preconditioned krylov solvers for bea the performance of a number of preconditioned krylov methods is analysed for a large variety of boundary element formulations low and high order element two dimensional 2 d and three dimensional 3 d regular singular and hypersingular collocation and symmetric galerkin single and multi zone thermal and elastic continuous and discontinuous boundary formulations with and without condensation are considered preconditioned conjugate gradient cg solvers in standard form and a form effectively operating on the normal equations cgn generalized minimal residual gmres conjugate gradient squared cgs and stabilized bi conjugate gradient bi cgstab krylov solvers are employed in this study both the primitive and preconditioned matrix operators are depicted graphically to illustrate the relative amenability of the alternative formulations to solution via kryiov methods and to contrast and explain their computational performances a notable difference between 2 d and 3 d bea operators is readily visualized in this manner numerical examples are presented and the relative conditioning of the various discrete bea operators is reflected in the performance of the krylov equation solvers a preconditioning scheme which was found to be uncompetitive in the collocation bea context is shown to make iterative solution of symmetric galerkin bea problems more economical than employing direct solution techniques we conclude that the preconditioned krylov techniques are competitive with or superior to direct methods in a wide range of boundary formulated problems and that their performance can be partially correlated with certain problem characteristics

geometric polar tracking from bearings only and doppler bearing measurements bearings only tracking bot and doppler bearing tracking dbt perform target motion analysis from measurements of bearings doppler and bearings respectively the state equations are simple for both the target and observer in the rectangular coordinates hence bot and dbt mostly work in that coordinate by developing the trigonometric relations between target and observer postions over time this paper first derives the pseudolinear equations for direct range and bearing estimation it then provides a generalized total least squares gtls and a maximum likelihood solution polar tracking has two advantages over rectangular first for applications that require range and bearing polar output avoids a coordinate conversion at every output instant second polar equations often have a smaller bias than rectangular consequently polar estimates can give a closer to the optimum initialization for iterative algorithms simulation results have validated the theoretical development confirming the near optimality of the gtls and maximum likelihood solutions

a mass matrix formulation for three dimensional dynamic fracture mechanics in this paper the dual reciprocity boundary element method is developed for the analysis of three dimensional elastodynamic fracture mechanics mixed mode problems the dual boundary element method is used to calculate the unknowns of boundary displacement and traction and the domain integrals in the elastodynamic equation are transformed into boundary integrals by the use of the dual reciprocity method dynamic stress intensity factors are determined by the crack opening displacement cod in the time domain several numerical examples are presented to demonstrate the accuracy of the method

a multi level fast multipole bem for 3 d elastodynamics in the frequency domain to reduce computational complexity and memory requirement for 3 d elastodynamics using the boundary element method bem a multi level fast multipole bem fm bem is proposed the diagonal form for the expansion of the elastodynamic fundamental solution is used with a truncation parameter adjusted to the subdivision level a feature necessary for achieving optimal computational efficiency both the single level and mul ti level forms of the elastodynamic fm bem are considered with emphasis on the latter crucial implementation issues including the truncation of the multipole expansion the optimal number of levels the direct and inverse extrapolation steps are examined in detail with the backing of numerical experiments a complexity analysis for both the single level and multi level versions is conducted the correctness and computational performances of the proposed elastodynamic fmm are demonstrated on numerical examples featuring up to o 10 6 dofs run on a single processor pc and including the diffraction of an incident p plane wave by a semi spherical or semi ellipsoidal canyon representative of topographic site effects

