spectral hp least squares finite element formulation for the navier stokes equations we consider the application of least squares finite element models combined with spectral hp methods for the numerical solution of viscous flow problems the paper presents the formulation validation and application of a spectral hp algorithm to the numerical solution of the navier stokes equations governing two and three dimensional stationary incompressible and low speed compressible flows the navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity or velocity gradients as additional independent variables and the least squares method is used to develop the finite element model high order element expansions are used to construct the discrete model the discrete model thus obtained is linearized by newton s method resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method spectral convergence of the l2 least squares functional and l2 error norms is verified using smooth solutions to the two dimensional stationary poisson and incompressible navier stokes equations numerical results for flow over a backward facing step steady flow past a circular cylinder three dimensional lid driven cavity flow and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

a semi local spectral hp element solver for linear elasticity problems summary we develop an efficient semi local method for speeding up the solution of linear systems arising in spectral hp element discretization of the linear elasticity equations the main idea is to approximate the element wise residual distribution with a localization operator we introduce in this paper and subsequently solve the local linear system additionally we decouple the three directions of displacement in the localization operator hence enabling the use of an efficient low energy preconditioner for the conjugate gradient solver this approach is effective for both nodal and modal bases in the spectral hp element method but here we focus on the modal hierarchical basis in numerical tests we verify that there is no loss of accuracy in the semi local method and we obtain good parallel scalability and substantial speed up compared to the original formulation in particular our tests include both structure only and fluid structure interaction problems with the latter modeling a 3d patient specific brain aneurysm copyright 2014 john wiley sons ltd

from electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex the electrostatic interpretation of the jacobi gauss quadrature points is exploited to obtain interpolation points suitable for approximation of smooth functions defined on a simplex moreover several new estimates based on extensive numerical studies for approximation along the line using jacobi gauss lobatto quadrature points as the nodal sets are presented the electrostatic analogy is extended to the two dimensional case with the emphasis being on nodal sets inside a triangle for which two very good matrices of nodal sets are presented the matrices are evaluated by computing the lebesgue constants and they share the property that the nodes along the edges of the simplex are the gauss lobatto quadrature points of the chebyshev and legendre polynomials respectively this makes the resulting nodal sets particularly well suited for integration with conventional spectral methods and supplies a new nodal basis for h p finite element methods

basis functions for triangular and quadrilateral high order elements in this paper we present a unified description of new spectral bases suitable for high order hp finite element discretizations on hybrid two dimensional meshes consisting of triangles and quadrilaterals all bases presented are for c0 continuous discretizations and are described both as modal and as mixed modal nodal expansions general jacobi polynomials of mixed weights are employed that accommodate automatic exact numerical quadratures generalized tensor products and variable expansion order in each element the approximation properties of the bases are analyzed in the context of the projection linear advection and diffusion operators

spatial prediction with mobile sensor networks using gaussian processes with built in gaussian markov random fields in this paper a new class of gaussian processes is proposed for resource constrained mobile sensor networks such a gaussian process builds on a gmrf with respect to a proximity graph over a surveillance region the main advantages of using this class of gaussian processes over standard gaussian processes defined by mean and covariance functions are its numerical efficiency and scalability due to its built in gmrf and its capability of representing a wide range of non stationary physical processes the formulas for predictive statistics such as predictive mean and variance are derived and a sequential field prediction algorithm is provided for sequentially sampled observations for a special case using compactly supported weighting functions we propose a distributed algorithm to implement field prediction by correctly fusing all observations simulation and experimental results illustrate the effectiveness of our approach

a dffd simulation method combined with the spectral element method for solid fluid interaction problems a 2d simulation method for a rigid body moving in an incompressible viscous fluid is proposed it combines one of the immersed boundary methods the dffd direct forcing fictitious domain method with the spectral element method the former is employed for efficiently capturing the two way fsi fluid structure interaction and the geometric flexibility of the latter is utilized for any possibly co existing stationary and complicated solid or flow boundary a pseudo body force is imposed within the solid domain to enforce the rigid body motion and a lagrangian mesh composed of triangular elements is employed for tracing the rigid body in particular a so called sub cell scheme is proposed to smooth the discontinuity at the fluid solid interface and to execute integrations involving eulerian variables over the moving solid domain the accuracy of the proposed method is verified through an observed agreement of the simulation results of some typical flows with analytical solutions or existing literatures the direct forcing fictitious domain method and the spectral element method are combined direct interpolation of eulerian variables onto lagrangian mesh is not necessary non fluctuating pressure fields are obtained with a smoothed pseudo body force the proposed method possesses a spectral accuracy both small and large solid to fluid density ratios are applicable

