edge elements on anisotropic meshes and approximation of the maxwell equations this paper deals with some edge element methods on a class of anisotropic meshes based on tetrahedra and prismatic pentahedral elements anisotropic local interpolation error estimates are derived for all these types of elements and for functions from classical and weighted sobolev spaces as a particular application the numerical approximation of the maxwell equations in domains with edges is investigated using nedelec s edge elements where anisotropic finite element meshes are appropriate some anisotropic regularity results of the solutions of maxwell equations on such domains are proved some numerical tests are described and inverse estimates are established both showing that our theoretical orders of convergence are optimal

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

central limit theorems and uniform laws of large numbers for arrays of random fields over the last decades spatial interaction models have been increasingly used in economics however the development of a sufficiently general asymptotic theory for nonlinear spatial models has been hampered by a lack of relevant central limit theorems clts uniform laws of large numbers ullns and pointwise laws of large numbers llns these limit theorems form the essential building blocks towards developing the asymptotic theory of m estimators including maximum likelihood and generalized method of moments estimators the paper establishes a clt ulln and lln for spatial processes or random fields that should be applicable to a broad range of data processes

testing for factor loading structural change under common breaks abstract this paper proposes a new test for factor loading structural change in dynamic factor models we first show that the leading test proposed by breitung and eickmeier 2011 exhibits nonmonotonic power essentially because the breaks are considered as spurious factors with stable factor loadings the proposed test eliminates the effects of the spurious factors by maximizing the test statistic over possible numbers of the original factors monte carlo simulations and an empirical example using u s treasury yield curve data clearly illustrate the usefulness of the proposed test

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

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

an iga discontinuous galerkin method on the union of overlapped patches abstract in isogeometric analysis iga the discontinuous galerkin method iga dg is often applied when the domain is composed of multiple non uniform rational b splines nurbs patches these patches are often required to be c 0 continuous to make the iga dg available and this requirement brings some problems to the cad process this paper extends the iga dg method to solve problems on the union of the overlapped patches with this method igaodg a problem on the overlapped domain is seen as multiple sub problems on the non trimmed patches and then the continuities of traces of the numerical solutions are penalized on the boundaries of non trimmed elements with the coefficients deduced from the classical dg method comparing with the iga methods which apply the cad boolean operations to deal with the overlapped domains the presented method carries out the integrations in the non trimmed patches thus no additional integration scheme needs to be considered to achieve the gaussian integration precision discussions on the presented discretization scheme and its convergence analysis show that this method is available on the domain created by the union of the matched mismatched and overlapped patches as predicted in the convergence analysis the presented method gives the optimal convergence rates in our numerical examples finally through one of its engineering applications this paper shows how to extend igaodg to solve problems that are defined on the trimmed patches

using the structure of subfields in the construction of goppa codes and extended goppa codes it is shown that for some location sets and some integral multiple power galois fields that some new general subclasses of goppa codes may be defined which have improved lower bounds to code dimension and minimum distance compared with ordinary goppa codes some previously published results are shown to be particular cases of these general subclasses of codes a new subclass of reversible goppa codes is also presented examples of code construction for these subclasses demonstrating the improved code parameters are presented for both non binary and binary codes

some estimates for h p k refinement in isogeometric analysis in this paper we propose a theoretical study of the approximation properties of nurbs spaces which are used in isogeometric analysis we obtain error estimates that are explicit in terms of the mesh size h the degree p and the global regularity measured by the parameter k our approach covers the approximation with global regularity from c 0 up to c k 1 with 2k 1 p notice that the interesting case of higher regularity up to k p is still open however our results give an indication of the role of the smoothness k in the approximation properties and offer a first mathematical justification of the potential of isogeometric analysis based on globally smooth nurbs