an asymptotically unbiased estimator for bearings only and doppler bearing target motion analysis bearings only bo and doppler bearing db target motion analysis tma attempt to obtain a target trajectory based on bearings and on doppler and bearing measurements respectively from an observer to the target the bo tma and db tma problems are nontrivial because the measurement equations are nonlinearly related to the target location parameters the pseudolinear formulation provides a linear estimator solution but the resulting location estimate is biased the instrumental variable method and the numerical maximum likelihood approach can eliminate the bias their convergence behavior however is not easy to control this paper proposes an asymptotically unbiased estimator of the tracking problem the proposed method applies least squares minimization on the pseudolinear equations with a quadratic constraint on the unknown parameters the resulting estimator is shown to be solving the generalized eigenvalue problem the proposed solution does not require initial guesses and does not have convergence problems sequential forms of the proposed algorithms for both bo tma and db tma are derived the sequential algorithms improve the estimation accuracy as a new measurement arrives and do not require generalized eigenvalue decomposition for solution update the proposed estimator achieves the cramer rao lower bound crlb asymptotically for gaussian noise before the thresholding effect occurs

transient elastodynamic antiplane crack analysis of anisotropic solids abstract transient elastodynamic analysis of an antiplane crack in anisotropic solids is presented a time domain traction boundary integral equation bie method is applied for this purpose the traction bie is hypersingular and has the crack opening displacement as its fundamental unknown quantity unlike the usual time domain bie method the present formulation applies a convolution quadrature developed by lubich lubich c 1988a b convolution quadrature and discretized operational calculus numer math 52 129 145 part i 413 425 part ii which requires only the laplace domain instead of the time domain green s functions the spatial variation of the crack opening displacement is approximated by an infinite series of chebyshev polynomials which take the local behavior of the crack opening displacement at crack tips into account by using a galerkin method the time domain bie is converted into a system of linear algebraic equations which can be solved step by step special attention is devoted to the computation of dynamic stress intensity factors of an antiplane crack in generally anisotropic solids numerical results for isotropic solids are presented and compared with the well known analytical results of thau and lu thau s a lu t h 1970 diffraction of transient horizontal shear waves by a finite crack and a finite rigid ribbon int j enggn sci 8 857 874 to check the accuracy and efficiency of the present time domain bie method the effect of the material anisotropy on the dynamic stress intensity factors is analyzed via several numerical examples

threshold region performance of maximum likelihood direction of arrival estimators this paper presents a performance analysis of the maximum likelihood ml estimator for finding the directions of arrival doas with a sensor array the asymptotic properties of this estimator are well known in this paper the performance under conditions of low signal to noise ratio snr and a small number of array snapshots is investigated it is well known that the ml estimator exhibits a threshold effect i e a rapid deterioration of estimation accuracy below a certain snr or number of snapshots this effect is caused by outliers and is not captured by standard techniques such as the crame spl acute r rao bound and asymptotic analysis in this paper approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ml estimator with high accuracy both the deterministic ml and stochastic ml estimators are treated for the single source and multisource estimation problems these approximations alleviate the need for time consuming computer simulations when evaluating the threshold region performance for the special case of a single stochastic source signal and a single snapshot it is shown that the ml estimator is not statistically efficient as snr spl rarr spl infin due to the effect of outliers

a theory of pseudoskeleton approximations abstract let an m n matrix a be approximated by a rank r matrix with an accuracy e we prove that it is possible to choose r columns and r rows of a forming a so called pseudoskeleton component which approximates a with o e r m n accuracy in the sense of the 2 norm on the way to this estimate we study the interconnection between the volume i e the determinant in the absolute value and the minimal singular value r of r r submatrices of an n r matrix with orthogonal columns we propose a lower bound better than one given by chandrasekaran and ipsen and by hong and pan for the maximum of r over all these submatrices and formulate a hypothesis on a tighter bound

