about the use of standard integration schemes for x fem in solid mechanics plasticity abstract the introduction of plasticity in an extended finite element x fem framework is very recent and arises several technical and scientific difficulties due to the moving position of integration points as the crack proceeds if a fixed grid is not used currently the existing analyses in plasticity with x fem are limited to monotonic plasticity approximated by non linear elasticity using the hrr field decomposition however such an analysis cannot be applied in fatigue where cyclic plasticity plays a major role in crack propagation the aim of this study is to tackle one of the difficulties induced by cyclic plastic computation the projection of the internal variables during crack propagation the discontinuous heaviside function in the elements cut by the crack is replaced by a new continuous enrichment function this new function is polynomial and its degrees and coefficients depend on the type of element and on the position of the interface in the element the automatic determination of the new enrichment and its introduction in a linear and non linear framework have been implemented for linear elements in two dimensions and three dimensions and tested with convergence tests in elasticity and plasticity

fast and accurate computation of hypersingular integrals in galerkin surface integral equation formulations via the direct evaluation method hypersingular 4 d integrals arising in the galerkin discretization of surface integral equation formulations are computed by means of the direct evaluation method the proposed scheme extends the basic idea of the singularity cancellation methods usually employed for the regularization of the singular integral kernel by utilizing a series of coordinate transformations combined with a reordering of the integrations the overall algebraic manipulation results in smooth 2 d integrals that can be easily evaluated via standard quadrature rules finally the reduction of the dimensionality of the original integrals together with the smooth behavior of the associated integrands lead up to unmatched accuracy and efficiency

economical symmetrical quadrature rules for complete polynomials over a square domain it is of interest in numerical analysis to develop symmetrical quadrature rules for integration of complete polynomial functions over a square domain with minimum computational effort gaussian product quadrature rules integrate such functions with maximum effort symmetrical quadrature rules are developed and presented for integration of complete polynomial functions up to 21st order with minimum computational effort

extra dof free and linearly independent enrichments in gfem abstract a gfem without extra dof is developed without the extra dof the resulting linear system becomes independent in size of the order of local approximation the resulting pu approximation becomes free of linear dependence and the resulting stiffness matrix becomes good conditioned numerical studies show the new gfem s excellent convergence properties and excellent stability

integration of singular enrichment functions in the generalized extended finite element method for three dimensional problems a mapping method is developed to integrate weak singularities which result from enrichment functions in the generalized extended finite element method the integration scheme is applicable to 2d and 3d problems including arbitrarily shaped triangles and tetrahedra implementation of the proposed scheme in existing codes is straightforward numerical examples for 2d and 3d problems demonstrate the accuracy and convergence properties of the technique copyright 2008 john wiley sons ltd

implicit solution of the unsteady euler equations for high order accurate discontinuous galerkin discretizations efficient solution techniques for high order accurate time dependent problems are investigated for solving the two dimensional non linear euler equations in this work the spatial discretization consists of a high order accurate discontinuous galerkin dg approach implicit time integration techniques are considered exclusively in order to avoid the stability restrictions of explicit methods standard backwards differencing methods bdf1 and bdf2 as well as a second order crank nicholson cn2 and a fourth order implicit runge kutta irk4 scheme are considered in an attempt to balance the spatial and temporal accuracy of the overall approach the implicit system arising at each time step is solved using a p multigrid approach which is shown to produce h independent convergence rates while remaining relatively insensitive to the time step size the crank nicholson methodology although not l stable demonstrates superior performance compared to the bdf2 scheme for the problems chosen in this work however the fourth order accurate implicit runge kutta scheme is found to be the most efficient in terms of computational cost for a given accuracy level as compared to the lower order schemes in spite of the added cost per time step and the benefits of this scheme increase for tighter error tolerances

application of group representation theory to derive hermite interpolation polynomials on a triangle current methods used to devise sets of hermite interpolation polynomials of minimal order that ensure c n continuity across triangular element boundaries in two dimensions are not readily extensible to higher dimensions the extension of such methods is especially difficult when the number of degrees of freedom afforded by data at points is different from the number of degrees of freedom determined by the coefficients of a complete polynomial basis to a particular order this work introduces a formalism based on group representation theory that can accomplish this task in general the method is introduced through the derivation of c 1 continuous hermite polynomials that interpolate data at the three vertices of an equilateral triangular element these interpolation polynomials are reported here for the first time the polynomials derived here are compared to the standard polynomials defined in a right triangle by using the two sets of polynomials to solve the laplace equation over finite elements the methodology presented here is of use in higher dimensional elements when the complete polynomial degrees of freedom exceed the total c n degrees of freedom at the nodes

time varying input and state delay compensation for uncertain nonlinear systems a robust controller is developed for uncertain second order nonlinear systems subject to simultaneous unknown time varying state delays and known sufficiently small time varying input delays in addition to additive sufficiently smooth disturbances an integral term composed of previous control values facilitates a delay free open loop error system and the development of the feedback control structure a stability analysis based on lyapunov krasovskii lk functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying numerical simulations illustrate robustness of the developed method to various combinations of simultaneous input and state delays

spectral element method for elastic and acoustic waves in frequency domain numerical techniques in time domain are widespread in seismic and acoustic modeling in some applications however frequency domain techniques can be advantageous over the time domain approach when narrow band results are desired especially if multiple sources can be handled more conveniently in the frequency domain moreover the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain in this paper we present a spectral element method sem in frequency domain to simulate elastic and acoustic waves in anisotropic heterogeneous and lossy media the sem is based upon the finite element framework and has exponential convergence because of the use of gll basis functions the anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems compared with the conventional finite element method the number of unknowns in the sem is significantly reduced and higher order accuracy is obtained due to its spectral accuracy to account for the acoustic solid interaction the domain decomposition method ddm based upon the discontinuous galerkin spectral element method is proposed numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain

the aspherity of random walks the asphericity a of a random walk is defined and calculated for non self avoiding walks the definition of a generalises to self avoiding walks percolating clusters and other fractal objects and thus provides a generalised quantitative measure of the departure from spherical symmetry of the gross shape of these objects

entropy stable shock capturing space time discontinuous galerkin schemes for systems of conservation laws we present a streamline diffusion shock capturing spacetime discontinuous galerkin dg method to approximate nonlinear systems of conservation laws in several space dimensions the degrees of freedom are in terms of the entropy variables and the numerical flux functions are the entropy stable finite volume fluxes we show entropy stability of the formally arbitrarily high order accurate method for a general system of conservation laws furthermore we prove that the approximate solutions converge to the entropy measure valued solutions for nonlinear systems of conservation laws convergence to entropy solutions for scalar conservation laws and for linear symmetrizable systems is also shown numerical experiments are presented to illustrate the robustness of the proposed schemes

a paradigm for higher order polygonal elements in finite elasticity using a gradient correction scheme abstract recent studies have demonstrated that polygonal elements possess great potential in the study of nonlinear elastic materials under finite deformations on the one hand these elements are well suited to model complex microstructures e g particulate microstructures and microstructures involving different length scales and incorporating periodic boundary conditions on the other hand polygonal elements are found to be more tolerant to large localized deformations than the standard finite elements and to produce more accurate results in bending and shear with mixed formulations lower order mixed polygonal elements are also shown to be numerically stable on voronoi type meshes without any additional stabilization treatment however polygonal elements generally suffer from persistent consistency errors under mesh refinement with the commonly used numerical integration schemes as a result non convergent finite element results typically occur which severely limit their applications in this work a general gradient correction scheme is adopted that restores the polynomial consistency by adding a minimal perturbation to the gradient of the displacement field with the correction scheme the recovery of optimal convergence for solutions of displacement based and mixed formulations with both linear and quadratic displacement interpolants is confirmed by numerical studies of several boundary value problems in finite elasticity in addition for mixed polygonal elements the various choices of the pressure field approximations are discussed and their performance on stability and accuracy are numerically investigated we present applications of those elements in physically based examples including a study of filled elastomers with interphasial effect and a qualitative comparison with cavitation experiments for fiber reinforced elastomers

numerical analysis of a new mixed formulation for eigenvalue convection diffusion problems a mixed formulation is proposed and analyzed mathematically for coupled convection diffusion in heterogeneous medias transfer in solid parts driven by pure diffusion is coupled with convection diffusion transfer in fluid parts this study is carried out for translation invariant geometries general infinite cylinders and unidirectional flows this formulation brings to the fore a new convection diffusion operator the properties of which are mathematically studied its symmetry is first shown using a suitable scalar product it is proved to be self adjoint with compact resolvent on a simple hilbert space its spectrum is characterized as being composed of a double set of eigenvalues one converging towards infty and the other towards infty thus resulting in a nonsectorial operator the decomposition of the convection diffusion problem into a generalized eigenvalue problem permits the reduction of the original three dimensional problem into a two dimensional one despite the operator being nonse

simple cascade observer for a class of nonlinear systems with long output delays this note proposes a cascade observer for a class of nonlinear systems with global lipschitz nonlinearities in the presence of delayed output measurements the head of the cascade is a high gain observer while the remaining systems are state predictors providing an estimate of the actual state the key feature of the proposed observer is the introduction of a matrix design parameter that allows to tune the prediction process dominant dynamics with an identical simple structure for all the predictors the design of the observer is carried out by considering a set of conditions under which the exponential convergence to zero of the observation error is established in particular it is shown that the number of the subsystems in the cascade observer depends on the size of the delay and the lipschitz constant the observer is first designed assuming a constant time delay the underlying design approach is then appropriately adapted to deal with the time varying delay the effectiveness of the proposed observer with respect to two existing cascade observers is particularly highlighted through a comprehensive comparative analysis and simulation results

symmetric quadrature rules for tetrahedra based on a cubic close packed lattice arrangement a family of quadrature rules for integration over tetrahedral volumes is developed the underlying structure of the rules is based on the cubic close packed ccp lattice arrangement using 1 4 10 20 35 and 56 quadrature points the rules are characterized by rapid convergence positive weights and symmetry each rule is an optimal approximation in the sense that lower order terms have zero contribution to the truncation error and the leading order error term is minimized quadrature formulas up to order 9 are presented with relevant numerical examples

symmetric triangle quadrature rules for arbitrary functions abstract despite extensive research on symmetric polynomial quadrature rules for triangles as well as approaches to their calculation few studies have focused on non polynomial functions particularly on their integration using symmetric triangle rules in this paper we present two approaches to computing symmetric triangle rules for singular integrands by developing rules that can integrate arbitrary functions the first approach is well suited for a moderate amount of points and retains much of the efficiency of polynomial quadrature rules the second approach better addresses large amounts of points though it is less efficient than the first approach we demonstrate the effectiveness of both approaches on singular integrands which can often yield relative errors two orders of magnitude less than those from polynomial quadrature rules

volumetric testing parallel to the boundary surface for a nonconforming discretization of the electric field integral equation the volumetric monopolar rwg discretization of the electric field integral equation efie imposes no continuity constraint across edges in the surface discretization around a closed conductor the current is expanded with the monopolar rwg set and the electric field is tested over a set of tetrahedral elements attached to the boundary surface this scheme is facet oriented and therefore well suited for the scattering analysis of nonconformal meshes or composite objects the observed accuracy though is only competitive with respect to the rwg discretization for a restricted range of heights of the tetrahedral elements in this communication we introduce a novel implementation of the volumetric monopolar rwg discretization of the efie with testing over a set of wedges we show with rcs and near field results that this scheme offers improved accuracy for a wider range of heights than the approach with tetrahedral testing the application of the wedge testing to the even surface odd volumetric monopolar rwg discretization of the efie edge oriented and therefore less versatile shows similar accuracy as with tetrahedral testing which is a sign of robustness

