc more precisely those are essentially composites with carefully manufactured properties that yield desirable mechanical characteristics and properties such as optimal arrangement of the material minimum weight etc to this end the displacement fundamental solution or green s function corresponding to a point force for the non homogenous biharmonic equation in two dimensions are derived in this work by employing a conformal mapping technique in conjunction with the radon transformation these functions besides being useful in their own right can also be used within the context of integral equation formulations for the solution of boundary value problems finally a series of numerical examples that deal with the non homogeneous plate on elastic foundation problem serve to illustrate the present method

dynamic dispersion curves for non homogeneous anisotropic beams with cross sections of arbitrary geometry abstract to accurately predict the dynamic behaviour of spanwise uniform non homogeneous anisotrophic beams with arbitrary cross sectional geometry is an important part of engineering analysis classical one dimensional beam theory fails in this endeavour and development of more sophisticated one dimensional theories is an important task a basis for development of improved one dimensional theory is the dispersion curve analysis a means to find the dispersion curves is discussed in this paper the code is developed to calculate the dispersion curves as well as corresponding mode shapes the code is based on finite element discretization over the cross sectional domain use of this code provides benchmark results for the testing of any existing one dimensional theory as well as facilitating the construction of new one dimensional theories dispersion information can also be useful in non destructive evaluation as an example of a case where non classical effects are particularly important results obtained from this code for an i beam are presented qualitative comparisons with the well known case of isotropic rectangular beam is provided features that are common for all beams are emphasized along with pointing out qualitative differences that exist for beams other than rectangular or circular

abundance of strange attractors in 1976 he h non performed a numerical study of the family of diffeomorphisms of the plane ha b x y 1 ax2 y bx and detected for parameter values a l 4 b 0 3 what seemed to be a non trivial attractor with a highly intricate geometric structure this family has since then been the subject of intense research both numerical and theoretical but its dynamics is still far from being completely understood in particular one could not exclude the possibility that the attractor observed by h6non were just a periodic orbit with a very high period recently in a remarkable paper bc2 benedicks and carleson were able to show that this is not the case at least for a positive lebesgue measure set of parameter values near a 2 b o more precisely they showed that if b 0 is small enough then for a positive measure set of a values near a 2 the corresponding diffeomorphism ha b exhibits a strange attractor their argument is a very creative extension of the techniques they had previously developed in bull for the study of the quadratic family on the real line and no doubt it will be important for the understanding of several other situations of complicated nonhyperbolic dynamics when acquainted in 1985 with the work by benedicks and carleson then in progress palls suggested that one should in this context think of the h6non family as a particular although important model for the creation of a horseshoe and that the emphasis should be put on the occurrence of unfoldings of homoclinic tangencies he proposed that the correct setting for benedicks carleson s results is within this more general framework of homoclinic bifurcations and stated the following

mathematical boundary integral equation analysis of an embedded shell under dynamic excitations a boundary integral equation method is presented for the analysis of a thin cylindrical shell embedded in an elastic half space under axisymmetric excitations by virtue of a set of ring load green s functions for the shell and a group of dynamic fundamental solutions for the semi infinite medium the structure medium interaction problem of wave propagation is shown to be reducible to a set of coupled boundary integral equations through the analysis of an auxiliary pair of cauchy integral equations the singularities of the contact stress distributions arc rendered explicit with a direct incorporation of such analytical features into the formulation an effective computational procedure is developed which involves an interpolation of regular functions only typical results for the dynamic contact load distributions displacements and complex compliance functions are included as illustrations in addition to furnishing quantities of direct engineering interest this treatment is apt to be useful as a foundation for further rigorous as well as approximate developments for various related physical problems and boundary integral methods

wave scattering by cracks in inhomogeneous continua using biem elastic wave scattering by cracks in inhomogeneous geological continua with depth dependent material parameters and under conditions of plane strain is studied in this work a restricted case of inhomogeneity is considered where poisson s ratio is fixed at one quarter while both shear modulus and density profile vary with depth but proportionally to each other furthermore time harmonic conditions are assumed to hold for this type of material the body wave speeds remain macroscopically constant and it becomes possible to recover exact green functions for the crack free inhomogeneous continuum by using an algebraic transformation method proposed in earlier work as a first step in a subsequent step the complete elastodynamic fundamental solution along with its spatial derivatives and an asymptotic expansion for small argument are all derived in closed form using the radon transform next a non hypersingular traction based boundary integral equation method biem formulation for solving boundary value problems with internal cracks is presented specifically the biem is used for computing stress intensity factors and scattered wave displacement amplitudes for an inclined line crack in an otherwise inhomogeneous continuum that is being swept by either pressure waves or vertically polarized shear waves at an arbitrary angle of incidence with respect to the horizontal direction the numerical results obtained herein reveal substantial differences between homogeneous and continuously inhomogeneous materials containing a crack in terms of their dynamic response where the latter case is assumed to give a more realistic representation of geological deposits compared to the former one finally these types of examples plus the benchmark case used for validation serve to illustrate the present approach and to show its potential for solving complex problems not just in geophysics but also in mechanics

