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

global target aggregation and state agreement of nonlinear multi agent systems with switching topologies in this paper we discuss coordination problems of a group of autonomous agents including the target aggregation to a convex set and the state agreement the aggregation of the whole agent group consisting of leaders informed agents and followers to a given set is investigated with switching interconnection topologies described by the connectivity assumptions on the joint topology in the time interval t for any time t and then the state agreement problem is studied in a similar way an approach based on set stability and limit set analysis is given to study the multi agent convergence problems with the help of graph theory and convex analysis coordination conditions are obtained in some important cases and the results show that simple local rules can make the networked agents with first order nonlinear individual dynamics achieve desired collective behaviors

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

constrained consensus in continuous time multiagent systems under weighted graph this paper studies constrained consensus for continuous time multiagent systems where agents are subject to different state constraints a projection based consensus protocol is presented where a projection operator is used on top of the traditional consensus protocol in order to keep the state staying inside the constraint set this operator can ensure the smoothness of the state trajectory under projection and it will only be used when the state is close to the boundary of the constraint set and about to move outside under this protocol each individual agent only needs to know its own state and constraint set as well as the relative states to its neighboring agents with the assumption that all constraint sets are convex and have nonempty intersection it is proven that global consensus can be achieved without violating any state constraints during the transience

global stabilization of linear discrete time systems with bounded feedback abstract this paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws the main result proved is an analog of one proved for the continuous time case by the authors and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one the proof provides in principle an algorithm for the construction of such feedback laws which can be implemented either as cascades or as parallel connections single hidden layer neural networks of simple saturation functions

global leader following consensus of a group of general linear systems using bounded controls this paper studies the global leader following consensus problem for a multi agent system with bounded controls the follower agents and the leader agent are all described by a general linear system both a bounded state feedback control law and a bounded output feedback control law are constructed for each follower agent in the group the feedback law for each input of an agent uses a multi hop relay protocol in which the agent obtains the information of other agents through multi hop paths in the communication network the number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of eigenvalues at the origin and the number of pairs of non zero imaginary eigenvalues of the sub system corresponding to the input and the feedback gains are constructed from the adjacency matrix of the communication network it is shown that global leader following consensus is achieved under these feedback control laws when the communication topology among follower agents is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower

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

adaptive consensus of scale free multi agent system by randomly selecting links abstractthis paper investigates an adaptive consensus problem for distributed scale free multi agent systems sfmass by randomly selecting links where the degree of each node follows a power law distribution the randomly selecting links are based on the assumption that every agent decides to select links among its neighbours according to the received data with a certain probability accordingly a novel consensus protocol with the range of the received data is developed and each node updates its state according to the protocol by the iterative method and cauchy inequality the theoretical analysis shows that all errors among agents converge to zero and in the meanwhile several criteria of consensus are obtained one numerical example shows the reliability of the proposed methods

consensus of second order discrete time multi agent systems with fixed topology abstract this paper studies the consensus of second order discrete time multi agent systems with fixed topology first we formulate the problem and give some preliminaries then by algebraic graph theory and matrix theory the convergence of system matrix is analyzed our main results indicate that the consensus of second order system can be achieved if and only if the topology graph has a directed spanning tree and the values of the scaling parameters satisfy a range the eigenvalues of the corresponding laplacian matrix play a key role in reaching consensus finally numerical simulations are given to illustrate the results

on global leader following consensus of identical linear dynamic systems subject to actuator saturation abstract this paper studies the leader following consensus problem for a group of agents with identical linear systems subject to control input saturation we focus on two classes of linear systems neutrally stable systems and double integrator systems for neurally stable systems we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and with proper choices of relative potential functions global consensus can also be achieved over a switching communication topology for double integrator systems we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and with the help of a simple saturation function in the local feedback laws global consensus can also be achieved over a switching communication topology simulation results illustrate the theoretical results

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

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 general result on the stabilization of linear systems using bounded controls we present two constructions of controllers that globally stabilize linear systems subject to control saturation we allow essentially arbitrary saturation functions the only conditions imposed on the system are the obvious necessary ones namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold one of the constructions is in terms of a neural network type one hidden layer architecture while the other one is in terms of cascades of linear maps and saturations

