a critical evaluation of the resolution properties of b spline and compact finite difference methods resolution properties of b spline and compact finite difference schemes are compared using fourier analysis in periodic domains and tests based on solution of the wave and heat equations in finite domains with uniform and nonuniform grids results show that compact finite difference schemes have a higher convergence rate and in some cases better resolution however b spline schemes have a more straightforward and robust formulation particularly near boundaries on nonuniform meshes

isogeometric boundary element analysis using unstructured t splines we couple collocated isogeometric boundary element methods and unstructured analysis suitable t spline surfaces for linear elastostatic problems we extend the definition of analysis suitable t splines to encompass unstructured control grids unstructured meshes and develop basis functions which are smooth rational polynomials defined in terms of the bezier extraction framework and which pass standard patch tests we then develop a collocation procedure which correctly accounts for sharp edges and corners extraordinary points and t junctions this approach is applied to several three dimensional problems including a real world t spline model of a propeller we believe this work clearly illustrates the power of combining new analysis suitable computer aided design technologies with established analysis methodologies in this case the boundary element method

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

dispersive and dissipative behaviour of high order discontinuous galerkin finite element methods the dispersive and dissipative properties of hp version discontinuous galerkin finite element approximation are studied in three different limits for the small wave number limit hk 0 we show the discontinuous galerkin gives a higher order of accuracy than the standard galerkin procedure thereby confirming the conjectures of hu and atkins j comput phys 182 2 2002 516 if the mesh is fixed and the order p is increased it is shown that the dissipation and dispersion errors decay at a super exponential rate when the order p is much larger than hk finally if the order is chosen so that 2p 1 hk for some fixed constant 1 then it is shown that an exponential rate of decay is obtained

a 3d isogeometric be fe analysis with dynamic remeshing for the simulation of a deformable particle in shear flows abstract a three dimensional isogeometric coupled boundary element and finite element approach based on analysis suitable t splines is developed for the simulation of deformable capsules suspended in shear flows boundary element analysis is used to solve the fluid stokes equation whereas the hydrodynamic membrane load is computed via isogeometric analysis under the assumption that the membrane is a hyper elastic thin shell with negligible bending resistance the smoothness of the t spline basis functions accommodate large deformations of the capsule without the need for additional smoothing techniques and can be used to accurately compute the membrane load a balanced distribution of membrane elements can be constructed using an unstructured locally refined mesh these properties are coupled with an adaptive temporal implicit integration scheme several benchmark examples are solved to illustrate the accuracy and potential of the method the approach is then applied to simulate the dynamics of a capsule in a real geometry of a brain capillary

consistent treatment of boundaries with mortar contact formulations using dual lagrange multipliers abstract computational modelling of contact problems raises two basic questions which method should be used to enforce the contact conditions and how should this method be discretised the most popular enforcement methods are the lagrange multiplier method the penalty method and combinations of these two a frequently used discretisation method is the so called node to segment approach however this approach might lead to problems like jumps in contact forces loss of convergence or failure to pass the patch test thus in the last few years several segment to segment contact algorithms based on the mortar method were proposed combination of a mortar discretisation with a penalty based enforcement of the contact conditions leads to unphysical penetrations on the other hand a lagrange multiplier mortar method requires additional unknowns hence condensation of the lagrange multipliers is desirable to preserve the initial size of the system of equations this can be achieved by interpolating the lagrange multipliers with so called dual shape functions discretising two contacting bodies leads to opposed contact surface representations of finite element edges called slave and master elements respectively in current versions of dual lagrange multiplier mortar formulations an inconsistency at the boundary appears when only a part of a slave element instead of the entire element belongs to the contact area we present a modified definition of the dual shape functions in such slave elements the basic idea is to construct dual shape functions that fulfill the so called biorthogonality condition within the contact area this leads to consistent mortar matrices also in the boundary region to avoid ill conditioning of the stiffness matrix the modified mortar matrices are weighted with appropriate weighting factors in doing so the corresponding modified lagrange multiplier nodal values are of the same order as the unmodified ones various examples demonstrate the performance of the modified mortar contact algorithm

interior two dimensional acoustic modelling and modal analysis using isogeometric approach abstract in this paper the interior two dimensional acoustic modelling and modal analysis are presented in the framework of isogeometric analysis iga the acoustic domain governed by the helmholtz equation is parameterized and analysed by non uniform rational lagrange nurl basis which can construct exact geometry model inherently like non uniform rational b spines nurbs and can provide a more straightforward way than nurbs to impose dirichlet boundary conditions the verification and versatility of iga using nurl are assessed in the investigation of a unit square domain and a unit circular domain by comparison with analytical solutions furthermore a quadrilateral domain with concave or convex conics is studied and some innovative results are presented which can be the benchmark data for other algorithm researches the effects of geometric weight and aspect ratio on acoustic eigenvalue and eigenmode of the quadrilateral domain are investigated in detail

