a nitsche stabilized finite element method for frictional sliding on embedded interfaces part ii intersecting interfaces abstract we extend the weighted nitsche s method proposed in the first part of this study to include multiple intersecting embedded interfaces these intersections arise either inside a computational domain where two internal interfaces intersect or on the boundary of the computational domain where an internal interface intersects with the external boundary we propose a variational treatment of both the interfacial kinematics and the external dirichlet constraints within nitsche s framework we modify the numerical analysis to account for these intersections and provide an explicit expression for the weights and the method parameters that arise in the nitsche variational form in the presence of junctions finally we demonstrate the performance of the method for both perfectly tied interfaces and perfectly plastic sliding interfaces through several benchmark examples

a domain decomposition method based on weighted interior penalties for advection diffusion reaction problems we propose a domain decomposition method for advection diffusion reaction equations based on nitsche s transmission conditions the advection dominated case is stabilized using a continuous interior penalty approach based on the jumps in the gradient over element boundaries we prove the convergence of the finite element solutions of the discrete problem to the exact solution and propose a parallelizable iterative method the convergence of the resulting domain decomposition method is proved and this result holds true uniformly with respect to the diffusion parameter the numerical scheme that we propose here can thus be applied straightforwardly to diffusion dominated advection dominated and hyperbolic problems some numerical examples are presented in different flow regimes showing the influence of the stabilization parameter on the performance of the iterative method and we compare our method with some other domain decomposition techniques for advection diffusion equations

design parametrization and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules control design belongs to the most important and difficult tasks of control engineering and has therefore been treated by many prominent researchers and in many textbooks the systems being generally described by their transfer matrices or by rosenbrock equations and more recently also as behaviors our approach to controller design uses in addition to the ideas of our predecessors on coprime factorizations of transfer matrices and on the parametrization of stabilizing compensators a new mathematical technique which enables simpler design and also new theorems in spite of the many outstanding results of the literature 1 we use an injective cogenerator signal module f over the polynomial algebra d f s f an infinite field a saturated multiplicatively closed set t of stable polynomials and its quotient ring dt of stable rational functions this enables the simultaneous treatment of continuous and discrete systems and of all notions of stability called t stability we investigate stabilizing control design by output feedback of input output io behaviors and study the full feedback io behavior especially its autonomous part and not only its transfer matrix 2 the new technique is characterized by the permanent application of the injective cogenerator quotient signal module dtft and of quotient behaviors bt of df behaviors b 3 for the control tasks of tracking disturbance rejection model matching and decoupling and not necessarily proper plants we derive necessary and sufficient conditions for the existence of proper stabilizing compensators with proper and stable closed loop behaviors parametrize all such compensators as io behaviors and not only their transfer matrices and give new algorithms for their construction moreover we solve the problem of pole placement or spectral assignability for the complete feedback behavior the properness of the full feedback behavior ensures the absence of impulsive solutions in the continuous case and that of the compensator enables its realization by kalman state space equations or elementary building blocks we note that every behavior admits an io decomposition with proper transfer matrix but that most of these decompositions do not have this property and therefore we do not assume the properness of the plant 4 the new technique can also be applied to more general control interconnections according to willems in particular to two parameter feedback compensators and to the recent tracking framework of fiaz takaba trentelman in contrast to these authors however we pay special attention to the properness of all constructed transfer matrices which requires more subtle algorithms

new solution method of linear static output feedback design problem for linear control systems abstract a new method of construction of the linear static output feedback for linear control systems is offered the essence of this method consists in construction of an initial approximation of the feedback matrix such that a numerical sequence which generated by arbitrary iterative method and beginning from this initial approximation converges to an exact solution of the feedback design problem examples are given

a robust nitsche s formulation for interface problems abstract in this work we propose a novel weighting for the interfacial consistency terms arising in a nitsche variational form we demonstrate through numerical analysis and extensive numerical evidence that the choice of the weighting parameter has a great bearing on the stability of the method consequently we propose a weighting that results in an estimate for the stabilization parameter such that the method remains well behaved in varied settings ranging from the configuration of embedded interfaces resulting in arbitrarily small elements to such cases where a large contrast in material properties exists an important consequence of this weighting is that the bulk as well as the interfacial fields remain well behaved in the presence of a elements with arbitrarily small volume fractions b large material heterogeneities and c both large heterogeneities as well as arbitrarily small elements we then highlight the accuracy and efficiency of the proposed formulation through numerical examples focusing particular attention on interfacial quantities of interest

a finite element method for the simulation of strong and weak discontinuities in solid mechanics in this paper we introduce and analyze a finite element method for elasticity problems with interfaces the method allows for discontinuities internal to the elements in the approximation across the interface we propose a general approach that can handle both perfectly and imperfectly bonded interfaces without modifications of the code for the case of linear elasticity we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh we present numerical examples for the linear case as well as for contact and crack propagation model problems