finite element exterior calculus from hodge theory to numerical stability this article reports on the confluence of two streams of research one emanating from the fields of numerical analysis and scientific computation the other from topology and geometry in it we consider the numerical discretization of partial differential equations that are related to differential complexes so that de rham cohomology and hodge theory are key tools for exploring the well posedness of the continuous problem the discretization methods we consider are finite element methods in which a variational or weak formulation of the pde problem is approximated by restricting the trial subspace to an appropriately constructed piecewise polynomial subspace after a brief introduction to finite element methods we develop an abstract hilbert space framework for analyzing the stability and convergence of such discretizations in this framework the differential complex is represented by a complex of hilbert spaces and stability is obtained by transferring hodgetheoretic structures that ensure well posedness of the continuous problem from the continuous level to the discrete we show stable discretization is achieved if the finite element spaces satisfy two hypotheses they can be arranged into a subcomplex of this hilbert complex and there exists a bounded cochain projection from that complex to the subcomplex in the next part of the paper we consider the most canonical example of the abstract theory in which the hilbert complex is the de rham complex of a domain in euclidean space we use the koszul complex to construct two families of finite element differential forms show that these can be arranged in subcomplexes of the de rham complex in numerous ways and for each construct a bounded cochain projection the abstract theory therefore applies to give the stability and convergence of finite element approximations of the hodge laplacian other applications are considered as well especially the elasticity complex and its application to the equations of elasticity background material is included to make the presentation self contained for a variety of readers

a 3d isogeometric be fe analysis with dynamic remeshing for the simulation of a deformable particle in shear flows abstract a three dimensional isogeometric coupled boundary element and finite element approach based on analysis suitable t splines is developed for the simulation of deformable capsules suspended in shear flows boundary element analysis is used to solve the fluid stokes equation whereas the hydrodynamic membrane load is computed via isogeometric analysis under the assumption that the membrane is a hyper elastic thin shell with negligible bending resistance the smoothness of the t spline basis functions accommodate large deformations of the capsule without the need for additional smoothing techniques and can be used to accurately compute the membrane load a balanced distribution of membrane elements can be constructed using an unstructured locally refined mesh these properties are coupled with an adaptive temporal implicit integration scheme several benchmark examples are solved to illustrate the accuracy and potential of the method the approach is then applied to simulate the dynamics of a capsule in a real geometry of a brain capillary

testing for structural stability of factor augmented forecasting models abstract mild factor loading instability particularly if sufficiently independent across the different constituent variables does not affect the estimation of the number of factors nor subsequent estimation of the factors themselves see e g stock and watson 2009 this result does not hold in the presence of large common breaks in the factor loadings however in this case information criteria overestimate the number of breaks additionally estimated factors are no longer consistent estimators of true factors hence various recent research papers in the diffusion index literature focus on testing the constancy of factor loadings however forecast failure of factor augmented models can be due to either factor loading instability regression coefficient instability or both to address this issue we develop a test for the joint hypothesis of structural stability of both factor loadings and factor augmented forecasting model regression coefficients our proposed test statistic has a chi squared limiting distribution and we are able to establish the first order validity of block bootstrap critical values empirical evidence is also presented for 11 us macroeconomic indicators

interior two dimensional acoustic modelling and modal analysis using isogeometric approach abstract in this paper the interior two dimensional acoustic modelling and modal analysis are presented in the framework of isogeometric analysis iga the acoustic domain governed by the helmholtz equation is parameterized and analysed by non uniform rational lagrange nurl basis which can construct exact geometry model inherently like non uniform rational b spines nurbs and can provide a more straightforward way than nurbs to impose dirichlet boundary conditions the verification and versatility of iga using nurl are assessed in the investigation of a unit square domain and a unit circular domain by comparison with analytical solutions furthermore a quadrilateral domain with concave or convex conics is studied and some innovative results are presented which can be the benchmark data for other algorithm researches the effects of geometric weight and aspect ratio on acoustic eigenvalue and eigenmode of the quadrilateral domain are investigated in detail

whitney forms of higher degree low order whitney elements are widely used for electromagnetic field problems higher order approximations are receiving increasing interest but their definition remains unduly complex in this paper we propose a new simple construction for whitney p elements of polynomial degree higher than one that use only degrees of freedom associated to p chains we provide a basis for these elements on simplicial meshes and give a geometrical localization of all degrees of freedom properties of the higher order whitney complex are deeply investigated

a quasi hamiltonian discretization of the thermal shallow water equations the rotating shallow water rsw equations are the usual testbed for the development of numerical methods for three dimensional atmospheric and oceanic models however an arguably more useful set of equations are the thermal shallow water equations tsw which introduce an additional thermodynamic scalar but retain the single layer two dimensional structure of the rsw as a stepping stone towards a three dimensional atmospheric dynamical core this work presents a quasi hamiltonian discretization of the thermal shallow water equations using compatible galerkin methods building on previous work done for the shallow water equations structure preserving or quasi hamiltonian discretizations methods that discretize the hamiltonian structure of the equations of motion rather than the equations of motion themselves have proven to be a powerful tool for the development of models with discrete conservation properties by combining these ideas with an energy conserving poisson time integrator and a careful choice of galerkin spaces a large set of desirable properties can be achieved in particular for the first time total mass buoyancy and energy are conserved to machine precision in the fully discrete model