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

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

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

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

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

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

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

brief paper synchronization in networks of identical linear systems the paper investigates the synchronization of a network of identical linear state space models under a possibly time varying and directed interconnection structure the main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected the result can be interpreted as a generalization of classical consensus algorithms stronger conditions are shown to be sufficient but to some extent also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature

brief finite gain stabilization of discrete time linear systems subject to actuator saturation it is shown that for neutrally stable discrete time linear systems subject to actuator saturation finite gain l p stabilization can be achieved by linear output feedback for all p 1 an explicit construction of the corresponding feedback laws is given the feedback laws constructed also result in a closed loop system that is globally asymptotically stable and in an input to state estimate

finite time observers for multi agent systems without velocity measurements and with input saturations abstract this paper is devoted to the distributed finite time observers for multi agent systems where the control inputs are required to be bounded and the velocities are assumed to be not available for feedback an effective framework through defining a class of coordinated saturation functions is introduced under which both a first order finite time observer and a high order finite time observer are constructed by applying the homogeneous theory for stability analysis it is proven that all the states of the followers can converge to that of the leader in finite time under our proposed observers with mild modifications of our control strategies the foregoing results are then extended to the distributed finite time containment control problem where the states of the followers converge to the convex hull spanned by the multiple dynamic leaders numerical simulations are presented to demonstrate the efficiency of our methods

perturbing consensus for complexity a finite time discrete biased min consensus under time delay and asynchronism abstract in this paper we propose a discrete time biased min consensus protocol with finite time convergence by perturbing an existing min consensus protocol and investigate its convergence under time delay and a synchronous state update it is shown that a complex behavior that can address shortest path planning on a graph emerges from this modified consensus protocol theoretical analysis shows that the proposed protocol converges in finite time in real world networked systems there may exist inevitable time delay or asynchronism in state updates the convergence of biased min consensus under these non ideal situations is also theoretically analyzed to show the scalability and efficiency of the proposed protocol it is applied to large scale maze solving on a maze map containing 640 640 pixels which corresponds to a graph with 42 185 nodes in addition we also present an application of the proposed protocol to address the complete coverage problem which further demonstrates the potential of biased min consensus in robotic applications

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

brief paper an internal model principle is necessary and sufficient for linear output synchronization output synchronization of a network of heterogeneous linear state space models under time varying and directed interconnection structures is investigated it is shown that assuming stabilizability and detectability of the individual systems and imposing very mild connectedness assumptions on the interconnection structure an internal model requirement is necessary and sufficient for synchronizability of the network to polynomially bounded trajectories the resulting dynamic feedback couplings can be interpreted as a generalization of existing methods for identical linear systems

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

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

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

constrained consensus of asynchronous discrete time multi agent systems with time varying topology the union graph is assumed to be strongly connected over each finite interval an approach is proposed to transform the original network to a synchronous one we show that the linear part converges and the projection error vanishes over time in this paper the constrained consensus problem is studied for asynchronous discrete time multi agent system where each agent needs to lie in a closed convex constraint set while reaching consensus the communication graphs are assumed to be directed unbalanced dynamically changing in addition their union graph is assumed to be strongly connected among certain intervals of finite length to deal with the asynchronous communications among agents the original asynchronous system is equivalently transformed to the synchronous one by adding new agents by employing the properties of the projection on the convex sets the distance from the states of the agents in the newly constructed system to the intersection set of all agents constraint sets is estimated based on this estimation the original system is proven to reach consensus by showing that the linear parts of the newly constructed systems converge and the nonlinear parts vanish over time finally two numerical examples are provided to show the effectiveness of the theoretical results

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

network topology and communication data rate for consensusability of discrete time multi agent systems this paper investigates the joint effect of agent dynamic network topology and communication data rate on consensusability of linear discrete time multi agent systems neglecting the finite communication data rate constraint and under undirected graphs a necessary and sufficient condition for consensusability under a common control protocol is given which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability the result is established by solving a discrete time simultaneous stabilization problem a lower bound of the optimal convergence rate to consensus which is shown to be tight for some special cases is provided as well moreover a necessary and sufficient condition for formationability of multi agent systems is obtained as a special case the discrete time second order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence the effects of undirected graphs on consensability formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph laplacian matrix an extension to directed graphs is also made the consensus problem under a finite communication data rate is finally investigated

global consensus for discrete time multi agent systems with input saturation constraints in this paper we consider the global consensus problem for discrete time multi agent systems with input saturation constraints under fixed undirected topologies we first give necessary conditions for achieving global consensus via a distributed protocol based on relative state measurements of the agent itself and its neighboring agents we then focus on two special cases where the agent model is either neutrally stable or a double integrator for the neutrally stable case any linear protocol of a particular form which solves the consensus problem for the case without input saturation constraints also solves the global consensus problem for the case with input saturation constraints for the double integrator case we show that a subset of linear protocols which solve the consensus problem for the case without saturation constraints also solve the global consensus problem for the case with input saturation constraints the results are illustrated by numerical simulations