functional t observers abstract this article is a contribution to behavioral observer theory which was started by valcher and willems in 1999 and which was recently exposed by fuhrmann in a comprehensive survey article it is also a further development of the article on t observers by oberst and the author for a given continuous or discrete time linear time invariant behavior we assume that a linear function of a trajectory e g some components can be measured we are interested in estimating another linear function of this trajectory we generalize the notions of t observability and t observers introduced by oberst and the author t denotes a multiplicatively closed subset of the ring of operators for different choices of t t observability coincides with observability reconstructibility trackability or detectability a t observer is an exact dead beat tracking or asymptotic observer we show the equivalence of t observability and the existence of t observers and give a constructive parametrization of all t observers corresponding results for proper t observers are also presented partial observation of the state of a kalman state space system compare e g fuhrmann s work is a special case of our setting and so are the observers of certain unknown components of a behavior studied by bisiacco valcher and willems the first result on functional observers in context with rosenbrock equations or polynomial matrix descriptions is due to wolovich 1974

higher order meshing of implicit geometries part i integration and interpolation in cut elements abstract an accurate implicit description of geometries is enabled by the level set method level set data is given at the nodes of a higher order background mesh and the interpolated zero level sets imply boundaries of the domain or interfaces within the higher order accurate integration of elements cut by the zero level sets is described the proposed strategy relies on an automatic meshing of the cut elements firstly the zero level sets are identified and meshed by higher order surface elements secondly the cut elements are decomposed into conforming sub elements on the two sides of the zero level sets any quadrature rule may then be employed within the sub elements the approach is described in two and three dimensions without any requirements on the background meshes special attention is given to the consideration of corners and edges of the implicit geometries

a symmetric method for weakly imposing dirichlet boundary conditions in embedded finite element meshes summary in this paper we propose a way to weakly prescribe dirichlet boundary conditions in embedded finite element meshes the key feature of the method is that the algorithmic parameter of the formulation which allows to ensure stability is independent of the numerical approximation relatively small and can be fixed a priori moreover the formulation is symmetric for symmetric problems an additional element discontinuous stress field is used to enforce the boundary conditions in the poisson problem additional terms are required in order to guarantee stability in the convection diffusion equation and the stokes problem the proposed method is then easily extended to the transient navier stokes equations copyright 2012 john wiley sons ltd

weighted extended b spline approximation of dirichlet problems we describe a new finite element method which uses weighted extended b splines on a regular grid as basis functions for solving dirichlet problems on bounded domains in arbitrary dimensions this web method does not require any grid generation and can be implemented very efficiently it yields smooth high order accurate approximations with relatively low dimensional subspaces

implicit boundary method for determination of effective properties of composite microstructures a method that uses a structured grid to perform micromechanical analysis for determining effective properties of a composite microstructure is presented this approach eliminates the need for constructing a mesh that has nodes along the interfaces between constituent materials of the composite implicit boundary method is used to ensure that interface conditions are satisfied at the material boundaries in this method solution structures for test and trial functions are constructed using approximate step functions such that the interface conditions are satisfied even if there are no nodes on the material interface boundary since a structured grid does not conform to the geometry of the analysis domain the geometry of the microstructure is defined independently using equations of the interface boundary curves surfaces structured grids that overlap the geometry are easy to generate and the elements in the grid are regular shaped and undistorted a numerical example is presented to demonstrate that the proposed solution structure accurately models the solution across material interface and convergence analysis is performed to show that the method converges as the grid density is increased fiber reinforced microstructures are analyzed to compute the effective elastic properties using both 2d and 3d models to show that the results match closely with the ones available in the literature

a discontinuous galerkin based immersed boundary method with non homogeneous boundary conditions and its application to elasticity we propose a discontinuous galerkin based immersed boundary method for elasticity problems the resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous galerkin approximation special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non homogeneous essential and natural boundary conditions the role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension finally extensive two and three dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions

an unfitted nitsche method for incompressible fluid structure interaction using overlapping meshes we consider the extension of the nitsche method to the case of fluid structure interaction problems on unfitted meshes we give a stability analysis for the space semi discretized problem and show how this estimate may be used to derive optimal error estimates for smooth solutions irrespectively of the mesh interface intersection we also discuss different strategies for the time discretization using either fully implicit or explicit coupling loosely coupled schemes some numerical examples illustrate the theoretical discussion

an unfitted finite element method based on nitsche s method for elliptic interface problems in this paper we propose a method for the finite element solution of elliptic interface problem using an approach due to nitsche the method allows for discontinuities internal to the elements in the approximation across the interface we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh further we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

implicit boundary method for finite element analysis using non conforming mesh or grid in the finite element method fem a mesh is used for representing the geometry of the analysis and for representing the test and trial functions by piece wise interpolation recently analysis techniques that use structured grids have been developed to avoid the need for a conforming mesh the boundaries of the analysis domain are represented using implicit equations while a structured grid is used to interpolate functions such a method for analysis using structured grids is presented here in which the analysis domain is constructed by boolean combination of step functions implicit equations of the boundary are used in the construction of trial and test functions such that essential boundary conditions are guaranteed to be satisfied furthermore these functions are constructed such that internal elements through which no boundary passes have the same stiffness matrix this approach has been applied to solve linear elastostatic problems and the results are compared with analytical and finite element analysis solutions to show that the method gives solutions that are similar to the fem in quality but is less computationally expensive for dense mesh grid and avoids the need for a conforming mesh copyright 2007 john wiley sons ltd

