an isogeometric method for the reissner mindlin plate bending problem we present a new isogeometric method for the discretization of the reissner mindlin plate bending problem the proposed scheme follows a recent theoretical framework that makes possible the construction of a space of smooth discrete deflections wh and a space of smooth discrete rotations h such that the kirchhoff constraint is exactly satisfied at the limit therefore we obtain a formulation which is natural from the theoretical mechanical viewpoint and locking free by construction we prove that the method is uniformly stable and satisfies optimal convergence estimates finally the theoretical results are fully supported by numerical tests

recovery based error estimation and adaptivity using high order splines over hierarchical t meshes abstract an adaptive higher order method based on a generalization of polynomial rational splines over hierarchical t meshes pht rht splines is introduced while most problems considered in isogeometric analysis can be solved efficiently when the solution is smooth many non trivial simulations have rough solutions this can be caused for example by the presence of re entrant corners in the domain for such problems a tensor product basis is less suitable for resolving the singularities that appear as refinement propagates throughout the computational domain hierarchical bases and adaptivity allow for a more efficient way of dealing with singularities by adding more degrees of freedom only where they are necessary to improve the approximation in order to drive the adaptive refinement an efficient recovery based error estimator is proposed in this work the estimator produces a recovered solution which is a more accurate approximation than the computed numerical solution several 2d and 3d numerical investigations with pht splines of higher order and greater continuity show good performance compared to uniform refinement in terms of degrees of freedom and computational cost

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

local refinement of analysis suitable t splines we develop a local refinement algorithm for analysis suitable t splines which does not produce excessive propagation of control points we then demonstrate its use as an adaptive framework for isogeometric analysis analysis suitable t splines are a class of t splines which are linearly independent and form a partition of unity these properties coupled with local refinement make this class of t splines appealing as a basis for isogeometric analysis

an interpretive model of line continuation in human visual perception abstract continuation is a fundamental intuitive property of perceptual grouping in line segregation to explain this property a hypothetical model from the standpoint of computer engineering is presented in this paper this model includes four mechanisms i e signal beaming mechanism feedback transmitting mechanism image partitioning mechanism and image revising mechanism and a temporary 3 d space called rho space or quotient space the map of excitatory and inhibitory signals from an input image is first constructed by applying some functions of the so called simple cortical cells which are sensitive to the position and orientation of the stimulus the signal beaming mechanism and feedback transmitting mechanism interact in human behaviours such as walking to resolve problems such as continuity transition fuzziness and ambiguity by using these two mechanisms the constructed map is then converted into a three dimensional quotient space in which all the members voxels satisfy the equivalence relationships so that the image partitioning mechanism can accomplish the work of line segregation the image revising mechanism is further used to eliminate the jaggedness caused by the signal transmission so that the final result of line segregation is consistent with the one from human observation this interpretive model was built on a 32 bits workstation sun 3 160 the results of several image processing simulations suggest that the hypothetical model is feasible and reasonable

isogeometric analysis using polynomial splines over hierarchical t meshes for two dimensional elastic solids isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries one of the major drawbacks of nurbs based isogeometric finite elements is the inefficiency of local refinement in this study we present an alternative to nurbs based isogeometric analysis that allows for local refinement the idea is based on polynomial splines and exploits the flexibility of t meshes for local refinement the shape functions satisfy important properties such as non negativity local support and partition of unity several numerical examples are used to demonstrate the reliability of the present method

x fem in isogeometric analysis for linear fracture mechanics the extended finite element method x fem has proven to be an accurate robust method for solving problems in fracture mechanics x fem has typically been used with elements using linear basis functions although some work has been performed using quadratics in the current work the x fem formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics in comparison with x fem with conventional finite elements of equal degree the nurbs based isogeometric analysis gives equal asymptotic convergence rates and equal accuracy with fewer degrees of freedom dof results for linear through quartic nurbs basis functions are presented for a multiplicity of one or a multiplicity equal the degree

non linear analysis of shells with arbitrary evolving cracks using xfem a new formulation and numerical procedures are developed for the analysis of arbitrary crack propagation in shells using the extended finite element method the method is valid for completely non linear problems through the thickness cracks in sandwich shells are considered an exact shell kinematics is presented and a new enrichment of the rotation field is proposed which satisfies the director inextensibility condition to avoid locking an enhanced strain formulation is proposed for the 4 node cracked shell element a finite strain plane stress constitutive model based on the logarithmic corotational rate is employed a cohesive zone model is introduced which embodies the special characteristics of the shell kinematics stress intensity factors are calculated for selected problems and crack propagation problems are solved copyright 2004 john wiley sons ltd

