on the numerical integration of trimmed isogeometric elements abstract a numerical algorithm is proposed to construct efficient quadrature rules for trimmed isogeometric elements of arbitrary shape and topology as part of the standard finite element preprocessing step the constructed integration rule is unique to an element and it is considered to be optimal in the sense that the final quadrature points and weights satisfy the moment fitting equations within the trimmed domain up to a predefined tolerance the resulting quadrature points are in the interior of the trimmed domain and the positivity of the weights is preserved the accuracy and efficiency of the quadrature scheme are assessed and compared to traditionally employed integration techniques results indicate that the proposed integration rules are more precise and inhibit the proliferation of quadrature points observed in competing approaches selected problems of elastostatics elastodynamics and elasto plastic dynamics are used to further demonstrate the validity and efficacy of the method

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

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 practical finite element approximation of a semi definite neumann problem on a curved domain this paper considers the finite element approximation of the semi definite neumann problem u f in a curved domain n n 2 or 3 sigma frac partial u partial v g on and int limits omega u dx q a given constant for dataf andg satisfying the compatibility condition int limits omega f dx int limits partial omega g ds 0 due to perturbation of domain errors h the standard galerkin approximation to the above problem may not have a solution a remedy is to perturb the right hand side so that a discrete form of the compatibility condition holds using this approach we show that for a finite element space defined overd h a union of elements with approximation powerh k in thel 2 norm and with dist h ch k one obtains optimal rates of convergence in theh 1 andl 2 norms whether h is fitted h d h or unfitted h d h provided the numerical integration scheme has sufficient accuracy

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

a connection between normalized coprime factorizations and linear quadratic regulator theory given a transfer matrix described by a minimal state space triple a method is given for computing state space realizations for the numerator and denominator of a normalized stable right coprime factorization for the transfer matrix the method involves the solution of an algebraic riccati equation it allows the use of existing computational state space algorithms in finding normalized stable right coprime factorizations and avoids explicit calculations of spectral factors

asymptotic stability of infinite dimensional discrete time balanced realizations the question of power and asymptotic stability of infinite dimensional discrete time state space systems is investigated it is shown that every balanced realization is asymptotically stable conditions are given for balanced input normal or output normal realizations to be asymptotically and or power stable

embedded structural entities in nurbs based isogeometric analysis the core idea of this article is nested parametrization in the context of isogeometric analysis the method has been inspired by trimming procedures and can be applied to different applications like local modifications and enhancements of thin walled structures or coupling of two overlying elements by embedding one in the other a remodeling for an explicit representation of the boundaries is avoided which would be contradictory to the aim of isogeometric analysis of using the original cad model the nested entity is directly linked to the super element however its element formulation is independent of the super element formulation within this article the derivation implementation and application is shown in particular for one dimensional entities embedded into 2d domains consequently the definition of an embedded curve in the surface is required and realized by using nurbs curves in the parameter space of the corresponding surface this curve with its respective predefined base vectors serves as the basis for new element formulations or adaptation of already developed element formulations which are based on the geometric description of a curve in detail an adapted formulation of the recently developed nonlinear isogeometric spatial bernoulli beam by the authors is presented in this paper furthermore those embedded curves are used for line supports and loads as well as a mass manipulation the accuracy of the proposed element formulation is verified by several benchmark examples and the potential for future applications is briefly revealed

smart octrees accurately integrating discontinuous functions in 3d abstract this paper presents an efficient and accurate method for the integration of discontinuous functions on a background mesh in three dimensions this task is important in computational mechanics applications where internal interfaces are present in the computational domain the proposed method creates boundary conforming integration subcells for composed numerical quadrature even in the presence of sharp geometric features e g edges or vertices similar to the octree procedure the algorithm subdivides the cut elements into eight octants however the octant nodes are moved onto the interface which allows for a robust resolution of the intersection topology in the element while maintaining algorithmic simplicity numerical examples demonstrate that the method is able to deliver highly accurate domain integrals with a minimal number of quadrature points further examples show that the proposed method provides a viable alternative to standard octree based approaches when combined with the finite cell method