least squares estimation of large dimensional threshold factor models abstract this paper studies large dimensional factor models with threshold type regime shifts in the loadings we estimate the threshold by concentrated least squares and factors and loadings by principal components the estimator for the threshold is superconsistent with convergence rate that depends on the time and cross sectional dimensions of the panel and it does not affect the estimator for factors and loadings this has the same convergence rate as in linear factor models we propose model selection criteria and a linearity test empirical application of the model shows that connectedness in financial variables increases during periods of high economic policy uncertainty

approximation of eigenvalues in mixed form discrete compactness property and application to hp mixed finite elements abstract in this paper we discuss the discrete compactness property dcp which is a well known tool for the analysis of finite element approximations of maxwell s eigenvalues we restrict our presentation to maxwell s eigenvalues but the theory applies to more general situations and in particular to mixed finite element schemes that can be written in the framework of de rham complex and which enjoy suitable compactness properties we investigate the relationships between dcp and standard mixed conditions for the good approximation of eigenvalues as a consequence of our theory the convergence analysis of the rectangular hp version of raviart thomas finite elements for the approximation of laplace eigenvalues is presented as a corollary of the analogous result for hp edge elements applied to the approximation of maxwell s eigenvalues d boffi m costabel m dauge l demkowicz discrete compactness for the hp version of rectangular edge finite elements siam j numer anal 44 3 2006 979 1004

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

panel data models with interactive fixed effects and multiple structural breaks abstractin this article we consider estimation of common structural breaks in panel data models with unobservable interactive fixed effects we introduce a penalized principal component ppc estimation procedure with an adaptive group fused lasso to detect the multiple structural breaks in the models under some mild conditions we show that with probability approaching one the proposed method can correctly determine the unknown number of breaks and consistently estimate the common break dates furthermore we estimate the regression coefficients through the post lasso method and establish the asymptotic distribution theory for the resulting estimators the developed methodology and theory are applicable to the case of dynamic panel data models simulation results demonstrate that the proposed method works well in finite samples with low false detection probability when there is no structural break and high probability of correctly estimating the break numbers when the structural breaks exist we finall

discrete hodge operators many linear boundary value problems arising in computational physics can be formulated in the calculus of differential forms discrete differential forms provide a natural and canonical approach to their discretization however much freedom remains concerning the choice of discrete hodge operators that is discrete analogues of constitutive laws a generic discrete hodge operator is introduced and it turns out that most finite element and finite volume schemes emerge as its specializations we reap the possibility of a unified convergence analysis in the framework of discrete exterior calculus

law of the iterated logarithm for stationary processes there has been recent interest in the conditional central limit question for strictly stationary ergodic processes x 1 x 0 x 1 whose partial sums s n x 1 x n are of the form s n m n r n where m n is a square integrable martingale with stationary increments and r n is a remainder term for which e r n 2 o n here we explore the law of the iterated logarithm lil for the same class of processes letting denote the norm in l 2 p a sufficient condition for the partial sums of a stationary process to have the form s n m n r n is that n 3 2 e sn x 0 x 1 be summable a sufficient condition for the lil is only slightly stronger requiring n 3 2 log 3 2 n e sn x 0 x 1 to be summable as a by product of our main result we obtain an improved statement of the conditional central limit theorem invariance principles are obtained as well

the cost of continuity performance of iterative solvers on isogeometric finite elements in this paper we study how the use of a more continuous set of basis functions affects the cost of solving systems of linear equations resulting from a discretized galerkin weak form specifically we compare performance of linear solvers when discretizing using c 0 b splines which span traditional finite element spaces and c p 1 b splines which represent maximum continuity we provide theoretical estimates for the increase in cost of the matrix vector product as well as for the construction and application of black box preconditioners we accompany these estimates with numerical results and study their sensitivity to various grid parameters such as element size h and polynomial order of approximation p in addition to the aforementioned continuity of the basis finally we present timing results for a range of preconditioning options for the laplace problem we conclude that the matrix vector product operation is at most left 33p 2 middle 8 right times more expensive for the more cont