integration with respect to fractal functions and stochastic calculus i the classical lebesgue stieltjes integral b a fdg of real or complex valued functions on a finite interval a b is extended to a large class of integrands f and integrators g of unbounded variation the key is to use composition formulas and integration by part rules for fractional integrals and weyl derivatives in the special case of holder continuous functions f and g of summed order greater than 1 convergence of the corresponding riemann stieltjes sums is proved the results are applied to stochastic integrals where g is replaced by the wiener process and f by adapted as well as anticipating random functions in the anticipating case we work within slobodeckij spaces and introduce a stochastic integral for which the classical ito formula remains valid moreover this approach enables us to derive calculation rules for pathwise defined stochastic integrals with respect to fractional brownian motion

vector valued stochastic delay equations a weak solution and its markovian representation abstract a class of stochastic delay equations in a type 2 umd banach space e driven by the cylindrical wiener process is studied we investigate two concepts of solutions weak and generalised strong and give conditions under which they are equivalent we present an evolution equation approach in a banach space e p e l p 1 0 e proving that the solutions can be reformulated as e p valued markov processes based on the markovian representation we prove the existence and continuity of the solutions the results are applied to stochastic reaction diffusion equations with delays

application of pht splines in bending and vibration analysis of cracked kirchhoff love plates abstract in this work we present an extended geometry independent field approximation x gift formulation for cracked kirchhoff love plates the plate geometry is modeled by non uniform rational b splines nurbs while the solution is approximated by polynomial splines over hierarchical t meshes pht splines and enriched by the heaviside function and crack tip asymptotic expansions the adaptive refinement is driven by a recovery based error estimator the formulation is employed for bending and vibration analysis we compare different strategies for refinement enrichment and evaluation of fracture parameters the obtained results are shown to be in a good agreement with the reference solutions

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis abstract in this article we address adaptive methods for isogeometric analysis based on local refinement guided by recovery based a posteriori error estimates isogeometric analysis was introduced a decade ago and an impressive progress has been made related to many aspects of numerical methods and advanced applications however related to adaptive mesh refinement guided by a posteriori error estimators rather few attempts are pursued besides the use of classical residual based error estimators in this article we explore a feature common for isogeometric analysis iga namely the use of structured tensorial meshes that facilitates superconvergence behavior of the gradient in the galerkin discretization by utilizing the concept of structured mesh refinement using lr b splines our aim is to facilitate superconvergence behavior for locally refined meshes as well superconvergence behavior matches well with the use of recovery based a posteriori estimator in the superconvergent patch recovery spr procedure however to our knowledge so far the spr procedure has not been exploited in the iga community we start out by addressing the existence of derivative superconvergent points in the computed finite element solution based on b splines and lr b splines for an elliptic model problem 1d and 2d poisson then we present some recovery procedures for improving the derivatives or gradient of the isogeometric finite element solution where the spr procedure will be the main focus in particular we show that our spr procedure for the improvement of derivatives fulfills the desired consistency criteria at the end we develop a posteriori error estimator where the improved gradient obtained from the proposed recovery procedures is used numerical results are presented to illustrate the efficiency of using spr procedure for the improvement of derivatives or gradient of computed solution in isogeometric analysis then the proposed a posteriori error estimator based adaptive refinement methodology is tested to solve smooth and non smooth elliptic benchmark problems the focus is put on whether optimal convergence rates are obtained in the computed solution or not as well as the effectivity index of the proposed error estimators

extended isogeometric analysis for simulation of stationary and propagating cracks summary a novel approach based on a combination of isogeometric analysis iga and extended fem is presented for fracture analysis of structures the extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational b splines as basis functions for both the solution field approximation and the geometric description and it can reproduce crack tip singular fields and discontinuity across a crack iga has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two dimensional isotropic media concepts of the extended fem are used in iga to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip crack discontinuity is represented by the heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions also the lagrange multiplier method is used to impose essential boundary conditions moreover the subtriangles technique is utilized for improving the accuracy of integration by the gauss quadrature rule several two dimensional static and quasi static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed mode stress intensity factors are compared with analytical and extended fem results copyright 2011 john wiley sons ltd