two dimensional mortar contact methods for large deformation frictional sliding this paper presents a mortar based formulation for the solution of two dimensional frictional contact problems involving finite deformation and large sliding as is widely recognized traditional node to surface contact formulations have several drawbacks in solution of deformable to deformable contact problems including lack of general patch test passage degradation of spatial convergence rates and robustness issues associated with the faceted representation of contacting surfaces the mortar finite element method initially proposed as a technique to join dissimilarly meshed domains has been shown to preserve optimal convergence rates in tied contact problems see discretization methods and iterative solvers based on domain decomposition springer verlag heidelberg 2001 for a recent review and is examined here as an alternative spatial discretization method for large sliding contact in particular a novel description for frictional sliding conditions in large deformation mortar formulations is proposed in this work in recent years the mortar element method has already been successfully implemented to solve frictional contact problems with linearized kinematics see int j numer meth engng 1993 36 3451 however in the presence of large deformations and finite sliding one must face difficulties associated with the definition and linearization of contact virtual work in the case where the mortar projection has a direct dependence on the tangential relative motion along the interface in this paper such a formulation is presented with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics some novel techniques are proposed to treat the non smoothness in the contact geometry and the searching required to define mortar segments a number of numerical examples illustrate the performance and accuracy of the proposed formulation copyright 2004 john wiley sons ltd

extended isogeometric analysis with strong imposing essential boundary conditions for weak discontinuous problems using b splines abstract strong imposing dirichlet boundary conditions remain a challenge for extended isogeometric analysis xiga or extended finite element methods xfem this paper proposed a novel xiga method of using b splines boundary plus plus splines for bi material weak discontinuous problems because b spline basis functions satisfy the kronecker delta property the presented method allows strong imposing dirichlet boundary conditions on the boundaries and bi material interfaces in addition compared with other xiga methods the number of the basis functions and degrees of freedom dofs are significantly reduced in the process of conversion which save the computational resources numerical examples verify the efficiency and accuracy of the proposed method

plane wave interpolation in direct collocation boundary element method for radiation and wave scattering numerical aspects and applications the classical boundary element formulation for the helmholtz equation is rehearsed and its limitations with respect to the number of variables needed to model a wavelength are explained a new type of interpolation for the potential is then described in which the usual boundary element shape functions are modified by the inclusion of a set of plane waves propagating in a range of directions this is termed the plane wave basis boundary element method the modifications needed to the classical procedures in terms of integration of the element matrices and location of collocation points are described the well known singular value decomposition solution technique which is adopted here for the solution of the system matrix equation in its complex form is briefly outlined the conditioning of the system matrix is analysed for a simple radiation problem the corresponding diffraction problem is also analysed and results are compared with analytical and classical boundary element solutions the chief method is adopted to enhance the quality of the solution particularly in the vicinity of irregular frequencies the plane wave basis boundary element method is then applied to two problems scattering of plane waves by an elliptical cylinder and the multiple circular cylinder plane wave scattering problem in both cases results are compared with analytical solutions the results clearly demonstrate that the new method is considerably more efficient than the classical approach for a given number of degrees of freedom the frequency for which accurate results can be obtained using the new technique can be up to three or four times higher than that of the classical method this makes the method a powerful new addition to our tools for tackling high frequency radiation and scattering problems

extended isogeometric boundary element method xibem for three dimensional medium wave acoustic scattering problems a boundary element method bem based on non uniform rational b splines nurbs is used to find solutions to three dimensional wave scattering problems governed by the helmholtz equation the method is extended in a partition of unity sense multiplying the nurbs functions by families of plane waves this method is called the extended isogeometric boundary element method xibem in this paper the collocation xibem formulation is described and numerical results are given the numerical results are compared against closed form or converged solutions comparisons are made against the conventional boundary element method and the non enriched isogeometric bem igabem when compared to non enriched boundary element simulations using xibem significantly reduces the number of degrees of freedom required to obtain a solution of a given error thus with a fixed computational resource problems of a shorter wavelength can be solved

on the solvability of closest point projection procedures in contact analysis analysis and solution strategy for surfaces of arbitrary geometry abstract the uniqueness and existence of the closest point projection procedure widely used in contact mechanics are analyzed in the current article first a projection domain for c 2 continuous surfaces is created based on the geometrical properties of surfaces then any point from the projection domain has a unique projection onto the given surface it is shown that in order to construct a continuous projection domain for arbitrary globally c 1 or c 0 continuous surfaces a projection routine should be generalized and also include a projection onto a curved edge and onto corner points criteria of uniqueness and existence of the corresponding projection routine are given and discussed from the geometrical point of view some examples showing the construction of the projection domain as well as the necessity of a generalized projection routine are given

assessment of methods for computing the closest point projection penetration and gap functions in contact searching problems summary in computational contact mechanics problems local searching requires calculation of the closest point projection of a contactor point onto a given target segment it is generally supposed that the contact boundary is locally described by a convex region however because this assumption is not valid for a general curved segment of a three dimensional quadratic serendipity element an iterative numerical procedure may not converge to the nearest local minimum to this end several unconstrained optimization methods are tested the newton raphson method the least square projection the sphere and torus approximation method the steepest descent method the broyden method the broyden fletcher goldfarb shanno method and the simplex method the effectiveness and robustness of these methods are tested by means of a proposed benchmark problem it is concluded that the newton raphson method in conjunction with the simplex method significantly increases the robustness of the local contact search procedure of pure penalty contact methods whereas the torus approximation method can be recommended for contact searching algorithms which employ the lagrange method or the augmented lagrangian method copyright 2015 john wiley sons ltd

