imposing dirichlet boundary conditions in the extended finite element method this paper is devoted to the imposition of dirichlet type conditions within the extended finite element method x fem this method allows one to easily model surfaces of discontinuity or domain boundaries on a mesh not necessarily conforming to these surfaces imposing neumann boundary conditions on boundaries running through the elements is straightforward and does preserve the optimal rate of convergence of the background mesh observed numerically in earlier papers on the contrary much less work has been devoted to dirichlet boundary conditions for the x fem or the limiting case of stiff boundary conditions in this paper we introduce a strategy to impose dirichlet boundary conditions while preserving the optimal rate of convergence the key aspect is the construction of the correct lagrange multiplier space on the boundary as an application we suggest to use this new approach to impose precisely zero pressure on the moving resin front in resin transfer moulding rtm process while avoiding remeshing the case of inner conditions is also discussed as well as two important practical cases material interfaces and phase transformation front capturing copyright 2006 john wiley sons ltd

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

geometrically accurate efficient and flexible quadrature techniques for the tetrahedral finite cell method abstract we illustrate the importance of geometrically accurate volume quadrature for obtaining optimal accuracy with non boundary fitted finite element discretizations when the problem domain is defined by sharp boundaries we consider the tetrahedral finite cell method tetfcm and replace its recursive subdivision based integration approach with geometrically accurate quadrature rules that emanate from higher order geometric parametrizations of cut tetrahedral elements the element wise parametrization procedure relies on the identification of the intersection topology and a series of higher order mappings based on lagrange polynomials we demonstrate with several 3d examples that geometrically faithful local parametrization ensures optimal accuracy while significantly reducing the number of quadrature points with respect to recursive subdivision on the other hand we highlight the strength of subdivision quadrature in the context of a patient specific workflow for the simulation based performance analysis of coupled bone implant configurations in particular we show that accuracy flexibility and computational efficiency of the tetfcm critically depend on flexibly applying the two different quadrature variants for fuzzy imaging data and sharp boundary representations respectively

an embedded dirichlet formulation for 3d continua this paper presents a new approach for imposing dirichlet conditions weakly on non fitting finite element meshes such conditions also called embedded dirichlet conditions are typically but not exclusively encountered when prescribing dirichlet conditions in the context of the extended finite element method xfem the methods key idea is the use of an additional stress field as the constraining lagrange multiplier function the resulting mixed hybrid formulation is applicable to 1d 2d and 3d problems the method does not require stabilization for the lagrange multiplier unknowns and allows the complete condensation of these unknowns on the element level furthermore only non zero diagonal terms are present in the tangent stiffness which allows the straight forward application of state of the art iterative solvers like algebraic multigrid amg techniques within this paper the method is applied to the linear momentum equation of an elastic continuum and to the transient incompressible navier stokes equations steady and unsteady benchmark computations show excellent agreement with reference values the general formulation presented in this paper can also be applied to other continuous field problems

stabilized finite element methods for the velocity pressure stress formulation of incompressible flows abstract formulated in terms of velocity pressure and the extra stress tensor the incompressible navier stokes equations are discretized by stabilized finite element methods the stabilized methods proposed are analyzed for a linear model and extended to the navier stokes equations the numerical tests performed confirm the good stability characteristics of the methods these methods are applicable to various combinations of interpolation functions including the simplest equal order linear and bilinear elements

the enriched space time finite element method est for simultaneous solution of fluid structure interaction the paper introduces a weighted residual based approach for the numerical investigation of the interaction of fluid flow and thin flexible structures the presented method enables one to treat strongly coupled systems involving large structural motion and deformation of multiple flow immersed solid objects the fluid flow is described by the incompressible navier stokes equations the current configuration of the thin structure of linear elastic material with non linear kinematics is mapped to the flow using the zero iso contour of an updated level set function the formulation of fluid structure and coupling conditions uniformly uses velocities as unknowns the integration of the weak form is performed on a space time finite element discretization of the domain interfacial constraints of the multi field problem are ensured by distributed lagrange multipliers the proposed formulation and discretization techniques lead to a monolithic algebraic system well suited for strongly coupled fluid structure systems embedding a thin structure into a flow results in non smooth fields for the fluid based on the concept of the extended finite element method the space time approximations of fluid pressure and velocity are properly enriched to capture weakly and strongly discontinuous solutions this leads to the present enriched space time est method numerical examples of fluid structure interaction show the eligibility of the developed numerical approach in order to describe the behavior of such coupled systems the test cases demonstrate the application of the proposed technique to problems where mesh moving strategies often fail copyright 2007 john wiley sons ltd