distributed learning and cooperative control for multi agent systems this paper presents an algorithm and analysis of distributed learning and cooperative control for a multi agent system so that a global goal of the overall system can be achieved by locally acting agents we consider a resource constrained multi agent system in which each agent has limited capabilities in terms of sensing computation and communication the proposed algorithm is executed by each agent independently to estimate an unknown field of interest from noisy measurements and to coordinate multiple agents in a distributed manner to discover peaks of the unknown field each mobile agent maintains its own local estimate of the field and updates the estimate using collective measurements from itself and nearby agents each agent then moves towards peaks of the field using the gradient of its estimated field while avoiding collision and maintaining communication connectivity the proposed algorithm is based on a recursive spatial estimation of an unknown field we show that the closed loop dynamics of the proposed multi agent system can be transformed into a form of a stochastic approximation algorithm and prove its convergence using ljung s ordinary differential equation ode approach we also present extensive simulation results supporting our theoretical results

distributed parametric and nonparametric regression with on line performance bounds computation in this paper we focus on collaborative multi agent systems where agents are distributed over a region of interest and collaborate to achieve a common estimation goal in particular we introduce two consensus based distributed linear estimators the first one is designed for a bayesian scenario where an unknown common finite dimensional parameter vector has to be reconstructed while the second one regards the nonparametric reconstruction of an unknown function sampled at different locations by the sensors both of the algorithms are characterized in terms of the trade off between estimation performance communication computation and memory complexity in the finite dimensional setting we derive mild sufficient conditions which ensure that a distributed estimator performs better than the local optimal ones in terms of estimation error variance in the nonparametric setting we introduce an on line algorithm that allows the agents to simultaneously compute the function estimate with small computational communication and data storage efforts as well as to quantify its distance from the centralized estimate given by a regularization network one of the most powerful regularized kernel methods these results are obtained by deriving bounds on the estimation error that provide insights on how the uncertainty inherent in a sensor network such as imperfect knowledge on the number of agents and the measurement models used by the sensors can degrade the performance of the estimation process numerical experiments are included to support the theoretical findings

directional rates of change under spatial process models spatial process models are now widely used for inference in many areas of application in such contexts interest is often in the rate of change of a spatial surface at a given location in a given direction examples include temperature or rainfall gradients in meteorology pollution gradients for environmental data and surface roughness assessment for digital elevation models because the spatial surface is viewed as a random realization all such rates of change are random as well we formalize the notions of directional finite difference processes and directional derivative processes building upon the concept of mean square differentiability as developed by stein and banerjee and gelfand we obtain complete distribution theory results under the assumptions of a stationary gaussian process model either for the data or for spatial random effects we present inference under a bayesian framework which in this setting presents several advantages finally we illustrate our methodology with a simulated dat

an eigen based high order expansion basis for structured spectral elements we present an eigen based high order expansion basis for the spectral element approach with structured elements the new basis exhibits a numerical efficiency significantly superior in terms of the conditioning of coefficient matrices and the number of iterations to convergence for the conjugate gradient solver to the commonly used jacobi polynomial based expansion basis this basis results in extremely sparse mass matrices and it is very amenable to the diagonal preconditioning ample numerical experiments demonstrate that with the new basis and a simple diagonal preconditioner the number of conjugate gradient iterations to convergence has essentially no dependence or only a very weak dependence on the element order the expansion bases are constructed by a tensor product of a set of special one dimensional 1d basis functions the 1d interior modes are constructed such that the interior mass and stiffness matrices are simultaneously diagonal and have identical condition numbers the 1d vertex modes are constructed to be orthogonal to all the interior modes the performance of the new basis has been investigated and compared with other expansion bases