slow feature analysis unsupervised learning of invariances invariant features of temporally varying signals are useful for analysis and classification slow feature analysis sfa is a new method for learning invariant or slowly varying features from a vectorial input signal it is based on a nonlinear expansion of the input signal and application of principal component analysis to this expanded signal and its time derivative it is guaranteed to find the optimal solution within a family of functions directly and can learn to extract a large number of decorrelated features which are ordered by their degree of invariance sfa can be applied hierarchically to process high dimensional input signals and extract complex features sfa is applied first to complex cell tuning properties based on simple cell output including disparity and motion then more complicated input output functions are learned by repeated application of sfa finally a hierarchical network of sfa modules is presented as a simple model of the visual system the same unstructured network can learn translation size rotation contrast or to a lesser degree illumination invariance for one dimensional objects depending on only the training stimulus surprisingly only a few training objects suffice to achieve good generalization to new objects the generated representation is suitable for object recognition performance degrades if the network is trained to learn multiple invariances simultaneously

the extended generalized finite element method an overview of the method and its applications an overview of the extended generalized finite element method gefm xfem with emphasis on methodological issues is presented this method enables the accurate approximation of solutions that involve jumps kinks singularities and other locally non smooth features within elements this is achieved by enriching the polynomial approximation space of the classical finite element method the gefm xfem has shown its potential in a variety of applications that involve non smooth solutions near interfaces among them are the simulation of cracks shear bands dislocations solidification and multi field problems copyright 2010 john wiley sons ltd

the dynamics of the henon map the purpose of this paper is to develop machinery which is suitable for a study of the long time behavior of systems such as the henon map with expansion combined with strong contraction our study is modeled on the treatment of the one dimensional system x 1 ax 2 and we study the perturbation of a from the value a 2 and b small a surprising number of complications arise when b 0 the computer simulations give some indication of the complicated structure of the attractor but it can safely be stated that the real difficulties do not show up the central aim of the paper is to introduce what we consider the relevant concepts and techniques needed to study mappings such as the henon one

multivariate slow feature analysis and decorrelation filtering for blind source separation we generalize the method of slow feature analysis sfa for vector valued functions of several variables and apply it to the problem of blind source separation in particular to image separation it is generally necessary to use multivariate sfa instead of univariate sfa for separating multi dimensional signals for the linear case an exact mathematical analysis is given which shows in particular that the sources are perfectly separated by sfa if and only if they and their first order derivatives are uncorrelated when the sources are correlated we apply the following technique called decorrelation filtering use a linear filter to decorrelate the sources and their derivatives in the given mixture then apply the unmixing matrix obtained on the filtered mixtures to the original mixtures if the filtered sources are perfectly separated by this matrix so are the original sources a decorrelation filter can be numerically obtained by solving a nonlinear optimization problem this technique can also be applied to other linear separation methods whose output signals are decorrelated such as ica when there are more mixtures than sources one can determine the actual number of sources by using a regularized version of sfa with decorrelation filtering extensive numerical experiments using sfa and ica with decorrelation filtering supported by mathematical analysis demonstrate the potential of our methods for solving problems involving blind source separation

modeling and identification of an arbitrarily shaped scatterer using dynamic xfem with cubic splines abstract localization and shape identification of an arbitrarily shaped scatterer embedded in elastic heterogeneous media is investigated using the dynamic extended finite element method xfem the scatterer s geometry is represented using cubic splines whose parameters are adaptively updated in a gradient based minimization framework that is used to solve the inverse identification problem the dynamic xfem is employed to solve the forward wave propagation problem because it enables direct parametric modeling of the moving boundary of the scatterer over a stationary background mesh the use of open close cubic splines combined with xfem enables the effective construction of the complicated scatterer geometry by minimizing the number of unknown shape parameters a two phase divide and conquer approach is adopted to alleviate complications due to the potential manifestation of multiple solutions to the inverse problem and for increased computational efficiency in first phase the scatterer is localized using a simple geometric representation and the search is carried out using multiple independent inversions starting from different initial estimates incidentally this strategy is perfectly scalable in parallel computation in the second phase the geometric representation is adaptively refined using cubic splines to obtain an accurate estimate of the scatterer s shape several numerical experiments are provided which clearly show that the proposed approach is robust and can yield highly accurate results

