manifold based isogeometric analysis basis functions with prescribed sharp features abstract we introduce manifold based basis functions for isogeometric analysis of surfaces with arbitrary smoothness prescribed c 0 continuous creases and boundaries the utility of the manifold based surface construction techniques in isogeometric analysis was demonstrated in majeed and cirak cmame 2017 the respective basis functions are derived by combining differential geometric manifold techniques with conformal parametrisations and the partition of unity method the connectivity of a given unstructured quadrilateral control mesh in r 3 is used to define a set of overlapping charts each vertex with its attached elements is assigned a corresponding conformally parametrised planar chart domain in r 2 so that a quadrilateral element is present on four different charts on the collection of unconnected chart domains the partition of unity method is used for approximation the transition functions required for navigating between the chart domains are composed out of conformal maps the necessary smooth partition of unity or blending functions for the charts are assembled from tensor product b spline pieces and require in contrast to earlier constructions no normalisation creases are introduced across user tagged edges of the control mesh planar chart domains that include creased edges or are adjacent to the domain boundary require special local polynomial approximants in the partition of unity method three different types of chart domain geometries are necessary to consider boundaries and arbitrary number and arrangement of creases the new chart domain geometries are chosen so that it becomes trivial to establish local polynomial approximants that are always c 0 continuous across the tagged edges the derived non rational manifold based basis functions correspond to the vertices of the mesh and may have an arbitrary number of creases and prescribed smoothness this makes them particularly well suited for isogeometric analysis of kirchhoff love thin shells with kinks which require c 1 continuous basis functions that are c 0 continuous across the kinks we demonstrate the convergence and utility of the new basis functions with linear and nonlinear beam plate and shell examples

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

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

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

a hierarchical approach to adaptive local refinement in isogeometric analysis abstract adaptive local refinement is one of the key issues in isogeometric analysis in this article we present an adaptive local refinement technique for isogeometric analysis based on extensions of hierarchical b splines we investigate the theoretical properties of the spline space to ensure fundamental properties like linear independence and partition of unity furthermore we use concepts well established in finite element analysis to fully integrate hierarchical spline spaces into the isogeometric setting this also allows us to access a posteriori error estimation techniques numerical results for several different examples are given and they turn out to be very promising

functional approach to the error control in adaptive iga schemes for elliptic boundary value problems abstract this work presents a numerical study of functional type a posteriori error estimates for iga approximation schemes in the context of elliptic boundary value problems along with the detailed discussion of the most crucial properties of such estimates we present the algorithm of a reliable solution approximation together with the scheme of an efficient a posteriori error bound generation in this approach we take advantage of b thb spline s high smoothness for the auxiliary vector function reconstruction which at the same time allows to use much coarser meshes and decrease the number of unknowns substantially the most representative numerical results obtained during a systematic testing of error estimates are presented in the second part of the paper the efficiency of the obtained error bounds is analysed from both the error estimation indication and the computational expenses points of view several examples illustrate that functional error estimates alternatively referred to as the majorants and minorants of deviation from an exact solution perform a much sharper error control than for instance residual based error estimates simultaneously assembling and solving routines for an auxiliary variables reconstruction which generate the majorant or minorant of an error can be executed several times faster than the routines for a primal unknown

spline based deforming ellipsoids for interactive 3d bioimage segmentation we present a new fast active contour model a k a snake for image segmentation in 3d microscopy we introduce a parametric design that relies on exponential b spline bases and allows us to build snakes that are able to reproduce ellipsoids we design our bases to have the shortest possible support subject to some constraints thus computational efficiency is maximized the proposed 3d snake can approximate blob like objects with good accuracy and can perfectly reproduce spheres and ellipsoids irrespective of their position and orientation the optimization process is remarkably fast due to the use of gauss theorem within our energy computation scheme our technique yields successful segmentation results even for challenging data where object contours are not well defined this is due to our parametric approach that allows one to favor prior shapes in addition this paper provides a software that gives full control over the snakes via an intuitive manipulation of few control points