stabilisation and control design by partial output feedback and by partial interconnection we study stabilisation and control design by partial output feedback on the one hand and by partial interconnection according to willems on the other hand this article is based on the paper design parametrization and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules by i blumthaler and u oberst and the same technique is used both discrete and continuous behaviours and various notions of stability are treated simultaneously in the case of partial output feedback we require that both the compensator and the feedback behaviour have proper transfer matrices without presuming properness of the plant we obtain conditions ensuring the existence of such stabilising compensators which perform additional control tasks like for instance tracking and an algorithm for constructing a large class of such compensators in the case of stabilisation by interconnection no input output structures of plant or compensator are assumed but the controlled be

stabilising compensators for linear time varying differential systems abstractin this paper we describe a constructive test to decide whether a given linear time varying ltv differential system admits a stabilising compensator for the control tasks of tracking disturbance rejection or model matching and construct and parametrise all of them if at least one exists in analogy to the linear time invariant lti case the ring of stable rational functions noncommutative in the ltv situation and the kucera youla parametrisation play prominent parts in the theory we transfer blumthaler s thesis from the lti to the ltv case and sharpen complete and simplify the corresponding results in the book linear time varying systems by bourles and marinescu

exact imposition of inhomogeneous dirichlet boundary conditions based on weighted finite cell method and level set function abstract the imposition of inhomogeneous dirichlet boundary conditions idbcs is essential in numerical analysis of a structure it is especially difficult and no longer straightforward whenever non conformal mesh is used to discretize a structure the original contribution of this paper is to develop a weighted finite cell method fcm with high computing accuracy the commonly used transfinite interpolation in the computer aided design cad community is now extended to define boundary value function so that the idbcs are imposed exactly unlike existing weak imposition forms and weighted interpolation methods it is shown that the weighting function and boundary value function involved in the weighted fcm can directly be applied to the physical field independently of the mesh discretization besides level set function lsf is used to represent the geometry of the considered physical domain to verify the effectiveness convergence performance and the generality of the proposed method numerical examples ranging from purely elastic to thermoelastic problems are illustrated computing results are compared with analytical and fea solutions

weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non matching meshes this is the accepted version of the following article codina r and baiges j 2015 weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non matching meshes int j numer meth engng 104 624 654 doi 10 1002 nme 4815 which has been published in final form at http onlinelibrary wiley com doi 10 1002 nme 4815 abstract

imposition of essential boundary conditions in the material point method summary there is increasing interest in the material point method mpm as a means of modelling solid mechanics problems in which very large deformations occur e g in the study of landslides and metal forming however some aspects vital to wider use of the method have to date been ignored in particular methods for imposing essential boundary conditions in the case where the problem domain boundary does not coincide with the background grid element edges in this paper we develop a simple procedure originally devised for standard finite elements for the imposition of essential boundary conditions to the mpm expanding its capabilities to boundaries of any inclination to the authors knowledge this is the first time that a method has been proposed that allows arbitrary dirichlet boundary conditions zero and non zero values at any inclination to be imposed in the mpm the method presented in this paper is different from other mpm boundary approximation approaches in that i the boundaries are independent of the background mesh ii artificially stiff regions of material points are avoided and iii the method does not rely on spurious mirroring of the problem domain to imposed symmetry the main contribution of this work is equally applicable to standard finite elements and the mpm this article is protected by copyright all rights reserved

a new face oriented stabilized xfem approach for 2d and 3d incompressible navier stokes equations abstract we develop a new stabilized xfem based fixed grid approach for the transient incompressible navier stokes equations using cut elements our framework is based on a new flexible strategy to handle several degrees of freedom dofs at nodes required for complex shaped embedded meshes as they occur for fixed grid fluid structure interaction problems boundary conditions on embedded boundaries are imposed weakly using a nitsche type approach ghost penalty terms for velocity and pressure are added for stability reasons and to improve the conditioning of the system matrix the idea of ghost penalties previously developed for stokes problems is extended to the incompressible navier stokes equations by using face oriented fluid stabilizations for both viscous and convective dominated flows furthermore the need for additional terms to enforce boundary conditions for non viscous flows is addressed a detailed numerical study of our stabilized fluid formulation including studies of nitsche s parameter and the ghost penalty parameter shows optimal error convergence and a good system conditioning in the viscous and the convective dominated cases compared to other fixed grid fluid formulations our method is much more accurate and less sensitive to the location of the interface regarding the accuracy and the sensitivity with respect to the interface position a clear improvement could be observed for the viscous and pressure fluxes as well as for the imposition of the boundary condition results of a transient two dimensional high reynolds number flow over a cylinder and the flow over a thick plate in 3d confirm the applicability of the proposed method