bayesian wiv estimators for 3 d bearings only tma with speed constraints this paper develops bayesian weighted instrumental variable wiv estimators under equality and inequality speed constraints for the three dimensional 3 d bearings only target motion analysis tma problem which show improved estimation accuracies compared to their unconstrained counterpart incorporating the speed constraint information into our previously proposed bayesian wiv estimator imposes a quadratic constraint on this problem finding an optimal solution for the resulting non convex problem is by no means straightforward the main problem with iterative optimization methods such as the maximum a posteriori is that they require initialization and may converge to a local minimum if poorly initialized using advanced linear and nonlinear algebra techniques non iterative accurate estimators under equality and inequality constraints are developed for this problem furthermore it is proven that the proposed equality constrained estimator is approximately asymptotically unbiased and that the inequality constrained estimator is the optimal solution an approximate covariance matrix has also been developed for the constrained wiv under equality constraint simulation results indicate that the equality and inequality constrained estimators outperform their unconstrained counterpart in the simulated scenarios

a fast 3d dual boundary element method based on hierarchical matrices in this paper a fast solver for three dimensional bem and dbem is developed the technique is based on the use of hierarchical matrices for the representation of the collocation matrix and uses a preconditioned gmres for the solution of the algebraic system of equations the preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format special algorithms are developed to deal with crack problems within the context of dbem the structure of dbem matrices has been efficiently exploited and it has been demonstrated that since the cracks form only small parts of the whole structure the use of hierarchical matrices can be particularly advantageous test examples presented show that with the proposed technique substantial increase in number of elements over the crack surfaces leads only to moderate increases in memory storage and solution time

a novel power bearing approach and asymptotically optimum estimator for target motion analysis the problem of target motion analysis tma has been extensively investigated using bearing only bo doppler bearing db and other measurement data for radio frequency rf emitters signal powers follow the well known path loss law that can be utilized to aid localization and target tracking in bo tma leading to the novel power bearing pb approach as proposed in this paper our main contribution lies in the proof of the asymptotic optimality of the total least squares tls algorithm for pb tma under some mild condition the cramer rao lower bound crlb is employed to demonstrate the performance improvements of the pb tma over the bo tma our work shows the promise of the pb tma approach for rf signals

3d pseudolinear target motion analysis from angle measurements the paper presents a new pseudolinear estimator for 3d target motion analysis by a single moving ownship collecting azimuth and elevation angle measurements the 3d pseudolinear estimator is derived as a small noise approximation to the maximum likelihood estimator and consists of a 2d pseudolinear estimator for the xy components of the target motion parameters and a least squares estimator for the z component to improve the poor bias performance of the 3d pseudolinear estimator alternative estimators are proposed employing bias compensation and weighted instrumental variables a selective angle measurement implementation of weighted instrumental variables is presented to maintain a strong correlation between the instrumental variable matrix and the data matrix in the presence of large measurement noise the performance advantages of the selective angle measurement weighted instrumental variable estimator over the conventional maximum likelihood estimator are demonstrated via simulation examples

on the fast matrix multiplication in the boundary element method by panel clustering the boundary element method bem leads to a system of linear equations with a full matrix while fem yields sparse matrices this fact seems to require much computational work for the definition of the matrix for the solution of the system and in particular for the matrix vector multiplication which always occurs as an elementary in this paper a method for the approximate matrix vector multiplication is described which requires much less arithmetical work in addition the storage requirements are strongly reduced

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

characteristic exponents and invariant manifolds in hilbert space the multiplicative ergodic theorem and the construction almost everywhere of stable and unstable manifolds pesin theory are extended to differentiable dynamical systems on hilbert manifolds under some compactness assumptions the results apply to partial differential equations of evolution and also to non invertible maps of compact manifolds

a novel batch bayesian wiv estimator for three dimensional tma using bearing and elevation measurements in this paper we derive a novel batch bayesian weighted instrumental variable estimator for the three dimensional 3d target motion analysis tma problem using bearing and elevation measurements unlike most existing 3d estimators based on instrumental variables the proposed approach is able to incorporate a priori information into the estimation process and is proven to be approximately asymptotically unbiased an approximate asymptotic covariance matrix is also presented to evaluate the performance of the estimator simulation results show that the proposed estimator outperforms its non bayesian counterpart and has an estimation performance on par with the conventional iterative maximum a posteriori estimator while being orders of magnitude faster in a passive sonar tma problem moreover it was shown that the proposed approach can provide an accurate initialization for recursive estimators