time domain boundary element analysis of elastic wave interaction with a crack the mathematical formulation of the problem of transient wave interaction with a crack in a homogeneous isotropic linearly elastic solid has been reduced to the solution of an integral equation over the insonified crack face the integral equation relates the unknown crack opening displacement which depends on time and position to the incident wave field the integral equation has been solved numerically by a time stepping method in conjunction with a boundary element discretization of the crack surface for normal incidence of a longitudinal step stress wave on a penny shaped crack results as functions of time have been obtained for the crack opening displacement the elastodynamic mode i stress intensity factor and the scattered far field

approximate determination of dispersion relations and displacement fields associated with elastic waves in bars method based on matrix formulation of hamiltons principle a method for approximate determination of dispersion relations and displacement fields associated with elastic waves in long prismatic bars is established the method is based on a matrix formulation of hamilton s principle and utilizes co ordinate functions to model the displacements in the bar the method which involves the solution of an eigenvalue problem is suitable for use in a mathematical toolbox it is applied to wave propagation in bars with square and circular cross sections the results obtained agree well with the known exact and approximate solutions the convergence rate is illustrated by systematically changing the order of the co ordinate functions

elastodynamic green s functions for a smoothly heterogeneous half space in this paper the response of a vertically heterogeneous elastic half space with a smooth modulus variation under a set of time harmonic ring and point sources is derived analytically a method of evaluation via asymptotic decomposition for the singular green s functions is presented in the technique the green s functions are decomposed into an analytical part and a residual component capturing the corresponding singular behavior the analytical parts of the ring and point load green s functions are expressible in terms of the elliptic integrals and algebraic functions respectively the residual integrals which are regular can be evaluated by numerical contour integration to obtain correct results one must note and take into account the existence of multiple poles along the formal path of the inversion integrals the details of which are discussed in the paper to highlight the various aspects of the physical problem a set of illustrative numerical results is included

runge kutta convolution quadrature methods for well posed equations with memory runge kutta based convolution quadrature methods for abstract well posed linear and homogeneous volterra equations non necessarily of sectorial type are developed a general representation of the numerical solution in terms of the continuous one is given the error and stability analysis is based on this representation which for the particular case of the backward euler method also shows that the numerical solution inherits some interesting qualitative properties such as positivity of the exact solution numerical illustrations are provided

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

runge kutta convolution quadrature for operators arising in wave propagation an error analysis of runge kutta convolution quadrature is presented for a class of non sectorial operators whose laplace transform satisfies besides the standard assumptions of analyticity in a half plane re s 0 and a polynomial bound operatorname o s mu 1 there the stronger polynomial bound operatorname o s mu 2 in convex sectors of the form operatorname arg s leq pi 2 theta for 0 the order of convergence of the runge kutta convolution quadrature is determined by 2 and the underlying runge kutta method but is independent of 1 time domain boundary integral operators for wave propagation problems have laplace transforms that satisfy bounds of the above type numerical examples from acoustic scattering show that the theory describes accurately the convergence behaviour of runge kutta convolution quadrature for this class of applications our results show in particular that the full classical order of the runge kutta method is attained away from the scattering boundary

effects of material gradients on transient dynamic mode iii stress intensity factors in a fgm abstract this paper presents a transient dynamic crack analysis for a functionally graded material fgm by using a hypersingular time domain boundary integral equation method the spatial variations of the material parameters of the fgm are described by an exponential law a numerical solution procedure is developed for solving the hypersingular time domain traction bie to avoid the use of time dependent green s functions which are not available for general fgm a convolution quadrature formula is adopted for approximating the temporal convolution while a galerkin method is applied for the spatial discretization of the hypersingular time domain traction bie numerical results for the transient dynamic stress intensity factors for a finite crack in an infinite and linear elastic fgm subjected to an impact anti plane crack face loading are presented and discussed the effects of the material gradients of the fgm on the transient dynamic stress intensity factors and their dynamic overshoot over the corresponding static stress intensity factors are analyzed

arbitrary branched and intersecting cracks with the extended finite element method summary extensions of a new technique for the nite element modelling of cracks with multiple branches multiple holes and cracks emanating from holes are presented this extended nite element method x fem allows the representation of crack discontinuities and voids independently of the mesh a standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method a methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed computation of the stress intensity factors sif in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique copyright 2000 john wiley sons ltd

enriched element free galerkin methods for crack tip fields summary the element free galerkin efg method is a meshless method for solving partial di erential equations which uses only a set of nodal points and a cad like description of the body to formulate the discrete model it has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used an enriched efg formulation for fracture problems is proposed two methods are used 1 adding the asymptotic fields to the trial function and 2 augmenting the basis by the asymptotic fields a local mapping of the enriched fields for curved cracks is also described results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom 1997 by john wiley sons ltd

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

numerical modeling of acoustic emission in laminated tensile test specimens abstract acoustic emission from transverse matrix cracks and fiber fracture in typical laminated tensile test specimens is modeled the acoustic sources are described as time dependent displacement discontinuities which subsequently are translated to volume forces the transient waves are computed using a finite element model of the specimen s cross section the finite element modeling leads to a system of differential equations in the axial coordinate and time the differential equations are solved using fourier transforms and eigenmode superposition followed by inversion of the transforms through residue calculus and fft computed time histories for matrix cracking and fiber fracture are presented the highest frequency content in these signals corresponds typically to 300 khz a method to measure the average matrix crack propagation velocity is suggested

an explicit dynamics extended finite element method part 1 mass lumping for arbitrary enrichment functions this paper presents a general mass lumping technique for explicit dynamics simulations using the extended finite element method with arbitrary enrichment functions the proposed mass lumping technique is a generalization of previously published results for cracks and holes time step estimates are studied for crack singular enrichment functions and for hole enrichment in both cases we show that the critical time step does not tend to zero and is of the same order as that of the same unenriched element the performance of the method is demonstrated on several numerical examples that compare well with classical finite elements and previously published x fem results

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

the scaled boundary finite element method analytical solution in frequency domain the scaled boundary finite element equation a system of ordinary differential equations in the radial coordinate is solved analytically applying a series expansion an eigenvalue problem of a hamiltonian matrix is solved when the difference of two eigenvalues is an even number besides the power series logarithmic functions occur two sets of independent solutions are obtained the scaled boundary finite element method is thus a semi analytical procedure to solve partial differential equations with the polynomial approximation of finite elements in the two circumferential directions and a closed form solution in the radial direction applications to bounded and unbounded domains demonstrate excellent accuracy

a hypersingular boundary integral method for two dimensional screen and crack problems we analyze hypersingular integral equations on a curved open smooth arc in r 2 that model either curved cracks in an elastic medium or the scattering of acoustic and elastic waves at a hard screen by using the mellin transformation we obtain sharp regularity results for the solution of these equations in sobolev spaces in the form of singular expansions in particular we show that the expansions do not contain logarithmic singularities

a symmetric galerkin bem variational framework for multi domain interface problems in this paper we discuss an energy based variational framework for the solution of interior problems in multiplyconnected domains comprising multiple piecewise homogeneous subdomains using exclusively boundary integral equations the primary goal is to provide a unified variational setting that lends itself naturally to symmetric galerkin boundary element formulations in terms of dirichlet type variables only the approach hinges on the explicit imposition of the normal derivative of the classical integral representation of the interior solution on each subdomain via lagrange multipliers in the augmented lagrangian of the system we use maue type identities to resolve the hypersingular kernels leading to a scheme that requires only standard singleand double layer evaluations in addition the usual difficulty with multi valued normals at subdomain corners is treated here within the same variational framework by incorporating into the variational formulation the constraint equation between the limiting normal derivatives at either side of the corner the resulting scheme remains fully symmetric the numerical implementation avoids the explicit presence of neumann type unknowns on the boundaries through condensation at the subdomain level in all integral evaluations three or four point gauss quadrature rules are sufficient for accurate results we describe the theory and present illustrative examples for thermal and acoustic problems governed by laplace and helmholtz equations respectively this technique however can be applied without essential modification to more general problems 2004 published by elsevier b v