guaranteed error bounds and local indicators for adaptive solvers using stabilised space time iga approximations to parabolic problems abstract the paper is concerned with space time iga approximations to parabolic initial boundary value problems we deduce guaranteed and fully computable error bounds adapted to special features of such type of approximations and investigate their efficiency the derivation of error estimates is based on the analysis of the corresponding integral identity and exploits purely functional arguments in the maximal parabolic regularity setting the estimates are valid for any approximation from the admissible energy class and do not contain mesh dependent constants they provide computable and fully guaranteed error bounds for the norms arising in stabilised space time approximations furthermore a posterior error estimates yield efficient error indicators enhancing the performance of adaptive solvers and generate very successful mesh refinement procedures theoretical results are verified with a series of numerical examples in which approximate solutions and the corresponding fluxes are recovered by iga techniques the numerical results confirm the high efficiency of the method in the context of the two main goals of a posteriori error analysis estimation of global errors and mesh adaptation

a super smooth c1 spline space over planar mixed triangle and quadrilateral meshes abstract in this paper we introduce a c 1 spline space over mixed meshes composed of triangles and quadrilaterals suitable for fem based or isogeometric analysis in this context a mesh is considered to be a partition of a planar polygonal domain into triangles and or quadrilaterals the proposed space combines the argyris triangle cf argyris et al 1968 with the c 1 quadrilateral element introduced in brenner and sung 2005 kapl et al 2020 for polynomial degrees p 5 the space is assumed to be c 2 at all vertices and c 1 across edges and the splines are uniquely determined by c 2 data at the vertices values and normal derivatives at chosen points on the edges and values at some additional points in the interior of the elements the motivation for combining the argyris triangle element with a recent c 1 quadrilateral construction inspired by isogeometric analysis is two fold on one hand the ability to connect triangle and quadrilateral finite elements in a c 1 fashion is non trivial and of theoretical interest we provide not only approximation error bounds but also numerical tests verifying the results on the other hand the construction facilitates the meshing process by allowing more flexibility while remaining c 1 everywhere this is for instance relevant when trimming of tensor product b splines is performed in the presented construction we assume to have bi linear element mappings and piecewise polynomial function spaces of arbitrary degree p 5 the basis is simple to implement and the obtained results are optimal with respect to the mesh size for l l 2 as well as sobolev norms h 1 and h 2

adaptively refined multi patch b splines with enhanced smoothness a spline space suitable for isogeometric analysis iga on multi patch domains is presented our construction is motivated by emerging requirements in isogeometric simulations in particular iga spaces should allow for adaptive mesh refinement and they should guarantee the optimal smoothness of the discretized solution even across interfaces of adjacent patches given a domain manifold m consisting of individual patches isomorphic to the unit square or cube that are glued together along interfaces we present a construction of multi patch b splines defined on them their smoothness is enhanced by locally modifying or merging basis functions around the boundary of each patch the resulting multi patch b splines with enhanced smoothness mpbes possess the property of local linear independence and form a non negative partition of unity moreover their span can be characterized as the linear space of all piecewise polynomial functions on the domain manifold that possess certain smoothness properties subsequently adaptively refined mpbes are obtained by generalizing the construction of truncated hierarchical th b splines more precisely a nested sequence of spaces spanned by mpbes is considered corresponding to steps of local enrichment in addition an inversely nested sequence of subdomains which are submanifolds of m is used to specify the local refinement level of functions in these spaces finally truncated hierarchical mpbes are obtained by means of the selection and truncation mechanism of thb splines the desired properties of linear independence and convex partition of unity are maintained the paper presents several numerical examples which demonstrate potential applications of the new basis in isogeometric analysis

adaptive isogeometric analysis with hierarchical box splines abstract isogeometric analysis is a recently developed framework based on finite element analysis where the simple building blocks in geometry and solution space are replaced by more complex and geometrically oriented compounds box splines are an established tool to model complex geometry and form an intermediate approach between classical tensor product b splines and splines over triangulations local refinement can be achieved by considering hierarchically nested sequences of box spline spaces since box splines do not offer special elements to impose boundary conditions for the numerical solution of partial differential equations pdes we discuss a weak treatment of such boundary conditions along the domain boundary an appropriate domain strip is introduced to enforce the boundary conditions in a weak sense the thickness of the strip is adaptively defined in order to avoid unnecessary computations numerical examples show the optimal convergence rate of box splines and their hierarchical variants for the solution of pdes

