a test for second order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series summary many time series are not second order stationary and it is not appropriate to analyse them by using methods designed for stationary series the paper introduces a new test for second order stationarity that detects kinds of departures from stationarity that are different from those based on fourier methods the new test is also computationally fast designed to work with gaussian and a wide range of non gaussian time series and can locate non stationarities in time and scale the test is demonstrated on earthquake explosion infant electrocardiogram and simulated time series showing varying degrees of stationarity the second main contribution develops approximate confidence intervals for time varying autocovariances for locally stationary series as the usual bands computed for stationary series are not appropriate our new bands enable practitioners to assess time varying autocovariances statistically and are exhibited on localized autocovariances of explosion and simulated time series

isogeometric boundary element analysis using unstructured t splines we couple collocated isogeometric boundary element methods and unstructured analysis suitable t spline surfaces for linear elastostatic problems we extend the definition of analysis suitable t splines to encompass unstructured control grids unstructured meshes and develop basis functions which are smooth rational polynomials defined in terms of the bezier extraction framework and which pass standard patch tests we then develop a collocation procedure which correctly accounts for sharp edges and corners extraordinary points and t junctions this approach is applied to several three dimensional problems including a real world t spline model of a propeller we believe this work clearly illustrates the power of combining new analysis suitable computer aided design technologies with established analysis methodologies in this case the boundary element method

on some techniques for approximating boundary conditions in the finite element method we discuss the stabilization of finite element methods in which essential boundary conditions are approximated by babuska s method of lagrange multipliers and we show that there is a close connection with this technique and a classical method by nitsche

error analysis of nitsche s mortar method optimal a priori and a posteriori error estimates are derived for three variants of nitsche s mortar finite elements the analysis is based on the equivalence of nitsche s method and the stabilised mixed method nitsche s method is defined so that it is robust with respect to large jumps in the material and mesh parameters over the interface numerical results demonstrate the robustness of the a posteriori error estimators

a stabilized powell sabin finite element method for the 2d euler equations in supersonic regime in this paper a powell sabin finite element ps fem scheme is presented for the solution of the 2d euler equations in supersonic regime the spatial discretization is based on ps splines that are piecewise quadratic polynomials with a global continuity defined on conforming triangulations some geometrical issues related to the practical construction of the ps elements are discussed in particular the generation of the control triangles and the imposition of the boundary conditions a stabilized formulation is considered and a novel shock capturing technique in the context of continuous finite elements is proposed to reduce oscillations around the discontinuity and compared with the classical technique proposed by tezduyar and senga 2006 the code is verified using manufactured solutions and validated using two challenging numerical examples which allows to evaluate the performance of the ps discretization in capturing the shocks

isogeometric kirchhoff love shell formulations for general hyperelastic materials abstract we present formulations for compressible and incompressible hyperelastic thin shells which can use general 3d constitutive models the necessary plane stress condition is enforced analytically for incompressible materials and iteratively for compressible materials the thickness stretch is statically condensed and the shell kinematics are completely described by the first and second fundamental forms of the midsurface we use c 1 continuous isogeometric discretizations to build the numerical models numerical tests including structural dynamics simulations of a bioprosthetic heart valve show the good performance and applicability of the presented methods

wavelet threshold estimators for data with correlated noise wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level dependent soft threshold to the coefficients in the wavelet transform a variety of threshold choices is proposed including one based on an unbiased estimate of mean squared error the practical performance of the method is demonstrated on examples including data from a neurophysiological context the theoretical properties of the estimators are investigated by comparing them with an ideal but unattainable bench mark that can be considered in the wavelet context as the risk obtained by ideal spatial adaptivity and more generally is obtained by the use of an oracle that provides information that is not actually available in the data it is shown that the level dependent threshold estimator performs well relative to the bench mark risk and that its minimax behaviour cannot be improved on in order of magnitude by any other estimator the wavelet domain structure of both short and long range dependent noise is considered and in both cases it is shown that the estimators have near optimal behaviour simultaneously in a wide range of function classes adapting automatically to the regularity properties of the underlying model the proofs of the main results are obtained by considering a more general multivariate normal decision theoretic problem

validating stationarity assumptions in time series analysis by rolling local periodograms we propose a simple and powerful procedure to validate the assumption of weak stationarity in time series analysis our focus is on processes with a slowly varying autocovariance structure the procedure evaluates the supremum over time of the l2 distance between the local sample spectral density local periodogram calculated using a segment of observations falling within a rolling window and an estimator of the spectral density obtained using the entire time series at hand large sample properties of a basic deviation process are investigated and critical values of a supremum type test are obtained using an appropriate bootstrap procedure the finite sample size and power properties of the procedure are investigated by means of simulations real data examples demonstrate the ability of the procedure to detect possible changes in the autocovariance structure of a time series and to understand their nature