h and p adaptivity driven by recovery and residual based error estimators for pht splines applied to time harmonic acoustics abstract in this work we demonstrate the application of pht splines for time harmonic acoustic problems modeled by the helmholtz equation solutions of the helmholtz equation have two features global oscillations associated with the wave number and local gradients caused by geometrical irregularities we show that after a sufficient number of degrees of freedom is used to approximate global oscillations adaptive refinement can capture local features of the solution we compare residual based and recovery based error estimators and investigate the performance of p refinement the simulations are done in the context of recently introduced geometry independent field approximation gift where pht splines are only used to approximate the solution while the computational domain is parameterized with nurbs this approach builds on the natural adaptation ability of pht splines and avoids the re parameterization of the nurbs geometry during the solution refinement process

a generalized finite element formulation for arbitrary basis functions from isogeometric analysis to xfem many of the formulations of cm rent research interest including iosogeometric methods and the extended finite element method use nontraditional basis functions some such as subdivision surfaces may not have convenient analytical representations the concept of an element if appropriate at all no longer coincides with the traditional definition developing a new software for each new class of basis functions is a large research burden especially if the problems involve large deformations non linear materials and contact the objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis resulting in a formulation that can be implemented within the traditional structure of a finite clement program but that permits the use of arbitrary sets of basis functions that are defined only through the input file elements ranging from a traditional linear four node tetrahedron through a higher order element combining xfem and isogeometric analysis may be specified entirely through an input file without any additional programming examples of this framework to applications with lagrange elements isogeometric elements and xfem basis functions for fracture are presented

evolution equations driven by a fractional brownian motion abstract in this paper we study nonlinear stochastic evolution equations in a hilbert space driven by a cylindrical fractional brownian motion with hurst parameter h 1 2 and nuclear covariance operator we establish the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients and for some values of the parameter h this result is applied to stochastic parabolic equation perturbed by a fractional white noise in this case if the coefficients are lipschitz continuous and bounded the existence and uniqueness of a solution holds if h d 4 the proofs of our results combine techniques of fractional calculus with semigroup estimates

variational solutions for partial differential equations driven by a fractional noise abstract in this article we develop an existence and uniqueness theory of variational solutions for a class of nonautonomous stochastic partial differential equations of parabolic type defined on a bounded open subset d r d and driven by an infinite dimensional multiplicative fractional noise we introduce two notions of such solutions for them and prove their existence and their indistinguishability by assuming that the noise is derived from an l 2 d valued fractional wiener process w h with hurst parameter h 1 1 1 whose covariance operator satisfies appropriate integrability conditions and where 0 1 denotes the holder exponent of the derivative of the nonlinearity in the stochastic term of the equations we also prove the uniqueness of solutions when the stochastic term is an affine function of the unknown random field our existence and uniqueness proofs rest upon the construction and the convergence of a suitable sequence of faedo galerkin approximations while our proof of indistinguishability is based on certain density arguments as well as on new continuity properties of the stochastic integral we define with respect to w h

fractional gaussian noise enhanced information capacity of a nonlinear neuron model with binary signal input this paper reveals the effect of fractional gaussian noise with hurst exponent h 1 2 1 on the information capacity of a general nonlinear neuron model with binary signal input the fgn and its corresponding fractional brownian motion exhibit long range strong dependent increments it extends standard brownian motion to many types of fractional processes found in nature such as the synaptic noise in the paper for the subthreshold binary signal sufficient conditions are given based on the forbidden interval theorem to guarantee the occurrence of stochastic resonance while for the suprathreshold binary signal the simulated results show that additive fgn with hurst exponent h 1 2 1 could increase the mutual information or bits count the investigation indicated that the synaptic noise with the characters of long range dependence and self similarity might be the driving factor for the efficient encoding and decoding of the nervous system