direct least square fitting of hyperellipsoids this paper presents two new computationally efficient direct methods for fitting n dimensional ellipsoids to noisy data they conduct the fitting by minimizing the algebraic distance in subject to suitable quadratic constraints the hyperellipsoid specific hes method is an elaboration of existing ellipse and 3d ellipsoid specific fitting methods it is shown that hes is ellipsoid specific in n dimensional space a limitation of hes is that it may provide biased fitting results with data originating from an ellipsoid with a large ratio between the longest and shortest main axis the sum of discriminants sod method does not have such a limitation the constraint used by sod rejects a subset of non ellipsoidal quadrics which enables a high tendency to produce ellipsoidal solutions moreover a regularization technique is presented to force the solutions towards ellipsoids with sod the regularization technique is compatible also with several existing 2d and 3d fitting methods the new methods are compared through extensive numerical experiments with n dimensional variants of three commonly used direct fitting approaches for quadratic surfaces the results of the experiments imply that in addition to the superior capability to create ellipsoidal solutions the estimation accuracy of the new methods is better or equal to that of the reference approaches

unique representation of an inverse kinetic theory for incompressible newtonian fluids abstract fundamental aspects of inverse kinetic theories for the incompressible navier stokes equations m tessarotto m ellero rgd24 italy july 10 16 2004 aip conf proc 762 2005 108 m ellero m tessarotto physica a 355 2005 233 include the possibility of defining uniquely the kinetic equation underlying such models and furthermore the construction of a kinetic theory implying also the energy equation the latter condition is consistent with the requirement that fluid fields result classical solutions of the fluid equations these issues appear of potential relevance both from the mathematical viewpoint and for the physical interpretation of the theory purpose of this work is to prove that under suitable prescriptions the inverse kinetic theory can be determined to satisfy such requirements

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

a bubble stabilized finite element method for dirichlet constraints on embedded interfaces we examine a bubble stabilized finite element method for enforcing dirichlet constraints on embedded interfaces by embedded we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mesh as such the robust imposition of dirichlet constraints using a lagrange multiplier field is not trivial to focus issues we consider a simple one sided problem that is representative of a wide class of evolving interface problems the bulk field is decomposed into coarse and fine scales giving rise to coarse scale and fine scale one sided sub problems the fine scale solution is approximated with bubble functions permitting static condensation and giving rise to a stabilized form bearing strong analogy with a classical method importantly the method is simple to implement readily extends to multiple dimensions obviates the need to specify any free stabilization parameters and can lead to a symmetric positive definite system of equations the performance of the method is then examined through several numerical examples the accuracy of the lagrange multiplier is compared to results obtained using a local version of the domain integral method the variational multiscale approach proposed herein is shown to both stabilize the lagrange multiplier and improve the accuracy of the post processed fluxes copyright 2006 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 semi lagrangean time integration approach for extended finite element methods many computational problems incorporate discontinuities that evolve in time the extendend finite element method xfem is able to represent discontinuities sharply on fixed arbitrary meshes but numerical difficulties arise if these discontinuities move in time we point out that this issue is crucial for interface problems with strongly discontinuous fields on fixed grids a method using semi lagrangean techniques is proposed to adequately handle time integration based on finite difference schemes in the context of the xfem the basic idea is to adapt previous numerical solutions to the current interface position by tracking back virtual lagrangean particles to their previous positions where an appropriate solution can be extrapo lated from a smooth field convergence properties of the proposed method in time and space are thoroughly studied for two one dimensional model problems finally the method is applied to the particularly challenging problem of premixed combustion where the discontinuity appears at the flame front separating the burnt from the unburnt gases a two dimensional and a three dimensional expanding flame demonstrates that the method is sufficiently accurate to retain the properties of the overall nitsche type formulation for interface problems with embedded strong discontinuities

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

on strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method we consider a problem stemming from recent models of phase transitions in stimulus responsive hydrogels wherein a sharp interface separates swelled and collapsed phases extended finite element methods that approximate the local solution with an enriched basis such that the mesh need not explicitly fit the interface geometry are emphasized attention is focused on the weak enforcement of the normal configurational force balance and various options for evaluating the jump in the normal component of the solute flux at the interface we show that as the reciprocal interfacial mobility vanishes it plays the role of a penalty parameter enforcing a pure dirichlet constraint eventually triggering oscillations in the interfacial velocity we also examine alternative formulations employing a lagrange multiplier to enforce this constraint it is shown that the most convenient choice of basis for the lagrange multiplier results in oscillations in the multiplier field and a decrease in accuracy and rate of convergence in local error norms suggesting a lack of stability in the discrete formulation under such conditions neither the direct evaluation of the gradient of the approximation at the phase interface nor the interpretation of the lagrange multiplier field provide a robust means to obtain the jump in the normal component of solute flux fortunately the adaptation and use of local domain integral methodologies considerably improves the flux evaluations several example problems are presented to compare and contrast the various techniques and methods

residual free bubbles for embedded dirichlet problems abstract we examine a stabilized method employing residual free bubbles for enforcing dirichlet constraints on embedded finite element interfaces in particular we focus attention on problems where the underlying mesh is not explicitly fitted to the geometry of the interface the residual free bubble problem is derived for a simple case and extensions are discussed we show that under certain conditions stabilization only requires knowledge of the residual free bubble on the interface we then examine methods to approximate the residual free bubble a series of benchmark tests are used to demonstrate the accuracy and robustness of the method comparisons are made to nitsche s method employing an eigenvalue estimate for the global stability parameter particular emphasis is placed on the accuracy of flux evaluations on the interface finally we employ the method to simulate an evolving interface problem motivated by resin transfer molding

a new petrov galerkin smoothed aggregation preconditioner for nonsymmetric linear systems we propose a new variant of smoothed aggregation sa suitable for nonsymmetric linear systems the new algorithm is based on two key generalizations of sa restriction smoothing and local damping restriction smoothing refers to the smoothing of a tentative restriction operator via a damped jacobi like iteration restriction smoothing is analogous to prolongator smoothing in standard sa and in fact has the same form as the transpose of prolongator smoothing when the matrix is symmetric local damping refers to damping parameters used in the jacobi like iteration in standard sa a single damping parameter is computed via an eigenvalue computation here local damping parameters are computed by considering the minimization of an energy like quantity for each individual grid transfer basis function numerical results are given showing how this method performs on highly nonsymmetric systems

a weakly compressible hybridizable discontinuous galerkin formulation for fluid structure interaction problems abstract a scheme for the solution of fluid structure interaction fsi problems with weakly compressible flows is proposed in this work a novel hybridizable discontinuous galerkin hdg method is derived for the discretization of the fluid equations while the standard continuous galerkin cg approach is adopted for the structural problem the chosen hdg solver combines robustness of discontinuous galerkin dg approaches in advection dominated flows with higher order accuracy and efficient implementations two coupling strategies are examined in this contribution namely a partitioned dirichlet neumann scheme in the context of hybrid hdg cg discretizations and a monolithic approach based on nitsche s method exploiting the definition of the numerical flux and the trace of the solution to impose the coupling conditions numerical experiments show optimal convergence of the hdg and cg primal and mixed variables and superconvergence of the postprocessed fluid velocity the robustness and the efficiency of the proposed weakly compressible formulation in comparison to a fully incompressible one are also highlighted on a selection of two and three dimensional fsi benchmark problems