gaussian process regression for sensor networks under localization uncertainty in this paper we formulate gaussian process regression with observations under the localization uncertainty due to the resource constrained sensor networks in our formulation effects of observations measurement noise localization uncertainty and prior distributions are all correctly incorporated in the posterior predictive statistics the analytically intractable posterior predictive statistics are proposed to be approximated by two techniques viz monte carlo sampling and laplace s method such approximation techniques have been carefully tailored to our problems and their approximation error and complexity are analyzed simulation study demonstrates that the proposed approaches perform much better than approaches without considering the localization uncertainty properly finally we have applied the proposed approaches on the experimentally collected real data from a dye concentration field over a section of a river and a temperature field of an outdoor swimming pool to provide proof of concept tests and evaluate the proposed schemes in real situations in both simulation and experimental results the proposed methods outperform the quick and dirty solutions often used in practice

a stabilised nodal spectral element method for fully nonlinear water waves we present an arbitrary order spectral element method for general purpose simulation of non overturning water waves described by fully nonlinear potential theory the method can be viewed as a high order extension of the classical finite element method proposed by cai et al 1998 5 although the numerical implementation differs greatly features of the proposed spectral element method include nodal lagrange basis functions a general quadrature free approach and gradient recovery using global l 2 projections the quartic nonlinear terms present in the zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves we show how the scheme can be stabilised through a combination of over integration of the galerkin projections and a mild spectral filtering on a per element basis this effectively removes any aliasing driven instabilities while retaining the high order accuracy of the numerical scheme the additional computational cost of the over integration is found insignificant compared to the cost of solving the laplace problem the model is applied to several benchmark cases in two dimensions the results confirm the high order accuracy of the model exponential convergence and demonstrate the potential for accuracy and speedup the results of numerical experiments are in excellent agreement with both analytical and experimental results for strongly nonlinear and irregular dispersive wave propagation the benefit of using a high order possibly adapted spatial discretisation for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications

efficient visualization of high order finite elements a general method for the post processing treatment of high order finite element fields is presented the method applies to general polynomial fields including discontinuous finite element fields the technique uses error estimation and h refinement to provide an optimal visualization grid some filtering is added to the algorithm in order to focus the refinement on a visualization plane or on the computation of one single iso zero surface 2d and 3d examples are provided that illustrate the power of the technique in addition schemes and algorithms that are discussed in the paper are readily available as part of an open source project that is developed by the authors namely gmsh

a new triangular and tetrahedral basis for high order hp finite element methods in this paper we describe the foundations of a new hierarchical modal basis suitable for high order hp finite element discretizations on unstructured meshes it is based on a generalized tensor product of mixed weight jacobi polynomials the generalized tensor product property leads to a low operation count with the use of sum factorization techniques variable p order expansions in each element are readily implemented which is a crucial property for efficient adaptive discretizations numerical examples demonstrate the exponential convergence for smooth solutions and the ability of this formulation to handle easily very complex two and three dmensional computational domains employing standard meshes

space time coupled spectral hp least squares finite element formulation for the incompressible navier stokes equations we consider least squares finite element models for the numerical solution of the non stationary navier stokes equations governing viscous incompressible fluid flows the paper presents a formulation where the effects of space and time are coupled resulting in a true space time least squares minimization procedure as opposed to a space time decoupled formulation where a least squares minimization procedure is performed in space at each time step the formulation is first presented for the linear advection diffusion equation and then extended to the navier stokes equations the formulation has no time step stability restrictions and is spectrally accurate in both space and time to allow the use of practical c0 element expansions in the resulting finite element model the navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity as an additional independent variable and the least squares method is used to develop the finite element model of the governing equations high order element expansions are used to construct the discrete model the discrete model thus obtained is linearized by newton s method resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix free form spectral convergence of the l2 least squares functional and l2 error norms in space time is verified using a smooth solution to the two dimensional non stationary incompressible navier stokes equations numerical results are presented for impulsively started lid driven cavity flow oscillatory lid driven cavity flow transient flow over a backward facing step and flow around a circular cylinder the results demonstrate the predictive capability and robustness of the proposed formulation even though the space time coupled formulation is emphasized we also present the formulation and numerical results for least squares space time decoupled finite element models the numerical results show that the space time coupled formulation has superior predictive capabilities for flows demanding high space time resolution exemplified here by the transient flow over a backward facing step