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

bootstrapping factor augmented regression models abstract this paper proposes and theoretically justifies bootstrap methods for regressions where some of the regressors are factors estimated from a large panel of data we derive our results under the assumption that t n c where 0 c n and t are the cross sectional and the time series dimensions respectively thus allowing for the possibility that the factor estimation error enters the limiting distribution of the ols estimator as an asymptotic bias term as was recently discussed by ludvigson and ng 2011 we consider general residual based bootstrap methods and provide a set of high level conditions on the bootstrap residuals and on the idiosyncratic errors such that the bootstrap distribution of a rotated ols estimator is consistent we subsequently verify these conditions for a simple wild bootstrap residual based procedure

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

equilibrated residual error estimator for edge elements reliable a posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for the dual problem a cheap computation of such functions via equilibration is well known for scalar equations of second order we simplify and modify the equilibration such that it can be applied to the curl curl equation and edge elements the construction is more involved for edge elements since the equilibration has to be performed on subsets with different dimensions for this reason raviart thomas elements are extended in the spirit of distributions

an isogeometric boundary element method for electromagnetic scattering with compatible b spline discretizations abstract we outline the construction of compatible b splines on 3d surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method method of moments our approach makes use of non uniform rational b splines to represent model geometry and compatible b splines to approximate the surface current and adopts the isogeometric concept in which the basis for analysis is taken directly from cad geometry data the approach allows for high order approximations and crucially provides a direct link with cad data structures that allows for efficient design workflows after outlining the construction of div and curl conforming b splines defined over 3d surfaces we describe their use with the electric and magnetic field integral equations using a galerkin formulation we use bezier extraction to accelerate the computation of nurbs and b spline terms and employ h matrices to provide accelerated computations and memory reduction for the dense matrices that result from the boundary integral discretization the method is verified using the well known mie scattering problem posed over a perfectly electrically conducting sphere and the classic nasa almond problem finally we demonstrate the ability of the approach to handle models with complex geometry directly from cad without mesh generation

consistent factor estimation in dynamic factor models with structural instability abstract this paper considers the estimation of approximate dynamic factor models when there is temporal instability in the factor loadings we characterize the type and magnitude of instabilities under which the principal components estimator of the factors is consistent and find that these instabilities can be larger than earlier theoretical calculations suggest we also discuss implications of our results for the robustness of regressions based on the estimated factors and of estimates of the number of factors in the presence of parameter instability simulations calibrated to an empirical application indicate that instability in the factor loadings has a limited impact on estimation of the factor space and diffusion index forecasting whereas estimation of the number of factors is more substantially affected

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

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

hierarchical t splines analysis suitability bezier extraction and application as an adaptive basis for isogeometric analysis abstract in this paper hierarchical analysis suitable t splines hasts are developed the resulting spaces are a superset of both analysis suitable t splines and hierarchical b splines the additional flexibility provided by the hierarchy of t spline spaces results in simple highly localized refinement algorithms which can be utilized in a design or analysis context a detailed theoretical formulation is presented bezier extraction is extended to hasts simplifying the implementation of hasts in existing finite element codes the behavior of a simple hasts refinement algorithm is compared to the local refinement algorithm for analysis suitable t splines demonstrating the superior efficiency and locality of the hasts algorithm finally hasts are utilized as a basis for adaptive isogeometric analysis

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

high dimensional covariance matrix estimation in approximate factor models the variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems classical methods of estimating the covariance matrices are based on the strict factor models assuming independent idiosyncratic components this assumption however is restrictive in practical applications by assuming sparse error covariance matrix we allow the presence of the cross sectional correlation even after taking out common factors and it enables us to combine the merits of both methods we estimate the sparse covariance using the adaptive thresholding technique as in cai and liu j amer statist assoc 106 2011 672 684 taking into account the fact that direct observations of the idiosyncratic components are unavailable the impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied

a large deformation frictional contact formulation using nurbs based isogeometric analysis this paper focuses on the application of nurbs based isogeometric analysis to coulomb frictional contact problems between deformable bodies in the context of large deformations a mortar based approach is presented to treat the contact constraints whereby the discretization of the continuum is performed with arbitrary order nurbs as well as c0 continuous lagrange polynomial elements for comparison purposes the numerical examples show that the proposed contact formulation in conjunction with the nurbs discretization delivers accurate and robust predictions results of lower quality are obtained from the lagrange discretization as well as from a different contact formulation based on the enforcement of the contact constraints at every integration point on the contact surface copyright 2011 john wiley sons ltd

bivariate spline differential forms abstract in this paper we introduce some basic results of bivariate spline differential forms on general partitions a necessary and sufficient condition is obtained for the existence of closed spline differential forms on such partitions it is the extension and application of multivariate spline theory

estimation and inference in large heterogeneous panels with a multifactor error structure this paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure the unobserved factors and the individual specific errors are allowed to follow arbitrary stationary processes and the number of unobserved factors need not be estimated the basic idea is to filter the individual specific regressors by means of cross section averages such that asymptotically as the cross section dimension n tends to infinity the differential effects of unobserved common factors are eliminated the estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross sectional averages of the dependent variable and the individual specific regressors a number of estimators referred to as common correlated effects cce estimators are proposed and their asymptotic distributions are derived the small sample properties of mean group and pooled cce estimators are investigated by monte carlo experiments showing that the cce estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics and for relatively small values of n and t

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

weak coupling for isogeometric analysis of non matching and trimmed multi patch geometries nitsche s method can be used as a coupling tool for non matching discretizations by weakly enforcing interface constraints we explore the use of weak coupling based on nitsche s method in the context of higher order and higher continuity b splines and nurbs we demonstrate that weakly coupled spline discretizations do not compromise the accuracy of isogeometric analysis we show that the combination of weak coupling with the finite cell method opens the door for a truly isogeometric treatment of trimmed b spline and nurbs geometries that eliminates the need for costly reparameterization procedures we test our methodology for several relevant technical problems in two and three dimensions such as gluing together trimmed multi patches and connecting non matching meshes that contain b spline basis functions and standard triangular finite elements the results demonstrate that the concept of nitsche based weak coupling in conjunction with the finite cell method has the potential to considerably increase the flexibility of the design through analysis process in isogeometric analysis

optimal quadrature for univariate and tensor product splines abstract numerical integration is a core subroutine in many engineering applications including the finite element method fem isogeometric analysis is a fem technology that uses smooth b spline and nurbs basis functions traditionally gaussian quadrature was used for numerical integration but this yields suboptimal performance this is attributed to the fact that gaussian quadrature rules do not take inter element smoothness of the spline basis into account resulting in over integration the equations for exact quadrature are well known but prove notoriously hard to solve due to their nonlinear nature these generalized gauss rules were first introduced in hughes et al 2010 in the context of isogeometric analysis where newton iteration was utilized to study and tabulate several cases later homotopy continuation barto and calo 2015 was used as an alternative strategy for finding these rules in this paper we describe an algorithm to generalize on both of these techniques it is optimal in the sense that it will integrate a space of dimension n using no more than n 1 2 quadrature points the algorithm works on arbitrary nonuniform knot vectors of any polynomial degree and continuity and is demonstrated on polynomial orders up to 15 it extends to 2d and 3d integrals by tensor product

identification and estimation of a large factor model with structural instability this paper tackles the identification and estimation of a high dimensional factor model with unknown number of latent factors and a single break in the number of factors and or factor loadings occurring at unknown common date first we propose a least squares estimator of the change point based on the second moments of estimated pseudo factors and show that the estimation error of the proposed estimator is op 1 we also show that the proposed estimator has some degree of robustness to misspecification of the number of pseudo factors with the estimated change point plugged in consistency of the estimated number of pre and post break factors and convergence rate of the estimated pre and post break factor space are then established under fairly general assumptions the finite sample performance of our estimators is investigated using monte carlo experiments

solid t spline construction from boundary representations for genus zero geometry abstract this paper describes a novel method to construct solid rational t splines for complex genus zero geometry from boundary surface triangulations we first build a parametric mapping between the triangulation and the boundary of the parametric domain a unit cube after that we adaptively subdivide the cube using an octree subdivision project the boundary nodes onto the input triangle mesh and at the same time relocate the interior nodes via mesh smoothing this process continues until the surface approximation error is less than a pre defined threshold t mesh is then obtained by pillowing the subdivision result one layer on the boundary and its quality is improved templates are implemented to handle extraordinary nodes and partial extraordinary nodes in order to get a gap free t mesh the obtained solid t spline is c 2 continuous except for the local region around each extraordinary node and partial extraordinary node the boundary surface of the solid t spline is c 2 continuous everywhere except for the local region around the eight nodes corresponding to the eight corners of the parametric cube finally a bezier extraction technique is used to facilitate t spline based isogeometric analysis the obtained bezier mesh is analysis suitable with no negative jacobians several examples are presented in this paper to show the robustness of the algorithm