a coupling interface method for elliptic interface problems we propose a coupling interface method cim under cartesian grid for solving elliptic complex interface problems in arbitrary dimensions where the coefficients the source terms and the solutions may be discontinuous or singular across the interfaces it consists of a first order version cim1 and a second order version cim2 in one dimension the cim1 is derived from a linear approximation on both sides of the interface the method is extended to high dimensions through a dimension by dimension approach to connect information from each dimension a coupled equation for the first order derivatives is derived through the jump conditions in each coordinate direction the resulting stencil uses the standard 5 grid points in two dimensions and 7 grid points in three dimensions similarly the cim2 is derived from a quadratic approximation in each dimension in high dimensions a coupled equation for the principal second order derivatives u x k x k is derived through the jump conditions in each coordinate direction the cross derivatives are approximated by one side interpolation this approach reduces the number of grid points needed for one side interpolation the resulting stencil involves 8 grid points in two dimensions and 12 14 grid points in three dimensions a numerical study for the condition number of the resulting linear system of the cim2 in one dimension has been performed it is shown that the condition number has the same behavior as that of the discrete laplacian independent of the relative location of the interface in a grid cell further we also give a proof of the solvability of the coupling equations provided the curvature k of the interface satisfies kh

a new fictitious domain approach inspired by the extended finite element method the purpose of this paper is to present a new fictitious domain approach inspired by the extended finite element method introduced by moes dolbow and belytschko in internat j numer methods engrg 46 1999 pp 131 150 an optimal method is obtained thanks to an additional stabilization technique some a priori estimates are established and numerical experiments illustrate different aspects of the method the presentation is made on a simple poisson problem with mixed neumann and dirichlet boundary conditions the extension to other problems or boundary conditions is quite straightforward

exactly solvable disordered sphere packing model in arbitrary dimensional euclidean spaces we introduce a generalization of the well known random sequential addition rsa process for hard spheres in d dimensional euclidean space mathbb r d we show that all of the n particle correlation functions of this nonequilibrium model in a certain limit called the ghost rsa packing can be obtained analytically for all allowable densities and in any dimension this represents the first exactly solvable disordered sphere packing model in an arbitrary dimension the fact that the maximal density ensuremath phi ensuremath infty 1 2 d of the ghost rsa packing implies that there may be disordered sphere packings in sufficiently high d whose density exceeds minkowski s lower bound for bravais lattices the dominant asymptotic term of which is 1 2 d indeed we report on a conjectural lower bound on the density whose asymptotic behavior is controlled by 2 ensuremath 0 778 65 dots d thus providing the putative exponential improvement on minkowski s 100 year old bound our results suggest that the densest packings in sufficiently high dimensions may be disordered rather than periodic implying the existence of disordered classical ground states for some continuous potentials

imposing essential boundary conditions in mesh free methods imposing essential boundary conditions is a key issue in mesh free methods the mesh free interpolation does not verify the kronecker delta property and therefore the imposition of prescribed values is not as straightforward as for the finite element method the aim of this paper is to present a general overview on the existing techniques to enforce essential boundary conditions in galerkin based mesh free methods special attention is paid to the mesh free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of the galerkin weak form particular examples are used to analyze and compare their performance in different situations

stability and stabilization of multidimensional input output systems in this paper we discuss stability and stabilization of continuous and discrete multidimensional input output io behaviors of dimension r which are described by linear systems of complex partial differential resp difference equations with constant coefficients where the signals are taken from various function spaces in particular from those of polynomial exponential functions stability is defined with respect to a disjoint decomposition of the r dimensional complex space into a stable and an unstable region with the standard stable region in the one dimensional continuous case being the set of complex numbers with negative real part a rational function is called stable if it has no poles in the unstable region an io behavior is called stable if the characteristic variety of its autonomous part has no points in the unstable region this is equivalent to the stability of its transfer matrix and an additional condition the system is called stabilizable if there is a compensator io system such that the output feedback system is well posed and stable we characterize stability and stabilizability and construct all stabilizing compensators of a stabilizable io system parametrization the theorems and proofs are new but essentially inspired and influenced by and related to the stabilization theorems concerning multidimensional io maps as developed for instance by bose guiver shankar sule xu lin ying zerz and quadrat and of course the seminal papers of vidyasagar youla and others in the one dimensional case in contrast to the existing literature the theorems and proofs of this paper do not need or employ the so called fractional representation approach i e various matrix fraction descriptions of the transfer matrix thus avoiding the often lengthy matrix computations and seeming to be of interest even for one dimensional systems at least to the author an important mathematical tool new in systems theory is gabriel s localization theory which only in the case of ideal convex shankar sule unstable regions coincides with the usual one algorithmic tests for stability stabilizability and ideal convexity and the algorithmic construction of stabilizing compensators are addressed but still encounter many difficulties see in particular the open problems listed by xu e

an implicit boundary finite element method with extension to frictional sliding boundary conditions and elasto plastic analyses abstract implicit boundary methods which enrich the interpolation structure with implicit weight functions are straightforward methods for the enforcement of dirichlet boundary conditions in this article we follow the implicit boundary method that uses approximate step functions the step boundary method developed by kumar et al and provide modifications that have several advantages roller boundary conditions have wide practical applications in engineering however the step boundary method for roller boundary conditions with inclinations has yet to be fully formulated through to the final linear system of equations thus we provide a complete derivation that leads to simplified stiffness matrices compared to the original approach which can be implemented directly in fictitious domain finite element analysis the approach is then extended we believe for the first time to the nonlinear cases of frictional boundary conditions and elasto plastic material behaviour the proposed formulation and procedures are validated on a number of example problems that test different aspects of the method