local spectral analysis via a bayesian mixture of smoothing splines in many practical problems time series are realizations of nonstationary random processes these processes can often be modeled as processes with slowly changing dynamics or as piecewise stationary processes in these cases various approaches to estimating the time varying spectral density have been proposed our approach in this article is to estimate the log of the dahlhaus local spectrum using a bayesian mixture of splines the basic idea of our approach is to first partition the data into small sections we then assume that the log spectral density of the evolutionary process in any given partition is a mixture of individual log spectra we use a mixture of smoothing splines model with time varying mixing weights to estimate the evolutionary log spectrum the mixture model is fit using markov chain monte carlo techniques that yield estimates of the log spectra of the individual subsections in addition to an estimate of the local log spectral density the method yields pointwise credible intervals

wavelet processes and adaptive estimation of the evolutionary wavelet spectrum this article defines and studies a new class of non stationary random processes constructed from discrete non decimated wavelets which generalizes the cramer fourier representation of stationary time series we define an evolutionary wavelet spectrum ews which quantifies how process power varies locally over time and scale we show how the ews may be rigorously estimated by a smoothed wavelet periodogram and how both these quantities may be inverted to provide an estimable time localized autocovariance we illustrate our theory with a pedagogical example based on discrete non decimated haar wavelets and also a real medical time series example

an isogeometric analysis approach to gradient damage models continuum damage formulations are commonly used for the simulation of diffuse fracture processes implicit gradient damage models are employed to avoid the spurious mesh dependencies associated with local continuum damage models the c 0 continuity of traditional finite elements has hindered the study of higher order gradient damage approximations in this contribution we use isogeometric finite elements which allow for the construction of higher order continuous basis functions on complex domains we study the suitability of isogeometric finite elements for the discretization of higher order gradient damage approximations

a test for second order stationarity of a multivariate time series it is well known that the discrete fourier transforms dft of a second order stationary time series between two distinct fourier frequencies are asymptotically uncorrelated in contrast for a large class of second order nonstationary time series including locally stationary time series this property does not hold in this paper these starkly differing properties are used to define a global test for stationarity based on the dft of a vector time series it is shown that the test statistic under the null of stationarity asymptotically has a chi squared distribution whereas under the alternative of local stationarity asymptotically it has a noncentral chi squared distribution further if the time series is gaussian and stationary the test statistic is pivotal however in many econometric applications the assumption of gaussianity can be too strong but under weaker conditions the test statistic involves an unknown variance that is extremely difficult to directly estimate from the data to overcome this issue a scheme to estimate the unknown variance based on the stationary bootstrap is proposed the properties of the stationary bootstrap under both stationarity and nonstationarity are derived these results are used to show consistency of the bootstrap estimator under stationarity and to derive the power of the test under nonstationarity the method is illustrated with some simulations the test is also used to test for stationarity of ftse 100 and dax 30 stock indexes from january 2011 december 2012

a new non parametric stationarity test of time series in the time domain summary we propose a new double order selection test for checking second order stationarity of a time series to develop the test a sequence of systematic samples is defined via walsh functions then the deviations of the autocovariances based on these systematic samples from the corresponding autocovariances of the whole time series are calculated and the uniform asymptotic joint normality of these deviations over different systematic samples is obtained with a double order selection scheme our test statistic is constructed by combining the deviations at different lags in the systematic samples the null asymptotic distribution of the statistic proposed is derived and the consistency of the test is shown under fixed and local alternatives simulation studies demonstrate well behaved finite sample properties of the method proposed comparisons with some existing tests in terms of power are given both analytically and empirically in addition the method proposed is applied to check the stationarity assumption of a chemical process viscosity readings data set

a test for the absence of aliasing or local white noise in locally stationary wavelet time series aliasing is often overlooked in time series analysis but can seriously distort the spectrum autocovariance and their estimates we show that dyadic subsampling of a locally stationary wavelet process which can cause aliasing results in a process that is the sum of asymptotic white noise and another locally stationary wavelet process with a modified spectrum we develop a test for the absence of aliasing in a locally stationary wavelet series at a fixed location and illustrate it on simulated data and a wind energy time series a useful by product is a new test for local white noise the tests are robust to model misspecification in that it is unnecessary for the analysis and synthesis wavelets to be identical hence in principle the tests work irrespective of which wavelet is used to analyze the time series though in practice there is a tradeoff between increasing statistical power and time localization of the test