a cut finite element method for a model of pressure in fractured media we develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks the crack has its own pressure field and can cut through

reduced order compensators via balancing and central control design for a structural control problem real time control of a physical system necessitates controllers that are low order in this article we compare two balanced truncation methods as a means of designing low order controllers for a nonlinear cable mass system the first is the standard technique of balanced truncation the second linear quadratic gaussian lqg balanced truncation can be thought of as balancing based on the controller and states that are important from the perspective of control and filter design are retained the control design applied to each reduced order model is the central controller we provide an overview of the central controller and devote attention to the design of this controller in the presence of balancing also described in this article is a method for reducing computational time in solving algebraic riccati equations for the design of low order lqg balanced controllers

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

real solutions to control approximation and factorization problems during the past decades much of finite dimensional systems theory has been generalized to infinite dimensions however there is one important flaw in this theory it guarantees only complex solutions even when the data is real we show that the standard solutions of many classical problems with real data are also real we call a possibly matrix or operator valued holomorphic function g real real symmetric if g bar z overline g z for every z we show that if such a function can be presented as g nm 1 where n m in mathcal h infty then we have g n r m r 1 where n r m r in mathcal h infty are real and weakly right coprime consequently if a real function g has a stabilizing compensator i e a function k such that begin smallmatrix i k g i end smallmatrix 1 in mathcal h infty then g has a real doubly coprime factorization and a youla parameterization of all real stabilizing controllers if a system of the form dot x ax bu y cx du or of the form x

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

weakly enforced essential boundary conditions for nurbs embedded and trimmed nurbs geometries on the basis of the finite cell method summary enforcing essential boundary conditions plays a central role in immersed boundary methods nitsche s idea has proven to be a reliable concept to satisfy weakly boundary and interface constraints we formulate an extension of nitsche s method for elasticity problems in the framework of higher order and higher continuity approximation schemes such as the b spline and non uniform rational basis spline version of the finite cell method or isogeometric analysis on trimmed geometries furthermore we illustrate a significant improvement of the flexibility and applicability of this extension in the modeling process of complex 3d geometries with several benchmark problems we demonstrate the overall good convergence behavior of the proposed method and its good accuracy we provide extensive studies on the stability of the method its influence parameters and numerical properties and a rearrangement of the numerical integration concept that in many cases reduces the numerical effort by a factor two a newly composed boundary integration concept further enhances the modeling process and allows a flexible discretization independent introduction of boundary conditions finally we present our strategy in the framework of the modeling and isogeometric analysis process of trimmed non uniform rational basis spline geometries copyright 2013 john wiley sons ltd

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

an immersed finite element method with integral equation correction summary we propose a robust immersed finite element method in which an integral equation formulation is used to enforce essential boundary conditions the solution of a boundary value problem is expressed as the superposition of a finite element solution and an integral equation solution for computing the finite element solution the physical domain is embedded into a slightly larger cartesian box shaped domain and is discretized using a block structured mesh the defect in the essential boundary conditions which occurs along the physical domain boundaries is subsequently corrected with an integral equation method in order to facilitate the mapping between the finite element and integral equation solutions the physical domain boundary is represented with a signed distance function on the block structured mesh as a result only a boundary mesh of the physical domain is necessary and no domain mesh needs to be generated except for the non boundary conforming block structured mesh the overall approach is first presented for the poisson equation and then generalized to incompressible viscous flow equations as an example of fluid structure coupling the settling of a heavy rigid particle in a closed tank is considered copyright 2010 john wiley sons ltd

an isogeometric design through analysis methodology based on adaptive hierarchical refinement of nurbs immersed boundary methods and t spline cad surfaces we explore hierarchical refinement of nurbs as a basis for adaptive isogeometric and immersed boundary analysis we use the principle of b spline subdivision to derive a local refinement procedure which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions we test hierarchical refinement of nurbs for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases using the b spline version of the finite cell method we illustrate the potential of immersed boundary methods as a seamless isogeometric design through analysis procedure for complex engineering parts defined by t spline cad surfaces specifically a ship propeller and an automobile wheel we show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features

