a recursive approach to local mesh refinement in two and three dimensions abstract the newest vertex strategy for local refinement in two dimensions is reviewed and discussed a recursive algorithm for local refinement of tetrahedral meshes in three dimensions based on similar bisection strategy is described the recursive approach requires certain restrictions on the initial mesh on the other hand under this condition the refinement process can be kept as local as needed and it can be fully inverted simple data structures and derefinement algorithms are also outlined

variable selection for gaussian process models in computer experiments in many situations simulation of complex phenomena requires a large number of inputs and is computationally expensive identifying the inputs that most impact the system so that these factors can be further investigated can be a critical step in the scientific endeavor in computer experiments it is common to use a gaussian spatial process to model the output of the simulator in this article we introduce a new simple method for identifying active factors in computer screening experiments the approach is bayesian and only requires the generation of a new inert variable in the analysis however in the spirit of frequentist hypothesis testing the posterior distribution of the inert factor is used as a reference distribution against which the importance of the experimental factors can be assessed the methodology is demonstrated on an application in material science a computer experiment from the literature and simulated examples

exact 3d boundary representation in finite element analysis based on cartesian grids independent of the geometry summary this paper proposes a novel immersed boundary method where the embedded domain is exactly described by using its computer aided design cad boundary representation with non uniform rational b splines nurbs or t splines the common feature with other immersed methods is that the current approach substantially reduces the burden of mesh generation in contrast the exact boundary representation of the embedded domain allows to overcome the major drawback of existing immersed methods that is the inaccurate representation of the physical domain a novel approach to perform the numerical integration in the region of the cut elements that is internal to the physical domain is presented and its accuracy and performance evaluated using numerical tests the applicability performance and optimal convergence of the proposed methodology is assessed by using numerical examples in three dimensions it is also shown that the accuracy of the proposed methodology is independent on the cad technology used to describe the geometry of the embedded domain copyright 2015 john wiley sons ltd

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

designs for crossvalidating approximation models multifold crossvalidation is routinely used for assessing the prediction error of an approximation model for a black box function despite its popularity this method is known to have high variability to mitigate this drawback we propose an experimental design approach that borrows latin hypercube designs to construct a structured crossvalidation sample such that the input values in each fold achieve uniformity theoretical results show that the estimate of the prediction error of the proposed method has significantly smaller variability than its counterpart under independent and identically distributed sampling numerical examples corroborate the theoretical results copyright 2013 oxford university press

a construction method for orthogonal latin hypercube designs summary the latin hypercube design is a popular choice of experimental design when computer simulation is used to study a physical process these designs guarantee uniform samples for the marginal distribution of each single input a number of methods have been pro posed for extending the uniform sampling to higher dimensions we show how to construct latin hypercube designs in which all main effects are orthogonal our method can also be used to construct latin hypercube designs with low correlation of first order and second order terms our method generates orthogonal latin hypercube designs that can include many more factors than those proposed by ye 1998

on design orthogonality maximin distance and projection uniformity for computer experiments space filling designs are widely used in both computer and physical experiments column orthogonality maximin distance and projection uniformity are three basic and popular space filling criteria

a general rotation method for orthogonal latin hypercubes summaryorthogonal latin hypercubes provide a class of useful designs for computer experiments among the available methods for constructing such designs the method of rotation is particularly prominent due to its theoretical appeal as well as its space filling properties this paper presents a general method of rotation for constructing orthogonal latin hypercubes making the rotation idea applicable to many more situations than the original method allows in addition to general theoretical results many new orthogonal latin hypercubes are obtained and tabulated

injectivity of b spline biquadratic maps abstract the application of isogeometric analysis requires a full parametrization map of the physical domain this map is suitable for the analysis only if it is injective in this paper we give a necessary condition for the injectivity of a b spline biquadratic map moreover sufficient injectivity conditions which are easy to check in the practice are introduced a method for parametrizing planar regions using a biquadratic map is also proposed the method is simpler than others reported in the literature since it is based on the solution of an optimization problem without restrictions and only requires the construction of a quadrilateral mesh with optimal geometric properties finally we show that the proposed method can be successfully used to obtain high quality parametrizations of simply connected planar regions with irregular boundary

