automatic mesh generation and adaptation by using contours a general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing funstion the contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions where finite elements meshes of different element sizes zre generated using the available general purpose mesh generators

interpolating and meshing 3d surface grids summary in the boundary representation b rep model a three dimensional 3d surface is dened by a set of simpler surfaces called patches although there are many dierent ways to specify a patch a common case is that of a 4 sided patch represented by a structured grid of points for instance this kind of data can easily be obtained from a cad system as it is the mapping of regularly spaced points in a rectangular parametric domain it can also be obtained from some particular 3d scanning devices non rectangular topologies may also be encountered for instance the 3 sided patch which can be considered as a degenerate case of the 4 sided patch one side being of zero length in this paper we use the coons method to build a surface interpolating the vertices of such a grid the continuity of this parameterization makes it suitable for our indirect approach to surface meshing which is generally based on the generation of an anisotropic mesh in the parametric space moreover the indirect approach has been extended to the construction of anisotropic geometric surface meshes in 3d space allowing an accurate geometric representation of the surface with a minimal number of elements several examples demonstrate the capabilities of this method copyright 2003 john wiley sons ltd

brief paper synchronization of coupled harmonic oscillators in a dynamic proximity network in this paper we revisit the synchronization problems for coupled harmonic oscillators in a dynamic proximity network unlike many existing algorithms for distributed control of complex dynamical networks that require explicit assumptions on the network connectivity we show that the coupled harmonic oscillators can always be synchronized without imposing any network connectivity assumption moreover we also investigate the synchronization with a leader and show that all harmonic oscillators can asymptotically attain the position and velocity of the leader again without any assumption on connectivity of the followers numerical simulation illustrates the theoretical results

boundary recovery for three dimensional conforming delaunay triangulation we present an efficient boundary recovery method for conforming delaunay triangulation of three dimensional domains our method combines local transformations like edges faces swappings and modified constrained delaunay refinement like edges faces splittings to recover the missing boundary edges and faces its convergence is theoretically proved its effectiveness is also demonstrated through some meshing examples

relative efficiency of unequal cluster sizes in stepped wedge and other trial designs under longitudinal or cross sectional sampling background a cluster trial with unequal cluster sizes often has lower precision than one with equal clusters with a corresponding inflation of the design effect for parallel group trials adjustments to the design effect are available under sampling models with a single intracluster correlation design effects for equal clusters under more complex scenarios have appeared recently including stepped wedge trials under cross sectional or longitudinal sampling we investigate the impact of unequal cluster size in these more general settings results assuming a linear mixed model with an exchangeable correlation structure that incorporates cluster and subject autocorrelation we compute the relative efficiency re of a trial with clusters of unequal size under a size stratified randomization scheme as compared to an equal cluster trial with the same total number of observations if there are no within cluster time effects the re exceeds that for a parallel trial in general the re is a weighted average of the re for a parallel trial and the re for a crossover trial in the same clusters existing approximations for parallel designs are extended to the general setting increasing the cluster size by the factor 1 cv2 where cv is the coefficient of variation of cluster size leads to conservative sample sizes as in a popular method for parallel trials conclusion methods to assess experimental precision for single period parallel trials with unequal cluster sizes can be extended to stepped wedge and other complete layouts under longitudinal or cross sectional sampling in practice the loss of precision due to unequal cluster sizes is unlikely to exceed 12

a priori anisotropic mesh adaptation on implicitly defined surfaces mesh adaptation on surfaces demands particular care due to the important role played by the surface fitting we propose an adaptive procedure based on a new error analysis which combines a rigorous anisotropic estimator for the l 1 norm of the interpolation error with an anisotropic heuristic control of the geometric error we resort to a metric based adaptive algorithm which employs local operations to modify the initial mesh according to the information provided by the error analysis an extensive numerical validation corroborates the robustness of the error analysis as well as of the adaptive procedure

automatic metric 3d surface mesh generation using subdivision surface geometrical model part 1 construction of underlying geometrical model summary this paper proposes a new automatic mesh generation algorithm for 3d surface mesh generation the algorithm is base d on the metric specification approach and can generate anisotropic meshes on 3d surfaces it is based on a new geometrical model using the interpolating subdivision surface concept by using the subdivision surface concept the new mesh generator can generate finite element meshes to model a wide range of surfaces which may contain sharp features such as cusp and crease lines when comparing with other algorithms which use analytical surface patches as the underlying geometrical model the new mesh generation scheme can be used in applications such as large deformation or crack analyses in which the domains to be gridded are not well defined or involve changing boundary the presentation of the work is divided into two parts in part i i e the present paper a detailed description of the underlying geometrical model used will be given while in part ii attentions will be focused on the mesh generation algorithms and the performance of the mesh generator

distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks in this paper we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies first when the leaders are stationary and all followers share an inertial coordinate frame we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is fixed we partition the nonsymmetric laplacian matrix and explore its properties to derive the convergence results when the directed network topology is switching the commonly adopted decoupling technique based on the kronecker product in a high dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results the proposed coordinate transformation technique also has potential applications in other high dimensional distributed control scenarios and might be used to simplify the analysis of a high dimensional system to that of a one dimensional system when the decoupling technique based on the kronecker product cannot be applied second when the leaders are dynamic and all followers share an inertial coordinate frame we propose a distributed tracking control algorithm without velocity measurements when the directed network topology is fixed we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is switching we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high dimensional space we also show via some counterexamples that it is in general impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high dimensional space simulation results are presented as a proof of concept

synchronization control for nonlinear stochastic dynamical networks pinning impulsive strategy in this paper a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling pinning state feedback controllers have been proved to be effective for synchronization control of state coupled dynamical networks we will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks some generic mean square stability criteria are derived in terms of algebraic conditions which guarantee that the whole state coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes an effective method is given to select the nodes which should be controlled at each impulsive constants the proportion of the controlled nodes guaranteeing the stability is explicitly obtained and the synchronization region is also derived and clearly plotted numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper

containment control for coupled harmonic oscillators with multiple leaders under directed topology this paper investigates the problem of containment control for coupled harmonic oscillators with multiple leaders under directed topology using tools from matrix graph and stability theories necessary and sufficient conditions are obtained for coupled harmonic oscillators under continuous time and sampled data based protocols respectively when the continuous time protocol is used it is proved that every follower will ultimately converge to the convex hull spanned by the leaders if and only if there exists at least one leader that has a directed path to that follower at any time when the sampled data based protocol is used it is shown that the containment can be achieved if and only if 1 an appropriate sampling period is chosen and 2 for every follower there exists at least one leader that has a directed path to that follower at any time and we also give the containment conditions for coupled harmonic oscillators under undirected topology as a special case finally numerical simulations are

synchronization of sampled data coupled harmonic oscillators with control inputs missing abstract this paper is concerned with the synchronization problem of sampled data coupled harmonic oscillators with control inputs missing a distributed algorithm for synchronization in undirected networks of coupled harmonic oscillators is proposed based on the sampled data measurement with controller failures some generic criteria for such algorithm over respectively undirected fixed and switching network topologies are derived analytically compared with some existing works a distinctive feature of this work is to solve synchronization problem in undirected networks even if each oscillator intermittently exchanges the velocity information with its neighbors in terms of sampled data setting only at discrete moments subsequently numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results

adaptive tetrahedral mesh generation by constrained delaunay refinement this paper presents a tetrahedral mesh generation method for numerically solving partial differential equations using finite element or finite volume methods in three dimensional space the main issues are the mesh quality and mesh size which directly affect the accuracy of the numerical solution and the computational cost two basic problems need to be resolved namely boundary conformity and field points distribution the proposed method utilizes a special three dimensional triangulation so called constrained delaunay tetrahedraliwtion to conform the domain boundary and create field points simultaneously good quality tetrahedra and graded mesh size can be theoretically guaranteed for a large class of mesh domains in addition an isotropic size field associated with the numerical solution can be supplied the field points will then be distributed according to it good mesh size conformity can be achieved for smooth sizing informations the proposed method has been implemented various examples are provided to illustrate its theoretical aspects as well as practical performance

anisotropic centroidal voronoi tessellations and their applications in this paper we introduce a novel definition of the anisotropic centroidal voronoi tessellation acvt corresponding to a given riemann metric tensor a directional distance function is used in the definition to simplify the computation we provide algorithms to approximate the acvt using the lloyd iteration and the construction of anisotropic delaunay triangulation under the given riemannian metric the acvt is applied to the optimization of two dimensional anisotropic delaunay triangulation to the generation of surface cvt and high quality triangular mesh on general surfaces various numerical examples demonstrating the effectiveness of the proposed method are presented

robust finite time containment control for high order multi agent systems with matched uncertainties under directed communication graphs abstractin this paper we study the robust finite time containment control problem for a class of high order uncertain nonlinear multi agent systems modelled as high order integrator systems with bounded matched uncertainties when relative state information between neighbouring agents is available an observer based distributed controller is proposed for each follower using the sliding mode control technique which solves the finite time containment control problem under general directed communication graphs when only relative output information is available robust exact differentiators and high order sliding mode controllers are employed together with the distributed finite time observers it is shown that robust finite time containment control can still be achieved in this situation an application in the coordination of multiple non holonomic mobile robots is used as an example to illustrate the effectiveness of the proposed control strategies