bias compensation for the bearings only pseudolinear target track estimator the bearings only pseudolinear target track estimator is known to suffer from severe bias problems this paper presents a bias analysis for the pseudolinear estimator and develops a method of bias compensation resulting in a closed form reduced bias pseudolinear estimator the reduced bias estimator is then incorporated into an instrumental variable estimator to produce asymptotically unbiased target motion parameter estimates unlike batch iterative estimators the proposed instrumental variable estimator has a closed from solution and therefore avoids the convergence problems associated with iterative estimators the performance of the proposed instrumental variable estimator is illustrated by way of simulation examples and is shown to be almost identical to that of the computationally more demanding iterative maximum likelihood estimator

smooth invariant manifolds in banach spaces with nonuniform exponential dichotomy we establish the existence of smooth stable manifolds for semiflows defined by ordinary differential equations v a t v f t v in banach spaces assuming that the linear equation v a t v admits a nonuniform exponential dichotomy our proof of the ck smoothness of the manifolds uses a single fixed point problem in the unit ball of the space of ck functions with holder continuous kth derivative this is a closed subset of the space of continuous functions with the supremum norm by an apparently not so well known lemma of henry see proposition 3 the estimates showing that the functions maintain the original bounds when transformed under the fixed point operator are obtained through a careful application of the faa di bruno formula for the higher derivatives of the compositions see 31 and 35 as a consequence we obtain in a direct manner not only the exponential decay of solutions along the stable manifolds but also of their derivatives up to order k when the vector field is of class ck

a fast hierarchical dual boundary element method for three dimensional elastodynamic crack problems in this work a fast solver for large scale three dimensional elastodynamic crack problems is presented implemented and tested the dual boundary element method in the laplace transform domain is used for the accurate dynamic analysis of cracked bodies the fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the laplace parameter an aca adaptive cross approximation algorithm is used for the population of the low rank blocks and its performance at varying laplace parameters is investigated a preconditioned gmres is used for the solution of the resulting algebraic system of equations the preconditioners are built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format an original strategy based on the computation of some local preconditioners only is presented and tested to further speed up the overall analysis the reported numerical results demonstrate the effectiveness of the technique for both uncracked and cracked solids and show significant reductions in terms of both memory storage and computational time

smooth center manifolds for nonuniformly partially hyperbolic trajectories abstract we establish the existence of unique smooth center manifolds for ordinary differential equations v a t v f t v in banach spaces assuming that v a t v admits a nonuniform exponential trichotomy this allows us to show the existence of unique smooth center manifolds for the nonuniformly partially hyperbolic trajectories in addition we prove that the center manifolds are as regular as the vector field our proof of the c k smoothness of the manifolds uses a single fixed point problem in an appropriate complete metric space to the best of our knowledge we establish in this paper the first smooth center manifold theorem in the nonuniform setting

the solution of elastostatic and dynamic problems using the boundary element method based on spherical hankel element framework summary in this paper new spherical hankel shape functions are utilized to reformulate boundary element method for two dimensional 2d elastostatic and elastodynamic problems to this end the dual reciprocity dr boundary element method bem is reconsidered by employing new spherical hankel shape functions to approximate the state variables displacements and tractions of navier s differential equation using enrichment of a class of radial basis functions rbfs called spherical hankel rbfs hereafter the interpolation functions of a hankel boundary element framework has been derived for this purpose polynomial terms are added to the functional expansion that only uses spherical hankel rbf in the approximation in addition to polynomial function fields the participation of spherical bessel function fields has also increased robustness and efficiency in the interpolation it is very interesting that there is no runge phenomenon in equispaced hankel macroelements unlike equispaced classic lagrange ones several numerical examples are provided to demonstrate the effectiveness robustness and accuracy of the proposed hankel shape functions and in comparison with the classic lagrange ones they show much more accurate and stable results