a comparison of techniques for overcoming non uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering the partition of unity method has become an attractive approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements the non uniqueness of solution obtained from the conventional boundary integral equation cbie is well known the cbie derived through green s identities suffers from a problem of non uniqueness at certain characteristic frequencies two of the standard methods of overcoming this problem are the so called combined helmholtz integral equation formulation chief method and that of burton and miller the latter method introduces a hypersingular integral which may be treated in various ways in this paper we present the collocation partition of unity boundary element method pubem for the helmholtz problem and compare the performance of chief against a burton miller formulation regularised using the approach of li and huang

plane wave enriched partition of unity isogeometric analysis puiga for 2d helmholtz problems abstract in general numerical concerns in simulation of time harmonic acoustic waves are mainly due to the dispersion errors and the demands in modeling the problems with higher number of degrees of freedom per wavelength to obtain acceptable results as a remedy plane wave enriched partition of unity finite element method pufem was earlier proposed by melenk and babuska 1996 even though pufem gives accurate results with lesser degrees of freedom and shows exponential convergence it suffers from the approximate representation of geometry and leads to the boundary representation induced errors in this regard plane wave enriched pufem under isogeometric framework named partition of unity isogeometric analysis puiga is proposed for accurate geometry representation and smooth solution approximation which can lead to a better solution several benchmark problems are considered in the present study to illustrate the computational effectiveness of puiga

a discontinuous enrichment method for three dimensional multiscale harmonic wave propagation problems in multi fluid and fluid solid media an evanescent wave occurs when a propagating incident wave impinges on an interface between two fluid solid or fluid solid media at a subcritical angle mathematical properties of such a wave make it difficult to capture with standard finite element discretization schemes for this reason the discontinuous enrichment method dem developed in comput methods appl mech eng 2001 190 6455 6479 comput methods appl mech eng 2003 192 1389 1419 comput methods appl mech eng 2003 192 3195 3210 int j numer meth engng 2004 61 1938 1956 wave motion 2004 39 4 307 317 int j numer meth engng 2006 66 2086 2114 int j numer meth engng 2006 66 796 815 is extended here to the solution of a class of three dimensional evanescent wave problems in the frequency domain to this effect new dem elements for three dimensional elastodynamic problems are first proposed then these and other dem elements previously developed for the efficient solution of the helmholtz problem are further enriched with free space solutions of model evanescent wave problems in order to achieve high accuracy at practical mesh resolution for fluid fluid and fluid solid applications the performance of the extended dem elements is reported to be better than that of its basic helmholtz and navier counterparts and superior to that achieved by the classical high order polynomial finite element method copyright 2008 john wiley sons ltd

isogeometric analysis of free vibration of simple shaped elastic samples the paper is devoted to numerical solution of free vibration problems for elastic bodies of canonical shapes by means of a spline based finite element method fem called isogeometric analysis iga it has an advantage that the geometry is described exactly and the approximation of unknown quantities is smooth due to higher order continuous shape functions iga exhibits very convenient convergence rates and small frequency errors for higher frequency spectrum in this paper the iga strategy is used in computation of eigen frequencies of a block and cylinder as benchmark tests results are compared with the standard fem the rayleigh ritz method and available experimental data the main attention is paid to the comparison of convergence rate accuracy and time consumption of iga against fem and also to show a spline order and parameterization effects in addition the potential of iga in resonant ultrasound spectroscopy measurements of elastic properties of general anisotropy solids is discussed

a new family of continuous discontinuous three dimensional boundary elements with application to acoustic wave propagation this paper presents a new family of continuous discontinuous three dimensional boundary elements which has been implemented in a computer system for acoustic wave propagation in the frequency domain the system includes elements of different geometrical shapes order of interpolation and degree of continuity results of several tests are included to show the efficiency of the family of elements

an isogeometric approach of two dimensional acoustic design sensitivity analysis and topology optimization analysis for absorbing material distribution abstract a study of structural shape optimization and absorbing material distribution optimization of noise barrier structures based on the recently proposed isogeometric analysis method with exact geometric definitions is presented the acoustic scattering is approximated using the basis functions that represent the geometry a fast multipole method is applied to accelerate the solution of the boundary element method bem the burton miller formulation is used to overcome the fictitious frequency problem when a single helmholtz boundary integral equation is used for the exterior boundary value problem the strongly singular integrals in the burton miller formulation using the isogeometric bem are evaluated explicitly and directly particularly for the sensitivity formulation with a hyper singular integral the optimality criteria method is used for two types of optimization analyses shape optimization and material distribution topology optimization for the shape optimization the design variables can be set to the locations of the control points because the control points determine the shape of structure for the second optimization a new material interpolation scheme for acoustic problems based on the solid isotropic material with penalization simp method is given where the interpolation variable is not the real structural density used in a conventional simp but a fictitious material density that determines the normalized surface admittance several examples are presented to demonstrate the validity and efficiency of the proposed algorithm