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

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

arbitrary branched and intersecting cracks with the extended finite element method summary extensions of a new technique for the nite element modelling of cracks with multiple branches multiple holes and cracks emanating from holes are presented this extended nite element method x fem allows the representation of crack discontinuities and voids independently of the mesh a standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method a methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed computation of the stress intensity factors sif in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique copyright 2000 john wiley sons ltd

the hp d adaptive finite cell method for geometrically nonlinear problems of solid mechanics summary the finite cell method fcm combines the fictitious domain approach with the p version of the finite element method and adaptive integration for problems of linear elasticity it offers high convergence rates and simple mesh generation irrespective of the geometric complexity involved this article presents the integration of the fcm into the framework of nonlinear finite element technology however the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map as a consequence of the weak penalization nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries leading to a low algebraic rate of convergence therefore the fcm approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp d method which synergetically uses the h adaptivity of the integration scheme numerical experiments show that the hp d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map the hp d adaptive fcm is thus able to restore high convergence rates for the geometrically nonlinear case while preserving the easy meshing property of the original fcm accuracy and performance of the present scheme are demonstrated by several benchmark problems in one two and three dimensions and the nonlinear simulation of a complex foam sample copyright 2011 john wiley sons ltd

on methods for stabilizing constraints over enriched interfaces in elasticity summary enriched finite element approaches such as the extended finite element method provide a framework for constructing approximations to solutions of non smooth problems internal features such as boundaries are represented in such methods by using discontinuous enrichment of the standard finite element basis within such frameworks however imposition of interface constraints and or constitutive relations can cause unexpected difficulties depending upon how relevant fields are interpolated on un gridded interfaces this work address the stabilized treatment of constraints in an enriched finite element context both the lagrange multiplier and penalty enforcement of tied constraints for an arbitrary boundary represented in an enriched finite element context can lead to instabilities and artificial oscillations in the traction fields we demonstrate two alternative variational methods that can be used to enforce the constraints in a stable manner in a bubble stabilized approach fine scale degrees of freedom are added over elements supporting the interface the variational form can be shown to have a similar form to a second approach we consider nitsche s method with the exception that the stabilization terms follow directly from the bubble functions in this work we examine alternative variational methods for enforcing a tied constraint on an enriched interface in the context of two dimensional elasticity we examine several benchmark problems in elasticity and show that only nitsche s method and the bubble stabilization approach produce stable traction fields over internal boundaries we also demonstrate a novel difference between the penalty method and nitsche s method in that the latter passes the patch test exactly regardless of the stabilization parameter s magnitude results for more complicated geometries and triple interface junctions are also presented copyright 2008 john wiley sons ltd

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

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 mixed hybrid dirichlet formulation for wall bounded flow problems including turbulent flow abstract in this study a new method for the weak imposition of dirichlet boundary conditions in convection dominated convection diffusion and wall bounded turbulent flow problems is developed it is based on an embedded dirichlet formulation which utilises an additional discontinuous stress field for imposing boundary conditions values at outflow boundaries may not be sufficiently controllable on underresolved meshes e g when using nitsche s method for weak enforcement of dirichlet boundary conditions hence a consistent modification of an earlier proposed constant parameter embedded dirichlet formulation that allows to regain control if required is introduced a separate treatment of boundary conditions in wall normal and tangential direction is enabled this split is physically motivated and it turns out to be crucial for a successful application of the method on the one hand it allows for including a formulation based on the law of the wall in tangential direction on the other hand a consistent modification derived from theoretical considerations for convection diffusion problems is applied in wall normal direction preventing unphysical penetration of walls numerical results obtained for turbulent channel flow at modest friction reynolds number re 395 employing meshes with and without adequate resolution of the boundary layer are presented superior performance of the proposed method compared to strongly imposed boundary conditions is demonstrated by an error reduction of up to 50 for mean velocity results in the core of the channel on coarse discretisations