a new least squares stabilized nitsche method for cut isogeometric analysis we derive a new stabilized symmetric nitsche method for enforcement of dirichlet boundary conditions for elliptic problems of second order in cut isogeometric analysis cutiga we consider c1 spli

support varieties and representation types for basic classical lie superalgebras abstract let be an algebraically closed field of characteristic p 3 and g a restricted lie superalgebra over we introduce the definition of restricted cohomology for g and show its cohomology ring is finitely generated provided g is a basic classical lie superalgebra as a consequence we show that the restricted enveloping algebra of a basic classical lie superalgebra g is always wild except g sl 2 or g osp 1 2 or g c 2

borel weil theorem for algebraic supergroups abstract we study the structure of an algebraic supergroup and establish the borel weil theorem for to give a systematic construction of all simple supermodules over an arbitrary field especially when has a distinguished parabolic super subgroup we show that the set of all simple supermodules of is parameterized by the set of all dominant weights for the even part of prove a super analogue of the kempf vanishing theorem and give a description of euler characteristics

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

isogeometric analysis with trimming technique for problems of arbitrary complex topology trimming technique is a powerful and efficacious way of endowing an arbitrary complex topology to cad files created by using nurbs in the present work it is shown that any complex multiply connected nurbs domain can be described by using trimming curves only isogeometric analysis for linear elasticity problems of complex topology described in this way is presented for fully communicative interaction between cad and cae a specific searching algorithm and an integration scheme of trimmed elements are introduced to utilize the iges files exported from cad system for isogeometric analysis schemes for imposing essential and traction boundary conditions on trimming curves are presented it has been demonstrated that with the presented schemes trimmed cases in any complicated situations can be successfully treated with the examples of complex topology that could be described by employing trimming curves only effectiveness and robustness of present method are demonstrated

a balanced canonical form for discrete time minimal systems using characteristic maps abstract this paper presents a balanced canonical form for the class of discrete time minimal systems the main tool is to establish a bijection between the set of minimal systems and the class of minimal discrete time asymptotically stable systems of the same dimension this characteristic map is shown to preserve system equivalence and balancing the canonical form for discrete time minimal systems is then constructed by mapping the system to its discrete time asymptotically stable counterpart via the characteristic map transforming the resulting system to lyapunov balanced canonical form and returning to the original system class by means of the inverse characteristic map

robust untangling of curvilinear meshes this paper presents a technique that allows to untangle high order curvilinear meshes the technique makes use of unconstrained optimization where element jacobians are constrained to lie in a prescribed range through moving log barriers the untangling procedure starts from a possibly invalid curvilinear mesh and moves mesh vertices with the objective of producing elements that all have bounded jacobians bounds on jacobians are computed using the results of johnen et al 2012 2013 1 2 the technique is applicable to any kind of polynomial element for surface volume hybrid or boundary layer meshes a series of examples demonstrate both the robustness and the efficiency of the technique the final example involving a time explicit computation shows that it is possible to control the stable time step of the computation for curvilinear meshes through an alternative element deformation measure

condition number analysis and preconditioning of the finite cell method the isogeometric finite cell method in which a domain is immersed in a structured background mesh suffers from conditioning problems when cells with small volume fractions occur in this contribution we establish a rigorous scaling relation between the condition number of i fcm system matrices and the smallest cell volume fraction ill conditioning stems either from basis functions being small on cells with small volume fractions or from basis functions being nearly linearly dependent on such cells based on these two sources of ill conditioning an algebraic preconditioning technique is developed which is referred to as symmetric incomplete permuted inverse cholesky sipic a detailed numerical investigation of the effectivity of the sipic preconditioner in improving i fcm condition numbers and in improving the convergence speed and accuracy of iterative solvers is presented for the poisson problem and for two and three dimensional problems in linear elasticity in which nitche s method is applied in either the normal or tangential direction the accuracy of the preconditioned iterative solver enables mesh convergence studies of the finite cell method

isogeometric analysis on v reps first results abstract inspired by the introduction of volumetric modeling via volumetric representations v reps by massarwi and elber in 2016 in this paper we present a novel approach for the construction of isogeometric numerical methods for elliptic pdes on trimmed geometries seen as a special class of more general v reps we develop tools for approximation and local re parameterization of trimmed elements for three dimensional problems and we provide a theoretical framework that fully justifies our algorithmic choices we validate our approach both on two and three dimensional problems for diffusion and linear elasticity