nonsingular isogeometric boundary element method for stokes flows in 3d abstract isogeometric analysis iga is emerging as a technology bridging computer aided geometric design cagd most commonly based on non uniform rational b splines nurbs surfaces and engineering analysis in finite element and boundary element isogeometric methods fe iga and iga bem the nurbs basis functions that describe the geometry define also the approximation spaces in the fe iga approach the surfaces generated by the cagd tools need to be extended to volumetric descriptions a major open problem in 3d this additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of boundary integral equations leading to boundary element isogeometric analysis iga bem the main advantages of such an approach are given by the dimensionality reduction of the problem from volumetric based to surface based by the fact that the interface with cagd tools is direct and by the possibility to treat exterior problems where the computational domain is infinite by contrast these methods produce system matrices which are full and require the integration of singular kernels in this paper we address the second point and propose a nonsingular formulation of iga bem for 3d stokes flows whose convergence is carefully tested numerically standard gaussian quadrature rules suffice to integrate the boundary integral equations and carefully chosen known exact solutions of the interior stokes problem are used to correct the resulting matrices extending the work by klaseboer et al 2012 27 to iga bem

a natural framework for isogeometric fluid structure interaction based on bem shell coupling abstract the interaction between thin structures and incompressible newtonian fluids is ubiquitous both in nature and in industrial applications in this paper we present an isogeometric formulation of such problems which exploits a boundary integral formulation of stokes equations to model the surrounding flow and a non linear kirchhoff love shell theory to model the elastic behavior of the structure we propose three different coupling strategies a monolithic fully implicit coupling a staggered elasticity driven coupling and a novel semi implicit coupling where the effect of the surrounding flow is incorporated in the non linear terms of the solid solver through its damping characteristics the novel semi implicit approach is then used to demonstrate the power and robustness of our method which fits ideally in the isogeometric paradigm by exploiting only the boundary representation b rep of the thin structure middle surface

grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics summary the spatial discretisation of a continuum by the fem introduces dispersion errors to the numerical solution of stress wave propagation errors of phase and group velocities and the scatter of wave propagation are induced when these propagating phenomena are modelled by the fem the speed of a single harmonic wave depends on its frequency parasitic effects do not exist in an ideal unbounded continuum with higher order finite elements there are optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefronts in principle the dispersion errors and the spurious oscillations cannot be removed from these solutions but can be suppressed to a certain extent for reliable numerical solutions by the fem the dispersion errors should be analysed and determined the dispersion properties of a plane square biquadratic serendipity finite element are examined and compared with a bilinear one dispersion analysis is carried out for the consistent and lumped mass matrices a dispersive improved lumped mass matrix for biquadratic serendipity elements is proposed the paper closes with the recommendation of a choice of permissible dimensionless wavelengths for bilinear and biquadratic serendipity finite element meshes copyright 2013 john wiley sons ltd

isogeometric finite element data structures based on bezier extraction of t splines we develop finite element data structures for t splines based on bezier extraction generalizing our previous work for nurbs as in traditional finite element analysis the extracted bezier elements are defined in terms of a fixed set of polynomial basis functions the so called bernstein basis the bezier elements may be processed in the same way as in a standard finite element computer program utilizing exactly the same data processing arrays in fact only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same a byproduct of the extraction process is the element extraction operator this operator localizes the topological and global smoothness information to the element level and represents a canonical treatment of t junctions referred to as hanging nodes in finite element analysis and a fundamental feature of t splines a detailed example is presented to illustrate the ideas copyright 2011 john wiley sons ltd

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

the inside outside contact search algorithm for finite element analysis a new contact search algorithm inside outside algorithm for the sheet forming simulation has been developed and implemented in the dynamic explicit fe code dynamic the inside outside algorithm is derived based on the feature of the inside outside status of a nodal mesh normal vector in respect to a surface segment for the judgment of the contact of fe nodes with the tool surface this new algorithm includes local search local track and penetration calculation processes almost no additional cpu time is required for the local search process because the calculations for both global and local search are combined moreover the problems of conventional contact searching algorithms such as iterations for local search and the deadzone problem are resolved therefore the quick robust contact searching and accurate evaluation of penetration have been achieved the numerical results show that the new contact searching algorithm is more cost effective and robust than conventional ones 1997 john wiley sons ltd

pollution studies for high order isogeometric analysis and finite element for acoustic problems abstract it is well known that galerkin finite element methods suffer from pollution error when solving wave problems to reduce the pollution impact on the solution different approaches were proposed to enrich the finite element method with wave like functions so that the exact wavenumber is incorporated into the finite element approximation space solving wave problems with isogeometric analysis was also investigated in the literature where the superior behaviour of isogeometric analysis due to higher continuity in the underlying basis has been studied recently a plane wave enriched isogeometric analysis was introduced for acoustic problems however it remains unquantified the impact of these different approaches on the pollution or how they perform compared to each other in this work we show that isogeometric analysis outperforms finite element method in dealing with pollution we observe similar behaviour when both the methods are enriched with plane waves using higher order polynomials with fewer enrichment functions seems to improve the pollution compared to lower order polynomials with more functions however the latter still leads to smaller errors using similar number of degrees of freedom in conclusion we propose that partition of unity isogeometric analysis can be an efficient tool for wave problems as enrichment eliminates the need for domain re meshing at higher frequencies and also due to its ability to capture the exact geometry even on coarse meshes as well as its improved pollution behaviour