elastic wave identification of penetrable obstacles using shape material sensitivity framework this study deals with elastic wave identification of discrete heterogeneities inclusions in an otherwise homogeneous reference solid from limited aperture waveform measurements taken on its surface on adopting the boundary integral equation bie framework for elastodynamic scattering the inverse query is cast as a minimization problem involving experimental observations and their simulations for a trial inclusion that is defined through its boundary elastic moduli and mass density for an optimal performance of the gradient based search methods suited to solve the problem explicit expressions for the shape i e boundary and material sensitivities of the misfit functional are obtained via the adjoint field approach and direct differentiation of the governing bies making use of the message passing interface the proposed sensitivity formulas are implemented in a data parallel code and integrated into a nonlinear optimization framework based on the direct bie method and an augmented lagrangian whose inequality constraints are employed to avoid solving forward scattering problems for physically inadmissible or overly distorted trial inclusion configurations numerical results for the reconstruction of an ellipsoidal defect in a semi infinite solid show the effectiveness of the proposed shape material sensitivity formulation which constitutes an essential computational component of the defect identification algorithm

runge kutta methods for parabolic equations and convolution quadrature we study the approximation properties of runge kutta time discretizations of linear and semilinear parabolic equations including incompressible navier stokes equations we derive asymptotically sharp error bounds and relate the temporal order of convergence which is generally noninteger to spatial regularity and the type of boundary conditions the analysis relies on an interpretation of runge kutta methods as convolution quadratures in a different context these can be used as efficient computational methods for the approximation of convolution integrals and integral equations they use the laplace transform of the confolution kernal via a discrete operational calculus 23 refs 2 tabs

convolution quadrature and discretized operational calculus ii operational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations singular integrals power and logarithmic singularities finite part integrals multiple timescale convolution volterra integral equations wiener hopf integral equations frequency domain conditions which determine the stability of such equations can be carried over to the discretization

time domain fundamental solution to biot s complete equations of dynamic poroelasticity part i two dimensional solution abstract this paper develops transient fundamental solution for biot s full dynamic two dimensional equations of poroelasticity an explicit well posed laplace transform domain fundamental solution is obtained for the governing differential equations which are established in terms of solid displacements and fluid pressure in some limiting cases the solutions are shown to reduce to those of classical elastodynamics and steady state poroelasticity thus ensuring the validity of our result the closed form transient fundamental solutions both for the limiting case early time approximation and for the general case are derived from corresponding ones in the laplace transform domain by means of laplace transform techniques they represent the very first satisfactory fundamental solutions in the real time domain for full dynamic poroelasticity some characteristics of the solutions are investigated selected numerical results are presented to demonstrate the features of the waves and the accuracy of the solution is established by comparing them with laplace transform domain solutions to complete the ingredients for developing the bem the betti s reciprocal theorem is extended to the full dynamic poroelasticity based on which a time domain boundary integral equation is obtained

partition of unity enrichment for bimaterial interface cracks partition of unity enrichment techniques are developed for bimaterial interface cracks a discontinuous function and the two dimensional near tip asymptotic displacement functions are added to the finite element approximation using the framework of partition of unity this enables the domain to be modelled by finite elements without explicitly meshing the crack surfaces the crack tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack the concept of partition of unity facilitates the incorporation of the oscillatory nature of the singularity within a conforming finite element approximation the mixed mode complex stress intensity factors for bimaterial interfacial cracks are numerically evaluated using the domain form of the interaction integral good agreement between the numerical results and the reference solutions for benchmark interfacial crack problems is realized copyright 2004 john wiley sons ltd

simple bifurcations leading to hyperbolic attractors we prove the existence of a new stability boundary of periodic orbits in a high dimensional case thereby resolving the problem on a blue sky catastrophe in a general one parameter family we additionally establish the existence of a codimension one boundary which separates the morsesmale systems from systems with hyperbolic smalewilliams like attractors the route across this boundary is accomplished by the disappearance of a saddle node periodic orbit we also study the principal bifurcations of a torus breakdown which lead to anosov attractors and to multidimensional solenoids