analysis of the fully discrete fat boundary method the fat boundary method is a method of the fictitious domain class which was proposed to solve elliptic problems in complex geometries with non conforming meshes it has been designed to recover optimal convergence at any order despite of the non conformity of the mesh and without any change in the discrete laplace operator on the simple shape domain we propose here a detailed proof of this high order convergence and propose some numerical tests to illustrate the actual behaviour of the method

a weighted nitsche stabilized method for small sliding contact on frictional surfaces abstract we propose a weighted nitsche framework for small sliding frictional contact problems on three dimensional interfaces the proposed method inherits the advantages of both augmented lagrange multiplier and penalty methods while also addressing their shortcomings algorithmic details of the traction update and consistent linearization in the presence of nitsche terms are provided several benchmark numerical experiments are conducted and the results are compared with existing studies the results are encouraging and indicate accurate satisfaction of the non interpenetration constraint stable tractions and asymptotic quadratic convergence of the newton raphson method

stabilization pole placement and regular implementability in this paper we study control by interconnection of linear differential systems we give necessary and sufficient conditions for regular implementability of a given linear differential system we formulate the problems of stabilization and pole placement as problems of finding a suitable regularly implementable sub behavior of the manifest plant behavior the problem formulations and their resolutions are completely representation free and specified only in terms of the system dynamics control is viewed as regular interconnection a controller is a system that constrains the plant behavior through a distinguished set of variables namely the control variables the issue of implementation of a controller in the feedback configuration and its relation to regularity of interconnection is addressed freedom of disturbances in a plant and regular interconnection with a controller also turn out to be inter related

fictitious domain finite element methods using cut elements i a stabilized lagrange multiplier method we propose a fictitious domain method where the mesh is cut by the boundary the primal solution is computed only up to the boundary the solution itself is defined also by nodes outside the domain

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

imposing dirichlet boundary conditions in hierarchical cartesian meshes by means of stabilized lagrange multipliers this is the pre peer reviewed version of the following article tur m albelda j nadal e and rodenas j j 2014 imposing dirichlet boundary conditions in hierarchical cartesian meshes by means of stabilized lagrange multipliers int j numer meth engng 98 399 417 which has been published in final form at http dx doi org 10 1002 nme 4629 this article may be used for non commercial purposes in accordance with wiley terms and conditions for self archiving

nurbs plasticity yield surface representation and implicit stress integration for isotropic inelasticity in numerical analysis the failure of engineering materials is controlled through specifying yield envelopes or surfaces that bound the allowable stress in the material however each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case these equations impact on the numerical implementation specifically relating to stress integration of the models and therefore a separate algorithm must be constructed for each model this paper presents for the first time a way to construct yield surfaces using techniques from non uniform rational basis spline nurbs surfaces such that any isotropic convex yield envelope can be represented within the same framework these surfaces are combined with an implicit backward euler type stress integration algorithm to provide a flexible numerical framework for computational plasticity the algorithm is inherently stable as the iterative process starts and remains on the yield surface throughout the stress integration the performance of the algorithm is explored using both material point investigations and boundary value analyses demonstrating that the framework can be applied to a variety of plasticity models

on the parametrization of all regularly implementing and stabilizing controllers in this paper we deal with problems of controller parametrization in the context of behavioral systems given a full plant behavior a subbehavior of the manifest plant behavior is called regularly implementable if it can be achieved as the controlled behavior resulting from the interconnection of the full plant behavior with a suitable controller behavior in such a way that the controller does not impose restrictions that are already present in the plant we establish a parametrization of all controllers that regularly implement a given behavior we also obtain a parametrization of all stabilizing controllers

an implicit boundary approach for viscous compressible high reynolds flows using a hybrid remeshed particle hydrodynamics method abstract we present an implicit boundary particle method with background mesh adaptation we use a brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high reynolds numbers a penalty term is added to the navier stokes equations to impose the boundary conditions the boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid achieving an implicit approach for flow around complex boundaries geometries simulation the main idea of the brinkman penalisation method is to model the solid obstacle as a porous medium the governing equations for the compressible fluid and penalised navier stokes for the porous medium are solved simultaneously without need for interface conditions the accuracy of the method is tested for a number of benchmark problems starting with simple cases such as a periodic laminar flow in a channel poiseuille flow to more complex problems such as the lid driven cavity with high reynolds numbers the reflection and propagation of a compressible shock wave and finally swirling flow in a model two stroke diesel engine the remeshed particle mesh method coupled with brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions

a fictitious domain method for dirichlet problem and applications abstract in this article we discuss the solution of the dirichlet problem for a class of elliptic operators by a lagrange multiplier fictitious domain method this approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries the resulting saddle point system can be solved by an uzawa conjugate gradient algorithm in the case of two dimensional problems a quasi optimal preconditioner has been found by fourier analysis and numerical experiments confirm its nice scaling properties the resulting methodology is applied to a nonlinear time dependent problem namely the flow of a viscous plastic medium in a cylindrical pipe showing the potential of this methodology for some classes of nonlinear problems