global stabilisation of nonlinear delay systems with a compact absorbing set predictor based stabilization results are provided for nonlinear systems with input delays and a compact absorbing set the control scheme consists of an inter sample predictor a global observer an approximate predictor and a nominal controller for the delay free case the control scheme is applicable even to the case where the measurement is sampled and possibly delayed the closed loop system is shown to have the properties of global asymptotic stability and exponential convergence in the disturbance free case robustness with respect to perturbations of the sampling schedule and robustness with respect to measurement errors in contrast to existing predictor feedback laws the proposed control scheme utilizes an approximate predictor of a dynamic type which is expressed by a system described by integral delay equations additional results are provided for systems that can be transformed to systems with a compact absorbing set by means of a preliminary predictor feedback

compensation of wave actuator dynamics for nonlinear systems the problem of stabilization of pde ode cascades has been solved in the linear case for several pde classes whereas in the nonlinear case the problem has been solved only for the transport delay pde namely for compensation of an arbitrary delay at the input of a nonlinear plant motivated by a specific engineering application in off shore drilling we solve the problem of stabilization of the cascade of a wave pde with a general nonlinear ode due to the presence of nonlinearities of arbitrary growth and the time reversibility of the wave pde and due to the possibility of using arguments based on lyapunov functionals or explicit solutions several stability analysis approaches are possible we present stability results in the h 2 times h 1 and c 1 times c 0 norms for general nonlinear odes as well as in the h 1 times l 2 norm for linear odes we specialize our general design for wave pde ode cascades to the case of a wave pde whose uncontrolled end does not drive an ode but is instead governed by a nonlinear robin boundary condition a nonlinear spring as in the friction law in drilling this is the first global stabilization result for wave equations that incorporate non collocated destabilizing nonlinearities of superlinear growth we present two numerical examples one with a nonlinear ode and one with a nonlinear spring at the uncontrolled boundary of the wave pde

a finite element semi lagrangian method with l2 interpolation summary high order accurate methods for convection dominated problems have the potential to reduce the computational effort required for a given order of solution accuracy the state of the art in this field is more advanced for eulerian methods than for semi lagrangian slag methods in this paper we introduce a new slag method that is based on combining the modified method of characteristics with a high order interpolating procedure the method employs the finite element method on triangular meshes for the spatial discretization an l2 interpolation procedure is developed by tracking the feet of the characteristic lines from the integration nodes numerical results are illustrated for a linear advection diffusion equation with known analytical solution and for the viscous burgers equation the computed results support our expectations for a robust and highly accurate finite element slag method copyright 2012 john wiley sons ltd

pseudo spectral solution of extended graetz problem for combined pressure driven and electroosmotic flow in a triangular micro duct abstract thermally developing mixed electroosmotically and pressure driven flow in a triangular micro duct with a step change wall temperature is investigated both axial conduction graetz problem extended and joule heating effects are taken into consideration a new higher order accurate method is proposed the proposed method is based on pseudo spectral galerkin approach and the eigenfunctions of the helmholtz equation for a triangular geometry convergence of the method is investigated and the effect of the peclet pe number joule heating and debye huckel parameter on the temperature distribution and nusselt number nu are discussed in detail

an accurate approach for the calculation of mom matrix elements the method of moments solution on integral equations for electromagnetic scattering and radiation problems with rao wilton glisson rwg and n spl times rwg basis functions requires the calculation of singular double surface integrals over triangular subdomains in this paper an approach is presented to deal with the singularity and almost singularity in which the triangle subdomain is divided into several subtriangles and then the singular or almost singular integral is calculated over each of the subtriangles this approach is mainly based on the projection process and the local polar frame it can be used to deal with the singular double surface integrals of order 1 r and 1 r sup 2 in which vector functions may be of zeroth order and higher order numerical examples are provided to verify the validity of the method presented in this paper for dealing with the singularity and almost singularity

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

the two dimensional shapes of simple three and four junction ideal comb polymers we redesign and apply a scheme originally proposed by wei 1995 2 3 to produce numerical shape parameters with high precision for arbitrary tree branched polymers based on their kirchhoff matrix eigenvalue spectrum this algorithm and a monte carlo growth method on square and triangular lattices are employed to investigate the shapes of ideal three and four junction two dimensional comb polymers we find that the extrapolated values obtained by all of these methods are in excellent agreement with each other and the available theory we confirm that polymers with a complete set of interior branches display a more circular shape

on the application of two symmetric gauss legendre quadrature rules for composite numerical integration over a triangular surface this paper first presents a gauss legendre quadrature rule for the evaluation of i t f x y d x d y where f x y is an analytic function in x y and t is the standard triangular surface x y 0 x y 1 x y 1 in the two space x y we transform this integral into an equivalent integral s f x y frac x y d d where s is the 2 square in space 1 1 we then apply the one dimensional gauss legendre quadrature rules in and variables to arrive at an efficient quadrature rules with new weight coefficients and new sampling points then a second gauss legendre quadrature rule of composite type is obtained this rule is derived by discretising t into three new triangles tic i 1 2 3 of equal size which are obtained by joining centroid of t c 1 3 1 3 to the three vertices of t by use of affine transformations defined over each tic and the linearity property of integrals leads to the result i underover i 1 3 tic f x y d x d y frac 1 3 t g x y d x d y where g x y i 1n n f xic x y yic x y and x xic x y and y yic x y refer to affine transformations which map each tic into t the standard triangular surface we then write t g x y d x d y s g x y frac x y d d and a composite rule of integration is thus obtained we next propose the discretisation of the standard triangular surface t into n2 right isosceles triangular surfaces ti i 1 1 n2 each of which has an area equal to 1 2 n2 units we have again shown that the use of affine transformation over each ti and the use of linearity property of integrals lead to the result t f x y d x d y underover i 1 n n ti f x y d x d y frac 1 n2 t h x y d x d y where h x y i 1n n f xi x y yi x y and x xi x y y yi x y refer to affine transformations which map each ti in x y space into t a standard triangular surface t in the x y space we can now apply the two rules earlier derived to the integral t h x y d x d y this amounts to application of composite numerical integration of t into n2 and 3n2 triangles of equal sizes respectively we can now apply the rules which are derived earlier to the evaluation of the integral t f x y d x d y and each of these procedures converges to the exact value of the integral t f x y d x d y for sufficiently large value of n and the convergence is much faster for higher order rules we have demonstrated this aspect by applying the above composite integration method to some typical integrals 2007 elsevier inc all rights reserved

new approaches to shapes of arbitrary random walks abstract the problem of the shape of a random object such as a flexible polymer chain was first tackled by kuhn nearly thirty years after the answer to the probability distribution of its size was publicly sought for by pearson in 1905 since then significant progress in the field has been made but the important task of evaluatin both analytically and accurately averaged individual principal components of the shape or inertia tensor for a walk of a certain architectural type remains unfinished we have recently developed a new and general formalism for both exact and approximate calculations of these and other averages such as asphericity and prolateness parameters which is illustrated here for an end looped random walk and a self avoiding or edwards chain we find that this combined open and closed random walks has surprisingly larger shape asymmetry than a simply open walk despite its smaller size

indirect finite element evaluation of two dimensional finite part integral using fourier transformation a broad class of engineering problems in fracture mechanics thermal fluid transport and electromagnetic theory involve the evaluation of two dimensional finite part integrals of the form a method for evaluation of such integrals is developed by deriving an equivalent integral using fourier transformation this equivalent integral does not involve a kernel with singular behaviour consequently standard numerical integration methodologies with conventional analytical evaluation techniques can be used in the finite element computations the accuracy and convergence of the developed numerical procedure are successfully demonstrated by numerical examples for planar fracture geometries

implicit runge kutta methods for the discretization of time domain integral equations implicit runge kutta based schemes are proposed for solving the time domain integral equations of electromagnetic theory the proposed technique maps a laplace domain equation to a domain equation using the butcher tableau of the implicit runge kutta scheme a discrete time domain system is recovered by computing the inverse transform numerically the resulting technique is capable of third or fifth order accuracy in time and is stable independent of time step numerical results illustrate the accuracy and stability of the technique

adjoint sensitivity formulation for discontinuous galerkin discretizations in unsteady inviscid flow problems this paper presents an unsteady discrete adjoint algorithm for high order implicit discontinuous galerkin discretizations in time dependent inviscid flow problems the major function of the adjoint approach is to obtain the sensitivity information in a time dependent functional output which in turn is used to drive an unsteady shape optimization process to deliver a minimum of the objective functional a gradient based optimization strategy is investigated in which the sensitivity derivatives of the objective functional with respect to input variables are formulated in the context of high order discontinuous galerkin discretizations while special emphasis is given to the variations and linearizations of curvilinear boundary elements implicit temporal discretizations consisting of a second order backward euler scheme and a fourth order implicit runge kutta scheme are considered exclusively in this work where the corresponding adjoint problem is required to be solved in a backward time integration manner due to the associated transpose operation two numerical examples for the unsteady shape design techniques are presented to verify the derived sensitivity formulations and to demonstrate the performance of the adjoint approach the first involves an inverse shape optimization case by matching a time dependent target pressure profile for a two dimensional periodic vortical gust impinging on a rae 2822 airfoil and the second considers minimization of the acoustic noise produced by subsonic flow over a naca0012 airfoil with a 0 03c thick blunt trailing edge

generalized gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method new gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method for discontinuous functions we construct gauss like quadrature rules over arbitrarily shaped elements in two dimensions without the need for partitioning the finite element a point elimination algorithm is used in the construction of the quadratures which ensures that the final quadratures have minimal number of gauss points for weakly singular integrands we apply a polar transformation that eliminates the singularity so that the integration can be performed efficiently and accurately numerical examples in elastic fracture using the extended finite element method are presented to illustrate the performance of the new integration techniques

the mini mixed finite element for the stokes problem an experimental investigation abstract o h 3 2 superconvergence in pressure and velocity has been experimentally investigated for the two dimensional stokes problem discretized with the mini mixed finite element even though the classic mixed finite element theory for the mini element guarantees linear convergence for the total error recent theoretical results indicate that superconvergence of order o h 3 2 in pressure and of the linear part of the computed velocity to the piecewise linear nodal interpolation of the exact velocity is in fact possible with structured three directional triangular meshes the numerical experiments presented here suggest a more general validity of o h 3 2 superconvergence possibly to automatically generated and unstructured triangulations in addition the approximating properties of the complete computed velocity have been compared with the approximating properties of the piecewise linear part of the computed velocity finding that the former is generally closer to the exact velocity whereas the latter conserves mass better

generalized gaussian quadrature rules on arbitrary polygons in this paper we present a numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons these quadratures have desirable properties such as positivity of weights and interiority of nodes and can readily be used as software libraries where numerical integration within planar polygons is required we have used this algorithm for the construction of symmetric and non symmetric quadrature rules over convex and concave polygons while in the case of symmetric quadratures our results are comparable to available rules the proposed algorithm has the advantage of being flexible enough so that it can be applied to arbitrary planar regions for the integration of generalized classes of functions to demonstrate the efficiency of the new quadrature rules we have tested them for the integration of rational polygonal shape functions over a regular hexagon for a relative error of 10 8 in the computation of stiffness matrix entries one needs at least 198 evaluation points when the region is partitioned whereas 85 points suffice with our quadrature rule copyright 2009 john wiley sons ltd

robustness of nonlinear predictor feedback laws to time and state dependent delay perturbations much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state provided the dependence is known in this paper we consider the delay variations as unknown and study robustness of nominal constant delay predictor feedbacks under delay variations that depend on time and the state we show that when the delay perturbation and its rate have sufficiently small magnitude the local asymptotic stability of the closed loop system under the nominal predictor based design is preserved for the special case of linear systems and under only time varying delay perturbations we prove robustness of global exponential stability of the predictor feedback when the delay perturbation and its rate are small in any one of four different metrics we present two examples one that is concerned with the control of a dc motor through a network and one of a teleoperation like system