centroidal voronoi tessellation based finite element superconvergence in this article a finding on finite element superconvergence is reported the laplacian operator with dirichlet boundary condition is considered the linear finite element solutions have an o h2 0 5 superconvergence in l2 norm at nodes on an almost equilateral triangular mesh generated based on centroidal voronoi tessellation for an arbitrary 2d bounded domain extensive numerical examples are presented to demonstrate the superconvergence property copyright 2008 john wiley sons ltd

an algorithm for the intersection of quadrilateral surfaces by tracing of neighbours the use of discrete data to represent engineering structures as derivatives from intersecting components requires algorithms to perform boolean operations between groups of quadrilateral and triangular surfaces in the intersection process an accurate and efficient method for the determination of intersection lines is a crucial step for large scale and complex surface intersections an algorithm based on tracing the neighbours of intersecting quadrilaterals is proposed to determine the intersection lines a background grid is employed to limit the scope of searching for candidate quadrilaterals that may intersect this will drastically cut down the time of geometrical check for intersections between quadrilaterals making the surface intersection and mesh generation a quasi linear process with respect to the number of elements involved given the node numbers at the vertices of the candidate quadrilaterals the neighbour relationship is then established in the determination of intersection each quadrilateral is divided into two triangles and four fundamental cases are identified and treated systematically to enhance robustness and reliability tracing the neighbours for the determination of intersection lines not only greatly increases the efficiency of the process it also improves the reliability as branching and degenerated cases can all be dealt with in a consistent manner on the intersecting surfaces concerned examples on a great variety of surface and mesh characteristics are given to demonstrate the effectiveness and robustness of the algorithm

anisotropic and feature sensitive triangular remeshing using normal lifting this work describes an automatic method to anisotropically remesh an input bad quality mesh while preserving sharp features we extend the method of levy and bonneel 2012 based on the lifting of the input mesh in a 6d space position and normal and the optimization of a restricted voronoi diagram in that space the main advantage of this method is that it does not require any parameterization of the input geometry the remeshing is performed globally and triangles can overlap several input charts we improve this work by modifying the objective function minimized in the optimization process in order to take into account sharp features this new formulation is a generalization of the work of levy and liu 2010 which does not require any explicit tagging of the sharp features we provide efficient formulas to compute the gradient of our objective function thus allowing us to use a quasi newton solver liu and nocedal 1989 to perform the minimization

synchronization of coupled harmonic oscillators with local instantaneous interaction in this brief we propose a distributed algorithm for synchronization of coupled harmonic oscillators with local instantaneous interaction we provide convergence analysis for such algorithm without and with a leader over fixed and switching undirected network topologies respectively we also establish the conditions by which the coupled harmonic oscillators achieve synchronized oscillatory motions under instantaneous network connectivity it is shown that the coupled harmonic oscillators can be synchronized even each oscillator instantaneously exchanges the velocity information with its neighbors only at discrete moments subsequently numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results

a three dimensional parametric mesher with surface boundary layer capability abstract a novel parametric surface meshing technique is presented its distinctive feature relies on successive approximations of the cad geometry through a hierarchical process where geometric information is gathered incrementally a detailed review of zero and first order surface approximations and their impact on parametric surface meshing algorithms is performed the proposed approach emphasizes the use of three dimensional information in order to be as independent as possible of the parametrization to overcome limitations of meshing purely in the parametric plane the presented technique includes semi structured boundary layer surface mesh generation which is a critical capability for accurate solutions to flows around geometries that have leading edge features numerous examples illustrate the method s robustness and ability to high quality meshes for complex cad geometries

parametric surface meshing using a combined advancing front generalized delaunay approach an indirect method for meshing parametric surfaces conforming to a user specifiable size map is presented first from this size specification a riemannian metric is defined so that the desired mesh is one with unit length edges with respect to the related riemannian space the so called unit mesh then based on the intrinsic properties of the surface the riemannian structure is induced into the parametric space finally a unit mesh is generated completely inside the parametric space such that it conforms to the metric of the induced riemannian structure this mesh is constructed using a combined advancing front delaunay approach applied within a riemannian context the proposed method can be applied to mesh composite parametric surfaces several examples illustrate the efficiency of our approach copyright 2000 john wiley sons ltd