multistep and multistage convolution quadrature for the wave equation algorithms and experiments we describe how a time discretized wave equation in a homogeneous medium can be solved by boundary integral methods the time discretization can be a multistep runge kutta or a more general multistep multistage method the resulting convolutional system of boundary integral equations belongs to the family of convolution quadratures of lubich the aim of this work is twofold it describes an efficient robust and easily parallelizable method for solving the semidiscretized system the resulting algorithm has the main advantages of time stepping methods and of fourier synthesis at each time step a system of linear equations with the same system matrix needs to be solved yet computations can easily be done in parallel the computational cost is almost linear in the number of time steps and only the laplace transform of the time domain fundamental solution is needed the new aspect of the algorithm is that all this is possible without ever explicitly constructing the weights of the convolution quadrature this approach also readily allows the use of modern data sparse techniques to efficiently perform computation in space we investigate theoretically and numerically to which extent hierarchical matrix mathcal h matrix techniques can be used to speed up the space computation the second aim of this article is to perform a series of large scale 3d experiments with a range of multistep and multistage time discretization methods the backward difference formula of order 2 bdf2 the trapezoid rule and the 3 stage radau iia methods are investigated in detail one of the conclusions of the experiments is that the radau iia method often performs overwhelmingly better than the linear multistep methods especially for problems with many reflections yet in connection with hyperbolic problems bdfs have so far been predominant in the literature on convolution quadrature

a galerkin bem for transient acoustic scattering by an absorbing obstacle this paper deals with the numerical resolution of the so called time domain boundary integral equations the scattering problem by an absorbing obstacle serves as the model for this discussion a new system of retarded potential boundary integral equations rpbie is set up to solve the problem using an energy identity we are able to prove the unconditional stability for standard conforming galerkin approximation of the rpbie the actual space time boundary elements are described in some detail and their implementation has confirmed that stability in a wide range of situations and for large run times never reached before

two boundary integral equation methods for linear elastodynamics problems on unbounded domains abstract we consider transient 3d elastic wave propagation problems in unbounded isotropic homogeneous media which can be reduced to corresponding 2d ones for their solution we propose and compare two boundary integral equation approaches both based on the coupling of a discrete time convolution quadrature with a classical space collocation discretization in the first approach the pde problem is preliminarily replaced by the equivalent well known vector space time boundary integral equation formulation while in the second the same pde is replaced by a system of two coupled wave equations each one of which is then represented by the associated boundary integral equation the construction of these two approaches is described and discussed some numerical testing are also presented

on green s function for a three dimensional exponentially graded elastic solid the problem of a point force acting in an unbounded three dimensional isotropic elastic solid is considered kelvin solved this problem for homogeneous materials here the material is inhomogeneous it is functionally graded specifically the solid is exponentially graded which means that the lame moduli vary exponentially in a given fixed direction the solution for the green9s function is obtained by fourier transforms and consists of a singular part given by the kelvin solution plus a non singular remainder this grading term is not obtained in simple closed form but as the sum of single integrals over finite intervals of modified bessel functions and double integrals over finite regions of elementary functions knowledge of this new fundamental solution for graded materials permits the development of boundary integral methods for these technologically important inhomogeneous solids

transient elastic wave analysis of 3 d large scale cavities by fast multipole bem using implicit runge kutta convolution quadrature abstract existing boundary element methods bems have been proven to be efficient numerical techniques particularly in modeling wave propagation problems but still remain limitations in solving large scale problems the main disadvantages may be caused by several problems including high cost and large amount of computer memory for the computation a time domain bem in which a collocation method is used for the time discretization also shows numerical instability for small cfl courant friedrichs lewy number in this work we propose a new three dimensional 3 d approach for solving transient elastic wave propagation problems of large scale spherical and spheroidal cavities by the convolution quadrature bem accelerated by fast multipole method fmm using an implicit runge kutta scheme in abbreviation we name it as irk based cq fmbem two special techniques pertaining to the fmm including the scaling of modified spherical bessel functions and the truncation method are used to enhance the efficiency and stability of our proposed method this approach is found to be particularly suitable for 3 d large scale problems as its high accuracy stability of time marching process and computational efficiency these properties are subsequently illustrated through numerical examples dealing with large scale wave problems of 3 d single spherical and spheroidal cavities and multiple equally and irregularly spherical cavities the accuracy of the present formulation is verified by comparing the obtained results with available reference solutions in the literature some numerical aspects of time increments sizes and topological shapes of cavities and their influences on the deformations and the waveforms are investigated also detailed investigation of the computational efficiency of our proposed method such as cpu time required memory etc is presented all the implementation tasks are carried out using the tokyo tech supercomputer which is called tsubame 2 5 42