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

a new prediction scheme for input delay compensation in restricted feedback linearizable systems the input output inversion of a system under the effect of input delays typically relies on the ability to predict the future of the system s state indeed if the latter is known ahead of time one can cope with the input delay by using a prediction of the state instead of the state itself such methods are efficient when the plant is stable but become numerically unstable otherwise we present a new method to compensate input delays our approach relies on imposing a desired error dynamics which is designed to be linear and asymptotically stable at the origin then the state prediction is computed from the state reference trajectory and the predicted error dynamics in this technical note we concentrate on the case study of systems in strict feedback form and present a simple backstepping procedure

a new c1 finite element full heptic a new c1 finite element complete in 7th degree polynomial basis is described and compared with other c1 elements in an eigen elements analysis

adjoint based h p adaptive discontinuous galerkin methods for the 2d compressible euler equations in this paper we investigate and present an adaptive discontinuous galerkin algorithm driven by an adjoint based error estimation technique for the inviscid compressible euler equations this approach requires the numerical approximations for the flow i e primal problem and the adjoint i e dual problem which corresponds to a particular simulation objective output of interest the convergence of these two problems is accelerated by an hp multigrid solver which makes use of an element gauss seidel smoother on each level of the multigrid sequence the error estimation of the output functional results in a spatial error distribution which is used to drive an adaptive refinement strategy which may include local mesh subdivision h refinement local modification of discretization orders p enrichment and the combination of both approaches known as hp refinement the selection between h and p refinement in the hp adaptation approach is made based on a smoothness indicator applied to the most recently available flow solution values numerical results for the inviscid compressible flow over an idealized four element airfoil geometry demonstrate that both pure h refinement and pure p enrichment algorithms achieve equivalent error reductions at each adaptation cycle compared to a uniform refinement approach but requiring fewer degrees of freedom the proposed hp adaptive refinement strategy is capable of obtaining exponential error convergence in terms of degrees of freedom and results in significant savings in computational cost a high speed flow test case is used to demonstrate the ability of the hp refinement approach for capturing strong shocks or discontinuities while improving functional accuracy

on the application of two gauss legendre quadrature rules for composite numerical integration over a tetrahedral region in this paper we first present a gauss legendre quadrature rule for the evaluation of i f f t ff x y z dxdydz where f x y z is an analytic function in x y z and tis the standard tetrahedral region x y z 0 x y z i x y z 1 in three space x y z we then use a transformation x x y y and z z to change the integral into an equivalent integral i 1 1 1 1 1 1 f x y x y z d d d over the standard 2 cube in space 1 1 we then apply the one dimensional gauss legendre quadrature rules in and variables to arrive at an efficient quadrature rule with new weight coefficients and new sampling points then a second gauss legendre quadrature rule of composite type is obtained this rule is derived by discretising the tetrahedral region t into four new tetrahedra t c i i 1 2 3 4 of equal size which are obtained by joining the centroid of t c 1 4 1 4 1 4 to the four vertices of t by use of the affine transformations defined over each t c i and the linearity property of integrals leads to the result i 4 i 1 tci f x y z dxdydz 1 4 t g x y z dxdydz where g x y z 1 p 3 f x k x y z y k x y z z k x y z x k x k x y z y k y k x y z and z k z k x y z refer to an affine transformations which map each t c i into the standard tetrahedral region t we then write i t g x y z dxdydz 1 0 1 0 1 0 g x y z x y z d d d and a composite rule of integration is thus obtained we next propose the discretisation of the standard tetrahedral region t into p 3 tetrahedra t i i 1 1 p 3 each of which has volume equal to 1 6p 3 units we have again shown that the use of affine transformations over each t and the use of linearity property of integrals leads to the result t f x y z dxdydz p3 i 1 t c i f x y z dxdydz p3 1 t p f x p y p z p dx p dy p dz p 1 p3 t h x y z dxdydz where p3 h x y z 1 f x p x y z y p x y z z p x y z x p x p x y z y p y p x y z and z p z p x y z refer to the affine transformations which map each t i in x p y p z p space into a standard tetrahedron t in the x y z space we can now apply the two rules earlier derived to the integral t h x y z dxdydz this amounts to the application of composite numerical integration of t into p3 and 4p3 tetrahedra of equal sizes we have demonstrated this aspect by applying the above composite integration method to some typical triple integrals

singularity subtraction technique for high order polynomial vector basis functions on planar triangles in this paper a singularity subtraction technique is developed for computing the impedance matrix elements of various electromagnetic surface integral equation formulations with the galerkin method and high order basis functions analytical closed form formulas for computing surface integrals with r r sup n n spl ges 3 singularities times polynomial nodal shape functions of arbitrary order on a planar triangle are presented

a convergence analysis of an h version finite element method with high order elements for two dimensional elasto plasticity problems in this paper we will give an h version finite element method for a two dimensional nonlinear elasto plasticity problem a family of admissible constitutive laws based on the so called gauge function method is introduced first and then a high order h version semidiscretization scheme is presented the existence and uniqueness of the solution for the semidiscrete problem are guaranteed by using some special properties of the constitutive law and finally we will show that as the maximum element size h longrightarrow 0 the solution of the semidiscrete problem will converge to the solution of the continuous problem the high order h version discretization scheme introduced here is unusual if the partition of the spatial space only has rectangles or parallelograms involved then there would not be any limit on the element degree however if the partition of the spatial space has some triangular elements then only certain combinations of finite element spaces for displacement and stress functions can be used the discretization scheme also provides a useful idea for applications of hp version or high order h version finite element methods for two dimensional problems where the elasto plastic body is not a polygon such as a disk or an annulus