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

improved pseudolinear kalman filter algorithms for bearings only target tracking despite its stability and computational complexity advantages the pseudolinear kalman filter plkf suffers from severe bias problems in bearings only target tracking applications this paper develops new variants of the plkf with significant performance improvement first a detailed analysis of the plkf bias is provided for nearly constant velocity target dynamics this analysis uncovers the specific reasons of bias in state estimation and leads to a new bias compensated plkf bc plkf algorithm with the improved bias performance the bias arising from the correlation between the measurement vector and pseudolinear noise is tackled by a novel instrumental variable kalman filter ivkf while the method of instrumental variables has been successfully applied to batch pseudolinear estimation algorithms its extension to the plkf is new the ivkf embeds the method of recursive iv estimation into the bc plkf and employs the bc plkf to construct instrumental variable vectors with desired properties the ivkf is further improved by adopting the method of selective angle measurements sam which ensures that the performance of the ivkf is not degraded by a weak correlation between the instrumental variable vector and measurement vector in low signal to noise ratio snr situations comparative simulation examples are presented to demonstrate the performance improvement of the proposed recursive estimators the bc plkf ivkf and sam ivkf over the conventional plkf and the extended kalman filter the sam ivkf is observed to provide the best estimation performance among the proposed estimators by producing a negligible estimation bias and mean squared error close to the posterior cramer rao lower bound at moderate noise levels

fundamental properties and performance of conventional bearings only target motion analysis this paper considers the problem of estimating the position and velocity of an object from noise corrupted bearing measurements obtained by a single moving observation platform the process is inherently nonlinear and exhibits unusual observability properties that are geometry dependent a maximum likelihood estimate mle of the target motion analysis solution is developed and its performance analyzed a comparison is drawn between the mle and two previously reported methods a nonlinear modified instrumental variable estimate miv and the pseudo linear estimate ple both the miv and ple are shown to derive from approximations to the nonlinear measurement equation and therefore share some common properties with the mle the limits on performance that can be expected from processing bearing data are detailed specifically for long range to baseline geometries approximate expressions for the cramer rao bound are derived extension of the results to the practical filters approximately predicts numerically observed behavior for less restrictive geometries bounds are presented incorporation of a target speed constraint on the mle results in a transition to a lower dimensional problem as noise level and range increases monte carlo experimental results are presented and the improvements realized by the mle techniques are evident

time discontinuous linear traction approximation in time domain bem scalar wave propagation analysis in the present paper the traditional bem formulation for time domain scalar wave propagation analysis is extended to a new class of problems a procedure to consider linear time interpolation for boundary tractions is worked out time discontinuities are included by adding to the standard bem equation the integral equation for velocities numerical examples are presented in order to assess the accuracy of the proposed formulation 1998 john wiley sons ltd

some quick and efficient methods for bearing only target motion analysis batch processing estimation methods for a target s trajectory assumed to be linear and uniform based only on the observation of its bearings are presented first the observer is assumed to have constant velocity so that one can only estimate the target s motion up to a multiplicative constant this motion is parameterized by three bearings at three judiciously chosen times and some simple quick yet highly efficient estimators for them are proposed the case of an observer moving nonuniformly is then considered a quadratic estimator that is similar to the pseudolinear estimator but does not have bias is introduced for the case in which the observer s motion can be decomposed into a finite number of constant velocity segments two sets of quasi sufficient statistics that permit considerable saving in computation with no significant loss of efficiency are also introduced expressions for the covariance matrix of the estimators and for their cramer rao bounds are provided

nonuniform almost reducibility of nonautonomous linear differential equations abstract we prove that a linear nonautonomous differential system with nonuniform hyperbolicity on the half line can be written as diagonal system with a perturbation which is small enough moreover we show that the diagonal terms are contained in the nonuniform exponential dichotomy spectrum for this purpose we introduce the concepts of nonuniform almost reducibility and nonuniform contractibility which are generalizations of these notions originally defined in a uniform context