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

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

adaptive periodic event triggered consensus for multi agent systems subject to input saturation abstractthis paper investigates the distributed adaptive event triggered consensus control for a class of nonlinear agents each agent is subject to input saturation two kinds of distributed event triggered control scheme are introduced one is continuous time based event triggered scheme and the other is sampled data based event triggered scheme compared with the traditional event triggered schemes in the existing literatures the parameters of the event triggered schemes in this paper are adaptively adjusted by using some event error dependent adaptive laws the problem of simultaneously deriving the controller gain matrix and the event triggering parameter matrix and tackling the saturation nonlinearity is cast into standard linear matrix inequalities problem a convincing simulation example is given to demonstrate the theoretical results

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

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

simultaneous external and internal stabilization of linear systems with input saturation and non input additive sustained disturbances in this paper we study simultaneous external and internal stabilization of the linear system under input saturation and non input additive sustained disturbances for systems that are asymptotic null controllable with bounded control it is shown that a nonlinear dynamic feedback controller can be designed so that the closed loop states remain bounded for any initial condition and for two classes of sustained disturbances and that the equilibrium in the absence of disturbances is globally asymptotically stable

brief paper some necessary and sufficient conditions for second order consensus in multi agent dynamical systems this paper studies some necessary and sufficient conditions for second order consensus in multi agent dynamical systems first basic theoretical analysis is carried out for the case where for each agent the second order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant a necessary and sufficient condition is given to ensure second order consensus and it is found that both the real and imaginary parts of the eigenvalues of the laplacian matrix of the corresponding network play key roles in reaching consensus based on this result a second order consensus algorithm is derived for the multi agent system facing communication delays a necessary and sufficient condition is provided which shows that consensus can be achieved in a multi agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value finally simulation examples are given to verify the theoretical analysis

distributed h constrained consensus problem abstract this paper is concerned with the distributed h constrained consensus problem for multi agent systems the objective is to use local information to make all agents reach a consensus in a given convex set while satisfying a desired h performance index in the presence of external disturbances a nonlinear distributed algorithm is adopted to solve this constrained consensus problem to measure the effects of the disturbance on the consensus of all agents and the convergence of all agents to the convex set a nonlinear function is constructed as the h output function by analyzing the convexity of the convex set a sufficient condition is given to solve the constrained consensus problem with the desired h performance finally a numerical simulation example is provided to show the effectiveness of our theoretical results

distributed velocity constrained consensus of discrete time multi agent systems with nonconvex constraints switching topologies and delays in this technical note a distributed velocity constrained consensus problem is studied for discrete time multi agent systems where each agent s velocity is constrained to lie in a nonconvex set a distributed constrained control algorithm is proposed to enable all agents to converge to a common point using only local information the gains of the algorithm for all agents need not to be the same or predesigned and can be adjusted by each agent itself based on its own and neighbors information it is shown that the algorithm is robust to arbitrarily bounded communication delays and arbitrarily switching communication graphs provided that the union of the graphs has directed spanning trees among each certain time interval the analysis approach is based on multiple novel model transformations proper control parameter selections boundedness analysis of state dependent stochastic matrices1 exploitation of the convexity of stochastic matrices and the joint connectivity of the communication graphs numerical examples are included to illustrate the theoretical results

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

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

distributed consensus of second order multiagent systems with nonconvex velocity and control input constraints this paper is devoted to a distributed consensus problem for second order multiagent systems with nonconvex velocity and control input constraints a distributed control algorithm is introduced using local information it is shown that consensus can be achieved as long as the union of the communication graphs has directed spanning trees among each time interval of certain bounded length in the presence of arbitrarily bounded communication delays finally a numerical example is included to illustrate the theoretical results

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

graph laplacian based leaderless consensus for multi agent systems in t s form abstract the graph laplacian based leaderless consensus protocol design problem for nonlinear multi agent systems mas in takagi sugeno form is highly challenging the main reason is that the similarity transformation of the mas dynamics in an abbreviated form with the kronecker product is quite restricted we provide a positive answer to this problem

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

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

the approximate invariance of the average number of connections for the continuum percolation of squares at criticality we perform monte carlo simulations to determine the average excluded area aex of randomly oriented squares randomly oriented widthless sticks and aligned squares in two dimensions we find significant differences between our results for randomly oriented squares and previous analytical results for the same the sources of these differences are explained using our results for aex and monte carlo simulation results for the percolation threshold we estimate the mean number of connections per object bc at the percolation threshold for squares in 2 d we study systems of squares that are allowed random orientations within a specified angular interval our simulations show that the variation in bc is within 1 6 when the angular interval is varied from 0 to 2

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

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper