a variational principle for the formulation of partitioned structural systems a continuum based variational principle is presented for the formulation of the discrete governing equations of partitioned structural systems this application includes coupled substructures as well as subdomains obtained by mesh decomposition the present variational principle is derived by a series of modifications of a hybrid functional originally proposed by atluri for finite element development the interface is treated by a displacement frame and a localized version of the method of lagrange multipliers interior displacements are decomposed into rigid body and deformational components to handle floating subdomains both static and dynamic versions are considered an important application of the present principle is the treatment of nonmatching meshes that arise from various sources such as separate discretization of substructures independent mesh refinement and global local analysis the present principle is compared with that of a globalized version of the multiplier method copyright 2000 john wiley sons ltd

isogeometric collocation for elastostatics and explicit dynamics we extend the development of collocation methods within the framework of isogeometric analysis iga to multi patch nurbs configurations various boundary and patch interface conditions and explicit dynamic analysis the methods developed are higher order accurate stable with no hourglass modes and efficient in that they require a minimum number of quadrature evaluations the combination of these attributes has not been obtained previously within standard finite element analysis

sharp geometric rigidity of isometries on heisenberg groups we prove sharp geometric rigidity estimates for isometries on heisenberg groups our main result asserts that every 1 varepsilon quasi isometry on a john domain of the heisenberg group mathbb h n n 1 is close to some isometry up to proximity order sqrt varepsilon varepsilon in the uniform norm and up to proximity order varepsilon in the l p 1 norm we give examples showing the asymptotic sharpness of our results

a quadrature based superconvergent isogeometric frequency analysis with macro integration cells and quadratic splines abstract a quadrature based superconvergent isogeometric method is presented for efficient frequency analysis with macro integration cells and quadratic splines the present development particularly refers to the isogeometric analysis of scalar wave equations the single element two element and three element macro integration cells are proposed to develop a set of explicit superconvergent quadrature rules with a 6th order frequency accuracy in contrast to the 4th order frequency accuracy associated with the standard isogeometric formulation with consistent mass matrix the 1d quadrature rules with various macro integration cells are derived from the condition of exact integration of the higher order mass matrix as well as the stiffness matrix consequently 3 point 5 point and 7 point quadrature rules with identical precision are established for the single element two element and three element macro integration cells respectively by construction these quadrature rules exactly recover the isogeometric higher order mass matrix formulation with frequency superconvergence in 1d case the 2d and 3d superconvergent quadrature rules with versatile integration cells are directly constructed through the tensor product formulation of the 1d integration algorithms it is shown that the multidimensional isogeometric analysis employing the proposed quadrature rules for both mass and stiffness matrices does produce the frequency superconvergence simultaneously without the wave propagation direction dependence problem which needs special treatments for the multidimensional higher order mass matrix formulation the proposed approach is featured by its simplicity for numerical implementation and efficiency using macro integration cells numerical examples confirm the efficacy of the present methodology

high gain observer approach to disturbance attenuation using measurement feedback a procedure is developed for disturbance attenuation in a linear system via the use of measurement feedback a high gain observer is used to recover the disturbance attenuation properties asymptotically which can be achieved using full state feedback it is thus shown that the problem of disturbance attenuation via measurement feedback can be decomposed into two problems of disturbance attenuation via state feedback these problems of disturbance via state feedback can then be solved using existing methods based on the algebraic riccati equation

local to global results for spaces of mathrm bmo type we study a class of spaces jn p related to mathrm bmo in the abstract setting of a metric space with a doubling measure we obtain a reimann rychener type local to global result and also show that a boman type condition is sufficient to make the embedding of jn p into weak l p to hold we discuss certain necessary condition our abstract setting covers various situations at once and in particular includes all geodesic spaces