nonlinear perturbations of nonuniform exponential dichotomy on measure chains abstract this paper focuses on nonlinear perturbations of flows in banach spaces corresponding to a nonautonomous dynamical system on measure chains admitting a nonuniform exponential dichotomy we first define the nonuniform exponential dichotomy of linear nonuniformly hyperbolic systems on measure chains then establish a new version of the grobman hartman theorem for nonuniformly hyperbolic dynamics on measure chains with the help of nonuniform exponential dichotomies moreover we also construct stable invariant manifolds for sufficiently small nonlinear perturbations of a nonuniform exponential dichotomy in particular it is shown that the stable invariant manifolds are lipschitz in the initial values provided that the nonlinear perturbation is a sufficiently small lipschitz perturbation

bearings only target motion analysis via instrumental variable estimation this paper deals with the instrumental variable iv estimation for the problem of target motion analysis from bearing only measurements bo tma by taking asymptotical analysis of the iv estimation a systematic method for developing consistent iv estimate and the sufficient condition for its asymptotical normality are proposed the asymptotical covariance of iv estimate is also derived explicitly which can be used to evaluate its performance these results generalize the previous studies and enhance the application of the iv estimation in target tracking numerical examples are shown to verify the theoretical results

smoothness of invariant manifolds for nonautonomous equations for semiflows generated by ordinary differential equations v a t v admitting a nonuniform exponential dichotomy we show that for any sufficiently small perturbation f there exist smooth stable and unstable manifolds for the perturbed equation v a t v f t v as an application we establish the existence of invariant manifolds for the nonuniformly hyperbolic trajectories of a semiflow in particular we obtain smooth invariant manifolds for a class of vector fields that need not be c1 for any 0 1 to the best of our knowledge no similar statement was obtained before in the nonuniformly hyperbolic setting we emphasize that we do not need to assume the existence of an exponential dichotomy but only the existence of a nonuniform exponential dichotomy with sufficiently small nonuniformity when compared to the lyapunov exponents of the original linear equation furthermore for example in the case of stable manifolds we only need to assume that there exist negative lyapunov exponents while we also allow zero exponents our proof of the smoothness of the invariant manifolds is based on the construction of an invariant family of cones

robustness of nonuniform exponential dichotomies in banach spaces we give conditions for the robustness of nonuniform exponential dichotomies in banach spaces in the sense that the existence of an exponential dichotomy for a given linear equation x a t x persists under a sufficiently small linear perturbation we also establish the continuous dependence with the perturbation of the constants in the notion of dichotomy and of the angles between the stable and unstable subspaces our proofs exhibit implicitly the exponential dichotomies of the perturbed equations in terms of fixed points of appropriate contractions we emphasize that we do not need the notion of admissibility of bounded nonlinear perturbations we also obtain related robustness results in the case of nonuniform exponential contractions in addition we establish an appropriate version of robustness for nonautonomous dynamical systems with discrete time