common breaks in means and variances for panel data this paper establishes the consistency of the estimated common break point in panel data consistency is obtainable even when a regime contains a single observation making it possible to quickly identify the onset of a new regime we also propose a new framework for developing the limiting distribution for the estimated break point and show how to construct confidence intervals the least squares method is used for estimating breaks in means and the quasi maximum likelihood qml method is used to estimate breaks in means and in variances qml is shown to be more efficient than the least squares even if there is no change in the variances

testing for structural breaks in dynamic factor models in this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest procedures for testing for structural breaks it is shown that structural breaks severely inflate the number of factors identified by the usual information criteria the hypothesis of a structural break is tested by using lr lm and wald statistics the lm test which performs best in our monte carlo simulations is generalized to test for structural breaks in factor models where the break date is unknown and the common factors and idiosyncratic components are serially correlated the proposed test procedures are applied to datasets from the us and the euro area

a hybrid igafem igabem formulation for two dimensional stationary magnetic and magneto mechanical field problems abstract isogeometric analysis iga can bridge the gap between geometrical and numerical modelling to this end the same functions used in computer aided design are applied to represent geometry and approximate field variables in the numerical model the concept has already been implemented to solve field problems using finite element fem and boundary element methods bem but coupling of both methods has not been applied in the current work an isogeometric fem bem coupling is proposed and applied to two dimensional stationary magnetic field problems while fem is used to model magnetisable bodies allowing for heterogeneous structures and non linear constitutive behaviour the bem domain accounts for the surrounding free space both methods are coupled on the surface of the magnetisable body due to this hybrid igafem bem approach no meshing of free space is necessary and truncation errors are avoided for problems to be solved on open infinite or semi infinite domains once the solution for the magnetic problem is obtained using the hybrid method igafem is used to solve a magneto mechanical field problem with one sided coupling in a subdomain of the magnetic problem this one sided coupling is realised by a magnetic stress tensor computed from the solution of the stationary magnetic field problem from the comparison of error norms and convergence rates for nurbs and discretisations based on lagrangian polynomials smaller errors and similar convergence rates are found for the proposed method for the same polynomial order of the basis functions and a comparable mesh size

isogeometric methods for computational electromagnetics b spline and t spline discretizations in this paper we introduce methods for electromagnetic wave propagation based on splines and on t splines we define spline spaces which form a de rham complex and following the isogeometric paradigm we map them on domains which are piecewise spline or nurbs geometries we analyze their geometric and topological structure as related to the connectivity of the underlying mesh and we present degrees of freedom together with their physical interpretation the theory is then extended to the case of meshes with t junctions leveraging on the recent theory of t splines the use of t splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose

effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear deformable beams with varying curvature and torsion abstract we present a displacement based and a mixed isogeometric collocation iga c formulation for free form three dimensional shear deformable beams with high and rapidly varying curvature and torsion when such complex shapes are concerned the approach used to build the iga geometric model becomes relevant although iga c has been so far successfully applied to a wide range of problems the effects that different parameterization and knot placement techniques may have on the accuracy of collocation based formulations is still an unexplored field to fill this gap primal and mixed formulations are used combining two parameterization methods chord length and equally spaced with two knot placement techniques uniformly spaced and de boor with respect to the space varying frenet local frame we derive the strong form of the governing equations in a compact form through the definition of two matrix operators conveniently used to perform first and second order derivatives of the vector fields involved in the formulations this approach is very efficient and easy to implement within a collocation based scheme several challenging numerical experiments allow to test the different considered parameterizations and knot placement techniques revealing in particular that with the primal formulation an equally spaced parameterization is definitively the most recommended choice and it should always be used with an approximation degree of at least p 6 although some caution must be adopted when very high jacobians and small curvatures occur the same holds for the mixed formulation with the difference that p 4 is enough to yield accurate results