unstable invariant manifolds for stochastic pdes driven by a fractional brownian motion abstract in this paper we consider a class of stochastic partial differential equations spdes driven by a fractional brownian motion fbm with the hurst parameter bigger than 1 2 the existence of local random unstable manifolds is shown if the linear parts of these spdes are hyperbolic for this purpose we introduce a modified lyapunov perron transform which contains stochastic integrals by the singularities inside these integrals we obtain a special lyapunov perron s approach by treating a segment of the solution over time interval 0 1 as a starting point and setting up an infinite series equation involving these segments as time evolves using this approach we establish the existence of local random unstable manifolds in a tempered neighborhood of an equilibrium

rough evolution equations we generalize lyons rough paths theory in order to give a pathwise meaning to some nonlinear infinite dimensional evolution equation associated to an analytic semigroup and driven by an irregular noise as an illustration we discuss a class of linear and nonlinear 1d spdes driven by a space time gaussian noise with singular space covariance and brownian time dependence

stochastic analysis rough path analysis and fractional brownian motions in this paper we show by using dyadic approximations the existence of a geometric rough path associated with a fractional brownian motion with hurst parameter greater than 1 4 using the integral representation of fractional brownian motions we furthermore obtain a skohorod integral representation of the geometric rough path we constructed by the results in ly1 a stochastic integration theory may be established for fractional brownian motions and strong solutions and a wong zakai type limit theorem for stochastic differential equations driven by fractional brownian motions can be deduced accordingly the method can actually be applied to a larger class of gaussian processes with covariance functions satisfying a simple decay condition

stochastic calculus with respect to gaussian processes in this paper we develop a stochastic calculus with respect to a gaussian process of the form b t int t 0 k t s dw s where w is a wiener process and k t s is a square integrable kernel using the techniques of the stochastic calculus of variations we deduce change of variable formulas for the indefinite integrals and we study the approximation by riemann sums the particular case of the fractional brownian motion is discussed

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

an investigation into the closure process in human visual perception for line patterns closure property can provide a key to the image understanding in human visual perception it is a fundamental intuitive property of pattern grouping as advocated by the gestalt school of psychology the closure possesses a property to organize the world by filling in the gaps in the stimulation so that we perceive a whole object and not disjointed parts organization principle to investigate the organization principle in human visual perception for line patterns closure process and the function of visual receptive field are considered in this paper two corresponding methods from the viewpoint of computer science are presented and applied to the removal of the closure noise appearing in the binary dpc degraded paint character image one is called de disk expansion method based on the boundary information of stimulation to simulate the closure process the other is called vf visual receptive field method based on the lateral spread of excitation in neurophysiology to provide the effective vf for closure process the combination of de and vf methods is also developed a series of detailed experiments are given to illustrate the proposed algorithms and to compare the performance of the proposed algorithms with that of related existing methods morphology method and relaxation method experiments show that the proposed algorithms can obtain the better smoothing results and can reasonably simulate the closure process in human visual perception for line patterns

early warning signals for bifurcations in random dynamical systems with bounded noise abstract we consider discrete time one dimensional random dynamical systems with bounded noise which generate an associated set valued dynamical system we provide necessary and sufficient conditions for a discontinuous bifurcation of a minimal invariant set of the set valued dynamical system in terms of the derivatives of the so called extremal maps we propose an algorithm for reconstructing the derivatives of the extremal maps from a time series that is generated by iterations of the original random dynamical system we demonstrate that the derivative reconstructed for different parameters can be used as an early warning signal to detect an upcoming bifurcation and apply the algorithm to the bifurcation analysis of the stochastic return map of the koper model which is a three dimensional multiple time scale ordinary differential equation used as prototypical model for the formation of mixed mode oscillation patterns we apply our algorithm to data generated by this map to detect an upcoming transition

isogeometric finite element data structures based on bezier extraction of t splines we develop finite element data structures for t splines based on bezier extraction generalizing our previous work for nurbs as in traditional finite element analysis the extracted bezier elements are defined in terms of a fixed set of polynomial basis functions the so called bernstein basis the bezier elements may be processed in the same way as in a standard finite element computer program utilizing exactly the same data processing arrays in fact only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same a byproduct of the extraction process is the element extraction operator this operator localizes the topological and global smoothness information to the element level and represents a canonical treatment of t junctions referred to as hanging nodes in finite element analysis and a fundamental feature of t splines a detailed example is presented to illustrate the ideas copyright 2011 john wiley sons ltd