a weakly singular sgbem for analysis of cracks in 3d anisotropic media abstract a weakly singular symmetric galerkin boundary element method sgbem is developed for analysis of fractures in three dimensional anisotropic linearly elastic media the method constitutes a generalization of that by li et al s li m e mear l xiao symmetric weak form integral equation method for three dimensional fracture analysis comput methods appl mech engrg 151 1998 435 459 for isotropic media and is based upon a pair of weak form displacement and traction integral equations recently established by rungamornrat and mear j rungamornrat m e mear weakly singular weak form integral equations for cracks in three dimensional anisotropic media int j solids struct 45 2008 1283 1301 the formulation involves only weakly singular kernels and as a consequence standard c 0 elements can be employed in the numerical discretization the kernels possess a relatively simple form for general anisotropy which involves an equatorial line integral like that associated with the displacement fundamental solution despite their simple form it is still necessary to evaluate these kernels efficiently in the numerical implementation to do so certain symmetry properties associated with the specific material type under consideration are exploited and a simple yet accurate interpolation strategy is introduced another important aspect of the numerical treatment is the use of a special crack tip element which allows highly accurate mixed mode stress intensity factor data to be extracted as a function of position along the crack front this crack tip element was originally introduced by li et al s li m e mear l xiao symmetric weak form integral equation method for three dimensional fracture analysis comput methods appl mech engrg 151 1998 435 459 in their treatment of isotropic media and here it is extended to allow evaluation of the stress intensity factors for generally anisotropic media the element involves extra degrees of freedom associated with the nodes along the crack front with these quantities being directly related to the stress intensity factors and it is capable of representing the asymptotic behavior in the vicinity of the crack front to a sufficiently high order that relatively large crack tip elements can be utilized various examples are treated for cracks in an unbounded domain and for both embedded and surface breaking cracks in a finite domain and it is demonstrated that very accurate results can be obtained even with relatively coarse meshes

a fast dual boundary element method for 3d anisotropic crack problems in the present paper a fast solver for dual boundary element analysis of 3d anisotropic crack problems is formulated implemented and tested the fast solver is based on the use of hierarchical matrices for the representation of the collocation matrix the admissible low rank blocks are computed by adaptive cross approximation aca the performance of aca against the accuracy of the adopted computational scheme for the evaluation of the anisotropic kernels is investigated focusing on the balance between the kernel representation accuracy and the accuracy required for aca the system solution is computed by a preconditioned gmres and the preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format the effectiveness of the proposed technique for anisotropic crack problems has been numerically demonstrated highlighting the accuracy as well as the significant reduction in memory storage and analysis time in particular it has been numerically shown that the computational cost grows almost linearly with the number of degrees of freedom obtaining up to solution speedups of order 10 for systems of order 104 moreover the sensitivity of the performance of the numerical scheme to materials with different degrees of anisotropy has been assessed copyright 2009 john wiley sons ltd

utilization of modified polar coordinates for bearings only tracking previous studies have shown that the cartesian coordinate extended kalman filter exhibits unstable behavior characteristics when utilized for bearings only target motion analysis tma in contrast formulating the tma estimation problem in modified polar mp coordinates leads to an extended kalman filter which is both stable and asymptotically unbiased exact state equations for the mp filter are derived without imposing any restrictions on own ship motion thus prediction accuracy inherent in the traditional cartesian formulation is completely preserved in addition these equations reveal that mp coordinates are well suited for bearings only tma because they automatically decouple observable and unobservable components of the estimated state vector such decoupling is shown to prevent covariance matrix ill conditioning which is the primary cause of filter instability further investigation also confirms that the mp state estimates are asymptotically unbiased realistic simulation data are presented to support these findings and to compare algorithm performance with respect to the cramer rao lower bound ideal as well as the cartesian and pseudolinear filters

stable manifolds for nonautonomous equations without exponential dichotomy abstract we consider nonautonomous ordinary differential equations v a t v in banach spaces and under fairly general assumptions we show that for any sufficiently small perturbation f there exists a stable invariant manifold for the perturbed equation v a t v f t v which corresponds to the set of negative lyapunov exponents of the original linear equation the main assumption is the existence of a nonuniform exponential dichotomy with a small nonuniformity i e a small deviation from the classical notion of uniform exponential dichotomy in fact we showed that essentially any linear equation v a t v admits a nonuniform exponential dichotomy and thus the above assumption only concerns the smallness of the nonuniformity of the dichotomy this smallness is a rather common phenomenon at least from the point of view of ergodic theory almost all linear variational equations obtained from a measure preserving flow admit a nonuniform exponential dichotomy with arbitrarily small nonuniformity we emphasize that we do not need to assume the existence of a uniform exponential dichotomy and that we never require the nonuniformity to be arbitrarily small only sufficiently small our approach is related to the notion of lyapunov regularity which goes back to lyapunov himself although it is apparently somewhat forgotten today in the theory of differential equations