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

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

a functional approach to lqg balancing the paper has as its theme a circle of problems related to lqg balancing with a special emphasis on the related problems of model reduction and robust stabilization the aim is to present a unified point of view to both previously described problems the unification is achieved by focusing on the study of three functions and the relationships between them and the various operators that are associated with these functions with an arbitrary transfer function g one can associate canonically two objects the conjugate inner function which is based on the nrcf and the r which is associated with the lqg controller of the function g the approach that is taken is functional emphasizing operators a balanced realization of a stable g arises as a matrix representation of the shift realization with respect to a basis made out of suitably normalized hankel singular vectors a similar result holds for lqg balanced realizations here the underlying hankel operator we study is h r where r u m v n and u v s

lqg balancing for continuous time infinite dimensional systems in this paper we study the existence of linear quadratic gaussian lqg balanced realizations for continuous time infinite dimensional systems lqg balanced realizations are those for which the optimal cost operator for the system and its dual system are equal and diagonal the class of systems we consider is that of distributional resolvent linear systems which includes well posed linear systems as a subclass we prove the existence of lqg balanced realizations under a finite cost condition for both the system and its dual system we also show that an lqg balanced realization of a well posed transfer function is well posed we further show that approximately controllable and observable lqg balanced realizations are unique up to a unitary state space transformation finally we show that the spectrum of the product of the optimal cost operator of a system and its dual system is independent of the particular realization our method of proof shows the connections with coprime factorizations lyapunov balanced realizations and discrete time systems the main reason for studying lqg balanced realizations is that truncated lqg balanced realizations provide a good approximation of the original system we show that under certain conditions this is also true in the infinite dimensional case by proving an error bound in the gap metric

modular representations of the ortho symplectic supergroups a chevalley type integral basis for the ortho symplectic lie superalgebra is constructed the simple modules of the ortho symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified where a key combinatorial component comes from the mullineux conjecture on modular representations of the symmetric group a steinberg tensor product theorem for the ortho symplectic supergroup is also obtained

blended b spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis abstract we present a novel blended b spline method to construct bicubic tricubic splines over unstructured quadrilateral and hexahedral meshes for isogeometric analysis c 1 and truncated c 2 b spline functions are used in regular elements whereas c 0 and truncated c 1 b spline functions are adopted in boundary elements and interior irregular elements around extraordinary edges vertices the truncation mechanism is employed for a seamless transition from irregular to regular elements the resulting smoothness of the blended construction is c 2 continuous everywhere except c 0 continuous around extraordinary edges and c 1 continuous across the interface between irregular and regular elements the blended b spline construction yields consistent parameterization during refinement and exhibits optimal convergence rates spline functions in the blended construction form a non negative partition of unity are linearly independent and support bezier extraction such that the construction can be used in existing finite element frameworks several examples provide numerical evidence of optimal convergence rates

balanced canonical forms for minimal systems a normalized coprime factor approach abstract canonical forms are derived for the set of minimal systems of given order from a canonical form for a class of coinner transfer functions one of these canonical forms is in terms of so called riccati balanced coordinates the application of this work to model reduction is discussed

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

finite w superalgebras for basic lie superalgebras abstract we consider the finite w superalgebra u g f e for a basic lie superalgebra g f g f 0 g f 1 associated with a nilpotent element e g f 0 both over the field of complex numbers f c and over f k an algebraically closed field of positive characteristic in this paper we mainly present the pbw theorem for u g f e then the construction of u g f e can be understood well which in contrast with finite w algebras is divided into two cases in virtue of the parity of dim g f 1 1 this observation will be a basis of our sequent work on the dimensional lower bounds in the super kac weisfeiler property of modular representations of basic lie superalgebras cf 43 7 9