quantile spectral analysis for locally stationary time series summary classical spectral methods are subject to two fundamental limitations they can account only for covariance related serial dependences and they require second order stationarity much attention has been devoted lately to quantile based spectral methods that go beyond covariance based serial dependence features at the same time covariance based methods relaxing stationarity into much weaker local stationarity conditions have been developed for a variety of time series models here we combine those two approaches by proposing quantile based spectral methods for locally stationary processes we therefore introduce a time varying version of the copula spectra that have been recently proposed in the literature along with a suitable local lag window estimator we propose a new definition of local strict stationarity that allows us to handle completely general non linear processes without any moment assumptions thus accommodating our quantile based concepts and methods we establish a central limit theorem for the new estimators and illustrate the power of the proposed methodology by means of a simulation study moreover in two empirical studies namely of the standard poor s 500 series and a temperature data set recorded in hohenpeissenberg we demonstrate that the new approach detects important variations in serial dependence structures both across time and across quantiles such variations remain completely undetected and are actually undetectable via classical covariance based spectral methods

estimating linear dependence between nonstationary time series using the locally stationary wavelet model large volumes of neuroscience data comprise multiple nonstationary electrophysiological or neuroimaging time series recorded from different brain regions accurately estimating the dependence between such neural time series is critical since changes in the dependence structure are presumed to reflect functional interactions between neuronal populations we propose a new dependence measure derived from a bivariate locally stationary wavelet time series model since wavelets are localized in both time and scale this approach leads to a natural local and multi scale estimate of nonstationary dependence our methodology is illustrated by application to a simulated example and to electrophysiological data relating to interactions between the rat hippocampus and prefrontal cortex during working memory and decision making

symmetric and non symmetric variants of nitsche s method for contact problems in elasticity theory and numerical experiments a general nitsche method which encompasses symmetric and non symmetric variants is proposed for frictionless unilateral contact problems in elasticity the optimal convergence of the method is established both for two and three dimensional problems and lagrange affine and quadratic finite element methods two and three dimensional numerical experiments illustrate the theory

assessment of texture stationarity using the asymptotic behavior of the empirical mean and variance given textured images considered as realizations of 2 d stochastic processes a framework is proposed to evaluate the stationarity of their mean and variance existing strategies focus on the asymptotic behavior of the empirical mean and variance respectively em and ev known for some types of nondeterministic processes in this paper the theoretical asymptotic behaviors of the em and ev are studied for large classes of second order stationary ergodic processes in the sense of the wold decomposition scheme including harmonic and evanescent processes minimal rates of convergence for the em and the ev are derived for these processes they are used as criteria for assessing the stationarity of textures the experimental estimation of the rate of convergence is achieved using a nonparametric block sub sampling method our framework is evaluated on synthetic processes with stationary or nonstationary mean and variance and on real textures it is shown that anomalies in the asymptotic behavior of the empirical estimators allow detecting nonstationarities of the mean and variance of the processes in an objective way

bezier projection a unified approach for local projection and quadrature free refinement and coarsening of nurbs and t splines with particular application to isogeometric design and analysis abstract we introduce bezier projection as an element based local projection methodology for b splines nurbs and t splines this new approach relies on the concept of bezier extraction and an associated operation introduced here spline reconstruction enabling the use of bezier projection in standard finite element codes bezier projection exhibits provably optimal convergence and yields projections that are virtually indistinguishable from global l 2 projection bezier projection is used to develop a unified framework for spline operations including cell subdivision and merging degree elevation and reduction basis roughening and smoothing and spline reparameterization in fact bezier projection provides a quadrature free approach to refinement and coarsening of splines in this sense bezier projection provides the fundamental building block for h p k r adaptivity in isogeometric analysis

statistics of natural stochastic textures and their application in image denoising natural stochastic textures nsts characterized by their fine details are prone to corruption by artifacts introduced during the image acquisition process by the combined effect of blur and noise while many successful algorithms exist for image restoration and enhancement the restoration of natural textures and textured images based on suitable statistical models has yet to be further improved we examine the statistical properties of nst using three image databases we show that the gaussian distribution is suitable for many nst while other natural textures can be properly represented by a model that separates the image into two layers one of these layers contains the structural elements of smooth areas and edges while the other contains the statistically gaussian textural details based on these statistical properties an algorithm for the denoising of natural images containing nst is proposed using patch based fractional brownian motion model and regularization by means of anisotropic diffusion it is illustrated that this algorithm successfully recovers both missing textural details and structural attributes that characterize natural images the algorithm is compared with classical as well as the state of the art denoising algorithms