extended isogeometric analysis based on pht splines for crack propagation near inclusions summary adaptive local refinement is one of the main issues for isogeometric analysis iga in this paper an adaptive extended iga xiga approach based on polynomial splines over hierarchical t meshes pht splines for modeling crack propagation is presented the pht splines overcome certain limitations of non uniform rational b splines nurbs based formulations in particular they make local refinements feasible to drive the adaptive mesh refinement we present a recovery based error estimator for the proposed method the method is based on the xiga method in which discontinuous enrichment functions are added to the iga approximation and this method does not require remeshing as the cracks grow in addition crack propagation is modeled by successive linear extensions that are determined by the stress intensity factors sifs under linear elastic fracture mechanics the proposed method has been used to analyze numerical examples and the sifs results were compared with reference results the findings demonstrate the accuracy and efficiency of the proposed method this article is protected by copyright all rights reserved

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

local mild solutions for rough stochastic partial differential equations abstract we investigate mild solutions for stochastic evolution equations driven by a fractional brownian motion fbm with hurst parameter h 1 3 1 2 in infinite dimensional banach spaces using elements from rough paths theory we introduce an appropriate integral with respect to the fbm this allows us to solve pathwise our stochastic evolution equation in a suitable function space

linear independence of the t spline blending functions associated with some particular t meshes based on the local refinement algorithm addressed in sederberg et al 2004 17 we analyze the linear independence of the bi cubic t spline blending functions corresponding to particular t meshes

segmentation and association among lines and junctions for a line image abstract the relationships among line primitives and junctions for a line image are of great importance in pattern recognition with a conventional thinning method the thinning result may yield several short branches and multiple fork points at a junction which is the intersection of line primitives from the view of an original line image this is called the lability of the shape of the skeleton and will become an impediment in the construction of relationships among line primitives and junctions in this paper an effective approach to performing the segmentation and association among line primitives and junctions for a line image is presented the proposed approach cannot only segment the line primitives and junctions but also construct their relationships for the further interpretation of the given line image the segmentation is first performed by the analysis of line continuation to construct a map of uni olls orientation of the longest line in sight and a map of multi olls for an input line image the former is used to find the line primitives the latter to find the junctions next the two orientational maps are processed individually via a 2d median filter 2d labeling and partitioning and symmetry measuring then the line primitive containing the orientation and symmetry information and the junction containing the reasonable central point information are obtained finally the relationships among the found features are constructed by the transition of the orientation from the partitioned line primitives to the junctions the experimental results show that the proposed approach is feasible for the line type of characters under consideration

improved implementation and robustness study of the x fem for stress analysis around cracks numerical crack propagation schemes were augmented in an elegant manner by the x fem method the use of special tip enrichment functions as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh which is of industrial interest especially when a numerical model for crack propagation is desired this paper improves the implementation of the x fem method for stress analysis around cracks in three ways first the enrichment strategy is revisited the conventional approach uses a topological enrichment only the elements touching the front are enriched we suggest a geometrical enrichment in which a given domain size is enriched the improvements obtained with this enrichment are discussed second the conditioning of the x fem both for topological and geometrical enrichments is studied a preconditioner is introduced so that off the shelf iterative solver packages can be used and perform as well on x fem matrices as on standard fem matrices the preconditioner uses a local nodal cholesky based decomposition third the numerical integration scheme to build the x fem stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme a 2d benchmark problem is designed to show the improvements and the robustness

weakening the tight coupling between geometry and simulation in isogeometric analysis from sub and super geometric analysis to geometry independent field approximation gift this paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field the method inherits the main advantage of isogeometric analysis ie preserves the original exact computer aided design geometry for example given by nonuniform rational b splines but allows pairing it with an approximation space which is more suitable flexible for analysis for example t splines lr splines truncated hierarchical b splines and pht splines this generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain and therefore without weakening the link with the computer aided design model we demonstrate the use of the method with different choices of geometry and field spaces and show that despite the failure of the standard patch test the optimum convergence rate is achieved for nonnested spaces

stroke segmentation by bernstein be zier curve fitting abstract stroke segmentation is essential to the recognition of handwritten chinese characters here some new and reliable techniques are proposed first the thinning process is applied to each character to obtain the skeleton then a maximum circle technique is used to remove the spurious branches and merge the split 4 fork points all possible pairs of stroke segments connected at the same fork point are considered and the bernstein bezier curve is used to fit each pair to smooth the data and find its trend then from the result of this curve fitting we can decide which pair belongs to the same stroke finally the inflection points with very small radius of curvature are found and the stroke segmentation is carried out based on these inflection points experiments on some chinese characters show that the proposed new techniques are reliable and time saving compared with the direction method

stochastic heat equation driven by fractional noise and local time the aim of this paper is to study the d dimensional stochastic heat equation with a multiplicative gaussian noise which is white in space and has the covariance of a fractional brownian motion with hurst parameter h 0 1 in time two types of equations are considered first we consider the equation in the ito skorohod sense and later in the stratonovich sense an explicit chaos expansion for the solution is obtained on the other hand the moments of the solution are expressed in terms of the exponential moments of some weighted intersection local time of the brownian motion

abstract fractional cauchy problems with almost sectorial operators abstract of concern are the cauchy problems for linear and semilinear time fractional evolution equations involving in the linear part a linear operator a whose resolvent satisfies the estimate of growth 1 0 in a sector of the complex plane which occurs when one considers for instance the partial differential operators in the limit domain of dumb bell with a thin handle or in the space of holder continuous functions by constructing a pair of families of operators in terms of the generalized mittag leffler type functions and the resolvent operators associated with a for the first time and a deep analysis on the properties for these families we obtain the existence and uniqueness of mild solutions and classical solutions to the cauchy problems moreover we present three examples to illustrate the feasibility of our results

the existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion abstract in this paper we investigate the existence uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional brownian motion b q h t d x t a x t f t x t d t g t d b q h t with hurst parameter h 1 2 1 we also consider the existence of weak solutions

stochastic calculus for fractional brownian motion i theory in this paper a stochastic calculus is given for the fractional brownian motions that have the hurst parameter in 1 2 1 a stochastic integral of ito type is defined for a family of integrands so that the integral has zero mean and an explicit expression for the second moment this integral uses the wick product and a derivative in the path space some ito formulae or change of variables formulae are given for smooth functions of a fractional brownian motion or some processes related to a fractional brownian motion a stochastic integral of stratonovich type is defined and the two types of stochastic integrals are explicitly related a square integrable functional of a fractional brownian motion is expressed as an infinite series of orthogonal multiple integrals

thinning approach for noisy digital patterns abstract many problems difficult to solve by traditional computer algorithms can be explored by the principles of human visual perception from the hint of human visual symmetry a thinning approach for noisy digital patterns is presented in this paper it includes three main algorithms algorithm 1 is designed to find the effective circular range for each pixel containing the maximum effective information algorithm 2 is designed to compute the symmetry score of the pixel distribution in the circular range and convert the symmetry information into a gray scale image algorithm 3 provides a modified gray scale thinning algorithm for thinning the gray scale image to obtain a connected thin line experiments show that the thinning results obtained by the proposed method are properly acceptable whensnr 2 2 db and the connectedness of the thin line can be preserved

sample paths estimates for stochastic fast slow systems driven by fractional brownian motion we analyze the effect of additive fractional noise with hurst parameter h 1 2 on fast slow systems our strategy is based on sample paths estimates similar to the approach by berglund and gentz in the brownian motion case yet the setting of fractional brownian motion does not allow us to use the martingale methods from fast slow systems with brownian motion we thoroughly investigate the case where the deterministic system permits a uniformly hyperbolic stable slow manifold in this setting we provide a neighborhood tailored to the fast slow structure of the system that contains the process with high probability we prove this assertion by providing exponential error estimates on the probability that the system leaves this neighborhood we also illustrate our results in an example arising in climate modeling where time correlated noise processes have become of greater relevance recently

non planar 3d crack growth by the extended finite element and level sets part i mechanical model a methodology for solving three dimensional crack problems with geometries that are independent of the mesh is described the method is based on the extended finite element method in which the crack discontinuity is introduced as a heaviside step function via a partition of unity in addition branch functions are introduced for all elements containing the crack front the branch functions include asymptotic near tip fields that improve the accuracy of the method the crack geometry is described by two signed distance functions which in turn can be defined by nodal values consequently no explicit representation of the crack is needed examples for three dimensional elastostatic problems are given and compared to analytic and benchmark solutions the method is readily extendable to inelastic fracture problems copyright 2002 john wiley sons ltd