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

synchronization of coupled harmonic oscillators with local interaction this paper studies synchronization of coupled second order linear harmonic oscillators with local interaction we analyze convergence conditions over respectively directed fixed and switching network topologies by using tools from algebraic graph theory matrix theory and nonsmooth analysis it is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions examples are given to validate the convergence conditions the theoretical result is also applied to synchronized motion coordination of multi agent systems as a proof of concept

regridding surface triangulations an advancing front surface gridding technique that operates on discretely defined surfaces i e triangulations is presented different aspects that are required to make the procedure reliable for complex geometries are discussed notable among these are a the recovery of surface features and discrete surface patches from the discrete data b filtering based on point and side normals to remove undesirable data close to cusps and corners c the proper choice of host faces for ridges and d fast interpolation procedures suitable for complex geometries post generation surface recovery or repositioning techniques are discussed several examples ranging from academic to industrial demonstrate the utility of the proposed procedure forab initiosurface meshing from discrete data such as those encountered when the surface description is already given as discrete the improvement of existing surface triangulations as well as remeshing applications during runs exhibiting significant change of domain

tetrahedral mesh generation and optimization based on centroidal voronoi tessellations the centroidal voronoi tessellation based delaunay triangulation cvdt provides an optimal distribution of generating points with respect to a given density function and accordingly generates a high quality mesh in this paper we discuss algorithms for the construction of the constrained cvdt from an initial delaunay tetrahedral mesh of a three dimensional domain by establishing an appropriate relationship between the density function and the specified sizing field and applying the lloyd s iteration the constrained cvdt mesh is obtained as a natural global optimization of the initial mesh simple local operations such as edges faces flippings are also used to further improve the cvdt mesh several complex meshing examples and their element quality statistics are presented to demonstrate the effectiveness and efficiency of the proposed mesh generation and optimization method copyright 2003 john wiley sons ltd

containment control in mobile networks in this paper the problem of driving a collection of mobile robots to a given target destination is studied in particular we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader agents while the remaining agents only employ local interaction rules to this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop go rules for the leader agents non zenoness liveness and convergence of the resulting system are also analyzed

automatic metric 3d surface mesh generation using subdivision surface geometrical model part 2 mesh generation algorithm and examples in this paper a new metric advancing front surface mesh generation scheme is suggested this new surface mesh generator is based on a new geometrical model employing the interpolating subdivision surface concept the target surfaces to be meshed are represented implicitly by interpolating subdivision surfaces which allow the presence of various sharp and discontinuous features in the underlying geometrical model while the main generation steps of the new generator are based on a robust metric surface triangulation kernel developed previously a number of specially designed algorithms are developed in order to combine the existing metric advancing front algorithm with the new geometrical model as a result the application areas of the new mesh generator are largely extended and can be used to handle problems involving extensive changes in domain geometry numerical experience indicates that by using the proposed mesh generation scheme high quality surface meshes with rapid varying element size and anisotropic characteristics can be generated in a short time by using a low end pc finally by using the pseudo curvature element size controlling metric to impose the curvature element size requirement in an implicit manner the new mesh generation procedure can also generate finite element meshes with high fidelity to approximate the target surfaces accurately copyright 2003 john wiley sons ltd

an extended advancing front technique for closed surfaces mesh generation an extended advancing front technique aft with shift operations and riemann metric named as shifting aft is presented for finite element mesh generation on 3d surfaces especially 3d closed surfaces riemann metric is used to govern the size and shape of the triangles in the parametric space the shift operators are employed to insert a floating space between real space and parametric space during the 2d parametric space mesh generation in the previous work of closed surface mesh generation the virtual boundaries are adopted when mapping the closed surfaces into 2d open parametric domains however it may cause the mesh quality worsening problem in order to overcome this problem the aft kernel is combined with the shift operator in this paper the shifting aft can generate high quality meshes and guarantee convergence in both open and closed surfaces for the shifting aft it is not necessary to introduce virtual boundaries while meshing a closed surface hence the boundary discretization procedure is largely simplified and moreover better shaped triangles will be generated because there are no additional interior constraints yielded by virtual boundaries comparing with direct methods the shifting aft avoids costly and unstable 3d geometrical computations in the real space some examples presented in this paper have demonstrated the advantages of shift aft in 3d surface mesh generation especially for the closed surfaces copyright 2007 john wiley sons ltd

eqsm an efficient high quality surface grid generation method based on remeshing the eqsm method for the generation of unstructured triangular surface grids is presented the method is based on remeshing techniques and avoids the need for traditional mesh triangulation approaches such as the advancing front and the delaunay methods normalized edge lengths based on a metric derived from curvature or from a user specified spacing are employed as the remeshing criterion it is assumed that the geometry is input in the form of composite parametric surfaces with analytic definition or ferguson or nurbs type multiple patch representation examples based upon typical aircraft geometries are included to demonstrate how high quality grids can be efficiently generated on surfaces that exhibit a high degree of geometric complexity