isogeometric analysis using lr b splines abstract the recently proposed locally refined b splines denoted lr b splines by dokken et al 2013 6 may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided design and finite element analysis in this paper we propose local refinement strategies for adaptive isogeometric analysis using lr b splines and investigate its performance by doing numerical tests on well known benchmark cases the theory behind lr b spline is not presented in full details but the main conceptual ingredients are explained and illustrated by a number of examples

effortless quasi interpolation in hierarchical spaces we present a general and simple procedure to construct quasi interpolants in hierarchical spaces such spaces are composed of a hierarchy of nested spaces and provide a flexible framework for local refinement the proposed hierarchical quasi interpolants are described in terms of the so called truncated hierarchical basis assuming a quasi interpolant is selected for each space associated with a particular level in the hierarchy the hierarchical quasi interpolants are obtained without any additional manipulation the main properties like polynomial reproduction of the quasi interpolants selected at each level are locally preserved in the hierarchical construction we show how to construct hierarchical local projectors and the local approximation order of the underling hierarchical space is also investigated the presentation is detailed for the truncated hierarchical b spline basis and we discuss its extension to a more general framework

thb splines an effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis local refinement with hierarchical b spline structures is an active topic of research in the context of geometric modeling and isogeometric analysis by exploiting a multilevel control structure we show that truncated hierarchical b spline thb spline representations support interactive modeling tools while simultaneously providing effective approximation schemes for the manipulation of complex data sets and the solution of partial differential equations via isogeometric analysis a selection of illustrative 2d and 3d numerical examples demonstrates the potential of the hierarchical framework

further developments and tests of a progressive algorithm for multiple criteria decision making p korhonen h moskowitz and j wallenius 1986 developed a progressive algorithm and the supporting theory for modeling and solving multiple criteria decision problems with discrete alternatives a special feature of the algorithm is that it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision maker s dm s preference structure or value function the algorithm is based on progressively sampling the decision space obtaining preference information from the dm determining the likelihood of finding possibly surely better alternatives and based on this information continuing the search or terminating it by making the final choice we describe a computerized implementation and extensive computational tests of the algorithm as well as some of our experiences in applying and field testing it in practice we also consider several improvements and developments of the algorithm to further facilitate its use in practice

on the local linear independence of generalized subdivision functions characterizing the linear and local linear independence of the functions that span a linear space is a key task if the space is to be used computationally given a control net the spanning functions of one spatial coordinate of a generalized subdivision surface are called nodal functions they are the limit under subdivision of associating the value one with one control net node and zero with all others no characterization of independence of nodal functions has been published to date even for the two most popular generalized subdivision algorithms catmull clark subdivision and loop s subdivision this paper provides a road map for the verification of linear and local linear independence of generalized subdivision functions it proves the conjectured global independence of the nodal functions of both algorithms disproves local linear independence for higher valences and establishes linear independence on every surface region corresponding to a facet of the control net subtle exceptions even to global independence underscore the need for a detailed analysis to provide a sound basis for a number of recently developed computational approaches

on the completeness of hierarchical tensor product b splines abstract given a grid in r d consisting of d bi infinite sequences of hyperplanes possibly with multiplicities orthogonal to the d axes of the coordinate system we consider the spaces of tensor product spline functions of a given degree on a multi cell domain such a domain consists of finite set of cells which are defined by the grid a piecewise polynomial function belongs to the spline space if its polynomial pieces on adjacent cells have a contact according to the multiplicity of the hyperplanes in the grid we prove that the connected components of the associated set of tensor product b splines whose support intersects the multi cell domain form a basis of this spline space more precisely if the intersection of the support of a tensor product b spline with the multi cell domain consists of several connected components then each of these components contributes one basis function in order to establish the connection to earlier results we also present further details relating to the three dimensional case with single knots only a hierarchical b spline basis is defined by specifying nested hierarchies of spline spaces and multi cell domains we adapt the techniques from giannelli and juttler 2013 to the more general setting and prove the completeness of this basis in the sense that its span contains all piecewise polynomial functions on the hierarchical grid with the smoothness specified by the grid and the degrees under certain assumptions on the domain hierarchy finally we introduce a decoupled version of the hierarchical spline basis that allows to relax the assumptions on the domain hierarchy in certain situations such as quadratic tensor product splines the decoupled basis provides the completeness property for any choice of the domain hierarchy