optic disc segmentation based on variational model with multiple energies accurate and reliable optic disc od segmentation is important for retinal image analysis and retinal disease screening this paper presents a novel method to automatically segment od in fundus images based on variational model with multiple energies firstly a sparse coding based technique is designed to localize the od center based on which an initial boundary curve is then estimated by a circular hough transform next od segmentation is regarded as an energy minimization problem and a variational model integrating three energy terms is proposed to evolve the curve to the od boundary in the proposed model the first term named phase based boundary energy is designed to attract the evolution curve to the od boundary even the one with low contrast the second term named pca based shape energy constraints the evolution curve to a common od shape which can suppress the negative effect of bright interferences e g the bright lesions and myelinated nerve fibers in od segmentation the last one is the region energy which drives the evolution curve to the boundary of the homogeneous regions and hence improve the robustness of the model to the noises boundary and the initial position of evolution curve the proposed od segmentation method is evaluated on three public available databases i e the messidor onhsd and drions databases and the experimental results demonstrate that the proposed method outperforms the state of the art techniques highlightsa sparse coding based method is designed to localize the optic disc od in fundus image variational model integrating three energy terms is proposed to segment od boundary phase based edge stop function is designed in the boundary energy the proposed method is evaluated and analyzed on three public databases and outperforms the state of the art approaches

a mortar based frictional contact formulation for large deformations using lagrange multipliers abstract in this work a lagrange multiplier method is proposed to solve 2d coulomb frictional contact problems in the context of large deformations as the proposed formulation is based on the mortar method the constraints are imposed in a weak integral sense along the contact surface in order to compute the contact integrals we use a numerical integration based on the definition of the kinematical variables gap slip and their variations at the quadrature points the linearization of non linear equations virtual work and contact constraints is developed in order to apply a newton s method the examples show that the numerical integration still preserves the optimal rate of convergence of the finite element solution

digital topology and geometry in medical imaging a survey digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids such methods have been widely used in many medical imaging applications including image segmentation visualization manipulation interpolation registration surface tracking object representation correction quantitative morphometry etc digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability fidelity and efficiency this paper presents a comprehensive yet compact survey on results principles and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications specifically this paper reviews methods related to distance analysis and path propagation connectivity surface tracking image segmentation boundary and centerline detection topology preservation and local topological properties skeletonization and object representation correction and quantitative morphometry a common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity path propagation and neighborhood analysis

accuracy of finite difference and finite element modeling of the scalar and elastic wave equations numerical solutions of the scalar and elastic wave equations have greatly aided geophysicists in both forward modeling and migration of seismic wave fields in complicated geologic media and they promise to be invaluable in solving the full inverse problem this paper quantitatively compares finite difference and finite element solutions of the scalar and elastic hyperbolic wave equations for the most popular implicit and explicit time domain and frequency domain techniques in addition to versatility and ease of implementation it is imperative that one choose the most cost effective solution technique for a fixed degree of accuracy to be of value a solution technique must be able to minimize 1 numerical attenuation or amplification 2 polarization errors 3 numerical anisotropy 4 errors in phase and group velocities 5 extraneous numerical parasitic modes 6 numerical diffraction and scattering and 7 errors and transmission coefficients this paper shows that in homogeneous media the

a constrained optimization methodology for the detection phase in contact mechanics simulations the detection phase in computational contact mechanics can be subdivided into a global search and a local detection when potential contact is detected by the former a rigorous local detection determines which surface elements come or may come in contact in the current increment we first introduce a rigorous definition of the closest point for non differentiable lower dimensional manifolds we then simplify the detection by formulating an optimization problem subject to inequality constraints the formulation is then solved using different techniques from the field of mathematical optimization for both linear and quadratic finite element meshes the resulting general and robust detection scheme is tested on a set of problems and compared with other techniques commonly used in computational geometry

an isogeometric boundary element method for three dimensional potential problems abstract isogeometric analysis iga coupled with boundary element method i e igabem received a lot of attention in recent years in this paper we extend the igabem to solve 3d potential problems this method offers a number of key improvements compared with conventional piecewise polynomial formulations firstly the models for analysis in the igabem are exact geometrical representation no matter how coarse the discretization of the studied bodies is thus the igabem ensures that no geometrical errors are produced in the analysis process secondly a meshing process is no longer required which means redundant computations are eliminated to allow analysis to be carried out with greatly reduced pre processing to accurately evaluate the singular integrals appearing in our method the power series expansion method is employed the integration surface is on the real surface of the model rather than the interpolation surface i e no geometrical errors thus the value of integral is more accurate than the traditional boundary element method which can improve the computation accuracy of the igabem some numerical examples for 3d potential problems are used to validate the solutions of the present method with analytical and numerical solutions available

a two dimensional isogeometric boundary element method for elastostatic analysis the concept of isogeometric analysis where functions that are used to describe geometry in cad software are used to approximate the unknown fields in numerical simulations has received great attention in recent years the method has the potential to have profound impact on engineering design since the task of meshing which in some cases can add significant overhead has been circumvented much of the research effort has been focused on finite element implementations of the isogeometric concept but at present little has been seen on the application to the boundary element method the current paper proposes an isogeometric boundary element method bem which we term igabem applied to two dimensional elastostatic problems using non uniform rational b splines nurbs we find it is a natural fit with the isogeometric concept since both the nurbs approximation and bem deal with quantities entirely on the boundary the method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric bem implementation