the tetrahedral finite cell method higher order immersogeometric analysis on adaptive non boundary fitted meshes the finite cell method fcm is an immersed domain finite element method that combines higher order non boundary fitted meshes weak enforcement of dirichlet boundary conditions and adaptive quadrature based on recursive subdivision due to its ability to improve the geometric resolution of intersected elements it can be characterized as an immersogeometric method in this paper we extend the fcm so far only used with cartesian hexahedral elements to higher order non boundary fitted tetrahedral meshes based on a reformulation of the octree based subdivision algorithm for tetrahedral elements we show that the resulting tetfcm scheme is fully accurate in an immersogeometric sense that is the solution fields achieve optimal and exponential rates of convergence for h and p refinement if the immersed geometry is resolved with sufficient accuracy tetfcm can leverage the natural ability of tetrahedral elements for local mesh refinement in three dimensions its suitability for problems with sharp gradients and highly localized features is illustrated by the immersogeometric phase field fracture analysis of a human femur bone

mixed least squares finite element models for static and free vibration analysis of laminated composite plates abstract new mixed least squares finite element models are developed for static and free vibration analysis of laminated composite plates both models consider the first order shear deformation theory with generalized displacements and stress resultants as independent variables using equal and high order c 0 basis functions the mixed least squares formulation is a useful alternative to mixed weak form models as it develops into an unconstrained minimization variational problem and thereby allows the finite element approximating spaces to be chosen independently ultimately the model for static analysis yields a symmetric positive definite system of linear equations and the latest innovative model for free vibration analysis yields a symmetric quadratic eigenvalue problem the predictive capabilities of the proposed models are assessed by comparison with analytical solutions considering selected examples of both static and free vibration analysis of rectangular laminated composite plates with different boundary conditions and a range of side to thickness ratios from 10 to 500 in particular these mixed least squares models using high order basis functions are shown to be insensitive to shear locking

systematic and generic construction of shape functions for p adaptive meshes of multidimensional finite elements this paper presents a methodology for generating high order shape functions for the complete family of finite elements the geometric entities presented are the point line triangle quadrilateral tetrahedron pyramid prism and hexahedron the shape functions constructed are hierarchical and generate continuous approximation spaces the order of interpolation of the shape function can be determined independently for each edge face and volume the space of interpolation of order p for each element is complete this definition allows for the construction of hybrid meshes with any combination of these elements including elements of distinct dimension and or interpolation order the reader will observe that our systematic way of constructing shape functions can be extended to elements of higher dimension

consensus based distributed multiple model ukf for jump markov nonlinear systems this note studies the problem of distributed estimation for jump markov nonlinear systems jmnlss in a not fully connected sensor network based on the consensus theory a distributed unscented kalman filter ukf is first derived for nonlinear systems without jumping parameters and then it is extended to develop a distributed multiple model ukf for jmnlss the proposed filtering algorithm is illustrated via a simulation example involving tracking a maneuvering target

higher order triangular basis functions and solution performance of the cg method new sets of hierarchical higher order basis functions in fem for triangle elements are constructed using a systematic orthogonalization approach that yield better conditioning and investigated with different preconditioners jacobi icc ilu and sainv presented theoretical and numerical results indicate that certain preconditioners are insensitive to the condition number of the basis functions advantageous properties of basis functions in relation to preconditioners are viewed from the perspective of similarity and congruence transforms of the basis functions this provides an alternative view for a systematic construction of the basis functions that couples with a specific preconditioner to optimize the solution performance

robust distributed estimation for linear systems under intermittent information we provide a comprehensive solution to the estimation problem of the state for a linear time invariant system in a distributed fashion over networks that allow only intermittent information transmission by attaching to each node an observer that employs information received from its neighbors triggered by asynchronous communication events we propose a distributed state observer that guarantees global exponential stability of the zero estimation error set the design of parameters is formulated as linear matrix inequalities a thorough robustness analysis of the proposed observer to unmodeled dynamics unknown communication times as well as measurement and communication noise characterized in terms of input to state stability is presented these properties of the proposed observer are shown analytically and validated numerically