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

fast isogeometric solvers for explicit dynamics in finite element analysis solving time dependent partial differential equations with explicit time marching schemes requires repeatedly applying the inverse of the mass matrix for mass matrices that can be expressed as tensor products of lower dimensional matrices we present a direct method that has linear computational complexity i e o n o n where nn is the total number of degrees of freedom in the system we refer to these matrices as separable matrices for non separable mass matrices we present a preconditioned conjugate gradient method with carefully designed preconditioners as an alternative we demonstrate that these preconditioners which are easy to construct and cheap to apply o n o n can deliver significant convergence acceleration the performances of these preconditioners are independent of the polynomial order p independence and mesh resolution h independence for maximum continuity b splines as verified by various numerical tests

explicit time integration algorithms for structural dynamics with optimal numerical dissipation abstract a new predictor corrector explicit time integration algorithm is presented for solving structural dynamics problems the basis of the algorithm is the implicit generalized method developed by the authors like its implicit parent the explicit generalized method is a one parameter family of algorithms in which the parameter defines the high frequency numerical dissipation for a given value of high frequency dissipation the explicit generalized method minimizes low frequency dissipation the algorithm can be utilized effectively for structural dynamics calculations in which numerical dissipation is needed to reduce spurious oscillations parameter values are given that enable physical damping to be treated explicitly while maintaining second order accuracy without the need for an expensive second corrector pass

a formulation based on localized lagrange multipliers for bem fem coupling in contact problems this paper presents a unified formulation for the combination of the finite element method fem and the boundary element method bem in 3d frictional contact problems that is based on the use of localized lagrange multipliers llms resolution methods for the contact problem between non matching meshes have traditionally been based on a direct coupling of the contacting solids using classical lagrange multipliers these methods tend to generate strongly coupled systems that require a deep knowledge of the discretization characteristics on each side of the contact zone complicating the process of mixing different numerical techniques in this work a displacement contact frame is inserted between the fe and be interface meshes discretized and finally connected to the contacting substructures using llms collocated at the mesh interface nodes this methodology will provide a partitioned formulation which preserves software modularity and facilitates the connection of non matching fe and be meshes

biorthogonal bases with local support and approximation properties we construct locally supported basis functions which are biorthogonal to conforming nodal finite element basis functions of degree p in one dimension in contrast to earlier approaches these basis functions have the same support as the nodal finite element basis functions and reproduce the conforming finite element space of degree p 1 working with gaus lobatto nodes we find an interesting connection between biorthogonality and quadrature formulas one important application of these newly constructed biorthogonal basis functions are two dimensional mortar finite elements the weak continuity condition of the constrained mortar space is realized in terms of our new dual bases as a result local static condensation can be applied which is very attractive from the numerical point of view numerical results are presented for cubic mortar finite elements

isogeometric dual mortar methods for computational contact mechanics in recent years isogeometric analysis iga has received great attention in many fields of computational mechanics research especially for computational contact mechanics an exact and smooth surface representation is highly desirable as a consequence many well known finite element methods and algorithms for contact mechanics have been transferred to iga in the present contribution the so called dual mortar method is investigated for both contact mechanics and classical domain decomposition using nurbs basis functions in contrast to standard mortar methods the use of dual basis functions for the lagrange multiplier based on the mathematical concept of biorthogonality enables an easy elimination of the additional lagrange multiplier degrees of freedom from the global system this condensed system is smaller in size and no longer of saddle point type but positive definite a very simple and commonly used element wise construction of the dual basis functions is directly transferred to the iga case the resulting lagrange multiplier interpolation satisfies discrete inf sup stability and biorthogonality however the reproduction order is limited to one in the domain decomposition case this results in a limitation of the spatial convergence order to o h3 2 in the energy norm whereas for unilateral contact due to the lower regularity of the solution optimal convergence rates are still met numerical examples are presented that illustrate these theoretical considerations on convergence rates and compare the newly developed isogeometric dual mortar contact formulation with its standard mortar counterpart as well as classical finite elements based on first and second order lagrange polynomials

isogeometric mortar methods the application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically for the lagrange multiplier two choices of uniformly stable spaces are presented both of them are spline spaces but of a different degree in one case we consider an equal order pairing for which a cross point modification based on a local degree reduction is required in the other case the degree of the dual space is reduced by two compared to the primal this pairing is proven to be inf sup stable without any necessary cross point modification several numerical examples confirm the theoretical results and illustrate additional aspects

the john nirenberg inequality and a sobolev inequality in general domains abstract we extend the john nirenberg inequality and a limiting case of the sobolev inequality to domains which can have irregular boundaries