a new and flexible method for constructing designs for computer experiments we develop a new method for constructing good designs for computer experiments the method derives its power from its basic structure that builds large designs using small designs we specialize the method for the construc tion of orthogonal latin hypercubes and obtain many results along the way in terms of run sizes the existence problem of orthogonal latin hypercubes is completely solved we also present an explicit result showing how large or thogonal latin hypercubes can be constructed using small orthogonal latin hypercubes another appealing feature of our method is that it can easily be adapted to construct other designs we examine how to make use of the method to construct nearly orthogonal and cascading latin hypercubes

three dimensional isogeometrically enriched finite elements for frictional contact and mixed mode debonding abstract we present an isogeometric enrichment technique for three dimensional finite element computations applied to frictional contact and mixed mode debonding this is an extension of previous work that focused on two dimensional and frictionless problems to offer a more complete view of the enriched element s performance a comparison of the results to tri variate isogeometric discretizations and standard lagrangian elements is also included here the enrichment is applied by discretizing parts of the surface that require higher accuracy with isogeometric basis functions while the rest of the body uses lagrangian shape functions by using an isogeometric surface representation the higher continuity across element boundaries and higher order of interpolation can be exploited at the same time the generation of tri variate isogeometric meshes is avoided a convergence study without any surface effects involving only volume integrals shows that the enriched elements can also be beneficial for these problems the major advantage of the isogeometric element enrichment over standard tri linear elements is demonstrated in contact problems including normal and tangential tractions for both mixed mode cohesive debonding and frictional contact the enrichment increases robustness and leads to more accurate results than standard linear lagrangian elements all computations are also compared to results using tri variate isogeometric discretizations to give a complete picture of the element s performance it is also shown that the proposed enrichment formulation has advantages in mesh generation

multi layer designs for computer experiments space filling designs such as latin hypercube designs lhds are widely used in computer experiments however finding an optimal lhd with good space filling properties is computationally cumbersome on the other hand the well established factorial designs in physical experiments are unsuitable for computer experiments owing to the redundancy of design points when projected onto a subset of factor space in this work we present a new class of space filling designs developed by splitting two level factorial designs into multiple layers the method takes advantage of many available results in factorial design theory and therefore the proposed multi layer designs mlds are easy to generate moreover our numerical study shows that mlds can have better space filling properties than optimal lhds

simple transitive 2 representations of small quotients of soergel bimodules in all finite coxeter types but i2 12 i2 18 and i2 30 we classify simple transitive 2 representations for the quotient of the 2 category of soergel bimodules over the coinvariant algebra which

mapped b spline basis functions for shape design and isogeometric analysis over an arbitrary parameterization abstract it is well known that b spline surfaces are defined by a regular array of control vertices in case of models with arbitrary topology it is extremely difficult to maintain continuity conditions among neighboring surfaces the scenario is also true for applications in isogeometric analysis iga this paper presents a novel method for shape design and isogeometric analysis from a quadrilateral control mesh of arbitrary topology using mapped b spline basis functions based on an arbitrary input quadrilateral control mesh a global parameterization of the final surface is first defined through a gravity center method gcm a re parameterization method is then applied to map a b spline basis function to others that are explicitly defined and are tailored to each of the control vertices which can be either regular or extraordinary ones the final surface is defined by all the input control vertices with their corresponding mapped basis functions for practical implementation the surface can be evaluated patch by patch depending on the order of the b spline basis function used for mapping to others the global continuity of the resulting surface including at extraordinary points can be arbitrary higher order in the present paper a uniform cubic b spline basis function is used and the resulting surface is globally c 2 continuous several numerical examples are provided to demonstrate the proposed method for both shape design and isogeometric analysis