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

shell finite cell method a high order fictitious domain approach for thin walled structures abstract this article presents a generalization of the recently proposed finite cell method to thin walled structures this approach uses a combination of well known fictitious domain methods with high order hierarchical ansatz spaces known from the p version of the finite element method whereas the original concept embeds a three dimensional structure in a simple domain being meshed into a grid of cube shaped cells the extension presented in this paper applies the fictitious domain approach to a two dimensional master domain defined in the parameter plane of the geometric model implementation details are discussed and numerical benchmark problems show the high accuracy and computational efficiency of the new approach it is also remarked that the present approach can easily be carried over to isogeometric analysis opening an attractive possibility to simulate trimmed nurbs surfaces

a robust finite element method for nonhomogeneous dirichlet problems in domains with curved boundaries in this paper the authors consider a simple finite element method on an approximately polygonal domain using linear elements the dirichlet data are transferred in a natural way and the resulting linear system can be solved using multigrid techniques their analysis takes into account the change in domain and data transfer and optimal error estimates are obtained that are robust in the regularity of the boundary data provided they are at least square integrable it is proved that the natural extension of this finite element approximation to the original domain is optimal order accurate

subdivision stabilised immersed b spline finite elements for moving boundary flows an immersed finite element method is presented to compute flows with complex moving boundaries on a fixed cartesian grid the viscous incompressible fluid flow equations are discretized with b spline basis functions the two scale relation for b splines is used to implement an elegant and efficient technique to satisfy the lbb condition on non grid aligned fluid domains and at moving boundaries the boundary conditions are enforced with a consistent penalty method as originally proposed by nitsche in addition a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut cells the versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations

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 cut finite element method for coupled bulk surface problems on time dependent domains in this contribution we present a new computational method for coupled bulk surface problems on time dependent domains the method is based on a space time formulation using discontinuous piecewise linear elements in time and continuous piecewise linear elements in space on a fixed background mesh the domain is represented using a piecewise linear level set function on the background mesh and a cut finite element method is used to discretize the bulk and surface problems in the cut finite element method the bilinear forms associated with the weak formulation of the problem are directly evaluated on the bulk domain and the surface defined by the level set essentially using the restrictions of the piecewise linear functions to the computational domain in addition a stabilization term is added to stabilize convection as well as the resulting algebraic system that is solved in each time step we show in numerical examples that the resulting method is accurate and stable and results in well conditioned algebraic systems independent of the position of the interface relative to the background mesh

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

stable isogeometric analysis of trimmed geometries abstract we explore extended b splines as a stable basis for isogeometric analysis with trimmed parameter spaces the stabilization is accomplished by an appropriate substitution of b splines that may lead to ill conditioned system matrices the construction for non uniform knot vectors is presented the properties of extended b splines are examined in the context of interpolation potential and linear elasticity problems and excellent results are attained the analysis is performed by an isogeometric boundary element formulation using collocation it is argued that extended b splines provide a flexible and simple stabilization scheme which ideally suits the isogeometric paradigm

linkage principle for ortho symplectic supergroups abstract the purpose of the paper is to derive linkage principle for modular representations of ortho symplectic supergroups we follow the approach of doty and investigate in detail the representation theory of the ortho symplectic group s p o 2 1 and that of its frobenius thickening using the description of flags and adjacent borel supersubgroups we derive first the strong linkage for the frobenius thickening g r t of the ortho symplectic supergroup g of type s p o 2 m 2 n 1 and s p o 2 m 2 n based on this we derive the linkage principle for ortho symplectic supergroups s p o 2 m 2 n 1 and s p o 2 m 2 n

super duality and irreducible characters of ortho symplectic lie superalgebras we formulate and establish a super duality which connects parabolic categories o for the ortho symplectic lie superalgebras and classical lie algebras of bcd types this provides a complete and conceptual solution of the irreducible character problem for the ortho symplectic lie superalgebras in a parabolic category o which includes all finite dimensional irreducible modules in terms of classical kazhdan lusztig polynomials