a class of second order mckean vlasov stochastic evolution equations driven by fractional brownian motion and poisson jumps abstract this paper focuses on a class of second order mckean vlasov stochastic evolution equations driven by a fractional brownian motion and poisson jumps specifically we allow nonlinearities and the jump term to depend not only of the state of the solution but also on the corresponding probability law of the state the global existence and uniqueness of mild solutions is established under various growth conditions and a related stability result is discussed an example is presented to illustrate the applicability of the theory

adaptive isogeometric analysis by local h refinement with t splines isogeometric analysis based on non uniform rational b splines nurbs as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space which renders a purely local refinement impossible this paper demonstrates how this difficulty can be overcome by using t splines instead t splines allow the introduction of so called t junctions which are related to hanging nodes in the standard fem obeying a few straightforward rules rectangular patches in the parameter space of the t splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry furthermore it is shown how state of the art a posteriori error estimation techniques can be combined with refinement by t splines numerical examples underline the potential of isogeometric analysis with t splines and give hints for further developments

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

fast isogeometric boundary element method based on independent field approximation abstract an isogeometric boundary element method for problems in elasticity is presented which is based on an independent approximation for the geometry traction and displacement field this enables a flexible choice of refinement strategies permits an efficient evaluation of geometry related information a mixed collocation scheme which deals with discontinuous tractions along non smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions all these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations the system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis for the required geometrical bisection of the domain a strategy for the evaluation of bounding boxes containing the supports of nurbs basis functions is presented the versatility and accuracy of the proposed methodology are demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions

an extended isogeometric thin shell analysis based on kirchhoff love theory abstract an extended isogeometric element formulation xiga for analysis of through the thickness cracks in thin shell structures is developed the discretization is based on non uniform rational b splines nurbs the proposed xiga formulation can reproduce the singular field near the crack tip and the discontinuities across the crack it is based on the kirchhoff love theory where c 1 continuity of the displacement field is required this condition is satisfied by the nurbs basis functions hence the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy the performance and validity of the formulation is tested by several benchmark examples

stochastic averaging for a class of two time scale systems of stochastic partial differential equations abstract this paper focuses on systems of stochastic partial differential equations that have a slow component driven by a fractional brownian motion and a fast component driven by a fast varying diffusion we establish an averaging principle in which the fast varying diffusion process acts as a noise and is averaged out in the limit the slow process is shown to have a limit in the l 2 sense which is characterized by the solution of a stochastic partial differential equation driven by a fractional brownian motion whose coefficients are averages of that of the original slow process with respect to the stationary measure of the fast varying diffusion this averaging principle paves a way for reduction of computational complexity the implication is that one can ignore the complex original systems and concentrate on the average systems instead

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

an isogeometric meshfree coupling approach for analysis of cracks summary this paper presents a new concurrent simulation approach to couple isogeometric analysis iga with the meshfree method for studying of crack problems in the present method the overall physical domain is divided into two sub domains which are formulated with the iga and meshfree method respectively in the meshfree sub domain the moving least squares mls shape function is adopted for the discretization of the area around crack tips and the iga sub domain is adopted in the remaining area meanwhile the interface region between the two sub domains is represented by coupled shape functions the resulting shape function which comprises both iga and meshfree shape functions satisfies the consistency condition thus ensuring convergence of the method moreover the meshfree shape functions augmented with the enriched basis functions to predict the singular stress fields near a crack tip are presented the proposed approach is also applied to simulate the crack propagation under a mixed mode condition several numerical examples are studied to demonstrate the utility and robustness of the proposed method this article is protected by copyright all rights reserved

enriched isogeometric collocation for two dimensional time harmonic acoustics abstract in this work the isogeometric collocation iga c is paired with two types of enrichment plane wave pw and generalized harmonic polynomial ghp functions to solve 2d problems for the helmholtz equation a parametric study is conducted and a detailed assessment of the performance of the method in a number of benchmark problems is provided three different collocation methods are tested for the non enriched formulation namely greville abscissae ga approximated cauchy galerkin acg and superconvergent sc points showing that the acg scheme is the best choice in terms of overall error convergence rate and ease of solving the linear system then the influence of the number of shape functions in the original and enriched basis location and number of collocation points and wave number over both the convergence rate as well as the condition number of the stiffness matrix are studied the numerical results show that 1 there is an improvement over the non enriched formulation 2 the improvement depends on the choice of the number and type of enrichment and 3 the pollution error is not completely alleviated with the enriched formulations