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise

weighted t splines with application in reparameterizing trimmed nurbs surfaces abstract to facilitate isogeometric analysis this paper presents a new type of t spline named the weighted t spline which introduces a new weighting idea to t spline basis functions weighted t spline basis functions satisfy partition of unity and are linearly independent in addition we apply the bicubic weighted t splines to reparameterize trimmed nurbs surface patches edge interval extension is performed to reconstruct the trimming curve on the t spline surface and the trimming curve can be exactly preserved comparisons with standard t splines show that the weighted t splines can decrease the required number of control points and t mesh elements the surface error introduced by weighted t spline basis functions is bounded within 0 5 and the error introduced by the trimming curve is constrained within its three ring neighboring elements weighted t spline models are also applied to solve the linear elasticity problems and poisson s equation demonstrating that they can be used in isogeometric analysis

the schur algebra we study a class of endomomorphism algebras of certain q permutation modules over the hecke algebra of type b whose summands involve both parabolic and quasi parabolic subgroups and prove that these algebras are integrally free and quasi hereditary and are stable under base change some consequences for decomposition numbers are discussed the notion of a q schur algebra was introduced by dipper and james dj2 who used these algebras to parametrize the irreducible representations of the finite general linear groups in non describing characteristics with hindsight these algebras had already appeared earlier in an entirely different quantum group context ji inspired by physics in ji jimbo considered the endomorphism algebras of tensor spaces as hecke algebra modules in his context a q schur algebra can be viewed as a quotient of the quantized enveloping algebra associated to gln in pw these algebras were shown to be quasi hereditary the quasi heredity property is an embodiment in classical algebra of the geometric derived category stratification exhibited by perverse sheaves ps it means more applications can be deduced from a ring theoretic point of view see e g dps3 and the possibility is raised of even deeper results in the future as suggested by cps2 certainly these algebras play a central role in the representation theories of the finite and quantum general linear groups naturally one asks are there such algebras for types other than a our paper ds showed that there were similar quasi hereditary quotients of quantized enveloping algebras for all types of root systems however no connection with hecke algebras and finite groups of lie type was found there this paper aims at the same question and constructs possible algebras directly from hecke algebras hence from finite groups of lie type we restrict attention to the type b case imitating the definition of a q schur algebra we introduce the notion of a q schur algebra these algebras are the endomorphism algebras of certain modules over the hecke algebra of type b called tensor spaces whose summands involve not only parabolic subgroups but also quasi parabolic subgroups of the weyl group of type b a main result of our paper shows that qschur algebras are quasi hereditary we speculate that similar constructions exist for other classical types only type d remains actually since type c is equivalent received by the editors march 3 1997 and in revised form october 28 1998 2000 mathematics subject classification primary 20c08 20g05 20c33 the authors would like to thank arc for support under the large grant a69530243 as well as nsf and the universities of virginia and new south wales for their cooperation the first author also thanks the newton institute at cambridge for its hospitality c 2000 american mathematical society

construction of orthogonal and nearly orthogonal designs for computer experiments this paper presents new infinite families of orthogonal designs for computer experiments in cases where orthogonal designs cannot exist we construct alternative nearly orthogonal designs our designs can accommodate many factors and a large set of levels no iterative computer search is required to build up the desired orthogonal designs we develop and use new infinite classes of periodic golay pairs

simultaneous untangling and smoothing of tetrahedral meshes abstract the quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function the objective function is derived from some quality measure of the local submesh that is the set of tetrahedra connected to the adjustable or free node although these objective functions are suitable to improve the quality of a mesh in which there are non inverted elements they are not when the mesh is tangled this is due to the fact that usual objective functions are not defined on all r 3 and they present several discontinuities and local minima that prevent the use of conventional optimisation procedures otherwise when the mesh is tangled there are local submeshes for which the free node is out of the feasible region or this does not exist in this paper we propose the substitution of objective functions having barriers by modified versions that are defined and regular on all r 3 with these modifications the optimisation process is also directly applicable to meshes with inverted elements making a previous untangling procedure unnecessary this simultaneous procedure allows to reduce the number of iterations for reaching a prescribed quality to illustrate the effectiveness of our approach we present several applications where it can be seen that our results clearly improve those obtained by other authors

sliced orthogonal array based latin hypercube designs we propose an approach for constructing a new type of design called a sliced orthogonal array based latin hypercube design this approach exploits a slicing structure of orthogonal arrays with strength two and makes use of sliced random permutations such a design achieves one and two dimensional uniformity and can be divided into smaller latin hypercube designs with one dimensional uniformity sampling properties of the proposed designs are derived examples are given for illustrating the construction method and corroborating the derived theoretical results potential applications of the constructed designs include uncertainty quantification of computer models computer models with qualitative and quantitative factors cross validation and efficient allocation of computing resources supplementary materials for this article are available online

c2 interpolation t splines abstract in this work we construct a class of c 2 interpolation t spline called it spline basis functions over regular t meshes a new rule for determining the local knot vectors of the it spline basis functions is designed the resulting it spline basis functions are always linearly independent for regular t meshes in order to guarantee the partition of unity and compact support properties of the it spline basis functions several modified schemes are developed an iteration adjustment algorithm for adjusting the points on it spline surface to the targeted points is proposed some applications of the new it spline basis functions in fitting bivariate functions and open 3d meshes solving numerical pdes and iga are given

isogeometric analysis for csg models abstract the iga isogeometric analysis was developed as a bridge between cad and cae with its highly precise geometry representation however iga can only do little with the models that cad systems generated in csg constructive solid geometry manner because the trimmed domain exists this paper presents a method named constructive solid isogeometric analysis csiga to work for csg models that are composed of primitive solids with union subtraction and intersection operators first this work decomposes the csg models into several primitive solids represented by nurbs separately then cuts the primitives with their adjacent ones to produce a set of trimmed tri variable nurbs primitives and finally uses boolean operators to compose them as to the single trimmed solid an integration scheme is presented meanwhile a combination scheme has been developed to deal with the union of multiple trimmed solids by using a mortar method the formulation is verified by applying the isogeometric analysis on several solids which have theoretical solutions such as elliptic cylinder and combined brick and some tests on multiple trimmed solids are done too it is shown that the csiga method can deal with csg models efficiently

isogeometric triangular bernstein bezier discretizations automatic mesh generation and geometrically exact finite element analysis isogeometric analysis iga was introduced as a way to bypass the design to analysis bottleneck inherent in the traditional computer aided design cad through finite element analysis fea paradigm however an outstanding problem in the field of iga is that of surface to volume parameterization in cad packages solid objects are represented by a collection of nurbs or t spline bounding surfaces but to perform engineering analysis on real world problems we must find a way to parameterize the volumes of these objects as well this has proven to be difficult using traditional iga as the tensor product nature of trivariate nurbs and t splines limit their ability to create analysis suitable parameterizations of arbitrarily complex volumes to overcome the limitations of trivariate nurbs and t splines we propose the use of rational bernstein bezier tetrahedra to create analysis suitable volumetric parameterizations for isogeometric analysis in this paper which is part one of a two part series we present the methodology for discretizing two dimensional geometries using rational bernstein bezier triangles in addition to presenting finite element analysis methodologies based on rational bernstein bezier triangles we also introduce two new mesh generation strategies for automatically creating high quality geometrically exact curvilinear meshes we assess the quality of our mesh generation schemes using a suite of challenging two dimensional geometries and we verify the accuracy of our proposed numerical discretization approach using the method of manufactured solutions