exact shapes of random walks in two dimensions abstract since the random walk problem was first presented by pearson in 1905 the shape of a walk which is either completely random or self avoiding has attracted the attention of generations of researchers working in such diverse fields as chemistry physics biology and statistics among many advances in the field made in the past decade is the formulation of the three dimensional shape distribution function of a random walk as a triple fourier integral plus its numerical evaluation and graphical illustration however exact calculations of the averaged individual principal components of the shape tensor for a walk of a certain architectural type including an open walk have remained a challenge here we provide an exact analytical approach to the shapes of arbitrary random walks in two dimensions especially we find that an end looped random walk surprisingly has an even larger shape asymmetry than an open walk

mixed inner outer iteration technique based surface integral equations for fast solving em scattering from penetrable objects in this paper a mixed inner outer iteration technique based on surface integral equation is proposed for solving scattering problems from penetrable and homogeneous dielectric structures the most important novelty of the proposed technique is combining the tangential poggio miller chang harrington wu tsai as outer iteration and the electric magnetic current combined field integral equation as inner iteration respectively in this case the new method offers the guarantee of high accuracy with faster convergence especially for electrically dielectric structures in large scale furthermore it presents an excellent compatibility with sparse approximate inverse preconditioning numerical results are given to demonstrate the accuracy efficiency and compatibility of the proposed method

second order accurate derivatives and integration schemes for meshfree methods summary the consistency condition for the nodal derivatives in traditional meshfree galerkin methods is only the differentiation of the approximation consistency dac one missing part is the consistency between a nodal shape function and its derivatives in terms of the divergence theorem in numerical forms in this paper a consistency framework for the meshfree nodal derivatives including the dac and the discrete divergence consistency ddc is proposed the summation of the linear ddc over the whole computational domain leads to the so called integration constraint in the literature a three point integration scheme using background triangle elements is developed in which the corrected derivatives are computed by the satisfaction of the quadratic ddc we prove that such smoothed derivatives also meet the quadratic dac and therefore the proposed scheme possesses the quadratic consistency that leads to its name qc3 numerical results show that qc3 is the only method that can pass both the linear and the quadratic patch tests and achieves the best performances for all the four examples in terms of stability convergence accuracy and efficiency among all the tested methods particularly it shows a huge improvement for the existing linearly consistent one point integration method in some examples copyright 2012 john wiley sons ltd

monomial cubature rules since stroud a compilation a bibliography of references to cubature rules which have appeared since the publication of stroud s book 1971 is presented the standard regions that are treated in this paper are the n cube the n simplex the n sphere and the entire space

on the adaptive coupling of fem and bem in 2 d elasticity this paper concerns the combination of the finite element method fem and the boundary element method bem using the symmetric coupling as a model problem in two dimensions we consider the hencky material a certain nonlinear elastic material in a bounded domain with navier lame differential equation in the unbounded complementary domain using some boundary integral operators the problem is rewritten such that the galerkin procedure leads to a fem bem coupling and quasi optimally convergent discrete solutions beside this a priori information we derive an a posteriori error estimate which allows up to a constant factor the error control in the energy norm since information about the singularities of the solution is not available a priori in many situation and having in mind the goal of an automatic mesh refinement we state adaptive algorithms for the h version of the fem bem coupling illustrating numerical results are included

nonlinear predictors for systems with bounded trajectories and delayed measurements novel nonlinear predictors are studied for nonlinear systems with delayed measurements without assuming globally lipschitz conditions or a known predictor map but requiring instead bounded state trajectories the delay is constant and known these nonlinear predictors consists of a series of dynamic filters that generate estimates of the state vector and its maximum magnitude at different delayed time instants which differ from one another by a small fraction of the overall delay

output transformations and separation results for feedback linearisable delay systems abstractthe class of strict feedback systems enjoys special properties that make it similar to linear systems this paper proves that such a class is equivalent under a change of coordinates to the wider class of feedback linearisable systems with multiplicative input when the multiplicative terms are functions of the measured variables only we apply this result to the control problem of feedback linearisable nonlinear mimo systems with input and or output delays in this way we provide sufficient conditions under which a separation result holds for output feedback control and moreover a predictor based controller exists when these conditions are satisfied we obtain that the existence of stabilising controllers for arbitrarily large delays in the input and or the output can be proved for a wider class of systems than previously known

information transfer between incompatible finite element meshes application to coupled thermo viscoelasticity this article is concerned with information transfer between non matching finite element meshes such a feature is not new in the literature but we focus herein on a geometric approach to transfer solution fields in order to be as application independent as possible moreover the dedicated case concerns the transfer of finite element fields defined at integration points of the meshes and allows iterative exchange of fields in both directions to do so we propose an extension to the mortar technique that fulfills these goals and that does not suffer from a high computational cost the application is the simulation of a strongly coupled thermo viscoelastic problem with phase transition solved with a partitioning technique

numerical approximation of internal discontinuity interface problems this work focuses on the finite element discretization of boundary value problems whose solution features either a discontinuity or a discontinuous conormal derivative across an interface inside the computational domain the interface is characterized via a level set function the discontinuities are accounted for by using suitable extension operators whose numerical implementation requires a very low computational effort after carrying out the error analysis numerical results to validate our approach are presented in one two and three dimensions

general behavior and shear center location of prismatic anisotropic beams via power series abstract the behavior of a tip loaded anisotropic cantilever beam with an arbitrary cross section is studied using saint venant s semi inverse method along with a power series solution for the local in plane and out of plane deformation warping functions the power series coefficients are determined by solving a set of variationally derived linear algebraic equations using the resulting three dimensional displacement solutions the shear deformation associated with applied tip loads is investigated as well as the shear center location two different definitions of the shear center are presented for anisotropic beams by extending existing approaches developed for isotropic sections both of the extended definitions reveal the linear dependency of the shear center location on beam length numerical results are presented for three different cross sections ellipse triangle naca 0012 airfoil and two different materials al 6061 t6 off angle high strength graphite epoxy fibers