an explicit method with improved stability property a new explicit method is presented this method has an enhanced stability property when compared with the previously published explicit method j eng mech 2007 133 7 748 760 which is unconditionally stable for linear elastic and any instantaneous stiffness softening systems based on linearized analysis whereas it is only conditionally stable for any instantaneous stiffness hardening system in contrast to the previously published explicit method the most important improvement of the new explicit method is that it can have unconditional stability for general instantaneous stiffness hardening systems in addition to linear elastic and instantaneous stiffness softening systems since these stability results are obtained from a linearized stability analysis they are applicable to the non linear systems that satisfied the simplifications used for the analysis this explicit method is also shown to be second order accurate it is computationally efficient in the solution of a general structural dynamic problem where the total response is dominated by low frequency modes when compared with explicit methods such as the newmark explicit method and the family of explicit methods developed by tamma et al comput methods appl mech eng 2003 192 257 290 and implicit methods such as the constant average acceleration method some numerical examples are used to confirm the enhanced stability property and the efficiency in computing copyright 2008 john wiley sons ltd

symbol based multigrid methods for galerkin b spline isogeometric analysis we consider the stiffness matrices arising from the galerkin b spline isogeometric analysis discretization of classical elliptic problems by exploiting their specific spectral properties compactly described by a symbol we design an efficient multigrid method for the fast solution of the related linear systems the convergence rate of general purpose multigrid methods based on classical stationary smoothers is optimal i e bounded independently of the matrix size but it also worsens exponentially with respect to the spline degree the symbol allows us to give a detailed theoretical explanation of this exponential worsening in the case of the two grid scheme in addition thanks to a specific factorization of the symbol we are able to design an ad hoc multigrid method with an effective preconditioned cg or gmres smoother at the finest level in the spirit of the multi iterative idea the convergence rate of this multi iterative multigrid method is not only optimal but also robust i e bounded su

hybrid mixed discretization of elasto dynamic contact problems using consistent singular mass matrices summary an alternative spatial semi discretization of dynamic contact based on a modified hamilton s principle is proposed the modified hamilton s principle uses displac ement velocity and momentum as variables which allows their independent spatial discretization al ong with a local static condensation for velocity and momentum it leads to an approach with a hybrid mixed consistent mass matrix hmcmm an attractive feature of such a formulation is the possibility to construc t hybrid singular mass matrices hsmm with zero components at those nodes where contact is collocated this improves numerical stability of the semidiscrete problem the differential index of the underlying differential algebraic system is reduced from 3 to 1 and spurious oscillations in the contact pressure whi ch are commonly reported for formulations with lagrange multipliers are significantly reduced resu lts of numerical experiments for truss and timoshenko beam elements are discussed in addition the properties of the novel discretization scheme for an unconstrained dynamic problem are assessed by a dispersion analysis copyright c 2010 john wiley sons ltd received

isogeometric preconditioners based on fast solvers for the sylvester equation we consider large linear systems arising from the isogeometric discretization of the poisson problem on a single patch domain the numerical solution of such systems is considered a challenging task particularly when the degree of the splines employed as basis functions is high we consider a preconditioning strategy which is based on the solution of a sylvester like equation at each step of an iterative solver we show that this strategy which fully exploits the tensor structure that underlies isogeometric problems is robust with respect to both mesh size and spline degree although it may suffer from the presence of complicated geometry or coefficients we consider two popular solvers for the sylvester equation a direct one and an iterative one and we discuss in detail their implementation and efficiency for two dimensional 2d and three dimensional 3d problems on single patch or conforming multipatch nonuniform rational b splines nurbs geometries we present numerical experiments for problems

direct and sparse construction of consistent inverse mass matrices general variational formulation and application to selective mass scaling summary classical explicit finite element formulations rely on lumped mass matrices a diagonalized mass matrix enables a trivial computation of the acceleration vector from the force vector recently non diagonal mass matrices for explicit finite element analysis fea have received attention due to the selective mass scaling sms technique sms allows larger time step sizes without substantial loss of accuracy however an expensive solution for accelerations is required at each time step in the present study this problem is solved by directly constructing the inverse mass matrix first a consistent and sparse inverse mass matrix is built from the modified hamiltons principle with independent displacement and momentum variables usage of biorthogonal bases for momentum allows elimination of momentum unknowns without matrix inversions and directly yields the inverse mass matrix denoted here as reciprocal mass matrix rmm secondly a variational mass scaling technique is applied to the rmm it is based on the penalized hamiltons principle with an additional velocity variable and a free parameter using element wise bases for velocity and a local elimination yields variationally scaled rmm thirdly examples illustrating the efficiency of the proposed method for simplex elements are presented and discussed copyright 2014 john wiley sons ltd