q tensor space and q weyl modules we obtain the irreducible representations of the q schur algebra motivated by the fact that these representations give all the irreducible representations of gln q in the nondescribing characteristic the irreducible polynomial representations of the general linear groups in the describing characteristic are a special case of this construction the theory of polynomial representations of general linear groups is equivalent to the representation theory of schur algebras see green s book 5 and the bibliography therein in 4 we defined q analogues of schur algebras when q 1 these are the usual schur algebras and when q is a prime power representations of q schur algebras give a substantial part of the representation theory of finite general linear groups in the nondescribing characteristic case including all irreducible representations of these groups and important information about decomposition numbers it is natural to ask what features of the classical schur algebras have qanalogues in this paper we define q analogues of tensor space of weyl modules and of weight spaces thereby generalizing the main reslllts which appear in green s book 5 for example we classify the irreducible modules for qschur algebras we determine bases for q weyl modules compatible with weight spaces and we give results on composition multiplicities of the irreducible modules in q weyl modules the proofs are largely self contained so by specializing q to 1 we recover the corresponding results in 5 this paper therefore is relevant to the representation theory of symmetric groups and to the representation theory of general linear groups in the describing and in the nondescribing characteristics 1 the q schur algebra let r be a natural number let r be an integral domain and let q be a unit in r we denote the symmetric group on r letters by er the hecke algebra z is the r free r algebra with basis twlw e er where the multiplication is determined by the following rule if a i i 1 is a basic transposition in received by the editors august 15 1989 1980 mathematics subject classification 198 5 revision primary 1 6a64 1 6a6 5 secondary 20c30 this research was supported in part by nsf grant no dms 8802290 the authors gratefully acknowledge support received from nato grant no 0222 87 r 1991 american mathematical society 0002 9947 91 1 00 25 per page

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

resolutions over symmetric algebras with radical cube zero abstract let be a finite dimensional indecomposable weakly symmetric algebra over an algebraically closed field k satisfying j 3 0 let s 1 s r be representatives of the isomorphism classes of simple modules and let e be the r r matrix whose i j entry is dim k ext 1 s i s j if there exists an eigenvalue of e satisfying 2 then the minimal resolution of each non projective finitely generated module has exponential growth with radius of convergence 1 2 2 4 on the other hand if all eigenvalues of e satisfy 2 then the dimensions of the modules in the minimal projective resolution of each finitely generated module are either bounded or grow linearly in this case we classify the possibilities for the matrix e the proof is an application of the perron frobenius theorem

parametric mesh regularization for interpolatory shape design and isogeometric analysis over a mesh of arbitrary topology abstract isogeometric analysis iga over a mesh of arbitrary topology is a challenging task since the concept of iga was proposed in the literature one can find some results in iga over an irregular mesh based on approximating schemes while little work is reported so far using interpolatory schemes this paper presents a parametric mesh regularization pmr method for iga using mapped interpolatory basis functions over a mesh of arbitrary topology given a geometric model defined over a mesh of arbitrary topology a global parametric mesh is first defined from the given control mesh using a gravity center method gcm yuan and ma 2014 the resulting parametric mesh is further regularized such that it ensures absolute interpolatory modeling with mapped interpolatory basis functions necessary geometric rules are developed for the regularization process while maintaining the same mesh topological structure the interpolatory basis function used in this paper is a kind of truncated interpolatory basic function tibf studied in our early work yuan and ma 2013 it can also be applied to other mapped interpolatory basis functions in addition to the capability of interpolatory modeling the proposed pmr method can also be applied to approximating schemes which further enriches the capability of such schemes in both modeling and isogeometric analysis of some models in a more appropriate and convenient manner the proposed pmr method has also the potential in achieving higher order continuity at extraordinary vertices using higher order mapped interpolatory basis functions

schur weyl duality for infinitesimal q schur algebras sq 2 r 1 abstract using the result of s r doty d k nakano k m peters polynomial representations of frobenius kernels of gl 2 in contemp math vol 194 1996 pp 57 67 s konig c xi when is a cellular algebra quasi hereditary math ann 315 1999 281 293 we prove that a non semisimple infinitesimal schur algebra s 2 r 1 is not cellular furthermore we determine the structure of the endomorphism ring of tensor space as a module for the infinitesimal schur algebra s 2 r 1 up to morita equivalence both results generalize to the quantum case