isogeometric spline forests in this paper we present isogeometric spline forests an isogeometric spline forest is a hierarchical spline representation capable of representing surfaces or volumes of arbitrarily complex geometry and topological genus spline forests can accomodate arbitrary degree and smoothness in the underlying hierarchical basis as well as non uniform knot interval configurations we describe adaptive h refinement and coarsening algorithms for isogeometric spline forests and develop a bezier extraction framework which provides a simple and efficient single level finite element description of the complex multi level unstructured hierarchical spline basis we then demonstrate the potential of spline forests as a basis for analysis in the context of transient advection diffusion problems where fully integrated adaptivity is demonstrated for the first time in an isogeometric simulation in all cases the adaptive process remains local even in the case of moving fronts and preserves exact geometry at the coarsest level of the discretization the accuracy and robustness of the approach is demonstrated in all cases

isogeometric mortar methods the application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically for the lagrange multiplier two choices of uniformly stable spaces are presented both of them are spline spaces but of a different degree in one case we consider an equal order pairing for which a cross point modification based on a local degree reduction is required in the other case the degree of the dual space is reduced by two compared to the primal this pairing is proven to be inf sup stable without any necessary cross point modification several numerical examples confirm the theoretical results and illustrate additional aspects

dimension reduction and adaptation in conditional density estimation an orthogonal series estimator of the conditional density of a response given a vector of continuous and ordinal nominal categorical predictors is suggested the estimator is based on writing a conditional density as a sum of orthogonal projections on all possible subspaces of reduced dimensionality and then estimating each projection via a shrinkage procedure the shrinkage procedure uses a universal thresholding and a dyadic blockwise shrinkage for low and high frequencies respectively the estimator is data driven is adaptive to underlying smoothness of a conditional density and attains a minimax rate of the mean integrated squared error convergence furthermore if a conditional density depends only on a subgroup of predictors then the estimator seizes the opportunity and attains a corresponding minimax rate of convergence the latter property relaxes the notorious curse of dimensionality moreover the estimator is fast because neither projections nor shrinkages are computation intensive a nu

selecting the best choice in the full information group interview problem abstract we consider the problem of selecting the single best choice when several groups of choices are presented sequentially for evaluation in the so called group interview problem we assume that the values of choices are random observations from a known distribution function and derive the optimal search strategy that maximizes the probability of selecting the best among all choices under the optimal search strategy derived by means of a dynamic programming technique a decision maker simply selects the best choice in the group under consideration if its value is higher than the pre specified decision value for that group we also consider the optimal ordering strategy for the case where the decision maker is permitted to rearrange the sequence of groups for evaluation we show that the optimal search and ordering strategies can be applied to many sequential decision problems such as the store location problem

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

review papers recent developments in nonparametric density estimation abstract advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where re

blended b spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis abstract we present a novel blended b spline method to construct bicubic tricubic splines over unstructured quadrilateral and hexahedral meshes for isogeometric analysis c 1 and truncated c 2 b spline functions are used in regular elements whereas c 0 and truncated c 1 b spline functions are adopted in boundary elements and interior irregular elements around extraordinary edges vertices the truncation mechanism is employed for a seamless transition from irregular to regular elements the resulting smoothness of the blended construction is c 2 continuous everywhere except c 0 continuous around extraordinary edges and c 1 continuous across the interface between irregular and regular elements the blended b spline construction yields consistent parameterization during refinement and exhibits optimal convergence rates spline functions in the blended construction form a non negative partition of unity are linearly independent and support bezier extraction such that the construction can be used in existing finite element frameworks several examples provide numerical evidence of optimal convergence rates