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

novel higher order mass matrices for isogeometric structural vibration analysis abstract a set of novel higher order mass matrices are presented for isogeometric analysis of structural vibrations using nurbs the proposed method for the construction of higher order mass matrices contains two essential steps firstly based upon the standard consistent mass matrix a special reduced bandwidth mass matrix is designed this reduced bandwidth mass matrix meets the requirement of mass conservation while simultaneously preserves the same order of frequency accuracy as the corresponding consistent mass matrix subsequently a mixed mass matrix is formulated through a linear combination of the reduced bandwidth mass matrix and the consistent mass matrix the desired higher order mass matrix is then deduced from the mixed mass matrix by optimizing the linear combination parameter to achieve the most favorable order of accuracy both quadratic and cubic formulations are discussed in detail and it is shown that with regard to the vibration frequency the proposed higher order mass matrices have 6th and 8th orders of accuracy in contrast to the 4th and 6th orders of accuracy associated with the quadratic and cubic consistent mass matrices a generalization to two dimensional higher order mass matrix is further realized by the tensor product operation on the one dimensional reduced bandwidth and consistent mass matrices a series of benchmark examples congruously demonstrate that the proposed higher order mass matrices are capable of achieving the theoretically derived optimal accuracy orders for structural vibration analysis

construction of dual bases let b n b 0 b 1 b n n 0 1 n n n be the sets of linearly independent functions we give a simple method of construction the dual functions d n d 0 n d 1 n d n n 0 n n satisfying the following conditions spand n spanb n and d i j 0 i j n n where d i i 1 d i j 0 for i j and is a given inner product the proposed algorithm allows us to construct all the sets of the dual functions d 0 d 1 d n in the time o n 3 where n is a natural number four illustrative examples presenting the possible applications of obtained results are given

finite element and nurbs approximations of eigenvalue boundary value and initial value problems abstract we study the spectral approximation properties of finite element and nurbs spaces from a global perspective we focus on eigenfunction approximations and discover that the l 2 norm errors for finite element eigenfunctions exhibit pronounced spikes about the transition points between branches of the eigenvalue spectrum this pathology is absent in nurbs approximations by way of the pythagorean eigenvalue error theorem we determine that the squares of the energy norm errors of the eigenfunctions are the sums of the eigenvalue errors and the squares of the l 2 norm eigenfunction errors the spurious behavior of the higher eigenvalues for standard finite elements is well known and therefore inherited by the energy norm errors along with the spikes in the l 2 norm of the eigenfunction errors the eigenvalue pathology is absent for nurbs the implications of these results to the corresponding elliptic boundary value problem and parabolic and hyperbolic initial value problems are discussed

some new results on algebraic riccati equations arising in linear quadratic differential games and the stabilization of uncertain linear systems abstract this paper presents some new results on algebraic riccati equations arising in linear quadratic differential games the first result is a uniqueness result for solutions of the riccati equations under consideration the second result is concerned with riccati equations which arise in differential games in which the weighting on the minimizing control is allowed to approach zero it is shown that if a certain minimum phase condition is satisfied then the corresponding solution to the riccati equation will also approach zero

variationally consistent inertia templates for b spline and nurbs based fem inertia scaling and customization abstract in this contribution variationally consistent inertia templates for b spline and nurbs based finite elements are proposed as a unified concept for two different purposes customization of the template allows construction of masses and reciprocal masses with desired properties like higher order accuracy or improved dispersion behavior inertia scaling allows substantial speed up for explicit dynamics by increased critical time steps the derivation of the template is based on a three field parametrized functional as in previous works of the authors group but with modified primary variables namely displacement velocity and mass specific linear momentum the latter allows for mass preservation for non constant density throughout the domain and is therefore an enhancement to the formulation proposed in tkachuk and bischoff 2015 with the focus on b spline and nurbs based finite elements the proposed template provides alternatives to the row sum lumped mass matrix which is only 2nd order accurate independent of the polynomial order earlier proposed algebraically constructed higher order masses from the literature can be reconstructed in the variational setting described here as special instances furthermore higher order reciprocal masses can be constructed from the template they are especially attractive for explicit dynamics as there is no extra expense per time step compared with lumped mass for linear problems for non linear problems only small overhead is expected but this paper focuses on linear problems only and mainly undistorted meshes tuning the method towards inertia scaling a reduction of the maximum eigenfrequency by 25 40 is obtained in the examples herein whereas the accuracy is higher than for lumped or consistent mass