isogeometric analysis suitable trivariate nurbs models from standard b rep models abstract this paper presents an effective method to automatically construct trivariate spline models of complicated geometry and arbitrary topology required for nurbs based isogeometric analysis the input is a triangulation of the solid model s boundary the boundary surface is decomposed into a set of cuboids in two steps pants decomposition and cuboid decomposition the novelty of our method is the pants to cuboids decomposition algorithm the algorithm is completely automatic and very robust even for low quality and noisy meshes the set of cuboids composes a generalized polycube approximating very roughly the input model s geometry while faithfully replicating its topology due to its regular structure the polycube is suitable for serving as the parametric domain for the tensor product spline representation based on a discrete harmonic mapping between the cuboids boundary and the polycube s boundary surface and volume parameterizations are generated in order to fit the trivariate splines the efficiency and the robustness of the proposed approach are illustrated by several examples

a new approach to solid modeling with trivariate t splines based on mesh optimization abstract we present a new method to construct a trivariate t spline representation of complex genus zero solids for the application of isogeometric analysis the proposed technique only demands a surface triangulation of the solid as input data the key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain the unitary cube to do that an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure the control points of the trivariate t spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid the distribution of the interpolating points is adapted to the singularities of the domain in order to preserve the features of the surface triangulation

bridge designs for modeling systems with low noise for deterministic computer simulations gaussian process models are a standard procedure for fitting data these models can be used only when the study design avoids having replicated points this characteristic is also desirable for one dimensional projections of the design since it may happen that one of the design factors has a strongly nonlinear effect on the response latin hypercube designs have uniform one dimensional projections but are not efficient for fitting low order polynomials when there is a small error variance d optimal designs are very efficient for polynomial fitting but have substantial replication in projections we propose a new class of designs that bridge the gap between d optimal designs and d optimal latin hypercube designs these designs guarantee a minimum distance between points in any one dimensional projection allowing for the fit of either polynomial or gaussian process models subject to this constraint they are d optimal for a prespecified model

an algebraic model for chains on ωbg p we provide an interpretation of the homology of the loop space on the p completion of the classifying space of a finite group in terms of representation theory and demonstrate how to compute it we then give the following reformulation if f is an idempotent in kg such that f kg is the projective cover of the trivial module k and e 1 f then we exhibit isomorphisms for n 2 h n bg p k tor e kg e n 1 kg e e kg h n bg p k ext n 1 e kg e e kg e kg further algebraic structure is examined such as products and coproducts restriction and steenrod operations

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

efficient construction of multi block volumetric spline parameterization by discrete mask method isogeometric analysis attempts to unify the mathematical languages in design and analysis to realize the seamless integration of cad and cae in three dimensional isogeometric analysis parametric volume is employed as the computational domain for a given set of boundary information in this paper we propose a discrete mask method for the efficient construction of multi block volumetric parameterization based on a set of given boundary spline surfaces given the block partition information of a model the interior control points can be obtained efficiently by solving a sparse linear system the existence and uniqueness of the solution for the linear system are also proved after performing a pre process on the non compatible boundary surfaces the discrete coons mask is generalized to a unified form which provides more choices for the construction of inner control points the proposed method is not only suitable for the multi block case with c 1 continuity but can also be used for the case in which the boundary surfaces are of different degrees and with different number of control points and knot vectors several examples are presented to illustrate the effectiveness of the proposed method

efficient r adaptive isogeometric analysis with winslow s mapping and monitor function approach abstract motivated by the moving mesh method in conventional finite element analysis in this paper we propose an r adaptive isogeometric analysis framework by winslow s mapping and monitor function approach we construct a new monitor function based on the absolute curvature metric of the isogeometric solution surface in the proposed r adaptive framework the redistribution of the inner control points is performed to increase the density of control points in the regions where curvature based or error based monitor functions are maximum the new locations of the inner control points are obtained by solving governing pdes using isogeometric collocation method which is more efficient in solving large scale problems by employing winslow s mapping we ensure that the generated r adaptive parameterization is valid for isogeometric analysis and can be used as optimal initial grid for subsequent h refinements multiple two dimensional heat conduction examples are solved which confirm the effectiveness of the proposed method