divergence conforming discretization for stokes problem on locally refined meshes using lr b splines abstract to solve the incompressible flow problems using isogeometric analysis the div compatible spline spaces were originally introduced by buffa et al 2011 and later developed by evans 2011 in this paper we extend the div compatible spline spaces with local refinement capability using locally refined lr b splines over rectangular domains we argue that the spline spaces generated on locally refined meshes will satisfy compatibility provided they span the entire function spaces as governed by mourrain 2014 dimension formula we will in this work use the structured refined lr b splines as introduced by johannessen et al 2014 further we consider these div compatible lr b spline spaces to approximate the velocity and pressure fields in mixed discretization for stokes problem and a set of standard benchmark tests are performed to show the stability efficiency and the conservation properties of the discrete velocity fields in adaptive isogeometric analysis

estimation of large dimensional factor models with an unknown number of breaks abstract in this paper we study the estimation of a large dimensional factor model when the factor loadings exhibit an unknown number of changes over time we propose a novel three step procedure to detect the breaks if any and then identify their locations in the first step we divide the whole time span into subintervals and fit a conventional factor model on each interval in the second step we apply the adaptive fused group lasso to identify intervals containing a break in the third step we devise a grid search method to estimate the location of the break on each identified interval we show that with probability approaching one our method can identify the correct number of changes and estimate the break locations simulation studies indicate superb finite sample performance of our method we apply our method to investigate stock and watson s 2009 u s monthly macroeconomic dataset and identify five breaks in the factor loadings spanning 1959 2006

isogeometric analysis in electromagnetics b splines approximation abstract we introduce a new discretization scheme for maxwell equations in two space dimension inspired by the new paradigm of isogeometric analysis introduced in hughes et al 2005 16 we propose an algorithm based on the use of bivariate b splines spaces suitably adapted to electromagnetics we construct b splines spaces of variable interelement regularity on the parametric domain these spaces and their push forwards on the physical domain form a de rham diagram and we use them to solve the maxwell source and eigen problem our scheme has the following features i is adapted to treat complex geometries ii is spectral correct iii provides regular e g globally c 0 discrete solutions of maxwell equations

panel data models with interactive fixed effects this paper considers large n and large t panel data models with unobservable multiple interactive eects these models are useful for both micro and macro econometric modelings in earnings studies for example workers motivation persistence and diligence combined to influence the earnings in addition to the usual argument of innate ability in macroeconomics the interactive eects represent unobservable common shocks and their heterogeneous responses over cross sections since the interactive eects are allowed to be correlated with the regressors they are treated as fixed eects parameters to be estimated along with the common slope coecients the model is estimated by the least squares method which provides the interactive eect s counterpart of the within estimator we first consider model identification and then derive the rate of convergence and the limiting distribution of the interactive eect s estimator of the common slope coecients the estimator is shown to be p nt consistent this rate is valid even in the presence of correlations and heteroskedasticities in both dimensions a striking contrast with fixed t framework in which serial correlation and heteroskedasticity imply unidentification the asymptotic distribution is not necessarily centered at zero biased corrected estimators are derived we also derive the constrained estimator and its limiting distribution imposing additivity coupled with interactive eects the problem of testing additive versus interactive eects is also studied we also derive identification conditions for models with grand mean time invariant regressors and common regressors it is shown that there exists a set of necessary and sucient identification conditions for those models given identification the rate of convergence and limiting results continue to hold

estimating a common deterministic time trend break in large panels with cross sectional dependence abstract this paper develops an estimation procedure for a common deterministic time trend break in large panels the dependent variable in each equation consists of a deterministic trend and an error term the deterministic trend is subject to a change in the intercept slope or both and the break date is common for all equations the estimation method is simply minimizing the sum of squared residuals for all possible break dates both serial and cross sectional correlations are important factors that decide the rate of convergence and the limiting distribution of the break date estimate the rate of convergence is faster when the errors are stationary than when they have a unit root when there is no cross sectional dependence among the errors the rate of convergence depends on the number of equations and thus is faster than the univariate case when the errors have a common factor structure with factor loadings correlated with the intercept and slope change parameters the rate of convergence does not depend on the number of equations and thus reduces to the univariate case the limiting distribution of the break date estimate is also provided some monte carlo experiments are performed to assess the adequacy of the asymptotic results a brief empirical example using the us gdp price index is offered