stable manifolds for nonuniform polynomial dichotomies we establish the existence of smooth stable manifolds in banach spaces for sufficiently small perturbations of a new type of dichotomy that we call nonuniform polynomial dichotomy this new dichotomy is more restrictive in the nonuniform part but allow the uniform part to obey a polynomial law instead of an exponential more restrictive law we consider two families of perturbations for one of the families we obtain local lipschitz stable manifolds and for the other family assuming more restrictive conditions on the perturbations and its derivatives we obtain c1 global stable manifolds finally we present an example of a family of nonuniform polynomial dichotomies and apply our results to obtain stable manifolds for some perturbations of this family

parameter dependence of stable manifolds under nonuniform hyperbolicity abstract for a nonautonomous linear equation v a t v in a banach space with a nonuniform exponential dichotomy we show that the nonlinear equation v a t v f t v has stable invariant manifolds v which are lipschitz in the parameter provided that f is a sufficiently small lipschitz perturbation since any linear equation with nonzero lyapunov exponents has a nonuniform exponential dichotomy the above assumption is very general we emphasize that passing from a classical uniform exponential dichotomy to a general nonuniform exponential dichotomy requires a substantially new approach

cracks in three dimensions a dynamic dual boundary element analysis in this paper the dual boundary integral equation for three dimensional dynamic problems in laplace space is presented for the first time the dual boundary element method is used to calculate dynamic stress intensity factors for three dimensional cracked structures the application of laplace transforms to the time dependent equations of elasticity reduce the problem to a static one in laplace space the displacement and traction boundary integral equations for the transformed variables are established by somigliana s identity by applying the displacement integral equation on one of the crack surfaces and the traction boundary integral equation on the other a general mixed mode crack problem can be solved in a single region in the same way as a static problem the transformed mixed mode stress intensity factors are calculated from the transformed displacement discontinuities near the crack tip the dynamic stress intensity factors in the time domain are obtained by the use of durbin s inversion method the accuracy of this method is demonstrated by its application to embedded penny shaped and elliptical cracks and edge cracks

a single region time domain bem for dynamic crack problems abstract a time domain boundary element method which allows the analysis of dynamic crack problems by using a single region formulation is presented the present method generates the distinct set of boundary integral equations by applying the displacement equation to one of the crack surfaces and the traction equation to the other the boundary of the structure is divided into continuous semi discontinuous and discontinuous quadratic elements the temporal variation of boundary displacements and tractions is approximated by piecewise linear and constant functions respectively the dynamic stress intensity factors are calculated using the crack opening displacements and the path independent integral this method is used to study dynamic behaviour of stationary cracks in finite and infinite domains in two dimensional analysis the results for two examples are compared with other reported solutions showing good agreement

lyapunov regularity of impulsive differential equations abstract for linear impulsive differential equations we give a simple criterion for the existence of a nonuniform exponential dichotomy which includes uniform exponential dichotomies as a very special case for this we introduce the notion of lyapunov regularity for a linear impulsive differential equation in terms of the so called regularity coefficient the theory is then used to show that if the lyapunov exponents are nonzero then there is a nonuniform exponential behavior which can be expressed in terms of the lyapunov exponents of the differential equation and of the regularity coefficient we also consider the particular case of nonuniform exponential contractions when there are only negative lyapunov exponents having this relation in mind it is also of interest to provide alternative characterizations of lyapunov regularity and particularly to obtain sharp lower and upper bound for the regularity coefficient in particular we obtain bounds expressed in terms of the matrices defining the impulsive linear system and we obtain characterizations in terms of the exponential growth rate of volumes in addition we establish the persistence of the stability of a linear impulsive differential equation under sufficiently small nonlinear perturbations