orthogonal and nearly orthogonal designs for computer experiments we introduce a method for constructing a rich class of designs that are suitable for use in computer experiments the designs include latin hypercube designs and two level fractional factorial designs as special cases and fill the vast vacuum between these two familiar classes of designs the basic construction method is simple building a series of larger designs based on a given small design if the base design is orthogonal the resulting designs are orthogonal likewise if the base design is nearly orthogonal the resulting designs are nearly orthogonal we present two generalizations of our basic construction method the first generalization improves the projection properties of the basic method the second generalization gives rise to designs that have smaller correlations sample constructions are presented and properties of these designs are discussed

an interactive geometry modeling and parametric design platform for isogeometric analysis in this paper an interactive parametric design through analysis platform is proposed to help design engineers and analysts make more effective use of isogeometric analysis iga to improve their product design and performance we develop several rhinoceros rhino plug ins to take input design parameters through a user friendly interface generate appropriate surface and or volumetric models perform mechanical analysis and visualize the solution fields all within the same computer aided design cad program as part of this effort we propose and implement graphical generative algorithms for iga model creation and visualization based on grasshopper a visual programming interface to rhino the developed platform is demonstrated on two structural mechanics examples an actual wind turbine blade and a model of an integrally bladed rotor ibr in the latter example we demonstrate how the rhino functionality may be utilized to create conforming volumetric models for iga

a method of constructing space filling orthogonal designs abstractthis article presents a method of constructing a rich class of orthogonal designs that include orthogonal latin hypercubes as special cases two prominent features of the method are its simplicity and generality in addition to orthogonality the resulting designs enjoy some attractive space filling properties making them very suitable for computer 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

algebraic mesh quality metrics quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics the theory based on the jacobian and related matrices provides a means of constructing classifying and evaluating mesh quality metrics the jacobian matrix is factored into geometrically meaningful parts a nodally invariant jacobian matrix can be defined for simplicial elements using a weight matrix derived from the jacobian matrix of an ideal reference element scale and orientation invariant algebraic mesh quality metrics are defined the singular value decomposition is used to study relationships between metrics equivalence of the element condition number and mean ratio metrics is proved the condition number is shown to measure the distance of an element to the set of degenerate elements algebraic measures for skew length ratio shape volume and orientation are defined abstractly with specific examples given two combined metrics shape volume and shape volume orientation are algebraically defined and examples of such metrics are given algebraic mesh quality metrics are extended to nonsimplicial elements a series of numerical tests verifies the theoretical properties of the metrics defined

multiserial and special multiserial algebras and their representations abstract in this paper we study multiserial and special multiserial algebras these algebras are a natural generalization of biserial and special biserial algebras to algebras of wild representation type we define a module to be multiserial if its radical is the sum of uniserial modules whose pairwise intersection is either 0 or a simple module we show that all finitely generated modules over a special multiserial algebra are multiserial in particular this implies that in analogy to special biserial algebras being biserial special multiserial algebras are multiserial we then show that the class of symmetric special multiserial algebras coincides with the class of brauer configuration algebras where the latter are a generalization of brauer graph algebras we end by showing that any symmetric algebra with radical cube zero is special multiserial and so in particular it is a brauer configuration algebra

spline parameterization method for 2d and 3d geometries based on t mesh optimization abstract we present a method to obtain high quality spline parameterization of 2d and 3d geometries for their use in isogeometric analysis as input data the proposed method demands a boundary representation of the domain and it constructs automatically a spline transformation between the physical and parametric domains parameterization of the interior of the object is obtained by deforming isomorphically an adapted parametric t mesh onto the physical domain by applying a t mesh untangling and smoothing procedure which is the key of the method mesh optimization is based on the mean ratio shape quality measure the spline representation of the geometry is calculated by imposing interpolation conditions using the data provided by one to one correspondence between the meshes of the parametric and physical domains we give a detailed description of the proposed technique and show some examples also we present some examples of the application of isogeometric analysis in geometries parameterized with our method