stochastic shell models driven by a multiplicative fractional brownian motion abstract we prove existence and uniqueness of the solution of a stochastic shell model the equation is driven by an infinite dimensional fractional brownian motion with hurst parameter h 1 2 1 and contains a non trivial coefficient in front of the noise which satisfies special regularity conditions the appearing stochastic integrals are defined in a fractional sense first we prove the existence and uniqueness of variational solutions to approximating equations driven by piecewise linear continuous noise for which we are able to derive important uniform estimates in some functional spaces then thanks to a compactness argument and these estimates we prove that these variational solutions converge to a limit solution which turns out to be the unique pathwise mild solution associated to the shell model with fractional noise as driving process

extended finite element methods for thin cracked plates with kirchhoff love theory a modelization of cracked plates under bending loads in the xfem framework is addressed the kirchhoff love model is considered it is well suited for very thin plates commonly used for instance in aircraft structures reduced hct and fvs elements are used for the numerical discretization two kinds of strategies are proposed for the enrichment around the crack tip with for both of them an enrichment area of xed size i e independant of the mesh size parameter in the rst one each degree of freedom inside this area is enriched with the nonsmooth functions that describe the asymptotic displacement near the crack tip the second strategy consists in introducing these functions in the nite element basis with a single degree of freedom for each one an integral matching is then used in order to ensure the c1 continuity of the solution at the interface between the enriched and the non enriched areas finally numerical convergence results for these strategies are presented and discussed

imposing dirichlet boundary conditions with nitsche s method and spline based finite elements a key challenge while employing non interpolatory basis functions in finite element methods is the robust imposition of dirichlet boundary conditions the current work studies the weak enforcement of such conditions for b spline basis functions with application to both second and fourth order problems this is achieved using concepts borrowed from nitsche s method which is a stabilized method for imposing constraints on surfaces conditions for the stability of the system of equations are derived for each class of problem stability parameters in the nitsche weak form are then evaluated by solving a local generalized eigenvalue problem at the dirichlet boundary the approach is designed to work equally well when the grid used to build the splines conforms to the physical boundary of interest as well as to the more general case when it does not through several numerical examples the approach is shown to yield optimal rates of convergence copyright 2010 john wiley sons ltd

viability for stochastic functional differential equations with infinite memory driven by a fractional brownian motion abstract in this paper we prove a viability result for stochastic functional differential equation with infinite memory driven by a fractional brownian motion with hurst parameter 1 2 h 1 using pathwise approach

calculation of fracture mechanics parameters for an arbitrary three dimensional crack by the equivalent domain integral method summary in this paper an equivalent domain integral edi method and the attendant numerical algorithms arc presented for the computation of a near crack tip field parameter the vector je integral and its variation along the front of an arbitrary three dimensional crack in a structural component account is taken of possible non elastic strains present in the structure in this case the near tip je values may be significantly different from the far field values jf especially under non proportional loading

isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth abstract we present a novel numerical method to simulate crack growth in 3d directly from the computer aided design cad geometry of the component without any mesh generation the method is an isogeometric boundary element method igabem based on non uniform rational b splines nurbs nurbs basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations a stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements convergence studies in the crack opening displacement is performed for a penny shaped crack and an elliptical crack two approaches to extract stress intensity factors sifs the contour m integral and the virtual crack closure integral are compared using dual integral equations the results show remarkable accuracy in the computed sifs leading to smooth crack paths and reliable fatigue lives without requiring the generation of any mesh from the cad model of the component under consideration

hitting times for gaussian processes this is the publisher s version also available electronically from http www jstor org stable 25450587 seq 1 page scan tab contents

gradient type noises ii systems of stochastic partial differential equations abstract the present paper is the second and main part of a study of partial differential equations under the influence of noisy perturbations existence and uniqueness of function solutions in the mild sense are obtained for a class of deterministic linear and semilinear parabolic boundary initial value problems if the noise data are random the results may be seen as a pathwise approach to spde s for typical examples such as spatially one dimensional stochastic heat equations with additive or multiplicative perturbations of fractional brownian type we recover and extend known results in addition we propose to consider partial noises of low order