coupling adaptively refined multi patch spline discretizations via boundary compatibility abstract the present paper studies adaptive refinement on multi patch domains in isogeometric analysis in particular we investigate the gluing construction for adaptively refined spline spaces to obtain discretizations that are c 0 smooth across interfaces we will see that this is closely related to the concept of boundary compatibility of an adaptive spline construction given a spline basis or more generally a generating system if linear independence is not guaranteed on a d dimensional box domain there are two possibilities for constructing the spline basis on the domain boundary firstly one can simply restrict the basis functions to the boundary secondly one may restrict the underlying mesh to the boundary and construct the spline basis on the resulting mesh the two constructions do not necessarily produce the same set of functions if they do then the spline bases are said to be compatible we study this property for hierarchical hb and truncated hierarchical b splines thb splines and identify sufficient conditions these conditions are weaker for thb than for hb splines finally we demonstrate the importance of boundary compatibility for geometric modeling and for adaptive refinement in isogeometric analysis in particular when considering multi patch domains

cross validation and the estimation of conditional probability densities many practical problems especially some connected with forecasting require nonparametric estimation of conditional densities from mixed data for example given an explanatory data vector x for a prospective customer with components that could include the customer s salary occupation age sex marital status and address a company might wish to estimate the density of the expenditure y that could be made by that person basing the inference on observations of x y for previous clients choosing appropriate smoothing parameters for this problem can be tricky not in the least because plug in rules take a particularly complex form in the case of mixed data an obvious difficulty is that there exists no general formula for the optimal smoothing parameters more insidiously and more seriously it can be difficult to determine which components of x are relevant to the problem of conditional inference for example if the jth component of x is independent of y then that component is irrelevant to es

on nonparametric discrimination using density differences summary we propose a technique for nonparametric discrimination in which smoothing parameters are chosen jointly according to a criterion based on the difference between two densities the approach is suitable for categorical continuous and mixed data and uses information from both populations to determine the smoothing parameter for any one population in the case of categorical data optimal performance is sometimes achieved using negative smoothing parameters a property which does not emerge if the smoothing parameters are chosen individually

rank based selection strategies for the random walk process abstract in many decision situations such as hiring a secretary selling an asset or seeking a job the value of each offer applicant or choice is assumed to be an independent identically distributed random variable in this paper we consider a special case where the observations are auto correlated as in the random walk model for stock prices for a given random walk process of n observations we explicitly compute the probability that the j th observation in the sequence is the maximum or minimum among all n observations based on the probability distribution of the rank we derive several distribution free selection strategies under which the decision maker s expected utility of selecting the best choice is maximized we show that unlike in the classical secretary problem evaluating more choices in the random walk process does not increase the likelihood of successfully selecting the best

analysis suitable t splines are dual compatible abstract in this paper we define dual compatible dc t splines and we prove that analysis suitable as t splines are dual compatible we show that the classical construction of a dual basis for tensor product t splines easily generalizes to dc t spline spaces and we discuss in the last section of the paper how it paves the way to a mathematical theory of as t splines

isogeometric analysis with geometrically continuous functions on planar multi patch geometries abstract we generate a basis of the space of bicubic and biquartic c 1 smooth geometrically continuous isogeometric functions on bilinear multi patch domains r 2 the basis functions are obtained by suitably combining c 1 smooth geometrically continuous isogeometric functions on bilinearly parameterized two patch domains cf 18 they are described by simple explicit formulas for their spline coefficients these c 1 smooth isogeometric functions possess potential for applications in isogeometric analysis which is demonstrated by several examples such as the biharmonic equation in particular the numerical results indicate optimal approximation power

space of c 2 smooth geometrically continuous isogeometric functions on two patch geometries abstract the space of c 2 smooth geometrically continuous isogeometric functions on bilinearly parameterized two patch domains is considered the investigation of the dimension of the spaces of biquintic and bisixtic c 2 smooth geometrically continuous isogeometric functions on such domains is presented in addition c 2 smooth isogeometric functions are constructed to be used for performing l 2 approximation and for solving triharmonic equation on different two patch geometries the numerical results indicate optimal approximation order