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

chebyshev polynomials on symmetric matrices in this paper we evaluate chebyshev polynomials of the second kind on a class of symmetric integer matrices namely on adjacency matrices of simply laced dynkin and extended dynkin diagrams as an application of these results we explicitly calculate minimal projective resolutions of simple modules of symmetric algebras with radical cube zero that are of finite and tame representation type

simplification of surface mesh using hausdorff envelope this paper presents a new method for surface mesh simplification given an initial surface mesh denoted as reference mesh the goal is to reduce the number of mesh elements while preserving the geometric approximation as well as the shape quality of the resulting mesh two tolerance areas with respect to the reference mesh have been introduced to preserve the geometry of the surface the reference mesh is then simplified and optimized in terms of shape quality so that the resulting mesh belongs to these tolerance areas several examples of surface meshes are provided regarding different application areas in order to assess the efficiency of the simplification method

on the connection between maximin distance designs and orthogonal designs summarymaximin distance designs and orthogonal designs are widely used in computer and physical experiments we characterize a broad class of maximin distance designs by establishing new bounds on the minimum intersite distance for mirror symmetric and general u type designs we show that maximin distance designs and orthogonal designs are closely related and coincide under some conditions

orthogonal column latin hypercubes and their application in computer experiments abstract latin hypercubes have been frequently used in conducting computer experiments in this paper a class of orthogonal latin hypercubes that preserves orthogonality among columns is proposed applying an orthogonal latin hypercube design to a computer experiment benefits the data analysis in two ways first it retains the orthogonality of traditional experimental designs the estimates of linear effects of all factors are uncorrelated not only with each other but also with the estimates of all quadratic effects and bilinear interactions second it can facilitate nonparametric fitting procedures because one can select good space filling designs within the class of orthogonal latin hypercubes according to selection criteria

on the structure of end uk 2 ωk r let uk 2 be the infinitesimal quantum gl2 over k where k is a field containing an lth primitive root e of 1 with l 3 odd we will determine the basic algebra for end uk 2 k r where k is the natural module for uk 2

constructing analysis suitable parameterization of computational domain from cad boundary by variational harmonic method in isogeometric analysis parameterization of computational domain has great effects as mesh generation in finite element analysis in this paper based on the concept of harmonic mapping from the computational domain to parametric domain a variational harmonic approach is proposed to construct analysis suitable parameterization of computational domain from cad boundary for 2d and 3d isogeometric applications different from the previous elliptic mesh generation method in finite element analysis the proposed method focuses on isogeometric version and converts the elliptic pde into a nonlinear optimization problem in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal iso parametric structure near convex concave parts of the boundary several examples are presented to show the efficiency of the proposed method in 2d and 3d isogeometric analysis

strong multipatch c1 coupling for isogeometric analysis on 2d and 3d domains abstract the solution spaces of isogoemetric analysis iga constructed from p degree basis functions allow up to c p 1 continuity within one patch however for a multi patch domain the continuity is only c 0 at the boundaries between the patches in this study we present the construction of basis functions of degree p 2 which are c 1 continuous across the common boundaries shared by the patches the new basis functions are computed as a linear combination of the c 0 basis functions on the multi patch domains an advantage of the proposed method is that for the new basis functions the continuity within a patch is preserved without additional treatment of the functions in the interior of the patch we apply continuity constraints to the new basis functions to enforce c 1 continuity where the constraints are developed according to the concept of matched g k constructions always yield c k continuous isogeometric elements discussed in groisser and peters 2015 however for certain geometries the over constrained solution space will lead to c 1 locking collin and sangalli 2016 we discuss and show the usage of partial degree elevation to overcome this problem we demonstrate the potential of the c 1 basis functions for iga applications through several examples involving biharmonic equations