automatic detection of optic disc based on pca and mathematical morphology the algorithm proposed in this paper allows to automatically segment the optic disc from a fundus image the goal is to facilitate the early detection of certain pathologies and to fully automate the process so as to avoid specialist intervention the method proposed for the extraction of the optic disc contour is mainly based on mathematical morphology along with principal component analysis pca it makes use of different operations such as generalized distance function gdf a variant of the watershed transformation the stochastic watershed and geodesic transformations the input of the segmentation method is obtained through pca the purpose of using pca is to achieve the grey scale image that better represents the original rgb image the implemented algorithm has been validated on five public databases obtaining promising results the average values obtained a jaccard s and dice s coefficients of 0 8200 and 0 8932 respectively an accuracy of 0 9947 and a true positive and false positive fractions of 0 9275 and 0 0036 demonstrate that this method is a robust tool for the automatic segmentation of the optic disc moreover it is fairly reliable since it works properly on databases with a large degree of variability and improves the results of other state of the art methods

symmetry preserving algorithm for large displacement frictionless contact by the pre discretization penalty method a three dimensional contact algorithm based on the pre discretization penalty method is presented using the pre discretization formulation gives rise to contact searching performed at the surface gaussian integration points it is shown that the proposed method is consistent with the continuum formulation of the problem and allows an easy incorporation of higher order elements with midside nodes to the analysis moreover a symmetric treatment of mutually contacting surfaces is preserved even under large displacement increments the proposed algorithm utilizes the bfgs method modified for constrained non linear systems the effectiveness of quadratic isoparametric elements in contact analysis is tested in terms of numerical examples verified by analytical solutions and experimental measurements the symmetry of the algorithm is clearly manifested in the problem of impact of two elastic cylinders copyright 2004 john wiley sons ltd

a finite deformation mortar contact formulation using a primal dual active set strategy in recent years nonconforming domain decomposition techniques and in particular the mortar method have become popular in developing new contact algorithms here we present an approach for two dimensional frictionless multibody contact based on a mortar formulation and using a primal dual active set strategy for contact constraint enforcement we consider linear and higher order quadratic interpolations throughout this work so called dual lagrange multipliers are introduced for the contact pressure but can be eliminated from the global system of equations by static condensation thus avoiding an increase in system size for this type of contact formulation we provide a full linearization of both contact forces and normal non penetration and tangential frictionless sliding contact constraints in the finite deformation frame the necessity of such a linearization in order to obtain a consistent newton scheme is demonstrated by further interpreting the active set search as a semi smooth newton method contact nonlinearity and geometrical and material nonlinearity can be resolved within one single iterative scheme this yields a robust and highly efficient algorithm for frictionless finite deformation contact problems numerical examples illustrate the efficiency of our method and the high quality of results

an isogeometric boundary element method using adaptive integral method for 3d potential problems due to the merits of exact geometrical representation high accuracy no meshing process and only the boundary description of the problem etc the isogeometric boundary element method i e igabem has achieved rapid development in this paper based on the upper bound of the relative error of the gaussian quadrature formula we presented a 3d igabem using adaptive integration method for potential problems this method offers a number of key improvements compared with conventional igabem firstly the boundary element integrations can be computed easily and effectively at optimal computational cost secondly the adaptive algorithm can cope with the common situation where the sizes of adjacent cells are significantly different moreover the presented method can compute the nearly singular integrals easily owing to the use of subdivision technique to accurately evaluate the singular integrals appearing in our method the power series expansion method is employed the integration surface is on the real surface of the model rather than the interpolation surface i e no geometrical errors thus the value of integral is more accurate than the traditional boundary element method which can improve the computation accuracy of the igabem numerical tests show that the presented method has good performance in both exactness and convergence a general method is proposed to calculate the nearly singular integrals appearing in the 3d igabem the boundary element integrations can be computed easily and effectively at optimal computational cost the adaptive algorithm can be used to cope with the common situation where the sizes of adjacent cells are significantly different the power series expansion method is expanded to compute the singular integrals appearing in 3d igabem

fast and robust optic disc detection using pyramidal decomposition and hausdorff based template matching reports on the design and test of an image processing algorithm for the localization of the optic disk od in low resolution about 20 spl mu pixel color fundus images the design relies on the combination of two procedures 1 a hausdorff based template matching technique on edge map guided by 2 a pyramidal decomposition for large scale object tracking the two approaches are tested against a database of 40 images of various visual quality and retinal pigmentation as well as of normal and small pupils an average error of 7 on od center positioning is reached with no false detection in addition a confidence level is associated to the final detection that indicates the level of difficulty the detector has to identify the od position and shape