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

a test of stationarity for textured images this article proposes a test of stationarity for random fields on a regular lattice motivated by a problem arising from texture analysis our approach is founded on the locally stationary two dimensional wavelet ls2w process model for lattice processes that has previously been used for standard texture analysis tasks such as texture discrimination and classification we propose two variants of our stationarity test both of which can be performed on a single realization a feature of particular practical importance within texture analysis we illustrate our approach with pilled fabric data demonstrating that the test is capable of identifying visually subtle changes in stationarity supplementary material for this article is available online

texture classification by wavelet packet signatures this correspondence introduces a new approach to characterize textures at multiple scales the performance of wavelet packet spaces are measured in terms of sensitivity and selectivity for the classification of twenty five natural textures both energy and entropy metrics were computed for each wavelet packet and incorporated into distinct scale space representations where each wavelet packet channel reflected a specific scale and orientation sensitivity wavelet packet representations for twenty five natural textures were classified without error by a simple two layer network classifier an analyzing function of large regularity d sub 20 was shown to be slightly more efficient in representation and discrimination than a similar function with fewer vanishing moments d sub 6 in addition energy representations computed from the standard wavelet decomposition alone 17 features provided classification without error for the twenty five textures included in our study the reliability exhibited by texture signatures based on wavelet packets analysis suggest that the multiresolution properties of such transforms are beneficial for accomplishing segmentation classification and subtle discrimination of texture

isogeometric analysis of the cahn hilliard phase field model abstract the cahn hilliard equation involves fourth order spatial derivatives finite element solutions are not common because primal variational formulations of fourth order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally c 1 continuous there are a very limited number of two dimensional finite elements possessing c 1 continuity applicable to complex geometries but none in three dimensions we propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher order differential operators namely higher order accuracy robustness two and three dimensional geometric flexibility compact support and most importantly the possibility of c 1 and higher order continuity a nurbs based variational formulation for the cahn hilliard equation was tested on two and three dimensional problems we present steady state solutions in two dimensions and for the first time in three dimensions to achieve these results an adaptive time stepping method is introduced we also present a technique for desensitizing calculations to dependence on mesh refinement this enables the calculation of topologically correct solutions on coarse meshes opening the way to practical engineering applications of phase field methodology

the penalty free nitsche method and nonconforming finite elements for the signorini problem we design and analyse a nitsche method for contact problems compared to the seminal work of chouly and hild siam j numer anal 51 2013 pp 1295 1307 our method is constructed by expressing the contact conditions in a nonlinear function for the displacement variable instead of the lateral forces the contact condition is then imposed using the nonsymmetric variant of nitsche s method that does not require a penalty term for stability nonconforming piecewise affine elements are considered for the bulk discretization we prove optimal error estimates in the energy norm

structural break estimation for nonstationary time series models this article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive ar processes the number and locations of the piecewise ar segments as well as the orders of the respective ar processes are assumed unknown the minimum description length principle is applied to compare various segmented ar fits to the data the goal is to find the best combination of the number of segments the lengths of the segments and the orders of the piecewise ar processes such a best combination is implicitly defined as the optimizer of an objective function and a genetic algorithm is implemented to solve this difficult optimization problem numerical results from simulation experiments and real data analyses show that the procedure has excellent empirical properties the segmentation of multivariate time series is also considered assuming that the true underlying model is a segmented autoregression this procedure is shown to be consistent for estimating the location of

multiple change point detection for high dimensional time series via sparsified binary segmentation time series segmentation a k a multiple change point detection is a well established problem however few solutions are designed specifically for high dimensional situations in this paper our interest is in segmenting the second order structure of a high dimensional time series in a generic step of a binary segmentation algorithm for multivariate time series one natural solution is to combine cusum statistics obtained from local periodograms and cross periodograms of the components of the input time series however the standard maximum and average methods for doing so often fail in high dimensions when for example the change points are sparse across the panel or the cusum statistics are spuriously large in this paper we propose the sparsified binary segmentation sbs algorithm which aggregates the cusum statistics by adding only those that pass a certain threshold this sparsifying step reduces the impact of irrelevant noisy contributions which is particularly beneficial in high dimensions in order to show the consistency of sbs we introduce the multivariate locally stationary wavelet model for time series which is a separate contribution of this work