asymptotic theory for static behavior of elastic anisotropic i beams abstract end effects for prismatic anisotropic beams with thin walled open cross sections are analyzed by the variational asymptotic method the decay rates for disturbances at the ends of prismatic beams are evaluated and the most influential end disturbances are incorporated into a refined beam theory thus the foundations of vlasovs theory as well as restrictions on its applicability are obtained from the variational asymptotic point of view vlasovs theory is proved to be asymptotically correct for isotropic i beams the asymptotically correct generalization of vlasovs theory for static behavior of anisotropic beams is presented in light of this development various published generalizations of vlasovs theory for thin walled anisotropic beams are discussed comparisons with a numerical 3 d analysis are provided showing that the present approach gives the closest agreement of all published theories the procedure can be applied to any thin walled beam with open cross sections

xfem based crack detection scheme using a genetic algorithm a new computational tool is developed for the accurate detection and identification of cracks in structures to be used in conjunction with non destructive testing of specimens it is based on the solution of an inverse problem based on some measurements typically along part of the boundary of the structure that describe the response of the structure to vibration in a chosen frequency or a combination of frequencies the goal is to estimate whether the structure contains a crack and if so to find the parameters location size orientation and shape of the crack that produces a response closest to the given measurement data in some chosen norm the inverse problem is solved using a genetic algorithm ga the ga optimization process requires the solution of a very large amount of forward problems the latter are solved via the extended finite element method xfem this enables one to employ the same regular mesh for all the forward problems performance of the method is demonstrated via a number of numerical examples involving a cracked flat membrane various computational aspects of the method are discussed including the a priori estimation of the ill posedness of the crack identification problem copyright 2007 john wiley sons ltd

fast convolution quadrature for the wave equation in three dimensions this work addresses the numerical solution of time domain boundary integral equations arising from acoustic and electromagnetic scattering in three dimensions the semidiscretization of the time domain boundary integral equations by runge kutta convolution quadrature leads to a lower triangular toeplitz system of size n this system can be solved recursively in an almost linear time o n log 2 n but requires the construction of o n dense spatial discretizations of the single layer boundary operator for the helmholtz equation this work introduces an improvement of this algorithm that allows to solve the scattering problem in an almost linear time the new approach is based on two main ingredients the near field reuse and the application of data sparse techniques exponential decay of runge kutta convolution weights w n h d outside of a neighborhood of d n h where h is a time step allows to avoid constructing the near field i e singular and near singular integrals for most of the discretizations of the single layer boundary operators near field reuse the far field of these matrices is compressed with the help of data sparse techniques namely h matrices and the high frequency fast multipole method numerical experiments indicate the efficiency of the proposed approach compared to the conventional runge kutta convolution quadrature algorithm

runge kutta convolution quadrature for the boundary element method abstract time domain boundary element formulations can be established either directly in time domain or via laplace or fourier domain somewhere in between are the convolution quadrature based boundary element formulations which utilize the laplace domain fundamental solution but establish a time stepping procedure up to now in applications mostly backward differential formulas of second order are used as the underlying multistep method however in recent mathematical literature also runge kutta methods have been applied here the use of runge kutta methods is explained in detail and some numerical studies are given in these studies the backward difference based procedures are compared to runge kutta methods for a non smooth problem an l 2 norm of the error is used as the basis of comparison the convergence of which is investigated theoretically as well the results confirm that the usage of the new techniques is preferable with regard to less numerical oscillations in the solution and better representation of wave fronts

the lanczos algorithm applied to unsymmetric generalized eigenvalue problem application of the two sided lanczos recursion to the unsymmetric generalized eigenvalue problem is presented the system matrices are real and unsymmetric therefore the recursions are performed in real arithmetic and complex arithmetic is employed in the qr algorithm used to extract the eigenvalues of the transformed tridiagonal matrix the biorthonormal transformation of the unsymmetric generalized eigenvalue problem is considered in detail with appropriate proofs presented in appendices issues relating to the computer implementation of the unsymmetric generalized eigenvalue problem are discussed the example problems solved demonstrate the working of the algorithm in extracting the complex and or real eignevalues of an unsymmetric system of matrices also the algorithm is applied to extract a few of the eigenvalues of a large fluid structure interaction problem and the results are compared with the eigenfrequencies extracted by an unsymmetric subspace iteration procedure presented in the literature