evaluation of fractal dimension effectiveness for damage detection in retinal background abstract this work investigates the characterization of bright lesions in retinal fundus images using texture analysis techniques exudates and drusen are evidences of retinal damage in diabetic retinopathy dr and age related macular degeneration amd respectively an automatic detection of pathological tissues could make possible an early detection of these diseases in this work fractal analysis is explored in order to discriminate between pathological and healthy retinal texture after a deep preprocessing step in which spatial and colour normalization are performed the fractal dimension is extracted locally by computing the hurst exponent h along different directions the greyscale image is described by the increments of the fractional brownian motion model and the h parameter is computed by linear regression in the frequency domain the ability of fractal dimension to detect pathological tissues is demonstrated using a home made system based on fractal analysis and support vector machine able to achieve around a 70 and 83 of accuracy in e ophtha and diaretdb1 public databases respectively in a second experiment the fractal descriptor is combined with texture information extracted by the local binary patterns improving the bright lesion detection accuracy sensitivity and specificity values higher than 89 80 and 90 respectively suggest that the method presented in this paper is a robust algorithm for describing retina texture and can be useful in the automatic detection of dr and amd

modelling wave propagation in two dimensional structures using finite element analysis a method is described by which the dispersion relations for a two dimensional structural component can be predicted from a finite element fe model the structure is homogeneous in two dimensions but the properties might vary through the thickness this wave finite element wfe method involves post processing the mass and stiffness matrices found using conventional fe methods of a segment of the structure this is typically a 4 noded rectangular segment although other elements can be used periodicity conditions are applied to relate the nodal degrees of freedom and forces the wavenumbers real imaginary or complex and the frequencies then follow from various resulting eigenproblems the form of the eigenproblem depends on the nature of the solution sought and may be a linear quadratic polynomial or transcendental eigenproblem numerical issues are discussed examples of a thin plate an asymmetric laminated plate and a laminated foam cored sandwich panel are presented for the last two examples developing an analytical model is a formidable task at best the method is seen to give accurate predictions at very little computational cost furthermore since the element matrices are typically found using a commercial fe package the meshing capabilities and the wealth of existing element libraries can be exploited

extended isogeometric boundary element method xibem for two dimensional helmholtz problems isogeometric analysis is a topic of considerable interest in the field of numerical analysis the boundary element method bem requires only the bounding surface of geometries to be described this makes non uniform rational b splines nurbs which commonly describe the bounding curve or surface of geometries in cad software appear to be a natural tool for the approach this isogeometric analysis bem igabem provides accuracy benefits over conventional bem schemes due to the analytical geometry provided by nurbs when applied to wave problems it has been shown that enriching bem approximations with a partition of unity basis in what has become known as the pu bem allows highly accurate solutions to be obtained with a much reduced number of degrees of freedom this paper combines these approaches and presents an extended isogeometric bem xibem which uses partition of unity enriched nurbs functions this new approach provides benefits which surpass those of both the igabem and the pu bem two numerical examples are given a single scattering cylinder and a multiple scatterer made up of two capsules and a cylinder

a binary tree element subdivision method for evaluation of nearly singular domain integrals with continuous or discontinuous kernel abstract an adaptive and efficient volume element subdivision method using binary tree for evaluation of nearly singular domain integrals with continuous or discontinuous kernel in three dimensional 3 d boundary element method bem has been presented in the conventional subdivision method csm for evaluation of nearly singular integrals the patches are obtained by simply connecting the source point with each vertex of the element thus the accuracy of the integral obtained with csm is easily affected by the shape of the element and the location of the source point in contrast the proposed binary tree subdivision method btsm is more convenient to implement and can guarantee successful patch generation under any circumstances for accurate evaluation of nearly singular domain integrals with continuous or discontinuous kernel numerical results for volume elements of arbitrary type with various relative locations of the source point demonstrate robustness accuracy and efficiency of the proposed method

compatible description of tool surfaces and fem meshes for analysing sheet forming operations implementation of the 3 d finite element method fem of sheet forming operations has proceeded slowly in particular describing the arbitrary tool surfaces in an accurate and smooth manner with well behaved first and second derivatives has been a major obstacle a new geometric method suitable for representing any rigid tool surface has been developed and shown to be superior to the usual schemes the new method relies on the described tool surface for position data only the spatial derivatives are obtained by considering only the sheet mesh nodal positions this new scheme has been implemented with a rigid viscoplastic fem program using general surface descriptions based on b splines and linear inter polation analytic representations of a hemispherical and rounded square punch were also compared the comparisons show that the proposed method offers several advantages over other general formulations 1 the new representation is the proper one for formulating the equilibrium condition alternate forms can produce spurious results 2 the proposed method introduces inherently smooth surface derivatives that improve numerical stability even with crude surface resolution suitable test problems show covergence with the new method far past the divergence points of the simulations using the standard general surface description 3 the method is reasonably efficient with a time penalty of approximately 30 50 per cent unoptimized with respect to analytic surface descriptions

a dual mortar approach for 3d finite deformation contact with consistent linearization in this paper an approach for three dimensional frictionless contact based on a dual mortar formulation and using a primal dual active set strategy for direct constraint enforcement is presented we focus on linear shape functions but briefly address higher order interpolation as well the study builds on previous work by the authors for two dimensional problems first and foremost the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi smooth newton method are extended to the 3d case this allows for solving all types of nonlinearities i e geometrical material and contact within one single newton scheme owing to the dual lagrange multiplier approach employed this advantage is not accompanied by an undesirable increase in system size as the lagrange multipliers can be condensed from the global system of equations moreover it is pointed out that the presented method does not make use of any regularization of contact constraints numerical examples illustrate the efficiency of our method and the high quality of results in 3d finite deformation contact analysis