on the linear independence of truncated hierarchical generating systems motivated by the necessity to perform adaptive refinement in geometric design and numerical simulation the construction of hierarchical splines from generating systems spanning nested spaces has been recently studied in several publications linear independence can be guaranteed with the help of the local linear independence of the spline basis at each level the present paper extends this framework in several ways firstly we consider spline functions that are defined on domain manifolds while the existing constructions are limited to domains that are open subsets of r d secondly we generalize the approach to generating systems containing functions which are not necessarily non negative thirdly we present a more general approach to guarantee linear independence and present a refinement algorithm that maintains this property the three extensions of the framework are then used in several relevant applications doubly hierarchical b splines hierarchical zwart powell elements and three different types of hierarchical subdivision splines

reissner mindlin shell implementation and energy conserving isogeometric multi patch coupling summary a shear flexible isogeometric reissner mindlin shell formulation using non uniform rational b splines basis functions is introduced which is used for the demonstration of a coupling approach for multiple non conforming patches the six degrees of freedom formulation uses the exact surface normal vectors and curvature the shell formulation is implemented in an isogeometric analysis framework for computation of structures composed of multiple geometric entities to enable local model refinement as well as non matching domains coupling a conservative multi patch approach using lagrange multipliers for structured non uniform rational b splines patches is presented here an additional border frame mesh is used to couple geometries during structural analyses this frame interface approach avoids the problem of excessive constraints when multiple patches are coupled at one point first the shell formulation is verified with several reference cases then the influence of the frame interface discretization and frame penalty stiffness on the smoothness of the results is investigated the effects of the perturbed lagrangian method in combination with the frame interface approach is shown in addition results of models with t joint interface connections and perpendicular stiffener patches are presented copyright 2016 john wiley sons ltd

isogeometric analysis with c1 hierarchical functions on planar two patch geometries abstract adaptive isogeometric methods for the solution of partial differential equations rely on the construction of locally refinable spline spaces a simple and efficient way to obtain these spaces is to apply the multi level construction of hierarchical splines that can be used on single patch domains or in multi patch domains with c 0 continuity across the patch interfaces due to the benefits of higher continuity in isogeometric methods recent works investigated the construction of spline spaces with global c 1 continuity on two or more patches in this paper we show how these approaches can be combined with the hierarchical construction to obtain global c 1 continuous hierarchical splines on two patch domains a selection of numerical examples is presented to highlight the features and effectivity of the construction

truncated hierarchical catmull clark subdivision with local refinement in this paper we present a new method termed truncated hierarchical catmull clark subdivision thccs which generalizes truncated hierarchical b splines to control grids of arbitrary topology thccs basis functions satisfy partition of unity are linearly independent and are locally refinable thccs also preserves geometry during adaptive hh refinement and thus inherits the surface continuity of catmull clark subdivision namely c2c2 continuous everywhere except at the local region surrounding extraordinary nodes where the surface continuity is c1c1 adaptive isogeometric analysis is performed with thccs basis functions on a benchmark problem with extraordinary nodes local refinement on complex surfaces is also studied to show potential wide application of the proposed method

a class of smooth estimators for discrete distributions summary this paper presents a class of smooth weight function estimators for discrete distributions any estimator in the class depends on choosing a parameterized set of weights the resulting estimators are strongly consistent and asymptotically normal under mild regularity conditions a general procedure for choosing the weight function smoothing parameter is given along with specific solutions in some cases mean squared error comparisons with the maximum likelihood estimator based on large sample theory and small sample simulations are obtained typically the weight function estimates yield significantly smaller mean squared error in these comparisons

a progressive algorithm for modeling and solving multiple criteria decision problems we consider a decision maker dm who has a set of possible decision alternatives from which one a best is to be chosen however all decision alternatives are not at the dm s disposal initially nor is full knowledge of his her utility value function therefore the dm evaluates only the available subset of all decision alternatives from which he she chooses a most preferred one obviously this decision is not necessarily globally best two natural questions arise how good is the most preferred solution what are the chances of finding better solutions by considering additional alternatives we describe and illustrate a general progressive algorithm and the supporting theory for modeling and solving this problem when alternatives are introduced dynamically