on structural shape optimization using an embedding domain discretization technique summary this contribution presents a novel approach to structural shape optimization that relies on an embedding domain discretization technique the evolving shape design is embedded within a uniform finite element background mesh which is then used for the solution of the physical state problem throughout the course of the optimization we consider a boundary tracking procedure based on adaptive mesh refinement to separate between interior elements exterior elements and elements intersected by the physical domain boundary a selective domain integration procedure is employed to account for the geometric mismatch between the uniform embedding domain discretization and the evolving structural component thereby we avoid the need to provide a finite element mesh that conforms to the structural component for every design iteration as it is the case for a standard lagrangian approach to structural shape optimization still we adopt an explicit shape parametrization that allows for a direct manipulation of boundary vertices for the design evolution process in order to avoid irregular and impracticable design updates we consider a geometric regularization technique to render feasible descent directions for the course of the optimization this article is protected by copyright all rights reserved

stabilization of nonlinear delay systems using approximate predictors and high gain observers we provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only the solution is global employs the predictor approach over the period that combines the input and output delays addresses nonlinear systems with sampled measurements and with control applied using a zero order hold and requires that the sampling holding periods be sufficiently short though not necessarily constant our approach considers a class of globally lipschitz strict feedback systems with disturbances and employs an appropriately constructed successive approximation of the predictor map a high gain sampled data observer and a linear stabilizing feedback for the delay free system the obtained results guarantee robustness to perturbations of the sampling schedule and different sampling and holding periods are considered the approach is specialized to linear systems where the predictor is available explicitly

delay robustness of linear predictor feedback without restriction on delay rate robustness is established for the predictor feedback for linear time invariant systems with respect to possibly time varying perturbations of the input delay with a constant nominal delay the prior results have addressed qualitatively constant delay perturbations robustness of stability in l 2 norm of actuator state and delay perturbations with restricted rate of change robustness of stability in h 1 norm of actuator state the present work provides simple formulas that allow direct and accurate computation of the least upper bound of the magnitude of the delay perturbation for which the exponential stability in supremum norm on the actuator state is preserved while the prior work has employed lyapunov krasovskii functionals constructed via backstepping the present work employs a particular form of small gain analysis two cases are considered the case of measurable possibly discontinuous time varying perturbations and the case of constant perturbations

compensation of actuator dynamics governed by quasilinear hyperbolic pdes we present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by a certain class of quasilinear first order hyperbolic pdes since for such pde ode cascades the speed of propagation depends on the pde state itself which implies that the prediction horizon cannot be a priori known analytically the key design challenge is the determination of the predictor state we resolve this challenge and introduce a pde predictor feedback control law that compensates the transport actuator dynamics due to the potential formation of shock waves in the solutions of quasilinear first order hyperbolic pdes which is related to the fundamental restriction for systems with time varying delays that the delay rate is bounded by unity we limit ourselves to a certain feasibility region around the origin and we show that the pde predictor feedback law achieves asymptotic stability of the closed loop system providing an estimate of its region of attraction our analysis combines lyapunov like arguments and iss estimates since it may be intriguing as to what is the exact relation of the cascade to a system with input delay we highlight the fact that the considered pde ode cascade gives rise to a system with input delay with a delay that depends on past input values defined implicitly via a nonlinear equation the developed control design methodology is applied to the control of vehicular traffic flow at distant bottlenecks

the generalized graetz problem in finite domains we consider the generalized graetz problem associated with stationary convection diffusion inside a domain having any regular three dimensional translationally invariant section and finite or semi infinite extent our framework encompasses any previous extended and conjugated graetz generalizations and provides theoretical bases for computing the orthogonal set of generalized two dimensional graetz modes the theoretical framework includes both heterogeneous and possibly anisotropic diffusion tensors in the case of semi infinite domains the existence of a bounded solution is shown from the analysis of two dimensional operator eigenvectors which form a basis of l 2 in the case of finite domains a similar basis can be exhibited and the mode s amplitudes can be obtained from the inversion of newly defined finite domain operator our analysis includes both the theoretical and practical issues associated with this finite domain operator inversion as well as its interpretation as a multireflection ima

control of transport pde nonlinear ode cascades with state dependent propagation speed in this paper we deal with the control of a transport partial differential equation nonlinear ordinary differential equation pde nonlinear ode cascade system in which the transport coefficient depends on the ode state we develop a pde based predictor feedback boundary control law which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed loop system the stability proof is based on an infinite dimensional backstepping transformation and a lyapunov like argument the relation of the pde ode cascade with a state dependent propagation speed to an ode system with a state dependent input delay which is defined implicitly via an integral of past values of the ode state is also highlighted and the corresponding equivalent predictor feedback design is presented together with an alternative proof of global asymptotic stability of the closed loop system based on the construction of a lyapunov functional the practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process

fast matlab assembly of fem matrices in 2d and 3d we propose an effective and flexible way to assemble finite element stiffness and mass matrices in matlab we apply this for problems discretized by edge finite elements typical edge finite elements are raviart thomas elements used in discretizations of h div spaces and nedelec elements in discretizations of h curl spaces we explain vectorization ideas and comment on a freely available matlab code which is fast and scalable with respect to time

the shapes of ideal five junction comb polymers in two and three dimensions abstract this work investigates a variety of properties of eleven and fourteen branch five junction comb polymers in the ideal regime in two and three dimensions a method based on the kirchhoff matrix eigenvalue spectrum for arbitrary tree branched polymers is used to compute shape properties and a scheme originally proposed by benhamous 2004 is used to produce an exact equation for the form factor of the fourteen branch comb polymers a monte carlo growth algorithm is also employed to compute the same properties it is found that the values obtained by all of these methods are in fine agreement with each other and available theory