quadrature schemes for arbitrary convex concave volumes and integration of weak form in enriched partition of unity methods abstract quadrature schemes are constructed based on moment fitting equations to integrate polynomials over arbitrary convex concave volumes that arise among others in enriched partition of unity finite element methods epum the building block of the scheme involves the divergence theorem of multivariable calculus which is used to integrate the base functions an efficient and robust point distribution method is proposed and the quadrature weights at the corresponding points are obtained by solving a least squares problem the method is applied initially to integrate given polynomial functions over complex volumes and further to simulate simple three dimensional fluid dynamic problems which involve very complex volumes when solved with epum accuracy of the present quadrature construction scheme is demonstrated by comparing the results with the available exact numerical solutions and efficiency of the method is proved by comparing the computational time with that of the widely used tessellation method

a stabilized nitsche cut finite element method for the oseen problem abstract we provide the numerical analysis for a nitsche based cut finite element formulation for the oseen problem which has been originally presented for the incompressible navier stokes equations by schott and wall 2014 and allows the boundary of the domain to cut through the elements of an easy to generate background mesh the formulation is based on the continuous interior penalty cip method of burman et al 2006 which penalizes jumps of velocity and pressure gradients over inter element faces to counteract instabilities arising for high local reynolds numbers and the use of equal order interpolation spaces for the velocity and pressure since the mesh does not fit the boundary dirichlet boundary conditions are imposed weakly by a stabilized nitsche type approach the addition of cip like ghost penalties in the boundary zone allows to prove that our method is inf supstable and to derive optimal order a priori error estimates in an energy type norm irrespective of how the boundary cuts the underlying mesh all applied stabilization techniques are developed with particular emphasis on low and high reynolds numbers two and three dimensional numerical examples corroborate the theoretical findings finally the proposed method is applied to solve the transient incompressible navier stokes equations on a complex geometry

fast multidimensional ellipsoid specific fitting by alternating direction method of multipliers many problems in computer vision can be formulated as multidimensional ellipsoid specific fitting which is to minimize the residual error such that the underlying quadratic surface is a multidimensional ellipsoid in this paper we present a fast and robust algorithm for solving ellipsoid specific fitting directly our method is based on the alternating direction method of multipliers which does not introduce extra positive semi definiteness constraints the computation complexity is thus significantly lower than those of semi definite programming sdp based methods more specifically to fit n data points into a p dimensional ellipsoid our complexity is o p 6 np 4 o p 3 where the former o results from preprocessing data once while that of the state of the art sdp method is o p 6 np 4 n frac 3 2 p 2 for each iteration the storage complexity of our algorithm is about frac 1 2 np 2 which is at most 1 4 of those of sdp methods extensive experiments testify to the great speed and accuracy advantages of our method over the state of the art approaches the implementation of our method is also much simpler than sdp based methods

an embedded mesh method in a multiple material ale abstract a new approach for treating the mechanical interactions of overlapping finite element meshes is presented referred to as embedded mesh methods here these overlapping mesh methods typically include a foreground solid mesh and a background euler fluid grid or solid mesh a number of different approaches have been used in previous work to characterize the interactions of the background and foreground meshes at the interface lagrange multipliers are well suited to enforce the continuity constraints but care must be taken such that the resulting formulation is stable several lagrange multiplier techniques are examined in this work and applied to coupling solid meshes and fluid structure interaction type problems in addition details regarding implementation in a two step multi material arbitrary lagrangian eulerian ale code are presented example problems demonstrate convergence and applicability to a range of problems in particular the fluid structure interaction examples focus on blast applications