low rank tensor methods in galerkin based isogeometric analysis abstract the global patch wise geometry map which describes the computational domain is a new feature in isogeometric analysis this map has a global tensor structure inherited from the parametric spline geometry representation the use of this global structure in the discretization of partial differential equations may be regarded as a drawback at first glance as opposed to the purely local nature of high order classical finite elements in this work we demonstrate that it is possible to exploit the regularity of this structure and to identify the great potential for the efficient implementation of isogeometric discretizations first we formulate tensor product b spline bases as well as the corresponding mass and stiffness matrices as tensors in order to reveal their intrinsic structure second we derive an algorithm for the separation of variables in the integrands arising in the discretization this is possible by means of low rank approximation of the integral kernels we arrive at a compact separated representation of the integrals the separated form implies an expression of galerkin matrices as kronecker products of matrix factors with small dimensions this representation is very appealing due to the reduction in both memory consumption and computation times our benchmarks performed using the c library g smo demonstrate that the use of tensor methods in isogeometric analysis possesses significant advantages

constructing iga suitable planar parameterization from complex cad boundary by domain partition and global local optimization abstract in this paper we propose a general framework for constructing iga suitable planar b spline parameterizations from given complex cad boundaries instead of the computational domain bounded by four b spline curves planar domains with high genus and more complex boundary curves are considered firstly some pre processing operations including bezier extraction and subdivision are performed on each boundary curve in order to generate a high quality planar parameterization then a robust planar domain partition framework is proposed to construct high quality patch meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments after the topology information generation of quadrilateral decomposition the optimal placement of interior bezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch partition with high quality finally after the imposition of c 1 g 1 continuity constraints on the interface of neighboring bezier patches with respect to each quad in the quadrangulation the high quality bezier patch parameterization is obtained by a local optimization method to achieve uniform and orthogonal iso parametric structures while keeping the continuity conditions between patches the efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton based parameterization approach

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

subdivision shells with exact boundary control and non manifold geometry we introduce several new extensions to subdivision shells that provide an improved level of shape control over shell boundaries and facilitate the analysis of shells with non smooth and non manifold joints to this end extended subdivision schemes are used that enable to relax the continuity of the limit surface along prescribed crease edges and to create surfaces with prescribed limit positions and normals furthermore shells with boundaries in the form of conic sections such as circles or parabolas are represented with rational subdivision schemes which are defined in analogy to rational b splines in terms of implementation the difference between the introduced and conventional subdivision schemes is restricted to the use of modified subdivision stencils close to the mentioned geometric features hence the resulting subdivision surface is in most parts of the domain identical to standard smooth subdivision surfaces the particular subdivision scheme used in this paper constitutes an improved version of the original loop s scheme and is as such based on triangular meshes as in the original subdivision shells surfaces created with the modified scheme are used for interpolating the reference and deformed shell configurations at the integration points the subdivision surface is evaluated using a newly developed discrete parameterization approach in the resulting finite elements the only degrees of freedom are the mid surface displacements of the nodes and additional lagrange parameters for enforcing normal constraints the versatility of the newly developed elements is demonstrated with a number of geometrically nonlinear shell examples copyright 2011 john wiley sons ltd

isogeometric collocation cost comparison with galerkin methods and extension to adaptive hierarchical nurbs discretizations abstract we compare isogeometric collocation with isogeometric galerkin and standard c 0 finite element methods with respect to the cost of forming the matrix and residual vector the cost of direct and iterative solvers the accuracy versus degrees of freedom and the accuracy versus computing time on this basis we show that isogeometric collocation has the potential to increase the computational efficiency of isogeometric analysis and to outperform both isogeometric galerkin and standard c 0 finite element methods when a specified level of accuracy is to be achieved with minimum computational cost we then explore an adaptive isogeometric collocation method that is based on local hierarchical refinement of nurbs basis functions and collocation points derived from the corresponding multi level greville abscissae we introduce the concept of weighted collocation that can be consistently developed from the weighted residual form and the two scale relation of b splines using weighted collocation in the transition regions between hierarchical levels we are able to reliably handle coincident collocation points that naturally occur for multi level greville abscissae the resulting method combines the favorable properties of isogeometric collocation and hierarchical refinement in terms of computational efficiency local adaptivity robustness and straightforward implementation which we illustrate by numerical examples in one two and three dimensions