enriched isogeometric collocation for two dimensional time harmonic acoustics abstract in this work the isogeometric collocation iga c is paired with two types of enrichment plane wave pw and generalized harmonic polynomial ghp functions to solve 2d problems for the helmholtz equation a parametric study is conducted and a detailed assessment of the performance of the method in a number of benchmark problems is provided three different collocation methods are tested for the non enriched formulation namely greville abscissae ga approximated cauchy galerkin acg and superconvergent sc points showing that the acg scheme is the best choice in terms of overall error convergence rate and ease of solving the linear system then the influence of the number of shape functions in the original and enriched basis location and number of collocation points and wave number over both the convergence rate as well as the condition number of the stiffness matrix are studied the numerical results show that 1 there is an improvement over the non enriched formulation 2 the improvement depends on the choice of the number and type of enrichment and 3 the pollution error is not completely alleviated with the enriched formulations

acoustic isogeometric boundary element analysis an isogeometric boundary element method based on t splines is used to simulate acoustic phenomena we restrict our developments to low frequency problems to establish the fundamental properties of the proposed approach using t splines the computer aided design cad and boundary element analysis are integrated without recourse to geometry clean up or mesh generation a regularized burton miller formulation is used resulting in integrals which are at most weakly singular we employ a collocation based approach to generate the linear system of equations the method is verified against closed form solutions and direct comparisons are made with conventional lagrangian discretizations it is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the t spline the method is then applied to a real world application to illustrate the potential for integrated engineering design and analysis

novel basis functions for the partition of unity boundary element method for helmholtz problems the bem is a popular technique for wave scattering problems given its inherent ability to deal with infinite domains in the last decade the partition of unity bem in which the approximation space is enriched with a linear combination of plane waves has been developed this significantly reduces the number of dofs required per wavelength it has been shown that the element ends are more susceptible to errors in the approximation than the mid element regions in this paper the authors propose that this is due to the use of a collocation approach in combination with a reduced order of continuity in the lagrangian shape function component of the basis functions it is demonstrated using numerical examples that choosing trigonometric shape functions rather than classical polynomial shape functions quadratic in this case provides accuracy benefits collocation schemes are investigated it is found that the somewhat arbitrary choice of collocating at equally spaced points about the surface of a scatterer is better than schemes based on the roots of polynomials or consideration of the fock domain

an isogeometric indirect boundary element method for solving acoustic problems in open boundary domains abstract this work introduces an indirect boundary element method bem within a nurbs based isogeometric framework for solving three dimensional acoustic problems in the frequency domain developments of isogeometric boundary elements so far have focused on the direct bem yet a multitude of common problems in acoustics involves open boundary surfaces which require a more involved indirect boundary element formulation the current work presents an indirect variational bem which makes use of nurbs shape functions additionally a novel technique for coupling strongly non conforming patches is introduced to allow the analysis of more complex geometries the proposed isogeometric indirect boundary element method is verified against analytical solutions and benchmarked against the conventional polynomial based indirect bem also two open boundary problems are studied including analyses over wider frequency ranges and one industrial type complex geometry containing multiple non conforming patches the proposed method is found to be not only significantly more efficient than its polynomial based counterpart but also very robust against strong non conformities in the nurbs descriptions

dispersion of elastic waves in the contact impact problem of a long cylinder numerical dispersion of two dimensional finite elements was studied the outcome of the dispersion study was verified by the numerical and analytical solutions to the longitudinal impact of two long cylindrical bars in accordance with the results of the dispersion analysis it was demonstrated that the quadratic elements showed better accuracy than the linear ones

isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth abstract we present a novel numerical method to simulate crack growth in 3d directly from the computer aided design cad geometry of the component without any mesh generation the method is an isogeometric boundary element method igabem based on non uniform rational b splines nurbs nurbs basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations a stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements convergence studies in the crack opening displacement is performed for a penny shaped crack and an elliptical crack two approaches to extract stress intensity factors sifs the contour m integral and the virtual crack closure integral are compared using dual integral equations the results show remarkable accuracy in the computed sifs leading to smooth crack paths and reliable fatigue lives without requiring the generation of any mesh from the cad model of the component under consideration

a multiple active contour model for cardiac boundary detection on echocardiographic sequences tracing of left ventricular epicardial and endocardial borders on echocardiographic sequences is essential for quantification of cardiac function the authors designed a method based on an extension of active contour models to detect both epicardial and endocardial borders on short axis cardiac sequences spanning the entire cardiac cycle they validated the results by comparing the computer generated boundaries to the boundaries manually outlined by four expert observers on 44 clinical data sets the mean boundary distance between the computer generated boundaries and the manually outlined boundaries was 2 80 mm spl sigma 1 28 mm for the epicardium and 3 61 spl sigma 1 68 mm for the endocardium these distances were comparable to interobserver distances which had a mean of 3 79 mm spl sigma 1 53 mm for epicardial borders and 2 67 mm spl sigma 0 88 mm for endocardial borders the correlation coefficient between the areas enclosed by the computer generated boundaries and the average manually outlined boundaries was 0 95 for epicardium and 0 91 for endocardium the algorithm is fairly insensitive to the choice of the initial curve thus the authors have developed an effective and robust algorithm to extract left ventricular boundaries from echocardiographic sequences