error analysis of some galerkin least squares methods for the elasticity equations the recent technique of stabilizing mixed finite element methods by augmenting the galerkin formulation with least squares terms calculated separately on each element is considered the error analysis is performed in a unified manner yielding improved results for some methods introduced earlier in addition a new formulation is introduced and analyzed method is used within two different contexts the first is in connection with the plain strain or three dimensional problems near the incompressible limit for which the poisson ratio equals one half it is well known that for these problems a standard lower order displacement finite element method will break down by now it is also well known how a working method can be obtained a new unknown the pressure is introduced and discretized with a finite element space different from that used for the displacements the finite element method obtained falls into the class of saddlepoint problems for which there is a general theory developed by brezzi and babuska 5 7 the application of this theory shows that the method converges optimally if the discrete spaces for the displacement and pressure satisfy a stability condition for a particular choice of displacement and pressure approximations it can be a difficult task to verify this babuska brezzi or inf sup condition during the last decade this problem has been intensively studied and the performances of many combinations are now known cf 18 and 23 26 for some recent extensions in addition there exists a general technique utilizing bubble functions by which a stable method can

the role of the bezier extraction operator for t splines of arbitrary degree linear dependencies partition of unity property nesting behaviour and local refinement we determine linear dependencies and the partition of unity property of t spline meshes of arbitrary degree using the bezier extraction operator local refinement strategies for standard semi standard and nonstandard t splines also by making use of the bezier extraction operator are presented for meshes of even and odd polynomial degrees a technique is presented to determine the nesting between two t spline meshes again exploiting the bezier extraction operator finally the hierarchical refinement of standard semi standard and non standard t spline meshes is discussed this technique utilises the reconstruction operator which is the inverse of the bezier extraction operator

automatic statistical analysis of bivariate nonstationary time series we propose a new method for analyzing bivariate nonstationary time series the proposed method is a statistical procedure that automatically segments the time series into approximately stationary blocks and selects the span to be used to obtain the smoothed estimates of the time varying spectra and coherence it is based on the smooth localized complex exponential slex transform which forms a library of orthogonal complex valued transforms that are simultaneously localized in time and frequency we show that the smoothed slex periodograms are consistent estimators report simulation results and apply the method to a two channel electroencephalogram dataset recorded during an epileptic seizure

wavelet transforms versus fourier transforms this note is a very basic introduction to wavelets it starts with an orthogonal basis of piecewise constant functions constructed by dilation and translation the wavelet transform maps each f x to its coefficients with respect to this basis the mathematics is simple and the transform is fast faster than the fast fourier transform which we briefly explain but approximation by piecewise constants is poor to improve this first wavelet we are led to dilation equations and their unusual solutions higher order wavelets are constructed and it is surprisingly quick to compute with them always indirectly and recursively

non uniform rational lagrange functions and its applications to isogeometric analysis of in plane and flexural vibration of thin plates abstract new basis functions were developed for isogeometric analysis iga to overcome the difficulties of iga using nurbs non uniform rational b splines on coping with dirichlet boundary conditions the new basis functions were constructed through nesting rational local lagrange interpolations like the t spline and were evaluated in similar procedure as the finite difference method explicit expressions for the new basis functions were presented due to their equivalence to the nurbs the new basis functions were named as non uniform rational lagrange nurl basis iga using nurl includes the finite element method as a special case but the geometry in iga using nurl is exact iga using nurl can carry out p refinement that has the nesting feature of the k refinement of nurbs dirichlet boundary conditions can be directly imposed in iga using nurl because the nurl are interpolation basis functions a method of directly transforming the tensor product basis of triangular patches to area coordinates was presented and the singularity problem at the edge degenerated to a single point was solved the methods developed in this work were applied to in plane and flexural vibration of thin plates comparisons with available results in literatures showed the fast convergence and high accuracy of iga using nurl and the transformation method for triangular patches introduction of a matlab toolbox of the nurl was appended

wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra we derive minimax rates for estimation in anisotropic smoothness classes this rate is attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension it is shown that this basis is superior to its one scale multiresolution analog if different degrees of smoothness in different directions are present as an important application we introduce a new adaptive wavelet estimator of the time dependent spectrum of a locally stationary time series using this model which was resently developed by dahlhaus we show that the resulting estimator attains nearly the rate which is optimal in gaussian white noise simultaneously over a wide range of smoothness classes moreover by our new approach we overcome the difficulty of how to choose the right amount of smoothing i e how to adapt to the appropriate resolution for reconstructing the local structure of the evolutionary spectrum in the time frequency plane