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

an extended finite element method lagrange multiplier based approach for fluid structure interaction abstract this paper presents a new fixed grid fluid structure interaction scheme that can be applied to the interaction of most general structures with incompressible flow it is based on an extended finite element method xfem based strategy the extended eulerian fluid field and the lagrangian structural field are partitioned and iteratively coupled using lagrange multiplier techniques for non matching grids the approach allows the simulation of the interaction of thin and bulky structures exhibiting large deformations finally qualitative examples and a benchmark computation demonstrate key features and accuracy of the method

the non symmetric nitsche method for the parameter free imposition of weak boundary and coupling conditions in immersed finite elements abstract we explore the use of the non symmetric nitsche method for the weak imposition of boundary and coupling conditions along interfaces that intersect through a finite element mesh in contrast to symmetric nitsche methods it does not require stabilization and therefore does not depend on the appropriate estimation of stabilization parameters we first review the available mathematical background recollecting relevant aspects of the method from a numerical analysis viewpoint we then compare accuracy and convergence of symmetric and non symmetric nitsche methods for a laplace problem a kirchhoff plate and in 3d elasticity our numerical experiments confirm that the non symmetric method leads to reduced accuracy in the l 2 error but exhibits superior accuracy and robustness for derivative quantities such as diffusive flux bending moments or stress based on our numerical evidence the non symmetric nitsche method is a viable alternative for problems with diffusion type operators in particular when the accuracy of derivative quantities is of primary interest

the finite cell method for linear thermoelasticity the recently introduced finite cell method fcm combines the fictitious domain idea with the benefits of high order finite elements while previous publications concentrated on single field applications this paper demonstrates that the advantages of the method carry over to the multi physical context of linear thermoelasticity the ability of the method to converge with exponential rates is illustrated in detail with a benchmark problem a second example shows that the finite cell method correctly captures the thermoelastic state of a complex problem from engineering practice both examples additionally verify that also for two field problems dirichlet boundary conditions can be weakly imposed on non conforming meshes by the proposed extension of nitsche s method

the 3l algorithm for fitting implicit polynomial curves and surfaces to data we introduce a completely new approach to fitting implicit polynomial geometric shape models to data and to studying these polynomials the power of these models is in their ability to represent nonstar complex shapes in two 2d and three dimensional 3d data to permit fast repeatable fitting to unorganized data which may not be uniformly sampled and which may contain gaps to permit position invariant shape recognition based on new complete sets of euclidean and affine invariants and to permit fast stable single computation pose estimation the algorithm represents a significant advancement of implicit polynomial technology for four important reasons first it is orders of magnitude taster than existing fitting methods for implicit polynomial 2d curves and 3d surfaces and the algorithms for 2d and 3d are essentially the same second it has significantly better repeatability numerical stability and robustness than current methods in dealing with noisy deformed or missing data third it can easily fit polynomials of high such as 14th or 16th degree fourth additional linear constraints can be easily incorporated into the fitting process and general linear vector space concepts apply

a localized mixed hybrid method for imposing interfacial constraints in the extended finite element method xfem the paper proposes an approach for the imposition of constraints along moving or fixed immersed interfaces in the context of the extended finite element method an enriched approximation space enables consistent representation of strong and weak discontinuities in the solution fields along arbitrarily shaped material interfaces using an unfitted background mesh the use of lagrange multipliers or penalty methods is circumvented by a localized mixed hybrid formulation of the model equations in a defined region in the vicinity of the interface the original problem is re stated in its auxiliary formulation the availability of the auxiliary variable enables the consideration of a variety of interface constraints in the weak form the contribution discusses the weak imposition of dirichlet and neumann type interface conditions as well as continuity requirements not fulfilled a priori by the enriched approximation the properties of the proposed approach applied to two dimensional linear scalar and vector valued elliptic problems are investigated by studying the convergence behavior

orthogonal distance fitting of implicit curves and surfaces dimensional model fitting finds its applications in various fields of science and engineering and is a relevant subject in computer machine vision and coordinate metrology in this paper we present two new fitting algorithms distance based and coordinate based algorithm for implicit surfaces and plane curves which minimize the square sum of the orthogonal error distances between the model feature and the given data points each of the two algorithms has its own advantages and is to be purposefully applied to a specific fitting task considering the implementation and memory space cost and possibilities of observation weighting by the new algorithms the model feature parameters are grouped and simultaneously estimated in terms of form position and rotation parameters the form parameters determine the shape of the model feature and the position rotation parameters describe the rigid body motion of the model feature the proposed algorithms are applicable to any kind of implicit surface and plane curve in this paper we also describe algorithm implementation and show various examples of orthogonal distance fit