observer based output feedback control of linear systems with input and output delays abstract this paper is concerned with observer based output feedback control of linear systems with both multiple input and output delays our recently developed truncated predictor feedback tpf approach for state feedback stabilization of time delay systems is generalized to the design of observers by imposing some restrictions on the open loop system two classes of observer based output feedback controllers one being finite dimensional and the other infinite dimensional are constructed it is further shown that the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time varying input and output delays it is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers but does not hold for the finite dimensional ones numerical examples are worked out to illustrate the effectiveness of the proposed approaches

stabilization of nonlinear systems with time varying input and state delays by approximate predictor in this paper the stabilization problem of nonlinear systems with time varying input and state delays is considered by an approximate predictor due to the introduction of state delays the nonlinear dynamic without state delays is used to predict the plant state and a new error term is introduced into the approximation error between the prediction value and the future state of the plant by lyapunov krasovskii functional and small gain argument the stability of the whole closed loop system is guaranteed provided that the sampling period the predictor accuracy and the upper bound of state delays satisfy an inequality constraint the effectiveness of the proposed results is illustrated by a numerical example

edged based smoothed point interpolation method for acoustic radiation with perfectly matched layer abstract it is known that for exterior acoustics the domain based finite element method always encounters the accuracy loss for high wavenumbers and the difficulty in dealing with the sommerfeld radiation condition in this work by using the polynomial and radial bases with specific node selection schemes the point interpolation method with the generalized gradient smoothing technique is employed to improve the accuracy for acoustic computations the appropriately softened acoustical stiffness of the discrete model is constructed based on the edge based smoothing domains via the gradient smoothing technique in addition the perfectly matched layer technique enables the smoothed point interpolation method to investigate exterior acoustics the complex coordinate transformation is utilized to determine the proper parameters for the perfectly matched layer through theoretical and numerical analyses several typical acoustic problems are analyzed revealing that better accuracy is obtained by the present method compared with the finite element method especially for high wavenumbers

exponential stabilization of linear systems with time varying delayed state feedback via partial spectrum assignment abstract we consider the problem of controlling a linear system when the state is available with a known time varying delay delayed state feedback control or the actuator is affected by a delay the solution proposed in this paper consists in partially assigning the spectrum of the closed loop system to guarantee the exponential zero state stability with a prescribed decay rate by means of a finite dimensional control law a non conservative bound on the maximum allowed delay for the prescribed decay rate is presented which holds for both cases of constant and time varying delays an advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required we compare the performance of our approach in terms of delay bound and input signal with another recent approach

compensation of input delay that depends on delayed input abstract for nonlinear systems we develop a pde based predictor feedback control design which compensates actuator dynamics governed by a transport pde with outlet boundary value dependent propagation velocity global asymptotic stability under the predictor feedback control law is established assuming spatially uniform strictly positive transport velocity the stability proof is based on a lyapunov like argument and employs an infinite dimensional backstepping transformation that is introduced an equivalent representation of the transport pde nonlinear ode cascade via a nonlinear system with an input delay that is defined implicitly through an integral of the past input is also provided and the equivalent predictor feedback control design for the delay system is presented the validity of the proposed controller is illustrated applying a predictor feedback bang bang boundary control law to a pde model of a production system with a queue consistent simulation results are provided that support the theoretical developments

on numerical integration in isogeometric subdivision methods for pdes on surfaces abstract subdivision surfaces offer great flexibility in capturing irregular topologies combined with higher order smoothness for instance loop and catmull clark subdivision schemes provide c 2 smoothness everywhere except at extraordinary vertices where the generated surfaces are c 1 smooth the combination of flexibility and smoothness leads to their frequent use in geometric modeling and makes them an ideal candidate for performing isogeometric analysis of higher order problems with irregular topologies e g thin shell problems in the neighborhood of extraordinary vertices however the resulting surfaces and the functions defined on them are non polynomial thus numerical integration based on quadrature has to be performed carefully to preserve the expected higher order consistency this paper presents a detailed case study of different quadrature schemes for isogeometric discretizations of partial differential equations on closed surfaces with loop s subdivision scheme as model problems we consider elliptic equations with the laplace beltrami and the surface bi laplacian operator as well as the associated eigenvalue problem for the laplace beltrami operator a particular emphasis is on the robustness of the approach in the vicinity of extraordinary vertices based on a series of numerical experiments different quadrature schemes are compared mid edge quadrature which can easily be implemented via a lookup table turns out to be a preferable choice due to its robustness and efficiency

delay adaptive control for nonlinear systems we present a systematic delay adaptive prediction based control design for nonlinear systems with unknown long actuator delay our approach is based on the representation of the constant actuator delay as a transport partial differential equation pde in which the convective speed is inversely proportional to the unknown delay we study two different frameworks assuming first that the actuator state is measured and relaxing afterward for the full state feedback case we prove global asymptotic convergence of the proposed adaptive controller while in the second case replacing the actuator state by its adaptive estimate we prove local regulation the relevance of the obtained results are illustrated by simulations of a biological activator repressor system

machine precision evaluation of singular and nearly singular potential integrals by use of gauss quadrature formulas for rational functions a new technique for machine precision evaluation of singular and nearly singular potential integrals with 1 r singularities is presented the numerical quadrature scheme is based on a new rational expression for the integrands obtained by a cancellation procedure in particular by using library routines for gauss quadrature of rational functions readily available in the literature this new expression permits the exact numerical integration of singular static potentials associated with polynomial source distributions the rules to achieve the desired numerical accuracy for singular and nearly singular static and dynamic potential integrals are presented and discussed and several numerical examples are provided

stabilization by means of approximate predictors for systems with delayed input sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented an approximate predictor is a mapping which approximates the exact values of the stabilizing input for the corresponding system with no delay a systematic procedure for the construction of approximate predictors is provided for globally lipschitz systems the resulting stabilizing feedback can be implemented by means of a dynamic distributed delay feedback law illustrative examples show the efficiency of the proposed control strategy