eigenvalues and pseudo eigenvalues of toeplitz matrices the eigenvalues of a nonhermitian toeplitz matrix a are usually highly sensitive to perturbations having condition numbers that increase exponentially with the dimension n an equivalent statement is that the resolvent zz a of a toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest exponentially large as a function of n even when z is far from the spectrum because of these facts the meaningfulness of the eigenvalues of nonhermitian toeplitz matrices for any but the most theoretical purposes should be considered suspect in many applications it is more meaningful to investigate the e pseudo eigenvalues the complex numbers z with ll zz a 11 l this paper analyzes the pseudospectra of toeplitz matrices and in particular relates them to the symbols of the matrices and thereby to the spectra of the associated toeplitz and laurent operators our results are reasonably complete in the triangular case and preliminary in the cases of nontriangular toeplitz matrices block toeplitz matrices and toeplitz like matrices with smoothly varying coefficients computed examples of pseudospectra are presented throughout and applications in numerical analysis are mentioned

c1 macroelements in adaptive finite element methods some interesting properties of composite basis functions for c1 macroelements are investigated including their use for constructing conforming c1 function spaces on non conforming adaptively refined meshes of particular interest is the classical cubic hsieh clough tocher 3 split triangle because of its simplicity and convergence properties in fourth order problems as compared with the powell sabin heindl 6 split and 12 split triangles a posteriori error indicators for adaptive refinement are developed numerical experiments demonstrate convergence rates and adaptive refinement performance based on a simplified error indicator is tested extensibility to analogous three dimensional tetrahedral elements is briefly discussed copyright 2006 john wiley sons ltd

from nurbs to nurps geometries abstract quadratic powell sabin splines and their rational extension the so called nurps surfaces are an interesting alternative for classical tensor product nurbs in the context of isogeometric analysis because they allow the use of local refinements while retaining a b spline like representation and exact description of conic sections in this paper we present a simple and effective strategy to convert a given planar geometry defined by a quadratic nurbs representation into a nurps representation suitable for the analysis

numerical solution of partial differential equations with powell sabin splines powell sabin splines are piecewise quadratic polynomials with global c 1 continuity they are defined on conforming triangulations of two dimensional domains and admit a compact representation in a normalized b spline basis recently these splines have been used successfully in the area of computer aided geometric design for the modelling and fitting of surfaces in this paper we discuss the applicability of powell sabin splines for the numerical solution of partial differential equations defined on domains with polygonal boundary a galerkin type pde discretization is derived for the variable coefficient diffusion equation special emphasis goes to the treatment of dirichlet and neumann boundary conditions finally an error estimator is developed and an adaptive mesh refinement strategy is proposed we illustrate the effectiveness of the approach by means of some numerical experiments

inverse inequalities on non quasi uniform meshes and application to the mortar element method we present a range of mesh dependent inequalities for piecewise constant and continuous piecewise linear finite element functions u defined on locally refined shape regular but possibly non quasi uniform meshes these inequalities involve norms of the form h u w s p for positive and negative s and where h is a function which reflects the local mesh diameter in an appropriate way the only global parameter involved is n the total number of degrees of freedom in the finite element space and we avoid estimates involving either the global maximum or minimum mesh diameter our inequalities include new variants of inverse inequalities as well as trace and extension theorems they can be used in several areas of finite element analysis to extend results previously known only for quasi uniform meshes to the locally refined case here we describe applications to i the theory of nonlinear approximation and ii the stability of the mortar element method for locally refined meshes

powell sabin b splines and unstructured standard t splines for the solution of the kirchhoff love plate theory exploiting bezier extraction the equations that govern kirchhoff love plate theory are solved using quadratic powell sabin b splines and unstructured standard t splines bezier extraction is exploited to make the formulation computationally efficient because quadratic powell sabin b splines result in inline image continuous shape functions they are of sufficiently high continuity to capture kirchhoff love plate theory when cast in a weak form unlike non uniform rational b splines nurbs which are commonly used in isogeometric analysis powell sabin b splines do not necessarily capture the geometry exactly however the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing and can make them competitive with respect to nurbs as no bending strip method for joined nurbs patches is needed this paper further illustrates how unstructured t splines can be modified such that they are inline image continuous around extraordinary points and that the blending functions fulfil the partition of unity property the performance of quadratic nurbs unstructured t splines powell sabin b splines and nurbs to nurps non uniform rational powell sabin b splines which are obtained by a transformation from a nurbs patch is compared in a study of a circular plate