improving smoothness and accuracy of modified butterfly subdivision scheme motivated by the increasing request of surface representation techniques suitable for biomedical imaging applications we construct a non stationary subdivision scheme for regular 3 directional grids which enjoys the following properties i interpolation ii affine invariance iii c2 smoothness iv approximation order 6 and v the capability of reproducing several trigonometric surfaces especially ellipsoids to study the smoothness properties of this new scheme via existing analysis tools we also construct an auxiliary stationary subdivision scheme enjoying properties i iv taking into account that when applied on regular 3 directional grids the modified butterfly scheme is c1 and has approximation order 4 the subdivision schemes derived in this paper can be considered improved variants of the modified butterfly scheme

optimal stopping on autoregressive schemes for j co 1 i i d random variables the autoregression x en axn 1 a2xn 2 yields a payoff yn en wkxk when stopped at time n 0 c as c oo the distributions of t and the remainder term rt xt c are asymptotically independent and determined for exponential and algebraic tailed distributions on en an asymptotic expression for the optimal payoff is given and c c y is calculated so that t yields a payoff asymptotically optimal and asymptotic to c as y 1

on numerical integration in isogeometric subdivision methods for pdes on surfaces abstract subdivision surfaces offer great flexibility in capturing irregular topologies combined with higher order smoothness for instance loop and catmull clark subdivision schemes provide c 2 smoothness everywhere except at extraordinary vertices where the generated surfaces are c 1 smooth the combination of flexibility and smoothness leads to their frequent use in geometric modeling and makes them an ideal candidate for performing isogeometric analysis of higher order problems with irregular topologies e g thin shell problems in the neighborhood of extraordinary vertices however the resulting surfaces and the functions defined on them are non polynomial thus numerical integration based on quadrature has to be performed carefully to preserve the expected higher order consistency this paper presents a detailed case study of different quadrature schemes for isogeometric discretizations of partial differential equations on closed surfaces with loop s subdivision scheme as model problems we consider elliptic equations with the laplace beltrami and the surface bi laplacian operator as well as the associated eigenvalue problem for the laplace beltrami operator a particular emphasis is on the robustness of the approach in the vicinity of extraordinary vertices based on a series of numerical experiments different quadrature schemes are compared mid edge quadrature which can easily be implemented via a lookup table turns out to be a preferable choice due to its robustness and efficiency

extended truncated hierarchical catmull clark subdivision abstract in this paper we present an extended truncated hierarchical catmull clark subdivision ethccs method which improves the efficiency of local refinement in truncated hierarchical catmull clark subdivision thccs based on the stam s method we first build a set of basis functions over arbitrary quadrilateral meshes and apply them to thccs then a new basis function insertion scheme is developed with the aid of the truncation mechanism which refines one ring neighboring elements rather than two ring neighborhoods therefore ethccs significantly improves the efficiency of local refinement compared with thccs as demonstrated by one benchmark problem and several complex models moreover ethccs is also proved to preserve the input geometry and produce nested spaces

dynamic programming formulation of the group interview problem with a general utility function abstract in many managerial decision situations such as buying an electronic appliance several groups of alternatives are presented sequentially and an accept or reject decision is made immediately after evaluating the alternatives in each group if each group contains only one alternative this optimal selection problem is known as the secretary problem which has a long and rich history of research devoted to developing solution strategies we propose a more generalized version of the secretary problem called the group interview problem in which each group contains more than one alternative and each group is presented and evaluated sequentially over time using a dynamic programming approach we derive a backward recursive equation for solving the group interview problem in which a decision maker s utility of selecting a certain choice is expressed as a general function depending on the specific form of this function we derive optimal selection strategies for various types of group interview problems such as minimum rank maximum utility best choice and one out of the p best choice problems