distributed kriged kalman filter for spatial estimation this paper considers robotic sensor networks performing spatially distributed estimation tasks a robotic sensor network is deployed in an environment of interest and takes successive point measurements of a dynamic physical process modeled as a spatio temporal random field taking a bayesian perspective on the kriging interpolation technique from geostatistics we design the distributed kriged kalman filter for predictive inference of the random field and of its gradient the proposed algorithm makes use of a novel distributed strategy to compute weighted least squares estimates when measurements are spatially correlated this strategy results from the combination of the jacobi overrelaxation method with dynamic average consensus algorithms as an application of the proposed algorithm we design a gradient ascent cooperative strategy and analyze its convergence properties in the absence of measurement errors via stochastic lyapunov functions we illustrate our results in simulation

on general balance in row column designs summary the purpose of this paper is to clarify the relationships between general balance in a row column design the commutivity of the information matrices of the row and column components and the concept of adjusted orthogonality the class of row column generalized cyclic incomplete block designs is defined and a characterization is given of the subclass having general balance

least squares finite element formulation for shear deformable shells abstract we present a least squares based finite element formulation for the numerical analysis of shear deformable shell structures the variational problem is obtained by minimizing the least squares functional defined as the sum of the squares of the shell equilibrium equations residuals measured in suitable norms of hilbert spaces the use of least squares principles leads to a variational unconstrained minimization problem where compatibility conditions between approximation spaces never arise i e stability requirements such as inf sup conditions never arise the proposed formulation retains the generalized displacements and stress resultants as independent variables and in view of the nature of the variational setting upon which the finite element model is built allows for equal order interpolation a p type hierarchical basis is used to construct the discrete finite element model based on the least squares formulation exponentially fast decay of the least squares functional is verified for increasing order of the modal expansions several well established benchmark problems are solved to demonstrate the predictive capability of the least squares based shell elements shell elements based on this formulation are shown to be effective in both membrane and bending dominated states

spectral element simulations of interactive particles in a fluid abstract this paper presents three dimensional simulations of interactive particles in a fluid the originality of this paper is the integrated eulerian lagrangian algorithms implemented with high order methods in both space and time for numerical solutions to navier stokes equations with additional source terms implementation of fourth order stiffly stable schemes was tested for time integration before they were used in computations in order to provide the h p type mesh refinement for extra flexibility to achieve higher spatial resolution a modal spectral element method was used to solve governing equations in three dimensions another originality is the efficiency in handling moving particles without adaptive or moving mesh simulation results were validated with experimental data and verified with exact solutions in addition numerical results were also compared with solutions at higher resolutions and good agreement was accomplished results indicate that algorithms and implementations are accurate and appropriate for investigating three dimensional interactive particles in a fluid involving many moving objects

some convergence results related to the jor iterative method for symmetric positive definite matrices the jacobi method for iteratively solving a set of linear algebraic equations is well known however it suffers from the drawback that it does not converge for all linear algebraic systems in science and engineering one often encounters algebraic systems of the form ax b where the matrix a is symmetric and positive definite in this paper we show that a slight variant of the jacobi method namely the jacobi overrelaxation jor method can be made to ensure convergence of the iterative scheme for such matrices thus we expand the applicability of jor iterative methods to all symmetric positive definite matrices in a manner which is computationally convenient and simple in particular we show that this variant scheme can be explicitly determined without the need for any eigenvalue computations we show that if eigenvalue computations are employed one can obtain the maximum rate of convergence by a proper choice of parameters for the jor scheme this maximum rate of convergence is also explicitly obtained

coordinated one step optimal distributed state prediction for a networked dynamical system a new recursive one step state prediction procedure is derived for a networked dynamic system under the coordination of a collaboration unit that provides optimal update gains for each individual subsystem utilizing merely system parameters this predictor estimates plant s local states based only on local system output measurements this estimator can be easily realized in a distributed way and can also be simply scaled to systems with a large amount of subsystems provided it has enough communication and storage capacities it is proved that when prediction error variances are adopted in performance comparisons the optimal gain matrix is usually unique recursive and explicit expressions are derived for both this optimal gain matrix and the covariance matrix of the corresponding prediction errors the optimal gain matrix for every subsystem in this distributed recursive predictor has been shown to be equal to that of the well known kalman filter utilizing only local system output measurements which makes it possible to robustify this state predictor using a sensitivity penalization approach numerical simulation results illustrate that prediction accuracy of the suggested procedure may sometimes be as good as that of the lumped kalman filter