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

truncated t splines fundamentals and methods in this paper we present truncated t splines as a new type of t splines suitable for both geometric design and analysis supporting highly localized refinement truncated t spline basis functions are piece wise polynomials that are linearly independent and form a partition of unity refinement of truncated t splines produces nested spline spaces furthermore we study truncated t splines and local refinement on the general domain 2 manifold with extraordinary points in the t mesh g1g1 continuity is attained around extraordinary points by properly capping quartic bezier patches where a constrained optimization problem is solved in the end we study benchmark problems using truncated t splines in the context of isogeometric analysis we also apply truncated t splines to complex geometries to show the smooth surfaces and simulation results under local refinement

linear quadratic gaussian balancing for discrete time infinite dimensional linear systems in this paper we study the existence of linear quadratic gaussian lqg balanced realizations for discrete time infinite dimensional systems lqg balanced realizations are those for which the smallest nonnegative self adjoint solutions of the control and filter riccati equations are equal we show that the control filter riccati equation has a nonnegative self adjoint solution if and only if the system is output input stabilizable our main result is that the transfer function of a discrete time linear system has an approximately controllable and observable lqg balanced realization iff it has an input and output stabilizable realization the corresponding control and filter riccati equations have unique nonnegative self adjoint solutions moreover approximately controllable and observable lqg balanced realizations are unique up to a unitary state space transformation finally we show that the spectrum of the product of the smallest nonnegative self adjoint solutions of the control and filter riccati equations is independent of the particular realization

from geometric design to numerical analysis a direct approach using the finite cell method on constructive solid geometry abstract during the last ten years increasing efforts were made to improve and simplify the process from computer aided design cad modeling to a numerical simulation it has been shown that the transition from one model to another i e the meshing is a bottle neck several approaches have been developed to overcome this time consuming step e g isogeometric analysis iga which applies the shape functions used for the geometry description typically b splines and nurbs directly to the numerical analysis in contrast to iga which deals with boundary represented models b rep our approach focuses on parametric volumetric models such as constructive solid geometries csg these models have several advantages as their geometry description is inherently watertight and they provide a description of the models interior to be able to use the explicit mathematical description of these models we employ the finite cell method fcm herein the only necessary input is a reliable statement whether an integration point lies inside or outside of the geometric model this paper mainly discusses such point in membership tests on various geometric objects like sweeps and lofts as well as several geometric operations such as filleting or chamfering we demonstrate that based on the information of the construction method of these objects the point in membership test can be carried out efficiently and robustly

a new set of invariants for linear systems application to reduced order compensator design a new set of invariants for linear systems weighting the contribution of each state component to the inherent closed loop lqg behavior of the system is presented together with applications to model order reduction and reduced order compensator design

isogeometric analysis with bezier tetrahedra abstract this paper presents an approach for isogeometric analysis of 3d objects using rational bezier tetrahedral elements in this approach both the geometry and the physical field are represented by trivariate splines in bernstein bezier form over the tetrahedrangulation of a 3d geometry given a nurbs represented geometry either untrimmed or trimmed we first convert it to a watertight geometry represented by rational triangular bezier splines rtbs for trimmed geometries a compatible subdivision scheme is developed to guarantee the watertightness the rtbs geometry preserves exactly the original nurbs surfaces except for an interface layer between trimmed surfaces where controlled approximation occurs from the watertight rtbs geometry a bezier tetrahedral partition is generated automatically by imposing continuity constraints on bezier ordinates of the elements we obtain a set of global c r smooth basis functions and use it as the basis for analysis numerical examples demonstrate that our method achieves optimal convergence in c r spaces and can handle complicated geometries

finite element approximation of the laplace beltrami operator on a surface with boundary we develop a finite element method for the laplace beltrami operator on a surface with boundary and nonhomogeneous dirichlet boundary conditions the method is based on a triangulation of the surfa

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

geometrical validity of curvilinear finite elements in this paper we describe a way to compute accurate bounds on jacobian determinants of curvilinear polynomial finite elements our condition enables to guarantee that an element is geometrically valid i e that its jacobian determinant is strictly positive everywhere in its reference domain it also provides an efficient way to measure the distortion of curvilinear elements the key feature of the method is to expand the jacobian determinant using a polynomial basis built using bezier functions that has both properties of boundedness and positivity numerical results show the sharpness of our estimates