campanato morrey spaces for the double phase functionals with variable exponents abstract our aim in this paper is to show that the riesz potential operator i of variable order embeds from variable exponent morrey spaces l p g to campanato morrey spaces in the case x p x x our result extends the recent work of rafeiro and samko 2019 and the authors mizuta et al 2020 we show that i embeds from morrey spaces l g of the double phase functionals x t t p x b x t q x to campanato morrey spaces where p and q satisfy log holder conditions p x q x and b is nonnegative bounded and holder continuous of order 0 1 we also discuss the continuity of riesz potentials i f of functions in l g and show that i embeds from l g to vanishing campanato morrey spaces

superconvergent isogeometric free vibration analysis of euler bernoulli beams and kirchhoff plates with new higher order mass matrices abstract a superconvergent isogeometric free vibration analysis is presented for euler bernoulli beams and kirchhoff plates this method is featured by new higher order mass matrices for the 1d euler bernoulli beam problem it is shown that a new higher order mass matrix can be directly established by optimizing a reduced bandwidth mass matrix the reduced bandwidth mass matrix is designed based upon the consistent mass matrix and it contains adjustable parameters to be determined via maximizing the order of accuracy of the vibration frequency as a result 4th and 6th orders of accuracy are observed for the proposed quadratic and cubic higher order mass matrices while their corresponding consistent mass matrices are 2nd and 4th order accurate respectively thus the higher order beam mass matrices have more superior frequency accuracy simultaneously with smaller bandwidth compared with their corresponding consistent mass matrices while for the 2d kirchhoff plate problem in order to compute arbitrary frequency in a superconvergent fashion a mixed mass matrix is formulated through a linear combination of the consistent mass matrix and the reduced bandwidth mass matrix then by introducing the wave propagation angle the higher order plate mass matrix can be rationally derived from the mixed mass matrix it is proved that the optimal combination parameter for higher order mass matrix depends on the wave propagation angle consequently a particular higher order mass matrix can always be set up for a superconvergent computation of arbitrary vibration frequency it is shown that the quadratic and cubic higher order mass matrices possess 4th and 6th orders of accuracy which are two orders higher than those of the consistent plate mass matrices the construction of higher order mass matrices and the analytical results for vibration frequencies are systematically demonstrated by a set of numerical examples

multi patch discontinuous galerkin isogeometric analysis for wave propagation explicit time stepping and efficient mass matrix inversion abstract we present a class of spline finite element methods for time domain wave propagation which are particularly amenable to explicit time stepping the proposed methods utilize a discontinuous galerkin discretization to enforce continuity of the solution field across geometric patches in a multi patch setting which yields a mass matrix with convenient block diagonal structure over each patch we show how to accurately and efficiently invert mass matrices in the presence of curved geometries by using a weight adjusted approximation of the mass matrix inverse this approximation restores a tensor product structure while retaining provable high order accuracy and semi discrete energy stability we also estimate the maximum stable timestep for spline based finite elements and show that the use of spline spaces results in less stringent cfl restrictions than equivalent c 0 or discontinuous finite element spaces finally we explore the use of optimal knot vectors based on l 2 n widths we show how the use of optimal knot vectors can improve both approximation properties and the maximum stable timestep and present a simple heuristic method for approximating optimal knot positions numerical experiments confirm the accuracy and stability of the proposed methods

inverse mass matrix via the method of localized lagrange multipliers summary an efficient method for generating the mass matrix inverse of structural dynamic problems is presented which can be tailored to improve the accuracy of target frequency ranges and or wave contents the present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditions and free edges or surfaces and constructs the free free inverse mass matrix employing the standard fem procedure the various boundary conditions are realized by the the method of localized lagrange multipliers in particular the present paper constructs the kernel inverse matrix by employing the standard fem elemental mass matrices it is shown that the accuracy of the present inverse mass matrix is almost identical to that of a conventional consistent mass matrix or a combination of lumped and consistent mass matrices numerical experiments with the proposed inverse mass matrix are carried out to validate its effectiveness when applied to vibration analysis of bars beams and plain stress problems this article is protected by copyright all rights reserved