a stabilized nitsche overlapping mesh method for the stokes problem we develop a nitsche based formulation for a general class of stabilized finite element methods for the stokes problem posed on a pair of overlapping non matching meshes by extending the least squares stabilization to the overlap region we prove that the method is stable consistent and optimally convergent to avoid an ill conditioned linear algebra system the scheme is augmented by a least squares term measuring the discontinuity of the solution in the overlap region of the two meshes as a consequence we may prove an estimate for the condition number of the resulting stiffness matrix that is independent of the location of the interface finally we present numerical examples in three spatial dimensions illustrating and confirming the theoretical results

optimal convergence analysis for the extended finite element method we establish some optimal a priori error estimate on some variants of the extended finite element method xfem namely the xfem with a cut off function and the standard xfem with a fixed enrichment area the results are established for the lame system homogeneous isotropic elasticity and the laplace problem the convergence of the numerical stress intensity factors is also investigated we show some numerical experiments which corroborate the theoretical results

nitsche s method for general boundary conditions we introduce a method for treating general boundary conditions in the finite element method generalizing an approach due to nitsche 1971 for approximating dirichlet boundary conditions we use poisson s equations as a model problem and prove a priori and a posteriori error estimates the method is also compared with the traditional galerkin method the theoretical results are verified numerically

cutfem discretizing geometry and partial differential equations we discuss recent advances on robust unfitted finite element methods on cut meshes these methods are designed to facilitate computations on complex geometries obtained for example from computer

a nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity in this note we propose a finite element method for incompressible or compressible elasticity problems with discontinuous modulus of elasticity or if compressible poisson s ratio the problem is written on mixed form using p1 continuous displacements and elementwise p0 pressures leading to the possibility of eliminating the pressure beforehand in the compressible case in the incompressible case the method is augmented by a stabilization term penalizing the pressure jumps we show a priori error estimates under certain regularity hypothesis in particular we prove that if the exact solution is sufficiently smooth in each subdomain then the convergence order is optimal

a new formulation for imposing dirichlet boundary conditions on non matching meshes generating matching meshes for problems with complex boundaries is often an intricate process and the use of non matching meshes appears as an appealing solution yet enforcing boundary conditions on non matching meshes is not a straightforward process especially when prescribing those of dirichlet type by combining a type of generalized finite element method gfem with the lagrange multiplier method a new technique for the treatment of essential boundary conditions on non matching meshes is introduced in this manuscript the new formulation yields a symmetric stiffness matrix and is straightforward to implement as a result the methodology makes possible the analysis of problems with the use of simple structured meshes irrespective of the problem domain boundary through the solution of linear elastic problems we show that the optimal rate of convergence is preserved for piecewise linear finite elements yet the formulation is general and thus it can be extended to other elliptic boundary value problems

a new implementation of the element free galerkin method abstract element free galerkin methods efg are methods for solving partial differential equations with moving least squares interpolants efg methods require only nodal data no element connectivity is needed in a previous implementation of the efg method lagrange multipliers were used to enforce the essential boundary condition however the use of lagrange multipliers increases the cost of solving the linear algebraic equations a new implementation is developed based on a modified variational principle in which the lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded in addition weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes the latter makes it very advantageous for modelling progressive cracking

an algebraic theory for design of controllers for linear multivariable systems part i structure matrices and feedforward design in this two part paper a theory is presented in which several control problems can be solved the theory is applicable to a general class of linear multivariable systems where the measured output does not have to be equal to the controlled output or the state the system may be affected by nonmeasurable disturbances only controllers which stabilize the system and have proper transfer functions are allowed i e the controllers have to be physically realizable it is shown that the solutions to control problems of servo type e g problems of model matching decoupling and invertibility are special cases of the solution to a more general problem analogously the solutions to problems of regulator type e g disturbance decoupling output regulation and pole placement are also speclal cases of the solution to a more general problem it is shown that problems of servo type and regulator type can be solved independently of each other in part i generalized polynomials are introduced as a mathematical framework structue matrices which describe how well a system can be controlled are defined finally problems of servo type are solved part ii mainly deals with problems of regulator type

a penalty free nonsymmetric nitsche type method for the weak imposition of boundary conditions in this paper we show that the nonsymmetric version of nitsche s method for the weak imposition of boundary conditions is stable without penalty term for nonconforming elements we prove the same result for the symmetric formulation as well we prove optimal h 1 error estimates and l 2 error estimates that are suboptimal with half an order in h both the pure diffusion and the convection diffusion problems are discussed

on the most compact regular lattices in large dimensions a statistical mechanical approach in this paper i will consider the computation of the maximum density of regular lattices in large dimensions using an approach based on statistical mechanics the starting point will be some theorems of rogers which are virtually unknown in the community of physicists using his approach one can find many similarities and differences with the problem of computing the entropy of a system of hard spheres the relation between the two problems is investigated in detail some conjectures are presented further investigation is needed in order to check their consistency