wavelet shrinkage asymptopia much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects curves densities spectral densities images from noisy data a now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems unfortunately the results have rarely moved into practice for a variety of reasons among them being similarity to known methods computational intractability and lack of spatial adaptivity we discuss a method for curve estimation based on n noisy data translate the empirical wavelet coefficients towards the origin by an amount 2 log n n the proposal differs from those in current use is computationally practical and is spatially adaptive it thus avoids several of the previous objections further the method is nearly minimax both for a wide variety of loss functions pointwise error global error measured in l p norms pointwise and global error in estimation of derivatives and for a wide range of smoothness classes including standard holder and sobolev classes and bounded variation this is a much broader near optimality than anything previously proposed we draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves finally the theory underlying the method is interesting as it exploits a correspondence between statistical questions and questions of optimal recovery and information based complexity

mixed and stabilized finite element methods for the obstacle problem we discretize the lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods a priori and a posteriori error estimates are derived and numerically verified

fitting time series models to nonstationary processes a general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation the asymptotic properties of the estimate are derived under the assumption of possible model misspecification for autoregressive processes with time varying coefficients the estimate is compared to the least squares estimate furthermore the behavior of estimates is explained when a stationary model is fitted to a nonstationary process

powell sabin b splines for smeared and discrete approaches to fracture in quasi brittle materials abstract non uniform rational b splines nurbs and t splines can have some drawbacks when modelling damage and fracture the use of powell sabin b splines which are based on triangles can by pass these drawbacks herein smeared as well as discrete approaches to fracture in quasi brittle materials using powell sabin b splines are considered for the smeared formulation an implicit fourth order gradient damage model is adopted since quadratic powell sabin b splines employ c 1 continuous basis functions throughout the domain they are well suited for solving the fourth order partial differential equation that emerges in this higher order damage model moreover they can be generated from an arbitrary triangulation without user intervention since powell sabin b splines are generated from a classical triangulation they are not necessarily boundary fitting and in that case they are not isogeometric in the strict sense for discrete fracture approaches the degree of continuity of t splines is reduced to c 0 at the crack tip hence stresses need to be evaluated and weighted at the integration points in the vicinity of the crack tip in order to decide when the critical stress is reached in practice stress fields are highly irregular around crack tips furthermore aligning a t spline mesh with the new crack segment can be difficult powell sabin b splines also remedy these drawbacks as they are c 1 continuous at the crack tip and stresses can be directly computed which vastly increases the accuracy and simplifies the implementation moreover re meshing is more straightforward using powell sabin b splines a current limitation is that in three dimensions there is no procedure yet for constructing powell sabin b splines on arbitrary tetrahedral meshes

isogeometric fluid structure interaction analysis with emphasis on non matching discretizations and with application to wind turbines abstract in this paper we develop a framework for fluid structure interaction fsi modeling and simulation with emphasis on isogeometric analysis iga and non matching fluid structure interface discretizations we take the augmented lagrangian approach to fsi as a point of departure here the lagrange multiplier field is defined on the fluid structure interface and is responsible for coupling of the two subsystems thus the fsi formulation does not rely on the continuity of the underlying function spaces across the fluid structure interface in order to produce the correct coupling conditions between the fluid and structural subdomains however in deriving the final fsi formulation the interface lagrange multiplier is formally eliminated and the formulation is written purely in terms of primal variables avoiding the use of lagrange multipliers adds efficiency to the proposed formulation as an added benefit the ability to employ non matching grids for multi physics simulations leads to significantly relaxed requirements that are placed on the geometry modeling and meshing tools for iga we show an application of the proposed fsi formulation to the simulation of the nrel 5 mw offshore wind turbine rotor where the aerodynamics domain is modeled using volumetric quadratic nurbs while the rotor structure is modeled using a cubic t spline based discretization of a rotation free kirchhoff love shell we conclude the article by showing fsi coupling of a t spline shell with a low order finite element method fem discretization of the aerodynamics equations this combined use of iga and fem is felt to be a good balance between speed robustness and accuracy of fsi simulations for this class of problems

adaptive covariance estimation of locally stationary processes it is shown that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions we model locally stationary processes with pseudo differential operators that are time varying convolutions an adaptive covariance estimation is calculated by searching first for a best local cosine basis which approximates the covariance by a band or a diagonal matrix the estimation is obtained from regularized versions of the diagonal coefficients in the best basis

locally adaptive estimation of evolutionary wavelet spectra we introduce a wavelet based model of local stationarity this model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time a notion of time varying wavelet spectrum is uniquely de ned as a wavelet type transform of the autocovariance function with respect to so called autocorrelation wavelets this leads to a natural representation of the autocovariance which is localized on scales we propose a pointwise adaptive estimator of the time varying spectrum the behavior of the estimator studied in homogeneous and inhomogeneous regions of the wavelet spectrum