mass lumping techniques in the spectral element method on the equivalence of the row sum nodal quadrature and diagonal scaling methods abstract in the context of wave propagation analysis the spectral element method sem in conjunction with a diagonal mass matrix is often the method of choice therefore it is of high importance to investigate the influence of different mass lumping schemes on the accuracy of the numerical results to this end we compare the performance of three established methods including the row sum method the nodal quadrature method and the diagonal scaling method the theoretical analysis of these methods reveals a close connection between them under certain conditions that are discussed in detail in this article we are able to show a direct equivalence between these three approaches in this regard the attainable accuracy of the numerical integration of the mass matrix plays an important role by means of several dynamic benchmark problems we verify the theoretical results and illustrate the convergence properties of the lumped mass matrix sem in comparison to a formulation based on the consistent mass matrix

dual and approximate dual basis functions for b splines and nurbs comparison and application for an efficient coupling of patches with the isogeometric mortar method abstract this contribution defines and compares different methods for the computation of dual basis functions for b splines and non uniform rational b splines nurbs they are intended to be used as test functions for the isogeometric mortar method but other fields of application are possible too three different concepts are presented and compared the first concept is the explicit formula for the computation of dual basis functions for nurbs proposed in the work of carl de boor these dual basis functions entail minimal support i e the support of the dual basis functions is equal to the support of the corresponding b spline basis functions in the second concept dual basis functions are derived from the inversion of the gram matrix these dual basis functions have global support along the interface the third concept is the use of approximate dual basis functions which were initially proposed for the use in harmonic analysis the support of these functions is local but larger than the support of the associated b spline basis functions we propose an extension of the approximate dual basis functions for nurbs basis functions after providing the general formulas we elaborate explicit expressions for several degrees of spline basis functions all three approaches are applied in the frame of the mortar method for the coupling of non conforming nurbs patches a method which allows complex discretizations with multiple intersecting interfaces is presented numerical examples show that the explicitly defined dual basis functions with minimal support severely deteriorate the global stress convergence behavior of the mechanical analysis this fact is in accordance with mathematical findings in literature which state that the optimal reproduction degree of arbitrary functions is not possible without extending the support of the dual basis functions the dual basis functions computed from the inverse of the gram matrix yield accurate numerical results but the global support yields significantly higher computational costs in comparison to computations of conforming meshes only the approximate dual basis functions yield accurate and efficient computations where neither accuracy nor efficiency is significantly deteriorated in comparison to computations of conforming meshes all basic cases of t intersections and star intersections are studied furthermore an example which combines all basic cases in a complex discretization is given the applicability of the presented method for the nonlinear case and for shell formulations is shown with the help of one numerical example

asymptotic h sup infinity disturbance attenuation based on perfect observation a design method of controllers which ensure internal stability and attain asymptotically h sup infinity disturbance attenuation is presented the design procedure consists of two steps 1 to design an h sup infinity state feedback control via an algebraic riccati equation approach and 2 under a certain minimum phase condition to recover the achievable performance asymptotically by applying high gain observers it makes use of the perfect observation for the design of high gain observers it is shown that the asymptotic recovery can be attained by using reduced order observers provided there is no direct feedthrough of controls and disturbances in observations

robust multigrid for isogeometric analysis based on stable splittings of spline spaces we present a robust and efficient multigrid method for single patch isogeometric discretizations using tensor product b splines of maximum smoothness our method is based on a stable splitting of the spline space into a large subspace of interior splines which satisfy a robust inverse inequality as well as one or several smaller subspaces which capture the boundary effects responsible for the spectral outliers which occur in isogeometric analysis we then construct a multigrid smoother based on an additive subspace correction approach applying a different smoother to each of the subspaces for the interior splines we use a mass smoother whereas the remaining components are treated with suitably chosen kronecker product smoothers or direct solvers we prove that the resulting multigrid method exhibits iteration numbers which are robust with respect to the spline degree and the mesh size furthermore it can be efficiently realized for discretizations of problems in arbitrarily high geometric dimensio

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case