estimation of planar curves surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation the author addresses the problem of parametric representation and estimation of complex planar curves in 2 d surfaces in 3 d and nonplanar space curves in 3 d curves and surfaces can be defined either parametrically or implicitly with the latter representation used here a planar curve is the set of zeros of a smooth function of two variables x y a surface is the set of zeros of a smooth function of three variables x y z and a space curve is the intersection of two surfaces which are the set of zeros of two linearly independent smooth functions of three variables x y z for example the surface of a complex object in 3 d can be represented as a subset of a single implicit surface with similar results for planar and space curves it is shown how this unified representation can be used for object recognition object position estimation and segmentation of objects into meaningful subobjects that is the detection of interest regions that are more complex than high curvature regions and hence more useful as features for object recognition

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 eulerian lagrangian method for fluid structure interaction based on level sets abstract we describe a method for fluid structure interaction with the interface and free surfaces defined by level sets the fluid is treated by an eulerian mesh whereas the solid or structure by a lagrangian mesh the level set method provides a compact framework for writing the weak form and for developing and computing the discretized equations lagrange multiplier methods and penalty methods are used to couple the fluid and structure results are presented for a few compressible fluid problems representative of high pressure waves

stability of incompressible formulations enriched with x fem abstract the treatment of near incompressibility is a major concern for applications involving rubber like materials or when important plastic flows occurs as in forming processes the use of mixed finite element methods is known to prevent the locking of the finite element approximation in the incompressible limit however it also introduces a critical condition for the stability of the formulation called the inf sup or lbb condition recently the finite element method has evolved with the introduction of the partition of unity method the extended finite element method x fem uses the partition of unity method to remove the need to mesh physical surfaces or to re mesh them as they evolve the enrichment of the displacement field makes it possible to treat surfaces of discontinuity inside finite elements in this paper some strategies are proposed for the enrichment of low order mixed finite element approximations in the incompressible setting the case of holes material interfaces and cracks are considered numerical examples show that for well chosen enrichment strategies the finite element convergence rate is preserved and the inf sup condition is passed

a fast algorithm for multidimensional ellipsoid specific fitting by minimizing a new defined vector norm of residuals using semidefinite programming a quadratic surface in n dimensional space is defined as the locus of zeros of a quadratic polynomial the quadratic polynomial may be compactly written in notation by an n 1 vector and a real symmetric matrix of order n 1 where the vector represents homogenous coordinates of an n d point and the symmetric matrix is constructed from the quadratic coefficients if an n d quadratic surface is an n d ellipsoid the leading n times n principal submatrix of the symmetric matrix would be positive or opposite definite as we know to impose a matrix being positive or opposite definite perhaps the best choice may be to employ semidefinite programming sdp from such straightforward and intuitive knowledge in the literature until 2002 calafiore first proposed a feasible method for multidimensional ellipsoid specific fitting using sdp which minimizes the 2 norm of the algebraic residual vector however the runtime of the method is significantly long and memory is often out when the number of fitted points is greater than several thousand in this paper we propose a fast and easily implemented algorithm for multidimensional ellipsoid specific fitting by minimizing a new defined vector norm of the algebraic residual vector using sdp which drastically decreases the size of the sdp problem while preserving accuracy the proposed fast method can handle several million fitted points without any difficulty

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

optimal estimation of contour properties by cross validated regularization the problem of estimating the properties of smooth continuous contours from discrete noisy samples is used as vehicle to demonstrate the robustness of cross validated regularization applied to a vision problem a method for estimation of contour properties based on smoothing spline approximations is presented generalized cross validation is to devise an automatic algorithm for finding the optimal value of the smoothing regularization parameter from the data the cross validated smoothing splines are then used to obtain optimal estimates of the derivatives of quantized contours experimental results are presented which demonstrate the robustness of the method applied to the estimation of curvature of quantized contours under variable scale rotation and partial occlusion these results suggest the application of generalized cross validation to other computer vision algorithms involving regularization

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100