efficient implementation of finite element methods on nonmatching and overlapping meshes in three dimensions in recent years a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on nonmatching or overlapping meshes examples of such methods are the fictitious domain method the extended finite element method and nitsche s method in all these methods integrals must be computed over cut cells or subsimplices which is challenging to implement especially in three space dimensions in this note we address the main challenges of such an implementation and demonstrate good performance of a fully general code for automatic detection of mesh intersections and integration over cut cells and subsimplices as a canonical example of an overlapping mesh method we consider nitsche s method which we apply to poisson s equation and a linear elastic problem

on interconnections control and feedback the purpose of this paper is to study interconnections and control of dynamical systems in a behavioral context we start with an extensive physical example which serves to illustrate that the familiar input output feedback loop structure is not as universal as we have been taught to believe this leads to a formulation of control problems in terms of interconnections subsequently we study interconnections of linear time invariant systems from this vantage point let us mention two of the results obtained the first one states that any polynomial can be achieved as the characteristic polynomial of the interconnection with a given plant provided the plant is not autonomous the second result states that any subsystem of a controllable system can be implemented by means of a singular feedback control law these results yield pole placement and stabilization of controllable plants as a special case these ideas are finally applied to the stabilization of a nonlinear system around an operating point

on the high density behavior of hamming codes with fixed minimum distance we discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n in the limit n d d n the problem is relevant for coding theory and the best available bounds state that the maximum density of the system falls in the interval 1 v d exp n being 0 and v d the volume of a sphere of radius d we find a solution of the equations describing the liquid up to an exponentially large value of widetilde rho v d but we show that this solution gives a negative entropy for the liquid phase for widetilde rho rsimn we then conjecture that a phase transition towards a different phase might take place and we discuss possible scenarios for this transition

stabilized low order finite elements for frictional contact with the extended finite element method abstract contact problem suffers from a numerical instability similar to that encountered in incompressible elasticity in which the normal contact pressure exhibits spurious oscillation this oscillation does not go away with mesh refinement and in some cases it even gets worse as the mesh is refined using a lagrange multipliers formulation we trace this problem to non satisfaction of the lbb condition associated with equal order interpolation of slip and normal component of traction in this paper we employ a stabilized finite element formulation based on the polynomial pressure projection ppp technique which was used successfully for stokes equation and for coupled solid deformation fluid diffusion using low order mixed finite elements for the frictional contact problem the polynomial pressure projection approach is applied to the normal contact pressure in the framework of the extended finite element method we use low order linear triangular elements tetrahedral elements for 3d for both slip and normal pressure degrees of freedom and show the efficacy of the stabilized formulation on a variety of plane strain plane stress and three dimensional problems

new upper bounds on sphere packings i we continue the study of the linear programming bounds for sphere packing introduced by cohn and elkies we use theta series to give another proof of the principal theorem and present some related results and conjectures this article is in the arxiv as arxiv math mg 0110010

optimal packings of superballs dense hard particle packings are intimately related to the structure of low temperature phases of matter and are useful models of heterogeneous materials and granular media most studies of the densest packings in three dimensions have considered spherical shapes and it is only more recently that nonspherical shapes e g ellipsoids have been investigated superballs whose shapes are defined by x1 2p x2 2p x3 2p 1 provide a versatile family of convex particles p0 5 with both cubic like and octahedral like shapes as well as concave particles 0p0 5 with octahedral like shapes in this paper we provide analytical constructions for the densest known superball packings for all convex and concave cases the candidate maximally dense packings are certain families of bravais lattice packings in which each particle has 12 contacting neighbors possessing the global symmetries that are consistent with certain symmetries of a superball we also provide strong evidence that our packings for convex superballs p0 5 are most likely the optimal ones the maximal packing density as a function of p is nonanalytic at the sphere point p 1 and increases dramatically as p moves away from unity two more nontrivial nonanalytic behaviors occur at p c 1 150 9 and p o ln 3 ln 4 0 792 4 for cubic and octahedral superballs respectively where different bravais lattice packings possess the same densities the packing characteristics determined by the broken rotational symmetry of superballs are similar to but richer than their two dimensional superdisk counterparts y jiao et al phys rev lett 100 245504 2008 and are distinctly different from that of ellipsoid packings our candidate optimal superball packings provide a starting point to quantify the equilibrium phase behavior of superball systems which should deepen our understanding of the statistical thermodynamics of nonspherical particle systems

weak impositions of dirichlet boundary conditions in solid mechanics a critique of current approaches and extension to partially prescribed boundaries abstract in this article we first review various approaches developed to date for the weak imposition of dirichlet boundary conditions in fictitious domain analysis for elasticity problems the hellinger reissner h r principle the linked lagrange multiplier llm method the implicit boundary method and the fat boundary method are discussed along with the well known lagrange multiplier penalty and nitsche s methods we state these approaches in a common form starting with energy functionals and weak forms and discretise using the fictitious domain finite element method previous formulations of these methods were in general developed for full prescription along the dirichlet boundary which generally implies no local effect of boundary inclination however partially prescribed conditions such as the structural roller boundary condition with inclination have wide practical applications in engineering here we provide techniques of imposing such boundary conditions in these methods in detail for those methods that contain algorithmic parameters such as the penalty and nitsche s methods extra computation or empirical estimation is necessary to decide values of the parameters and hence we discuss parametric and convergence behaviours through numerical examples to provide guidance on the choice of parameters

an algebraic theory for design of controllers for linear multivariable systems part ii feedback realizations and feedback design the study of general linear multivariable systems with possibly different controlled and measured outputs is continued in this part of the paper the structure matrices defined in part i are used to solve the feedback realization problem feedback realizable transfer functions are then used to solve problems of regulator type it is shown that the solutions to problems like disturbance deeoupling output regulation and pole placement are all special cases of the solution to a more general problem finally it is shown how the results of part i and part ii can be combined to solve problems of servo type and of regulator type simultaneously

implicit boundary method for analysis using uniform b spline basis and structured grid several analysis techniques such as extended finite element method x fem have been developed recently which use structured grid for the analysis implicit boundary method uses implicit equations of the boundary to apply boundary conditions in x fem framework using structured grids solution structures for test and trial functions are constructed using implicit equations such that the boundary conditions are satisfied even if there are no nodes on the boundary in this paper this method is applied for analysis using uniform b spline basis defined over a structured grid solution structures that are c1 or c2 continuous throughout the analysis domain can be constructed using b spline basis functions as a structured grid does not conform to the geometry of the analysis domain the boundaries of the analysis domain are defined independently using equations of the boundary curves surfaces compared with conforming mesh it is easier to generate structured grids that overlap the geometry and the elements in the grid are regular shaped and undistorted numerical examples are presented to demonstrate the performance of these b spline elements the results are compared with analytical solutions as well as with traditional finite element solutions convergence studies for several examples show that b spline elements provide accurate solutions with fewer elements and nodes compared with traditional fem they also provide continuous stress and strain in the analysis domain thus eliminating the need for smoothing stress strain results copyright 2008 john wiley sons ltd

mesh independent analysis of shell like structures summary mesh independent analysis is motivated by the desire to use accurate geometric models represented as equations rather than approximated by a mesh the trial and test functions are approximated or interpolated on a background mesh that is independent of the geometry this background mesh is easy to generate because it does not have to conform to the geometry essential boundary conditions can be applied using the implicit boundary method where the trial and test functions are constructed utilizing approximate step functions such that the boundary conditions are guaranteed to be satisfied this approach has been demonstrated for two dimensional 2d and three dimensional 3d structural analysis and is extended in this paper to model shell like structures the background mesh consists of 3d elements that use uniform b spline approximations and the shell geometry is assumed to be defined as parametric surfaces to allow arbitrarily complex shell like structures to be modeled several benchmark problems are used to study the validity of these 3d b spline shell elements copyright 2012 john wiley sons ltd

toy model for the mean field theory of hard sphere liquids we investigate a toy model of liquid based on simplified hypernetted chain equations in very large spatial dimension d the model does not exhibit a phase transition but several regimes of behavior when d infinity can be observed in different intervals of the density

a high order discontinuous galerkin nitsche method for elliptic problems with fictitious boundary we present a discontinuous galerkin method based on the classical method of nitsche for elliptic problems with an immersed boundary representation on a structured grid in such methods very small elements typically occur at the boundary leading to breakdown of the discrete coercivity as well as numerical instabilities in this work we propose a method that avoids using very small elements on the boundary by associating them to a neighboring element with a sufficiently large intersection with the domain this construction allows us to prove the crucial inverse inequality that leads to a coercive bilinear form and as a consequence we obtain optimal order a priori error estimates furthermore we prove a bound of the condition number of the stiffness matrix all the results are valid for polynomials of arbitrary order we also discuss the implementation of the method and present numerical examples in three dimensions

a finite element method for elliptic equations on surfaces in this paper a new finite element approach for the discretization of elliptic partial differential equations on surfaces is treated the main idea is to use finite element spaces that are induced by triangulations of an outer domain to discretize the partial differential equation on the surface the method is particularly suitable for problems in which there is a coupling with a flow problem in an outer domain that contains the surface we give an analysis that shows that the method has optimal order of convergence both in the h 1 and in the l 2 norm results of numerical experiments are included that confirm this optimality

a discontinuous galerkin based immersed boundary method a numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced the proposed method is conceptually simple and free of user defined parameters starting with a conforming finite element mesh the key ingredient is to switch those elements intersected by the dirichlet boundary to a discontinuous galerkin approximation and impose the dirichlet boundary conditions strongly by virtue of relaxing the continuity constraint at those elements boundary locking is avoided and optimal order convergence is achieved this is shown through numerical experiments in reaction diffusion problems copyright 2008 john wiley sons ltd

trajectory control and interconnection of 1d and nd systems in this paper we examine the relationship between control viewed as concatenation of trajectories and control viewed as interconnection of systems we show that for one dimensional linear time invariant systems the ability to obtain a given subsystem by regular interconnection a prerequisite for any feedback type structure is equivalent to the ability to drive any trajectory into that subsystem however in the case of multidimensional systems the former is a stronger property than the latter trajectory controllability can however be expressed as a regular interconnection of behaviors in an extended variable space by introducing latent or auxiliary variables this leads as a by product to the notion of controlling a system by means of latent variables