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

on the connection between the stabilized lagrange multiplier and nitsche s methods we derive nitsche s method for the domain decomposition through the stabilized lagrange multiplier method taking material parameters carefully into account this derivation naturally introduces parameter weighted average flux and stabilizing terms to nitsche s method we show stability and a priori analyses in the mesh dependent norms for both the stabilized method and nitsche s method and discuss connections between the proposed methods

haar fisz estimation of evolutionary wavelet spectra summary we propose a new haar fisz technique for estimating the time varying piecewise constant local variance of a locally stationary gaussian time series we apply our technique to the estimation of the spectral structure in the locally stationary wavelet model our method combines haar wavelets and the variance stabilizing fisz transform the resulting estimator is mean square consistent rapidly computable and easy to implement and performs well in practice we also introduce the haar fisz transform a device for stabilizing the variance of scaled x2 data and bringing their distribution close to gaussianity

an isogeometric analysis approach to gradient dependent plasticity summary gradient dependent plasticity can be used to achieve mesh objective results upon loss of well posedness of the initial boundary value problem due to the introduction of strain softening non associated flow and geometric non linearity a prominent class of gradient plasticity models considers a dependence of the yield strength on the laplacian of the hardening parameter usually an invariant of the plastic strain tensor this inclusion causes the consistency condition to become a partial differential equation in addition to the momentum balance at the internal moving boundary one has to impose appropriate boundary conditions on the hardening parameter or equivalently on the plastic multiplier this internal boundary condition can be enforced without tracking the elastic plastic boundary by requiring c1 continuity with respect to the plastic multiplier in this contribution this continuity has been achieved by using nurbs as shape functions both for the plastic multiplier and for the displacements one advantage of this isogeometric analysis approach is that the displacements can be interpolated one order higher making it consistent with the interpolation of the plastic multiplier this is different from previous approaches which have been exploited the regularising effect of gradient plasticity is shown for one and two dimensional boundary value problems this article is protected by copyright all rights reserved

acoustic isogeometric boundary element analysis an isogeometric boundary element method based on t splines is used to simulate acoustic phenomena we restrict our developments to low frequency problems to establish the fundamental properties of the proposed approach using t splines the computer aided design cad and boundary element analysis are integrated without recourse to geometry clean up or mesh generation a regularized burton miller formulation is used resulting in integrals which are at most weakly singular we employ a collocation based approach to generate the linear system of equations the method is verified against closed form solutions and direct comparisons are made with conventional lagrangian discretizations it is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the t spline the method is then applied to a real world application to illustrate the potential for integrated engineering design and analysis

isogeometric large deformation frictionless contact using t splines t spline based isogeometric analysis is applied to frictionless contact problems between deformable bodies in the context of large deformations the continuum is discretized with cubic t splines and cubic nurbs a gauss point to surface formulation is combined with the penalty method to treat the contact constraints in the discretized setting it is demonstrated that analysis suitable t splines coupled with local refinement accurately approximate contact pressures with far fewer degrees of freedom than nurbs both two and three dimensional examples are presented additionally all t spline analysis models are generated using commercially available t spline modeling software without intermediate mesh generation or geometry clean up steps

invariant tests for spatial stationarity using covariance structure we propose new tests for validating the ula model based on the received array data these tests use the structure of the covariance matrix of the data to decide whether the received data is spatially stationary invariance principles are used to ensure that the test has constant significance equivalent to a cfar test when the model is indeed true by eliminating the dependence on the covariance in addition a modification of the test is proposed for verifying stationarity within a specified subspace and heuristics are presented for distinguishing propagation effects from deviation from the ula model

isogeometric analysis with powell sabin splines for advection diffusion reaction problems abstract this paper presents the use of powell sabin splines in the context of isogeometric analysis for the numerical solution of advection diffusion reaction equations powell sabin splines are piecewise quadratic c 1 functions defined on a given triangulation with a particular macro structure we discuss the galerkin discretization based on a normalized powell sabin b spline basis we focus on the accurate detection of internal and boundary layers and on local refinements we apply the approach to several test problems and we illustrate its effectiveness by a comparison with classical finite element and recent isogeometric analysis procedures