autonomous coupled oscillators with hyperbolic strange attractors abstract we propose several examples of smooth low order autonomous dynamical systems which have apparently uniformly hyperbolic attractors the general idea is based on the use of coupled self sustained oscillators where due to certain amplitude nonlinearities successive epochs of damped and excited oscillations alternate because of additional phase sensitive coupling terms in the equations the transfer of excitation from one oscillator to another is accompanied by a phase transformation corresponding to some chaotic map in particular an expanding circle map or anosov map of a torus the first example we construct is a minimal model possessing an attractor of the smale williams type it is a four dimensional system composed of two oscillators the underlying amplitude equations are similar to those of the predator pray model the other three examples are systems of three coupled oscillators with a heteroclinic cycle this scheme presents more variability for the phase manipulations in the six dimensional system not only the smale williams attractor but also an attractor with arnold cat map dynamics near a two dimensional toral surface and a hyperchaotic attractor with two positive lyapunov exponents are realized

input power to waveguides calculated by a finite element method this paper considers the power injected into waveguide structures from forces that are concentrated along the waveguide but are otherwise arbitrary the motion of the structure is described by a set of coupled linear one dimensional wave equations these equations are in this work devised by the waveguide finite element method which is a versatile tool for describing wave motion in general structures that have uniform properties along one direction two separate procedures are derived the first is based on spatial and frequency averaging of a modal solution the second procedure is based on a spatial fourier transform which by nature assumes the waveguide to be infinite it is shown that in the limit of zero damping the two methods are identical subsequently input power to a stiffener in a railway car structure is calculated and compared with an in situ measurement showing a fair agreement

identification of a scatterer embedded in elastic heterogeneous media using dynamic xfem abstract a numerical approach for identifying a scatterer embedded in elastic heterogeneous media is described this scatterer may be a crack a void or an inclusion with properties that have detectable contrasts from those of the host medium the forward wave propagation problem is solved using the dynamic extended finite element method xfem which allows the boundary of the scatterer to be easily relocated over a stationary background mesh the inverse problem is cast as a minimization problem whereby the unknown shape parameters of the scatterer e g a line crack s center coordinates size and orientation are the updating parameters a gradient based method is utilized to solve the minimization problem in order to alleviate the potential manifestation of multiple solutions to the inverse problem various deployment patterns for multiple sensors are investigated and also a divide and conquer approach is adopted wherein a set of independent inversions using multiple initial guesses are carried out

flaw detection in sandwich plates based on time harmonic response using genetic algorithm an inverse identification technique is proposed to assess the presence location size and degree of flaw in the core layer of sandwich plates the time harmonic response of the sandwich plates is used as the input for inverse analysis the responses of the plates in forward analysis are predicted using finite element method fem based on mindlin plate theory the flaw is characterized by a set of parameters the genetic algorithm ga is applied to search the parameters to improve the efficiency of ga in searching for the true solution a two stage searching method is proposed numerical examples are given to illustrate the proposed technique

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

elastic wave scattering around cavities in inhomogeneous continua by the bem this work examines elastic wave scattering around cavities embedded in a continuum with depth dependent shear modulus and under conditions of plane strain a restricted case of inhomogeneity is considered where the poisson ratio is fixed at 0 25 and where the density profile also varies but proportionally to the shear modulus for this specific case the wave speeds remain macroscopically constant and it becomes possible to recover the exact green functions by using an algebraic transformation method these functions are subsequently used as kernels in a standard 2d boundary element formulation defined in the laplace transform domain the final step involves an inverse laplace transformation whereby the transient behavior of cavities in the aforementioned inhomogeneous continuum can be recovered two basic examples are solved namely the circular cylindrical cavity under sudden internal explosion and under a pressure wave sweep in the latter case it is possible to investigate the effect that the angle of wave incidence has on the displacement and stress that develop along the cavity s perimeter given the fact that the shear modulus is changing along the vertical direction these examples serve to illustrate the present approach and to reveal some interesting differences that are observed in transient wave scattering phenomena between homogeneous and continuously inhomogeneous models where the latter models yield a more realistic representation of geological formations

on models with non rough poincare homoclinic curves abstract the possibility of an a priori complete description of finite parameter models including systems with structurally unstable poincare homoclinic curves is studied the main result reported here is that systems having a countable set of moduli of equivalence and systems having infinitely many degenerate periodic and homoclinic orbits are dense in the newhouse regions of non stability we discuss the question of correctly setting a problem for the analysis of models of such type

high order contrasts for independent component analysis this article considers high order measures of independence for the independent component analysis problem and discusses the class of jacobi algorithms for their optimization several implementations are discussed we compare the proposed approaches with gradient based techniques from the algorithmic point of view and also on a set of biomedical data