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

anisotropic nurbs approximation in isogeometric analysis abstract we investigate the approximation error of mapped nurbs spaces such as those used in isogeometric analysis in accordance to the isoparametric paradigm we extend the results of 6 to the case of anisotropic meshes such as those needed in the presence of boundary layers the theoretical results cover anisotropic h refinement and are supported by numerical tests involving different geometries

estimation and inference of change points in high dimensional factor models abstract in this paper we consider the estimation of break points in high dimensional factor models where the unobserved factors are estimated by principal component analysis pca the factor loading matrix is assumed to have a structural break at an unknown time we establish the conditions under which the least squares ls estimator is consistent for the break date our consistency result holds for both large and small breaks we also find the ls estimator s asymptotic distribution simulation results confirm that the break date can be accurately estimated by the ls even if the magnitudes of breaks are small in two empirical applications we implement the method to estimate break points in the u s stock market and u s macroeconomy respectively

the cost of continuity a study of the performance of isogeometric finite elements using direct solvers we study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis the problem of choice is the canonical laplace equation in three dimensions from this study we conclude that for a fixed number of unknowns and polynomial degree of approximation a higher degree of continuity k drastically increases the cpu time and ram needed to solve the problem when using a direct solver this paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause

isogeometric analysis using t splines on two patch geometries we develop optimal approximation estimates for t splines in the case of geometries obtained by gluing two standard tensor product patches we derive results both for the t spline space in the parametric domain and the mapped t nurbs in the physical one a set of numerical tests in complete accordance with the theoretical developments is also presented

on the central limit theorem for stationary mixing random fields a simple proof of a central limit theorem for stationary random fields under mixing conditions is given generalizing some results obtained by more complicated methods e g bernstein s method

inferential theory for factor models of large dimensions this paper develops an inferential theory for factor models of large dimensions the principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator if normality is assumed we derive the rate of convergence and the limiting distributions of the estimated factors factor loadings and common components the theory is developed within the framework of large cross sections n and a large time dimension t to which classical factor analysis does not apply we show that the estimated common components are asymptotically normal with a convergence rate equal to the minimum of the square roots of n and t the estimated factors and their loadings are generally normal although not always so the convergence rate of the estimated factors and factor loadings can be faster than that of the estimated common components these results are obtained under general conditions that allow for correlations and heteroskedasticities in both dimensions stronger results are obtained when the idiosyncratic errors are serially uncorrelated and homoskedastic a necessary and sufficient condition for consistency is derived for large n but fixed t

a geometry preserving conservative mesh to mesh isogeometric interpolation algorithm for spatial adaptivity of the multigroup second order even parity form of the neutron transport equation abstract in this paper a method is presented for the application of energy dependent spatial meshes applied to the multigroup second order even parity form of the neutron transport equation using isogeometric analysis iga the computation of the inter group regenerative source terms is based on conservative interpolation by galerkin projection the use of non uniform rational b splines nurbs from the original computer aided design cad model allows for efficient implementation and calculation of the spatial projection operations while avoiding the complications of matching different geometric approximations faced by traditional finite element methods fem the rate of convergence was verified using the method of manufactured solutions mms and found to preserve the theoretical rates when interpolating between spatial meshes of different refinements the scheme s numerical efficiency was then studied using a series of two energy group pincell test cases where a significant saving in the number of degrees of freedom can be found if the energy group with a complex variation in the solution is refined more than an energy group with a simpler solution function finally the method was applied to a heterogeneous seven group reactor pincell where the spatial meshes for each energy group were adaptively selected for refinement it was observed that by refining selected energy groups a reduction in the total number of degrees of freedom for the same total l 2 error can be obtained

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 divergence conforming b splines for the unsteady navier stokes equations divergence conforming b splines are developed for application to the incompressible navier stokes equations on geometrically mapped domains these enable smooth pointwise divergence free solutions and thus satisfy mass conservation in the strongest possible sense semi discrete methods based on divergence conforming b splines are shown to conserve linear and angular momentum and satisfy balance laws for energy vorticity enstrophy and helicity these are geometric structure preserving quantities and numerical simulations that are sensitive to them are shown to be qualitatively correct and quantitatively accurate the methods developed are anticipated to open new doors to the practical calculation of complex flows and to studies of their physical behavior